NORMA
E U R OP E A
Recipienti a pressione non esposti a fiamma - Parte 3:
Progettazione
UNI EN 13445-3
AGOSTO 2021
Unfired pressure vessels - Part 3: Design
La norma specifica i requisiti per la progettazione dei recipienti a
pressione non esposti a fiamma trattati dalla UNI EN 13445-1:2021
e costruiti in acciaio in conformità alla UNI EN 13445-2:2021.
TESTO INGLESE
La presente norma è la versione ufficiale in lingua inglese della
norma europea EN 13445-3 (edizione maggio 2021).
La presente norma sostituisce la UNI EN 13445-3:2019.
ICS
23.020.30
© UNI
Riproduzione vietata. Legge 22 aprile 1941 N° 633 e successivi aggiornamenti.
Tutti i diritti sono riservati. Nessuna parte del presente documento può essere riprodotta o diffusa
con un mezzo qualsiasi, fotocopie, microfilm o altro, senza il consenso scritto dell’UNI.
UNI EN 13445-3:2021
Pagina I
PREMESSA NAZIONALE
La presente norma costituisce il recepimento, in lingua inglese,
della norma europea EN 13445-3 (edizione maggio 2021), che
assume così lo status di norma nazionale italiana.
La presente norma è stata elaborata sotto la competenza dell’ente
federato all’UNI
CTI - Comitato Termotecnico Italiano
La presente norma è stata ratificata dal Presidente dell’UNI ed è
entrata a far parte del corpo normativo nazionale il 5 agosto 2021.
Le norme UNI sono elaborate cercando di tenere conto dei punti di vista di tutte le parti
interessate e di conciliare ogni aspetto conflittuale, per rappresentare il reale stato
dell’arte della materia ed il necessario grado di consenso.
Chiunque ritenesse, a seguito dell’applicazione di questa norma, di poter fornire
suggerimenti per un suo miglioramento o per un suo adeguamento ad uno stato dell’arte
in evoluzione è pregato di inviare i propri contributi all’UNI, Ente Italiano di Normazione,
che li terrà in considerazione per l’eventuale revisione della norma stessa.
Si richiama l'attenzione sulla possibilità che alcuni degli elementi del presente documento
possono essere oggetto di brevetti. UNI non deve essere ritenuto responsabile di aver citato
tali brevetti.
Le norme UNI sono revisionate, quando necessario, con la pubblicazione di nuove edizioni o
di aggiornamenti.
È importante pertanto che gli utilizzatori delle stesse si accertino di essere in possesso
dell’ultima edizione e degli eventuali aggiornamenti.
Si invitano inoltre gli utilizzatori a verificare l’esistenza di norme UNI corrispondenti alle
norme EN o ISO ove citate nei riferimenti normativi.
UNI EN 13445-3:2021
© UNI
Pagina II
EN 13445-3
EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
May 2021
ICS 23.020.30
Supersedes EN 13445-3:2014
English Version
Unfired pressure vessels - Part 3: Design
Récipients sous pression non soumis à la flamme Partie 3: Conception
Unbefeuerte Druckbehälter - Teil 3: Konstruktion
This European Standard was approved by CEN on 24 February 2021.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2021 CEN
All rights of exploitation in any form and by any means reserved
worldwide for CEN national Members.
UNI EN 13445-3:2021
Ref. No. EN 13445-3:2021 E
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Contents
Page
European foreword ............................................................................................................................................................... 7
1
Scope ............................................................................................................................................................................. 8
2
Normative references ............................................................................................................................................. 8
3
Terms and definitions ............................................................................................................................................ 9
4
Symbols and abbreviations ................................................................................................................................12
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Basic design criteria ..............................................................................................................................................14
General .......................................................................................................................................................................14
Corrosion, erosion and protection...................................................................................................................14
Load cases .................................................................................................................................................................17
Design methods ......................................................................................................................................................24
Thickness calculations (DBF) ............................................................................................................................26
Joint coefficient .......................................................................................................................................................27
Design requirements of welded joints ...........................................................................................................28
6
6.1
6.2
6.6
6.7
Maximum allowed values of the nominal design stress for pressure parts .....................................31
General .......................................................................................................................................................................31
Steels (except castings), other than austenitic steels covered by 6.4 and 6.5, with a
minimum rupture elongation, as given in the relevant technical specification for the
material, below 30 % ............................................................................................................................................32
Alternative route for steels (except castings), other than austenitic steels covered by
6.4 and 6.5, with a minimum rupture elongation, as given in the relevant technical
specification for the material, below 30 % ...................................................................................................32
Austenitic steels (except castings) with a minimum rupture elongation, A%, as given in
the relevant technical specification for the material, such as 30%≤A%<35% ...............................33
Austenitic steels (except castings) with a minimum rupture elongation, A%, as given in
the relevant technical specification for the material, such as A% 35% ...........................................33
Cast steels..................................................................................................................................................................34
Nominal design stress of anchor bolting .......................................................................................................35
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
Shells under internal pressure .........................................................................................................................35
Purpose ......................................................................................................................................................................35
Specific definitions ................................................................................................................................................35
Specific symbols and abbreviations ................................................................................................................36
Cylindrical and spherical shells ........................................................................................................................36
Dished ends ..............................................................................................................................................................37
Cones and conical ends ........................................................................................................................................42
Nozzles which encroach into the knuckle region .......................................................................................51
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
Shells under external pressure .........................................................................................................................55
Purpose ......................................................................................................................................................................55
Specific definitions ................................................................................................................................................55
Specific symbols and definitions ......................................................................................................................56
General .......................................................................................................................................................................59
Cylindrical shells ....................................................................................................................................................60
Conical shell .............................................................................................................................................................80
Spherical shells .......................................................................................................................................................88
Vessel ends ...............................................................................................................................................................89
9
Openings in shells ..................................................................................................................................................
89
UNI EN 13445-3:2021
6.3
6.4
6.5
2
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.1
9.2
9.3
9.4
9.5
9.6
9.7
Purpose...................................................................................................................................................................... 89
Specific definitions ................................................................................................................................................ 90
Specific symbols and abbreviations ................................................................................................................ 91
General ...................................................................................................................................................................... 94
Isolated openings ................................................................................................................................................ 105
Multiple openings ............................................................................................................................................... 123
Openings close to a shell discontinuity ....................................................................................................... 134
10
10.1
10.2
10.3
10.4
10.5
10.6
10.7
Flat ends ................................................................................................................................................................. 142
Purpose................................................................................................................................................................... 142
Specific definitions ............................................................................................................................................. 142
Specific symbols and abbreviations ............................................................................................................. 143
Unpierced circular flat ends welded to cylindrical shells .................................................................... 144
Unpierced bolted circular flat ends.............................................................................................................. 151
Pierced circular flat ends ................................................................................................................................. 154
Flat ends of non-circular or annular shape ............................................................................................... 159
11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
Flanges .................................................................................................................................................................... 163
Purpose................................................................................................................................................................... 163
Specific definitions ............................................................................................................................................. 163
Specific symbols and abbreviations ............................................................................................................. 164
General ................................................................................................................................................................... 166
Narrow face gasketed flanges......................................................................................................................... 170
Full face flanges with soft ring type gaskets.............................................................................................. 186
Seal welded flanges ............................................................................................................................................ 189
Reverse narrow face flanges ........................................................................................................................... 189
Reverse full face flanges ................................................................................................................................... 192
Full face flanges with metal to metal contact............................................................................................ 196
12
12.1
12.2
12.3
12.4
12.5
12.6
Bolted domed ends ............................................................................................................................................. 199
Purpose................................................................................................................................................................... 199
Specific definitions ............................................................................................................................................. 199
Specific symbols and abbreviations ............................................................................................................. 199
General ................................................................................................................................................................... 199
Bolted domed ends with narrow face gaskets.......................................................................................... 199
Bolted domed ends with full face joints...................................................................................................... 201
13
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
Heat Exchanger Tubesheets ............................................................................................................................ 203
Purpose................................................................................................................................................................... 203
Specific definitions ............................................................................................................................................. 203
Specific symbols and abbreviations ............................................................................................................. 203
U-tube tubesheet heat exchangers ............................................................................................................... 206
Fixed tubesheet heat exchangers .................................................................................................................. 220
Floating tubesheet heat exchangers ............................................................................................................ 249
Tubesheet characteristics ............................................................................................................................... 267
Maximum permissible tube to tubesheet joint stress ........................................................................... 274
Maximum permissible longitudinal compressive stress for tubes ................................................... 275
Design of tubesheet flange extension with a narrow face gasket...................................................... 278
Design of tubesheet flange extension with a full face gasket .............................................................. 282
Special tube-to-tubesheet welded joints .................................................................................................... 285
14
14.1
14.2
14.3
14.4
14.5
14.6
14.7
Expansion bellows .............................................................................................................................................. 289
Purpose................................................................................................................................................................... 289
Specific definitions ............................................................................................................................................. 289
Specific symbols and abbreviations ............................................................................................................. 291
Conditions of applicability............................................................................................................................... 293
U-shaped unreinforced bellows .................................................................................................................... 295
U-shaped reinforced bellows .......................................................................................................................... 310
Toroidal bellows ................................................................................................................................................. 319
UNI EN 13445-3:2021
3
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.8 Fabrication ............................................................................................................................................................ 325
14.9 Inspection and testing ....................................................................................................................................... 327
14.10 Bellows subjected to axial, lateral or angular displacements ............................................................ 329
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
Pressure vessels of rectangular section...................................................................................................... 335
Purpose ................................................................................................................................................................... 335
Specific definitions ............................................................................................................................................. 335
Specific symbols and abbreviations ............................................................................................................. 335
General .................................................................................................................................................................... 337
Unreinforced vessels ......................................................................................................................................... 337
Reinforced vessels .............................................................................................................................................. 346
Openings................................................................................................................................................................. 355
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
16.10
16.11
16.12
16.13
16.14
Additional non-pressure loads....................................................................................................................... 357
Purpose ................................................................................................................................................................... 357
Specific definitions ............................................................................................................................................. 357
Specific symbols and abbreviations ............................................................................................................. 358
Local loads on nozzles in spherical shells .................................................................................................. 359
Local loads on nozzles in cylindrical shells ............................................................................................... 370
Line loads ............................................................................................................................................................... 379
Lifting lugs ............................................................................................................................................................. 385
Horizontal vessels on saddle supports........................................................................................................ 391
Horizontal vessels on ring supports............................................................................................................. 406
Vertical vessels on bracket supports ........................................................................................................... 411
Vertical vessels with supporting legs .......................................................................................................... 416
Vertical vessels with skirts .............................................................................................................................. 418
Vertical vessels with ring supports .............................................................................................................. 451
Global loads on cylindrical shells .................................................................................................................. 462
17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
Simplified assessment of fatigue life ............................................................................................................ 474
Purpose ................................................................................................................................................................... 474
Specific definitions ............................................................................................................................................. 474
Specific symbols and abbreviations ............................................................................................................. 477
Conditions of applicability ............................................................................................................................... 479
General .................................................................................................................................................................... 480
Determination of allowable number of pressure and thermal cycles ............................................. 488
Assessment rule................................................................................................................................................... 513
Design and manufacture................................................................................................................................... 513
Testing..................................................................................................................................................................... 514
18
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
18.10
18.11
18.12
Detailed assessment of fatigue life ............................................................................................................... 515
Purpose ................................................................................................................................................................... 515
Specific definitions ............................................................................................................................................. 515
Specific symbols and abbreviations ............................................................................................................. 519
Limitations ............................................................................................................................................................ 521
General .................................................................................................................................................................... 522
Welded material .................................................................................................................................................. 525
Unwelded components and bolts .................................................................................................................. 530
Elastic-plastic conditions ................................................................................................................................. 534
Fatigue action ....................................................................................................................................................... 536
Fatigue strength of welded components .................................................................................................... 540
Fatigue strength of unwelded components ............................................................................................... 560
Fatigue strength of steel bolts ........................................................................................................................ 565
19
19.1
19.2
19.3
19.4
Creep design.......................................................................................................................................................... 568
Purpose ................................................................................................................................................................... 568
Specific definitions ............................................................................................................................................. 568
Specific symbols and abbreviations ............................................................................................................. 568
Design in the creep range............................................................................................................. ................. 569
...
UNI EN 13445-3:2021
4
EN 13445-3:2021 (E)
Issue 1 (2021-05)
19.5
19.6
19.7
19.8
Nominal Design stress in the creep range ................................................................................................. 570
Weld joint factor in the creep range ............................................................................................................ 574
Pressure loading of predominantly non-cyclic nature in the creep range .................................... 574
Design procedures for DBF ............................................................................................................................. 574
20
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
20.9
Design rules for reinforced flat walls .......................................................................................................... 578
General ................................................................................................................................................................... 578
Stayed flat walls ................................................................................................................................................... 578
Specific definitions for stayed flat walls ..................................................................................................... 578
Required thickness of stayed flat walls ...................................................................................................... 578
Required dimensions and layout of staybolts and stays ...................................................................... 578
Requirements for threaded staybolts ......................................................................................................... 579
Requirements for welded-in staybolts and welded stays .................................................................... 579
Tables for stayed flat walls .............................................................................................................................. 580
Figures for Stayed Flat Walls .......................................................................................................................... 580
21
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
Circular flat ends with radial reinforcement ribs ................................................................................... 584
Purpose................................................................................................................................................................... 584
Specific definitions ............................................................................................................................................. 584
Specific symbols and abbreviations ............................................................................................................. 586
Ends without additional peripheral bending moment.......................................................................... 587
Ends with additional peripheral bending moment ................................................................................ 589
Openings ................................................................................................................................................................ 593
Welds ....................................................................................................................................................................... 593
Central Ring .......................................................................................................................................................... 594
22
22.1
22.2
22.3
22.4
22.5
22.6
22.7
22.8
22.9
22.10
Static analysis of tall vertical vessels on skirts ........................................................................................ 595
Purpose................................................................................................................................................................... 595
Specific definitions ............................................................................................................................................. 595
Specific symbols and abbreviations ............................................................................................................. 595
Loads ....................................................................................................................................................................... 596
Load combinations ............................................................................................................................................. 600
Stress analysis of pressure vessel shells and skirts ............................................................................... 600
Design of joint between skirt and pressure vessel (at dished end or cylindrical shell) ........... 601
Design of anchor bolts and base ring assembly ....................................................................................... 601
Foundation loads ................................................................................................................................................ 601
Vortex shedding .................................................................................................................................................. 602
Annex A (normative) Design requirements for pressure bearing welds .................................................... 606
Annex B (normative) Design by Analysis – Direct Route ................................................................................... 630
Annex C (normative) Design by analysis — Method based on stress categories ...................................... 662
Annex D (informative) Verification of the shape of vessels subject to external pressure .................... 684
Annex E (normative) Procedure for calculating the departure from the true circle of cylinders
and cones ............................................................................................................................................................... 691
Annex F (normative) Allowable external pressure for vessels outside circularity tolerance ............. 694
Annex G (normative) Alternative design rules for flanges and gasketed flange connections ............. 696
Annex H (informative) Gasket factors m and y ..................................................................................................... 746
Annex I (normative) Additional information on heat exchanger tubesheet design ................................ 749
Annex J (normative) Alternative method for the design of heat exchanger tubesheets ........................ 753
Annex K (informative) Additional information on expansion bellows design .......................................... 802
Annex L (informative) Basis for design rules related to additional non-pressure loads ...................... 809
Annex M (informative) In service monitoring of vessels operating in fatigue or creep service ......... 811
UNI EN 13445-3:2021
5
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex N (informative) Bibliography to Clause 18................................................................................................ 814
Annex O (informative) Physical properties of steels .......................................................................................... 815
Annex P (normative) Classification of weld details to be assessed using principal stresses ............... 823
Annex Q (normative) Simplified procedure for the fatigue assessment of unwelded zones................ 836
Annex R (informative) Coefficients for creep-rupture model equations for extrapolation of
creep-rupture strength ..................................................................................................................................... 837
Annex S (informative) Extrapolation of the nominal design stress based on time-independent
behaviour in the creep range.......................................................................................................................... 844
Annex T (normative) Design by experimental methods .................................................................................... 849
Annex U (informative) Guidance on negligibility of additional thermal cycles in fatigue and
ratcheting assessment....................................................................................................................................... 863
Annex V (informative) Consider a buffer for unknown nozzle loads — Opening design for
unknown nozzle loads ....................................................................................................................................... 872
Annex Y (informative) History of EN 13445-3 ....................................................................................................... 873
Annex ZA (informative) Relationship between this European Standard and the essential
requirements of Directive 2014/68/EU aimed to be covered ............................................................ 874
6
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
European foreword
This document (EN 13445-3:2021) has been prepared by Technical Committee CEN/TC 54 “Unfired pressure
vessels”, the secretariat of which is held by BSI.
This European Standard shall be given the status of a national standard, either by publication of an identical text
or by endorsement, at the latest by November 2021, and conflicting national standards shall be withdrawn at
the latest by November 2021.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document has been prepared under a standardization request given to CEN by the European Commission
and the European Free Trade Association, and supports essential requirements of EU Directive(s).
For relationship with EU Directive(s), see informative Annex ZA, which is an integral part of this document.
List of all parts in the EN 13445 series can be found on the CEN website.
Although these Parts may be obtained separately, it should be recognised that the Parts are inter-dependant. As
such the manufacture of unfired pressure vessels requires the application of all the relevant Parts in order for
the requirements of the Standard to be satisfactorily fulfilled.
Corrections to the standard interpretations where several options seem possible are conducted through the
Migration Help Desk (MHD). Information related to the Help Desk can be found at http://www.unm.fr
(en13445@unm.fr). A form for submitting questions can be downloaded from the link to the MHD website.
After subject experts have agreed an answer, the answer will be communicated to the questioner. Corrected
pages will be given specific issue number and issued by CEN according to CEN Rules. Interpretation sheets will
be posted on the website of the MHD.
This document supersedes EN 13445-3:2014. This new edition incorporates the Amendments which have been
approved previously by CEN members, and the corrected pages up to Issue 5 without any further technical
change. Annex Y provides details of significant technical changes between this European Standard and the
previous edition.
Amendments to this new edition may be issued from time to time and then used immediately as alternatives to
rules contained herein. It is intended to deliver a new Issue of EN 13445:2021 each year, starting with the
precedent as Issue 1, consolidating these Amendments and including other identified corrections.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to announce this European Prestandard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
UNI EN 13445-3:2021
7
EN 13445-3:2021 (E)
Issue 1 (2021-05)
1 Scope
This Part of this document specifies requirements for the design of unfired pressure vessels covered by EN
13445-1:2021 and constructed of steels in accordance with EN 13445-2:2021.
EN 13445-5:2021EN 13445-5:2021, Annex C specifies requirements for the design of access and inspection
openings, closing mechanisms and special locking elements.
NOTE
This Part applies to design of vessels before putting into service. It may be used for in service calculation
or analysis subject to appropriate adjustment.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references, the
latest edition of the referenced document (including any amendments) applies.
EN 286-2:1992, Simple unfired pressure vessels designed to contain air or nitrogen — Part 2: Pressure vessels
for air braking and auxiliary systems for motor vehicles and their trailers
EN 764-1:2015+A1:2016, Pressure equipment — Terminology — Part 1: Pressure, temperature, volume,
nominal size
EN 764-2:2012, Pressure equipment — Part 2: Quantities, symbols and units
EN 764-3:2002, Pressure equipment — Part 3: Definition of parties involved
EN 837-1:1996, Pressure gauges — Part 1: Bourdon tube pressure gauges — Dimensions, metrology,
requirements and testing
EN 837-3:1996, Pressure gauges — Part 3: Diaphragm and capsule pressure gauges — Dimensions,
metrology, requirements and testing
EN 1092-1:2018, Flanges and their joints — Circular flanges for pipes, valves, fittings and accessories, PNdesignated — Part 1: Steel flanges
EN 1591-1:2013, Flanges and their joints — Design rules for gasketed circular flange connections —
Calculation method
EN 1708-1:2010, Welding — Basic weld joint details in steel — Part 1: Pressurized components
EN 1990:20021), Eurocode — Basis of structural design
EN 1992-1-1:2005, Eurocode 2 — Design of concrete structures — Part 1-1: General rules and rules for
buildings
EN 1991-1-4:20052), Eurocode 1: Actions on structures — Part 1-4: General actions — Wind actions
1) EN 1990:2002 is impacted by the stand-alone amendment EN 1990:2002/A1:2005 and the corrigendum
EN 1990:2002/AC:2010.
2) EN 1991-1-4:2005 is impacted by the stand-alone amendment EN 1991-1-4:2005/A1:2010 and the corrigendum
EN 1991-1-4:2005/AC:2010.
8
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
EN 1991-1-6:2005, Eurocode 1 — Actions on structures — Part 1-6: General actions — Actions during
execution
EN 1998-1:2004, Design of structures for earthquake resistance — Part 1: General rules, seismic actions and
rules for buildings
EN 10204:2004, Metallic products – Type of inspection documents
EN 10222-1:1998, EN 10222-1:1998/A1:2002, Steel forgings for pressure purposes — Part 1: General
requirements for open die forgings
EN 12195-1:2010, Load restraining on road vehicles — Safety — Part 1: Calculation of securing forces
EN 13445-1:2021, Unfired pressure vessels — Part 1: General
EN 13445-2:2021, Unfired pressure vessels — Part 2: Materials
EN 13445-4:2021, Unfired pressure vessels — Part 4: Fabrication
EN 13445-5:2021EN 13445-5:2021, Unfired pressure vessels — Part 5: Inspection and testing
EN 13445-8:2021, Unfired pressure vessels — Part 8: Additional requirements for pressure vessels of
aluminium and aluminium alloys
EN 13555:2014, Flanges and their joints — Gasket parameters and test procedures relevant to the design
rules for gasketed circular flange connections
EN ISO 4014:2011, Hexagon head bolts — Product grades A and B (ISO 4014:2011)
EN ISO 4016:2011, Hexagon head bolts — Product grade C (ISO 4016:2011)
EN ISO 15613:2004, Specification and qualification of welding procedures for metallic materials —
Qualification based on pre-production welding test
ISO 261:1998, ISO general purpose metric threads — General plan
3 Terms and definitions
For the purposes of this Part of this document, the terms and definitions given in EN 13445-1:2021, EN 134452:2021 and the following apply:
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http://www.electropedia.org/
— ISO Online browsing platform: available at http://www.iso.org/obp
NOTE
EN 13445-1:2021 and EN 13445-2:2021 have adopted terminology, symbols and definitions of EN 7641:2015+A1:2016, EN 764-2:2012 and EN 764-3:2002.
3.1
action
imposed thermo-mechanical influence which causes stress and/or strain in a structure, e.g. an imposed
pressure, force, temperature
UNI EN 13445-3:2021
9
EN 13445-3:2021 (E)
Issue 1 (2021-05)
3.2
analysis thickness
effective thickness available to resist the loading depending on the load case, see 5.3.2
3.3
assumed thickness
thickness assumed by the designer between the minimum required shell thickness e and the shell analysis
thickness ea
3.4
calculation pressure
differential pressure used for the purpose of the design calculations for a component
[SOURCE: EN 764-1:2015+A1:2016]
3.5
calculation temperature
temperature used for the purpose of the design calculations for a component
[SOURCE: EN 764-1:2015+A1:2016]
3.6
chamber
fluid space within a unit of pressure equipment
[SOURCE: EN 764-1:2015+A1:2016]
3.7
component
part of pressure equipment which can be considered as an individual item for the calculation
[SOURCE: EN 764-1:2015+A1:2016]
3.8
creep range
temperature range in which material characteristics used in design are time dependent
Note 1 to entry: See also 5.1.
3.9
cryogenic applications
applications involving liquefied gases at low temperature
3.10
design pressure
pressure at the top of each chamber of the pressure equipment chosen for the derivation of the calculation
pressure of each component
[SOURCE: EN 764-1:2015+A1:2016]
Note 1 to entry: Any other location may be specified.
10
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
3.11
design temperature
temperature chosen for the derivation of the calculation temperature of each component
[SOURCE: EN 764-1:2015+A1:2016]
3.12
differential pressure
pressure which algebraic value is equal to the pressure difference on either side of a separation wall
[SOURCE: EN 764-1:2015+A1:2016]
3.13
governing weld joint
main full penetration butt joint the design of which, as a result of membrane stresses, governs the
thickness of the component
3.14
load case
combination of coincident actions
3.15
main joint
weld joint assembling main pressure bearing parts
3.16
maximum permissible pressure
maximum pressure obtained from the design by formulae or relevant procedures of EN 13445-3:2021 for a
given compoment in a given load case, or for the whole pressure vessel the minimum of these maximum
permissible pressures of all compoments
Note 1 to entry: The differences of the nominal design stress f, the analysis thickness ea and the joint coefficient z for
the calculation of the maximum permissible pressure in different load cases are specified in 5.3.2.
Note 2 to entry: If no explicit formula is given for the maximum permissible pressure Pmax then Pmax may be calculated
as pressure which gives the required thickness equal to the analysis thickness.
Note 3 to entry: The maximum permissible pressure Pmax used for the simplified assessment of fatigue life in
Clause 17 and for the calculation of the equivalent full pressure in 5.4.2 is calculated for normal operating load cases.
3.17
minimum possible fabrication thickness
minimum possible thickness after fabrication
3.18
nominal design stress
stress value to be used in the formulae for the calculation of pressure components
3.19
nominal thickness
thickness as specified on the drawings
3.20
test pressure
pressure to which the equipment is subjected for test purposes
[SOURCE: EN 764-1:2015+A1:2016]
UNI EN 13445-3:2021
11
EN 13445-3:2021 (E)
Issue 1 (2021-05)
3.21
test temperature
temperature at which the pressure test of the pressure equipment is carried out
[SOURCE: EN 764-1:2015+A1:2016]
3.22
volume
internal volume of a chamber, including the volume of nozzles to the first connection (flange, coupling,
weld) and excluding the volume of internal permanent parts (e.g. baffles, agitators)
[SOURCE: EN 764-1:2015+A1:2016]
3.23
weld throat thickness of a fillet weld
height of the inscribed isosceles triangle measured from the theoretical root point
4 Symbols and abbreviations
For the purposes of this Part of this document, the general symbols and abbreviations shall be in accordance
with EN 13445-1:2021, EN 13445-2:2021 and Table 4-1:
12
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 4-1 — Symbols, quantities and units c
Symbol
a
e
en
emin
ea
c
f
d
exp
test
neq
P
Pd
Pmax
PS, Ps
Ptest
ReH
Rm
Rm/T
Rp0,2
Rp0,2/T
Rp1,0
Rp1,0/T
T
Td
Ttest
TS max , TS min
V
z

Quantity
weld throat thickness
required thickness
nominal thickness
minimum possible fabrication thickness
analysis thickness
corrosion allowance
nominal design stress
maximum value of the nominal design stress for normal operating load cases
maximum value of the nominal design stress for exceptional load cases
maximum value of the nominal design stress for testing load cases
number of equivalent full pressure cycles (see 5.4.2)
calculation pressure
design pressure
maximum permissible pressure
maximum allowable pressure
test pressure
upper yield strength
tensile strength
tensile strength at temperature T
0,2 % proof strength
0,2 % proof strength at temperature T
1,0 % proof strength
1,0 % proof strength at temperature T
calculation temperature
design temperature
test temperature
maximum/minimum allowable temperatures
Unit
mm
mm
mm
mm
mm
mm
MPa
MPa
MPa
MPa
MPa a
MPa a
MPa a
MPa a
MPa a
MPa
MPa
MPa
MPa
MPa
MPa
MPa
°C
°C
°C
°C
volume
joint coefficient
Poisson's ratio
mm3 b
—
—
a MPa for calculation purpose only, otherwise the unit may be bar (1 MPa = 10 bar).
b mm3 for calculation purpose only, otherwise the unit should be litre.
c Formulae used in this standard are dimensional.
UNI EN 13445-3:2021
13
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5 Basic design criteria
5.1 General
EN 13445-3:2021 is applicable only when:
a) materials and welds are not subject to localized corrosion in the presence of products which the
vessel is to contain or which can be present in the vessel under reasonably foreseeable conditions.
b) either all calculation temperatures are below the creep range or a calculation temperature is in the
creep range and time dependent material characteristics are available in the materials standard.
NOTE
See definition 3.8 of creep range.
For the purpose of design, the creep range is the temperature range in which time independent material
characteristics are no more governing in the determination of the nominal design stress.
The material strength characteristics used shall be related to the specified lifetimes in the various creep load
cases
5.2 Corrosion, erosion and protection
5.2.1 General
Whenever the word "corrosion" is used in this standard it shall be taken to mean corrosion, oxidation, scaling,
abrasion, erosion and all other forms of wastage.
NOTE 1
Stress corrosion cracking may occur under certain conditions of temperature and environment. A
corrosion allowance is not an appropriate way of dealing with stress corrosion. Under such conditions, consideration
shall be given to the materials used and the residual stresses in the fabricated vessel.
NOTE 2
It is impossible to lay down definite precautionary guidelines to safeguard against the effects of corrosion
owing to the complex nature of corrosion itself, which may occur in many forms, including but not limited to the
following:
—
chemical attack where the metal is dissolved by the reagents. It may be general over the whole surface or
localized (causing pitting) or a combination of the two;
—
rusting caused by the combined action of moisture and air;
—
erosion corrosion where a reagent otherwise innocuous flows over the surface at velocity greater than some
critical value;
—
high temperature oxidation (scaling).
Consideration should be given to the effect which corrosion (both internal and external) may have upon the useful life
of the vessel. When in doubt, corrosion tests should be undertaken. These should be carried out on the actual metal
(including welds or combination of metals) under exposure to the actual chemicals used in service. Corrosion tests
should be continued for a sufficiently long period to determine the trend of any change in the rate of corrosion with
respect to time.
NOTE 3
It is very dangerous to assume that the major constituent of a mixture of chemicals is the active agent, as in
many cases small traces of a substance can exert an accelerating or inhibiting effect out of all proportion to the
amount present. Fluid temperatures and velocities from corrosion test data should be equivalent to those met in
operation.
14
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5.2.2 Additional thickness to allow for corrosion
In all cases where reduction of the wall thickness is possible as a result of surface corrosion or erosion, of one or
other of the surfaces, caused by the products contained in the vessel or by the atmosphere, a corresponding
additional thickness sufficient for the design life of the vessel components shall be provided. The value shall be
stated on the design drawing of the vessel. The amounts adopted shall be adequate to cover the total amount
of corrosion expected on either or both surfaces of the vessel.
A corrosion allowance is not required when corrosion can be excluded, either because the materials, including
the welds, used for the pressure vessel walls are corrosion resistant relative to the contents and the loading or
are reliably protected (see 5.2.4).
No corrosion allowance is required for heat exchanger tubes and other parts in similar heat exchanger duty,
unless a specific corrosive environment requires one.
This corrosion allowance does not ensure safety against the risk of deep corrosion or stress corrosion cracking,
in these cases a change of material, cladding, etc. is the appropriate means.
Where deep pitting may occur, suitably resistant materials shall be selected, or protection applied to the
surfaces.
5.2.3 Inter-relation of thickness definitions
The inter-relation of the various definitions of thickness is shown in Figure 5-1.
UNI EN 13445-3:2021
15
EN 13445-3:2021 (E)
Issue 1 (2021-05)
m
e
c
ea
e m in
e
en
eex
Key
e
is the required thickness;
en
is the nominal thickness;
emin
ea
is the minimum possible fabrication thickness (emin = en - e);
is the analysis thickness (ea = emin – c);
c
is the corrosion allowance;
e
m
is the absolute value of the possible negative tolerance on the nominal thickness (e.g. taken from the material standards);
eex
is the allowance for possible thinning during manufacturing process;
is the extra thickness to make up to the nominal thickness.
Figure 5-1 — Relationship of thickness definitions
5.2.4 Linings and coatings
Only completely impervious, sufficiently thick and chemically stable layers with an average life not less than that
of the pressure vessel shall be considered to be reliable protection against corrosion, but thin layers (like
painting, electroplating, tinning, etc.) and coatings which are known to have to be renewed during the lifetime
of the pressure vessel components shall not be used. For plastic coatings the suitability shall be justified, taking
into account, among other factors, the risk of diffusion. The test of corrosion protection outlined in EN 2862:1992 is not considered to be adequate for the pressure vessels covered by this standard.
Vessels may be fully or partially lined (or coated) with corrosion-resistant material. Linings should be integrally
bonded to the vessel base metal. Loose or intermittently attached linings may be used taking the following into
consideration:
— sufficient ductility of the lining to accommodate any strain likely to be imposed on it during service and
testing conditions, differential thermal expansion being taken into consideration;
— for non-metallic coatings, the surface finish of the base material.
Provided contact between the corrosive agent and the vessel base material is excluded, no corrosion allowance
needs be provided against internal wastage of the base material.
16
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5.2.5 Wear plates
Where severe conditions of erosion and abrasion arise, local protective or wear plates shall be fitted directly in
the path of the impinging material.
5.3 Load cases
5.3.1 Actions
In the design of a vessel the following actions shall be taken into account, where relevant:
a) internal and/or external pressure;
b) maximum static head of contained fluid under operating conditions;
c) weight of the vessel;
d) maximum weight of contents under operating conditions;
e) weight of water under hydraulic pressure test conditions;
f)
wind, snow and ice loading;
g) earthquake loading;
h) other loads supported by or reacting on the vessel, including loads during transport and installation.
When necessary, consideration shall be given to the effect of the following loads in cases where it is not
possible to demonstrate the adequacy of the proposed design e.g. by comparison with the behaviour of
other vessels:
i)
stresses caused by supporting lugs, ring, girders, saddles, internal structures or connecting piping or
intentional offsets of median lines on adjacent components;
j)
shock loads caused by water hammer or surging of the vessel contents;
k) bending moments caused by eccentricity of the centre of the working pressure relative to the neutral
axis of the vessel;
l)
stresses caused by temperature differences including transient conditions and by differences in
coefficients of thermal expansion;
m) stresses caused by fluctuations of pressure, temperature, and external loads applied to the vessel;
n) stresses caused by the decomposition of unstable fluids.
NOTE
The combination of actions is given in 5.3.2.4.
5.3.2 Classification of load cases
5.3.2.1
Normal operating load cases
Normal operating load cases are those acting on the pressure vessel during normal operation, including start-up
and shutdown.
UNI EN 13445-3:2021
17
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For normal operating load cases the following calculation parameters shall be used:
— the calculation pressure P as defined in 5.3.10;
— the nominal design stresses f = fd as defined in 6.1.3 at calculation temperature;
— the analysis thickness is ea = emin – c as defined in 5.2.3;
— the joint coefficient z as specified in Table 5.6-1.
5.3.2.2
Exceptional load cases
Exceptional load cases are those corresponding to events of very low occurrence probability requiring the safe
shutdown and inspection of the vessel or plant. Examples are pressure loading of secondary containment or
internal explosion.
For exceptional load cases the following calculation parameters shall be used:
— the calculation pressure P as defined in 5.3.10;
— the nominal design stresses f = fexp as defined in 6.1.2 and 6.1.3 at calculation temperature;
— the analysis thickness is ea = emin – c as defined in 5.2.3;
— the joint coefficient z = 1,0 as specified in 5.6.
5.3.2.3
Testing load cases
Testing load cases are:
— Testing load cases for final assessment related to tests after manufacture defined by EN 134455:2021EN 13445-5:2021,
or
— Testing load cases in service related to repeated tests during the life time defined by the user.
For testing load cases for final assessment the following calculation parameters shall be used:
— the test pressure Ptest = Pt as defined in EN 13445-5:2021EN 13445-5:2021;
— the nominal design stresses f = ftest as defined in 6.1.2 and 6.1.3 at test temperature;
— the analysis thickness is ea = emin with emin as defined in 5.2.3 (no corrosion allowance);
— the joint coefficient z = 1,0 as specified in 5.6.
For testing load cases in service the following calculation parameters shall be used:
— the test pressure Ptest = test pressure in service as defined by the user taking into account possible
national regulation. The modification of the test pressure for vessels with hydrostatic pressure
according to EN 13445-5:2021EN 13445-5:2021, 10.2.3.3.1 b) shall be applied using the user specified
test pressure in service instead of Pt;
18
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— the nominal design stresses f = ftest as defined in 6.1.2 and 6.1.3 at test temperature;
— the analysis thickness is ea = emin – c as defined in 5.2.3;
— the joint coefficient z = 1,0 as specified in 5.6.
5.3.2.4
Load combinations
5.3.2.4.1
General
Load combinations of non-pressure loads in Table 5.3.2.4-1 are used in connection with calculations according
to Clause 16 and Annex C (linear elastic behaviour). The basic calculation of pressure envelope by design
pressures and temperatures shall be made before Clause 16 (or Annex C) calculations. The load combinations in
Table 5.3.2.4-1 are minimum to be taken into account, if they are relevant. There may also be other loads.
5.3.2.4.2
Specific definitions
5.3.2.4.2.1
Dead loads
Maximum dead load (Gmax) is the weight of the whole un-corroded vessel with all internals (trays, packing, etc.),
attachments, insulation, fire protection, piping, platforms and ladders.
Corroded dead load (Gcorr) is defined as Gmax but with the weight of the corroded vessel.
Minimum dead load (Gmin) is the weight of the un-corroded vessel during the installation phase, excluding the
weight of items not already mounted on the vessel before erection (e.g. removable internals, platforms, ladders,
attached piping, insulation and fire protection).
NOTE
weight.
A scaffold is normally self-supported. In this case, the weight of the scaffold is not included in the vessel
Transport dead load (Gtrans) is the case, when vessel has the removable internals and insulation already mounted
on the vessel in the workshop.
5.3.2.4.2.2
Live loads
Live loads (L) used in this clause are weight loads of the contents (fluids or solids in the bottom of the vessel, on
trays and in packing) and traffic loads on platforms and ladders by personnel and machinery.
5.3.2.4.2.3
Wind loads
Wind loads (W) are horizontal global pressure loads caused by wind and acting on the projected area of the
vessel and its attachments, as influenced by the force coefficients (see EN 1991-1-4:2005).
5.3.2.4.2.4
Earthquake loads
Earthquake loads (E) are quasi-static horizontal forces on the vessel sections caused by seismic accelerations at
the base of vessel calculated by the “lateral force method of analysis” (see EN 1998-1:2004).
UNI EN 13445-3:2021
19
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5.3.2.4.2.5
Forces from attached external piping
Reaction forces from attached external piping are forces resulting from weight (G), wind (W), earthquake (E)
and other additional forces (F) as far as they influence the global equilibrium of the vessel (see 22.4.6 for
columns).
NOTE
Forces and moments on nozzles and supports on the vessel caused by attached external piping can act as
internal and/or external loads. Internal loads are those that cause local loads only and have no influence on the global
equilibrium because they are self-compensating. Furthermore, attached pipes can either load the vessel or restrain it
depending on their layout. Consideration of these aspects is given in the recommendations in 22.4.6.
5.3.2.4.3
Specific symbols and abbreviations
The following specific symbols and abbreviations are used in Table 5.3.2.4-1 in addition to those in Clause 4:
E
earthquake load (see 5.3.2.4.2.4)
F
additional loads from piping (thermal expansion loads) (see 5.3.2.4.2.5)
fB,op
nominal design stress for operation conditions for anchor bolts, see Formula (6.7–1)
Gmin
minimum dead loads (see 5.3.2.4.2.1)
Gmax
maximum dead loads (see 5.3.2.4.2.1)
Gcorr
corroded dead loads (see 5.3.2.4.2.1)
Gtrans
transport dead loads (see 5.3.2.4.2.1)
L
live loads of each loading case (contents, etc.) (see 5.3.2.4.2.2)
Pi
internal calculation pressure as defined in 5.3.10 for P > 0 (including hydrostatic pressure)
Pe
external calculation pressure as defined in 5.3.10 for P < 0 (e.g. vacuum)
W
wind load (see5.3.2.4.2.4)
σc,all
maximum allowable compressive stress for operation conditions in accordance with 16.14.8, with σe as
defined in 8.4 and with a safety factor of 1,5 in Formula (16.14–29)
σc,all,test
maximum allowable compressive stress for test conditions in accordance with 16.14.8, with σe as defined in
8.4 and with safety factor 1,05 in Formula (16.14–29)
&
operator which means: superposition of the different load types for the axial and lateral forces, the bending
moments and the resulting shear and longitudinal stresses using the beam theory for non-pressure loads
and the membrane theory for pressure loads
20
UNI EN 13445-3:2021
Pi, Gmax, L, F, W
Pe, Gmax, L, F, W
Gmax, L, F, W
Gcorr, W
Gmin, W
Pi, Gmax, L, E
Pe, Gmax, L, E
Gmax, L, E
Ptest, Gmax, Ltest, W Ptest & Gmax & Ltest & 0,6·W
Gmax
Gtrans
LC1
LC2
LC3
LC4
LC5
LC6
LC7
LC8
LC9
LC10
LC11
ftest
ftest
ftest
fexpc
fexpc
fexpc
fd
fd
fd
fd
fd
fd
σc,all,test
σc,all,test
σc,all,test
σc,all,test
σc,all,test
σc,all,test
σc,all
σc,all
σc,all
σc,all
σc,all
σc,all
Allowable compressive
stress for shells
N/A
N/A
fB,op
1,2· fB,op
1,2· fB,op
1,2· fB,op
fB,op
fB,op
fB,op
fB,op
fB,op
fB,op
external
Transport
Lifting (Crane)
Test with test pressure, test
filling and wind
Operation without pressure but
with earthquake
Operation
with
external
pressure and earthquake
Operation with internal pressure
and earthquake
Installation
Shut down (no pressure,
contents and thermal reactions)
Operation without pressure but
with wind
Operation
with
pressure and wind
Operation with internal pressure
and wind
Operation with internal pressure
Allowable tensile stress Explanations
for anchor bolts
After exceptional load case the vessel shall have re-inspection.
c
UNI EN 13445-3:2021
Real operating pressure may be used instead of 0,9*Pi, if it is limited either naturally (e.g. steam temperature) or by safety related control and instrumentation system.
b
a
21
Transport load case shall be taken into account on basis of manufacturer’s risk analysis for the vessel, if it proves to be critical for the vessel depending on the transport way (road, ship or
train). If no special regulations are specified the following transport loads shall be considered: downwards: 1,4 Gtrans, sidewards and upwards: 0,5*Gtrans driving direction: 0,8*Gtrans. The transport
loads shall be agreed with transport company so that the transport will not damage the vessel (see EN 12195-1).
a
≥ 1,5*Gmax
Gmax & L & E
Pe & Gmax & L & E
0,9·Pi & Gmax & L & E
Gmin & 0,7·W
Gcorr & 1,1·W
Gmax & L & F & 1,1·W
Pe & Gmax & L & F & 1,1·W
0,9·Pi & Gmax & L & F & 1,1·Wb
Pi & Gmax
Pi, Gmax
LC0
Load combination including Allowable tensile
weighting factors
stress for shells
Types of load
included
Load
Case
Table 5.3.2.4–1 — Load combinations d
EN 13445-3:2021 (E)
Issue 1 (2021-05)
22
The global effect of additional piping loads on shell stresses or anchoring shall be taken into account by designer, if considered relevant.
UNI EN 13445-3:2021
For LC10 and LC11: In calculation of allowable bending stress σb,all for transport and lifting cases according to 16.6.6, the nominal design stress ftest can be used instead of f
and K2 shall be set equal 1,05.
For LC6, LC7 and LC8: For Earthquake Loading conditions the simultaneous presence of wind loading need not be considered (see EN 1990:2002+A1:2005, Annex A)
For LC9: The reduced factor for the wind load is in accordance with EN 1991-1-6:2005 for duration times < 3 d.
For LC5: The wind load in this case depends on configuration at this time (with or without scaffold, platforms, insulation). The reduced factor for the wind load is in
accordance with EN 1991-1-6:2005 for duration times < 12 months.
For LC3 and LC8: These load cases are not required when both loading cases LC1 and LC2, or LC6 and LC7 are applicable, i.e. internal and external pressure are applied.
For LC1 and LC6: The factor 0,9 is applied to the internal calculation pressure Pi because the internal operating pressure is normally 10 % below PS due to the pressure
limiting device.
For LC1 and LC2: If more than one combination of coincident design pressure and design temperature exists then all combinations shall be investigated.
Alternatively a single combination of the maximum pressure and maximum temperature of all the cases may be used. It is not certain that the governing condition of
coincident pressure and temperature is also governing for the load combinations.
Remarks
EN 13445-3:2021 (E)
Issue 1 (2021-05)
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5.3.3 Failure modes considered in this Part
a) gross plastic deformation (GPD);
b) plastic instability (burst);
c) elastic or plastic instability (buckling);
d) progressive deformation (PD);
e) fatigue;
f)
creep rupture;
g) creep deformation;
h) creep fatigue.
NOTE 1
For more detailed information on failure modes see Annex B.
NOTE 2
Plastic instability is covered by the limits on GPD.
5.3.4 Maximum allowable pressure PS of a vessel (or a chamber)
The maximum allowable pressure PS of a vessel (or a chamber), for normal operating load cases, shall be
defined at a specified location. This shall be the location of connection of protective and/or limiting devices or
the top of the vessel (or chamber) or, if not appropriate, any point specified.
1)
For internal pressure, the maximum allowable pressure shall not be less than:
a) the differential pressure which will exist at the same specified location in the vessel (or chamber)
when the pressure relieving device starts to relieve;
b) the maximum differential pressure which can be attained in service at the same specified location
where this pressure is not limited by a relieving device;
2)
For external pressure, the absolute value of the maximum allowable pressure shall not be less than:
a) the absolute value of the differential pressure which will exist at the same specified location in
the vessel (or chamber) when the pressure relieving device starts to relieve;
b) the largest absolute value of the differential pressure which can be attained in service at the same
specified location where this pressure is not limited by a relieving device.
5.3.5 Design pressure of a vessel (or a chamber)
The absolute value of the design pressure Pd for normal operating load cases shall not be smaller than the
absolute value of PS.
UNI EN 13445-3:2021
23
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5.3.6 Maximum/minimum allowable temperatures TSmax and TSmin of a vessel (or a chamber)
TSmax and TSmin shall be specified for normal operating load cases.
5.3.7 Design temperature of a vessel (or a chamber)
The design temperature Td shall be not less than the maximum fluid temperature corresponding to the
coincident design pressure.
If the maximum allowable temperature TSmax is below 20 °C, the design temperature shall be 20 °C.
5.3.8 Design pressure - temperature combinations for normal operating load cases
More than one set of coincident design pressures and temperatures are permissible.
5.3.9 Design pressure-temperature combinations for testing or exceptional load cases
Design pressure-temperature combinations corresponding to testing or exceptional load cases (see 5.3.2) are
also permissible.
5.3.10 Calculation pressure of a component
The calculation pressure P shall be based on the most severe condition of coincident differential pressure and
temperature. It shall include the static and dynamic head where applicable, and shall be based on the
maximum possible differential pressure in absolute value between the inside and outside of the vessel (or
between the two adjacent chambers).
Vessels subject to external pressure shall be designed for the maximum differential pressure in absolute value
to which the vessel may be subjected in service. Vessels subject to vacuum shall be designed for a full pressure
of 0,1 MPa unless it can be shown that the amount of partial vacuum is limited, e.g. by a vacuum break valve or
similar device, in which case a lower design pressure between 0,1 MPa and the set pressure of this safety
device may be agreed.
5.3.11 Calculation temperature of a component
The calculation temperature T shall not be less than the actual metal temperature expected in service or,
where the through thickness temperature variation is known, the mean wall temperature. The calculation
temperature shall include an adequate margin to cover uncertainties in temperature prediction. Where
different metal temperatures can confidently be predicted for different parts of the vessel, the calculation
temperature for any point in the vessel may be based on the predicted metal temperature.
5.4 Design methods
5.4.1 General
This Part provides requirements for the design of pressure vessels or pressure vessel parts using design by
formulae (DBF):
In addition, two series of methods may be used to supplement or replace DBF:
24
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) methods based on design by analysis (DBA), namely Design by Analysis – Direct Route covered by
Annex B and Design by Analysis – Method based on Stress Categories, covered by Annex C;
b) methods based on experimental techniques, covered by Annex T.
5.4.2 Vessels of all testing groups, pressure loading predominantly of non-cyclic nature
The DBF requirements specified in Clauses 7 to 16, Annexes G and J, and in Clause 19 (for testing subgroups 1c and 3c only) and the DBA requirements of Annex B and Annex C provide satisfactory designs for
pressure loading of non-cyclic nature, i.e. when the number of full pressure cycles or equivalent full pressure
cycles is less than or equal to 500.
n
eq
(5.4-1)
 500
The equivalent number of full pressure cycles
n
eq


 P
i
n 
i  P
 m ax




n
eq
is given by:
3
(5.4-2)
In the above equation, Pmax is the maximum permissible pressure Pmax calculated for the whole vessel (see 3.16)
in the normal operating load case (see 5.3.2.1).
For simplification, Pmax may be replaced by the calculation pressure P.
NOTE
The value of 500 equivalent full pressure cycles is only a rough indication. It can be assumed that for
components with irregularities of profile, strongly varying local stress distributions, subjected to additional nonpressure loads, fatigue damage can occur before 500 cycles.
Cyclic thermal loads can be neglected if:
— for start-up and shutdown cycles, the number shall not exceed 2 000 and the rate of temperature
change at the surface shall be less than 60 °C per hour for ferritic steel sections. The designer can
specify a higher rate of surface temperature change based on favourable/good industry experience
and practice;
— if the requirements of Annex U are satisfied for operating conditions.
If these conditions on pressure and thermal loads are met, then no fatigue analysis is necessary and the
standard requirements of non-destructive testing given in EN 13445-5 shall be applied.
If these conditions cannot be met, then a fatigue assessment is necessary according to either Clause 17 or
Clause 18
5.4.3 Vessels of testing group 4
Pressure vessels to testing group 4, as defined in EN 13445-5:2021EN 13445-5:2021, are intended for
predominantly non-cyclic operation and calculation temperatures below the creep range. They are limited for
operation up to 500 full pressure cycles or equivalent full pressure cycles.
NOTE
When the number of equivalent full pressure cycles has reached 500, a hydraulic test should be
performed and followed by a complete visual examination. If the test is successfully passed, then the operation can
be continued for a new 500 cycles period.
UNI EN 13445-3:2021
25
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5.4.4 Vessels of testing group 1, 2, and 3, working below the creep range, pressure loading of
predominantly cyclic nature
If the number of full pressure cycles or equivalent full pressure cycles is likely to exceed 500, the calculations of
vessels of testing group 1, 2 and 3 shall be completed by a simplified fatigue analysis, as given in Clause 17 or, if
necessary, by a detailed fatigue analysis, as given in Clause 18.
In addition Clauses 17 and 18 specify conditions for the determination of critical zones where additional
requirements on weld imperfections and NDT shall be applied, as defined in EN 13445-5:2021EN 13445-5:2021,
Annex G.
5.4.5 Fatigue analysis of bellows
Specific fatigue curves are given in Clause 14 for bellows.
5.4.6 Design by analysis
If for a part no requirement is supplied in Clauses 7 to 16, Annexes G and J, the rules given in Annexes B and C
shall be applied.
The rules of Annex B, Design by Analysis – Direct Route, are applicable to vessels or vessel parts designed to
testing group 1 only.
5.4.7 Experimental techniques
Experimental techniques may be used to verify the adequacy of the design. These methods may be applied
without calculation when the product of the maximum allowable pressure PS and the volume V is less than
6 000 barL otherwise they supplement a design by formulae or a design by analysis. The rules of Annex T shall
be applied.
5.4.8 Prevention of brittle fracture
Detailed recommendations to safeguard against brittle fracture of steel vessels are given in EN 13445-2:2021,
Annex B.
5.5 Thickness calculations (DBF)
5.5.1 Determination of the required thickness
Unless otherwise stated, all design calculations shall be made in the corroded condition with a consistent set of
dimensions (thickness, diameter, etc.).
The formulae in this Part comprise either:
— a direct method to give the required thickness; or
— an iterative check that the analysis thickness is adequate.
Tolerances and fabrication allowances shall be additional, as shown in Figure 5-1.
NOTE
Possible limitations of the thickness may exist in requirements dealing with details.
5.5.2 Clad components
Corrosion-resistant claddings may be included in the calculation of the required wall-thickness against design
pressure only in the case of cladding of integrally-bonded type (i.e. explosion cladding, weld cladding, or such
other methods).
26
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
In the case of design against instability, the strength of the cladding shall not be taken into account.
DBF rules of Clauses 7 to 16 can be applied with an equivalent thickness which takes into account the presence
of the cladding. The nominal design stress to use is that for the base material: m1.
If the nominal design stress of the cladding m2 is greater or equal to that of the base material, the equivalent
thickness eeq is equal to the sum of the analysis thickness for the cladding and the base material.
e
eq
 e
a, m1
 e
(5.5-1)
a, m2
If the nominal design stress of the cladding is less than that of the base material, the equivalent thickness is:
e
eq
where
 e
a, m1
 e
a, m2

f m2
f
(5.5-2)
m1
subscript m1 is used for base material, and
subscript m2 is used for cladding.
In the fatigue analysis checks of Clauses 17 and 18, the presence of the cladding shall be considered with
respect to both the thermal analysis and the stress analysis. However when the cladding is of the integrallybonded type and the nominal thickness of the cladding is not more than 10 % of the total nominal thickness of
the component, the presence of the cladding may be neglected, i.e. the model is based on the base material
geometry.
5.6 Joint coefficient
For the calculation of the required thickness of certain welded components (e.g. cylinders, cones and spheres),
the design formulae contain z , which is the joint coefficient of the governing welded joint(s) of the
component.
Examples of governing welded joints are:
— longitudinal or helical welds in a cylindrical shell;
— longitudinal welds in a conical shell;
— any main weld in a spherical shell/head;
— main welds in a dished head fabricated from two or more plates.
The following welded joints are not governing welded joints:
— circumferential weld between a cylindrical or conical shell and a cylinder, cone, flange or end other
than hemispherical;
— welds attaching nozzles to shells;
— welds subjected exclusively to compressive stress.
NOTE
Circumferential joints may become governing joints due to external loads.
UNI EN 13445-3:2021
27
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For the normal operating load cases, the value of z is given in Table 5.6-1. It is related to the testing group of
the governing welded joints. Testing groups are specified in EN 13445-5:2021EN 13445-5:2021, Clause 6.
Table 5.6-1 — Joint coefficient and corresponding testing group
z
1
0,85
0,7
Testing Group
1, 2
3
4
In parent material, away from governing joints, z = 1.
For exceptional and testing conditions, a value of 1 shall be used, irrespective of the testing group.
5.7 Design requirements of welded joints
5.7.1 General requirements
The manufacturer shall choose the most suitable joints to meet the standard requirements. In particular, he
shall take account of the following parameters:
— grade and properties of the metals used;
— operating conditions: e.g. loading of predominantly non-cyclic nature or cyclic nature; dangerous or
corrosive fluid;
— applicable testing groups, see EN 13445-5:2021EN 13445-5:2021, 6.6.1.1;
— manufacturing means.
Annex A gives requirements and recommendations for pressure bearing welds. Specific requirements are
included when Design by Analysis – Direct Route of Annex B is used for vessels or vessel parts working in the
creep range.
5.7.2 Longitudinal joints
The components of cylindrical or conical shells, spherical components, and domed or flat ends shall be
assembled by butt welding, using a welding procedure that ensures full penetration.
The mean lines of the components that form longitudinal joints of cylindrical or conical shells as well as joints
on spherical shells shall be aligned in the vicinity of the welded joint within the manufacturing tolerance limits
given in EN 13445-4:2021. Bending effects shall be taken into account in the design.
5.7.3 Circumferential joints
The mean lines of components of same thickness shall be aligned within the tolerance limits of EN 134454:2021.
The mean lines of components of different thicknesses may be non-aligned, but the offset shall not exceed the
alignment of inner or outer surfaces within the tolerances limits given in EN 13445-4:2021.
28
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5.7.4 Special requirements for certain types of joints
5.7.4.1
Joggle joints
Joggle joints, where used, shall satisfy the following conditions:
a) testing groups 3 or 4 for non-cyclic operation, or, in addition, testing groups 1 or 2 for cryogenic
applications;
b) circumferential seams attaching head to shell; all circumferential seams for cryogenic applications;
c) materials 1.1, 1.2 or 8.1;
d) material thickness not exceeding 8 mm; 12 mm for cryogenic applications;
e) diameter not exceeding 1 600 mm, otherwise a full size weld procedure test is required for diameters
exceeding 1 600 mm. The diameter of the test piece shall not be less than the nominal diameter and
not be larger than twice the nominal diameter. The test shall be performed and recorded in
accordance with EN ISO 15613:2004. For cryogenic applications the diameter is not limited.
f) calculation temperature
— -10 °C  T  120 °C for materials 1.1 and 1.2;
— -196 °C  T  120 °C for materials 8.1;
— -40 °C  T  120 °C for materials 1.1 and 1.2, for cryogenic applications.
g) non-corrosive conditions;
h) manufacturing tolerances of EN 13445-4:2021.
5.7.4.2
Joints with permanent backing strips
Joints with permanent backing strips shall be allowed if the following conditions are all satisfied:
a) testing groups 3 or 4 for non-cyclic operation, or, in addition, testing groups 1 or 2 for cryogenic
applications;
b) circumferential seams attaching head to shell; all circumferential seams for cryogenic applications;
c) materials 1.1, 1.2 or 8.1;
d) material thickness not exceeding 8 mm; 30 mm for cryogenic applications;
e) diameter not exceeding 1 600 mm, otherwise a full size weld procedure test is required for
diameters exceeding 1 600 mm. The diameter of the test piece shall not be less than the nominal
diameter and not be larger than twice the nominal diameter. The test shall be performed and
recorded in accordance with EN ISO 15613:2004. For cryogenic applications the diameter is not
limited.
UNI EN 13445-3:2021
29
EN 13445-3:2021 (E)
Issue 1 (2021-05)
f)
calculation temperature
— -10 °C  T  120 °C for materials 1.1 and 1.2;
— -196 °C  T  120 °C for materials 8.1;
— -40 °C  T  120 °C for materials 1.1 and 1.2, for cryogenic applications.
g) non-corrosive conditions;
h) manufacturing tolerances of EN 13445-4:2021 for thicknesses not exceeding 8 mm; half of these
tolerances for thicknesses exceeding 8 mm in cryogenic applications.
5.7.4.3
5.7.4.3.1
Lap joints
General case
Lap joints with fillet welds shall be used only when all the following conditions are fulfilled:
a) testing group 4;
b) circumferential joints attaching head to shell;
c) material thickness not exceeding 8 mm;
d) maximum diameter 1 600 mm;
e) materials 1.1;
f)
calculation temperature:
— -10 °C  T  120 °C;
g) non-corrosive conditions;
h) both sides of the lap shall be welded (see Figures C 31 and C 34) except for the cases C 32, C 33 and
C 35 in Table A-2;
i)
manufacturing tolerances of EN 13445-4:2021.
5.7.4.3.2
Connection of bellows
Cases B 2, B 3 and B 5 of Table A-9 shall be used only under non-corrosive conditions.
30
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
6 Maximum allowed values of the nominal design stress for pressure parts
6.1 General
6.1.1 This clause specifies maximum allowed values of the nominal design stress for pressure parts
other than bolts and physical properties of steels.
The values to be used within the creep range are given in Clause 19.
NOTE
Nominal design stresses for bolting materials are given in Clauses 11 and 12.
6.1.2 For a specific component of a vessel, i.e. specific material, specific thickness, there are different
values of the nominal design stress for the normal operating, testing, and exceptional load cases.
For exceptional load cases, a higher nominal design stress may be used (see 6.1.3). The manufacturer shall
prescribe, in the instructions for use, an inspection of the vessel before returning it to service after occurrence
of such an exceptional case.
In assessing testing or exceptional load cases, progressive deformation and fatigue requirements need not be
taken into consideration.
6.1.3 The maximum values of the nominal design stress for normal operating and testing load cases
shall be determined from the material properties as specified in 6.1.5 and the safety factors given in 6.2 to
6.5. The formulae for deriving the maximum values of nominal design stresses are given in Table 6-1.
The nominal safety factor for exceptional load cases shall not be less than that for the testing load cases.
6.1.4 Special considerations may require lower values of the nominal design stress, e.g. risk of stress
corrosion cracking, special hazard situations, etc.
6.1.5 For the tensile strength and the yield strength the values shall be those which apply to the
materials in the final fabricated condition and shall conform to the minimum values of the technical
documentation prepared in accordance with EN 13445-5:2021EN 13445-5:2021, Clause 5.
NOTE
4:2021.
These values will generally be achieved when the heat treatment procedures conform to EN 13445-
The minimum values, specified for the delivery condition, can be used for design purposes unless the heat
treatment is known to lead to lower values, in which case these lower values shall be used. If the weld metal
gives lower strength values after fabrication, these shall be used.
6.1.6 For the determination of the tensile strength and the yield strength above 20 °C procedure of EN
13445-2:2021, 4.2 shall be used.
6.1.7
For the definition of rupture elongation see EN 13445-2:2021, Clause 4.
UNI EN 13445-3:2021
31
EN 13445-3:2021 (E)
Issue 1 (2021-05)
6.2 Steels (except castings), other than austenitic steels covered by 6.4 and 6.5, with a
minimum rupture elongation, as given in the relevant technical specification for the
material, below 30 %
6.2.1 Normal operating load cases
The nominal design stress for normal operating load cases f shall not exceed fd, the smaller of the two following
values:
— the minimum yield strength or 0,2 % proof strength at calculation temperature, as given in the
technical specification for the material, divided by the safety factor 1,5; and
— the minimum tensile strength at 20 °C, as given in the technical specification for the material, divided
by the safety factor 2,4.
6.2.2 Testing load cases
The nominal design stress for testing conditions f shall not exceed ftest, the minimum yield strength or 0,2 %
proof strength at test temperature, as given in the technical specification for the material, divided by the safety
factor 1,05.
6.3 Alternative route for steels (except castings), other than austenitic steels covered by
6.4
and 6.5, with a minimum rupture elongation, as given in the relevant technical
specification for the material, below 30 %
6.3.1 General
Alternative route allows the use of higher nominal design stress with an equivalent overall level of safety if all
of the following conditions are met:
a) Material requirements as specified in EN 13445-2:2021 for Design by Analysis – Direct Route.
b) Restriction in construction and welded joints as specified in Clause 5 and in Annex A for Design by
Analysis – Direct Route.
c) All welds which must be tested by non-destructive testing (NDT) according to the requirements of
EN 13445-5:2021EN 13445-5:2021 shall be accessible to NDT during manufacture and also for inservice inspection.
d) Fatigue analysis according to Clause 17 or 18 in all cases.
e) Fabrication requirements as specified in EN 13445-4:2021 for Design by Analysis – Direct Route.
f)
NDT as specified in EN 13445-5:2021EN 13445-5:2021 for Design by Analysis – Direct Route.
g) Appropriate detailed instructions for in-service inspections are provided in the operating
instructions of the manufacturer.
NOTE
Until sufficient in-house experience can be demonstrated, the involvement of an independent body,
appropriately qualified, is recommended for the assessment of the design (calculations) and for assurance that all
requirements are met in materials, fabrication and NDT.
32
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
6.3.2 Normal operating load cases
The nominal design stress for normal operating load cases f shall not exceed fd, the smaller of the two following
values:
— the minimum yield strength or 0,2 % proof strength at calculation temperature, as given in the
technical specification for the material, divided by the safety factor 1,5; and
— the minimum tensile strength at 20 °C, as given in the technical specification for the material, divided
by the safety factor 1,875.
6.3.3 Testing load cases
The nominal design stress for testing conditions f shall not exceed ftest, the minimum yield strength or 0,2 %
proof strength at test temperature, as given in the technical specification for the material, divided by the safety
factor 1,05.
6.4 Austenitic steels (except castings) with a minimum rupture elongation, A%, as given
in the relevant technical specification for the material, such as 30%≤A%<35%
6.4.1 Normal operating load cases
The nominal design stress for normal operating load cases f shall not exceed fd, the minimum 1 % proof
strength at calculation temperature, as given in the technical specification for the material, divided by the
safety factor 1,5.
6.4.2 Testing load cases
The nominal design stress for testing load cases f shall not exceed ftest, the minimum 1 % proof strength at test
temperature, as given in the technical specification for the material, divided by the safety factor 1,05.
6.5 Austenitic steels (except castings) with a minimum rupture elongation, A%, as given
in the relevant technical specification for the material, such as A%35%
6.5.1 Normal operating load cases
The nominal design stress for normal operating load cases f shall not exceed fd the greater of the two values:
a) that derived from 6.4.1; or
b) if a value of Rm/T is available, the smaller of two values:
— the minimum tensile strength at calculation temperature, as given in the technical specification for
the material, divided by the safety factor 3,0; and
— the minimum 1 % proof strength at calculation temperature, as given in the technical specification
for the material divided by the safety factor 1,2.
6.5.2 Testing load cases
The nominal design stress for testing load cases f shall not exceed ftest, the greater of the two values:
a) the value derived from 6.4.2; and
b) the minimum tensile strength at test temperature, as given in the technical specification for the
material, divided by the safety factor 2.
UNI EN 13445-3:2021
33
EN 13445-3:2021 (E)
Issue 1 (2021-05)
6.6 Cast steels
6.6.1 Normal operating load cases
The nominal design stress for normal operating load cases f shall not exceed fd, the smaller of the following two
values:
— the minimum yield strength or 0,2 % proof strength at calculation temperature, as given in the
technical specification for the material divided by the safety factor 1,9;
— the minimum tensile strength at 20 °C, as given in the technical specification for the material, divided
by the safety factor 3,0.
6.6.2 Testing load cases
The nominal design stress for testing load cases f shall not exceed ftest, the minimum yield strength or 0,2 %
proof strength at test temperature, as given in the technical specification for the material, divided by the safety
factor 1,33.
NOTE
Physical properties of steels are given in Annex O.
Table 6-1 — Maximum allowed values of the nominal design stress for pressure parts other than
bolts
Steel designation
Steels other than
austenitic, as per 6.2
A ≤ 30%c
Steels other than
austenitic, as per 6.3:
Alternative route
A < 30% c
Austenitic steels as
per 6.4
30% ≤ A < 35% c
Austenitic steels as
per 6.5
A  35%c
Normal operating load cases a
Testing and exceptional load casesa b
f
 R p0,2/ T R
m/20
 min 
;
d

1,5
2,4





f
f
 R p0,2/ T R
m/20
 min 
;
d

1,5
1,875





f
f
 R p1,0/ T 

 
d


1,5


f
 R
p1,0/ T 
; min
 max  
d

1,5




f
 R p0,2/ T R
m/20
 min 
;
d

1,9
3

Cast steels as per 6.6
f
 R p1,0/ T

R
m/ T  

;


1, 2
3






f
f
test
 R p0,2/ T

test
 
1,05







test
 R p0,2/ T

test
 
1,05







test
 R p1,0/ T

test
 
1
,
05







test
 R
 p1,0/ T test
 max 
 
1,05
 
test
 R p0,2/ T

test
 
1,33


a
Yield strength R eH may be used instead of R p0,2 if the latter is not available from the material standard.
b
See 5.3.2 and 6.1.2.
For definition of rupture elongation, see EN 13445-2:2021, Clause 4.
c
34
  R
  m/ T test
;
 
2

 





UNI EN 13445-3:2021



 
EN 13445-3:2021 (E)
Issue 1 (2021-05)
6.7 Nominal design stress of anchor bolting
The nominal design stress for the anchor bolts for the operation condition shall be calculated as follows:
𝑅p0,2/TB
𝑓𝐵,𝑜𝑝 = min {
1,65
;
𝑅m/20
}
2,062 5
(6.7-1)
where
TB
is design temperature for anchor bolts
NOTE
In most cases the design temperature TB of the anchor bolts will be 20 °C and will generally be much
lower than the design temperature of the vessel.”.
7 Shells under internal pressure
7.1 Purpose
This clause provides requirements for design against internal pressure of axisymmetric shells - cylinders,
spheres, parts of spheres, dished ends, cones and cone to cylinder intersections. Methods are also provided for
the design of offset cones connecting two cylinders and for nozzles encroaching into the knuckle region of
dished ends.
7.2 Specific definitions
The following definitions apply in addition to those in Clause 3.
7.2.1
cylinder
right circular cylinder
7.2.2
torispherical end
dished end, made up of a spherical cap, a toroidal knuckle and a cylindrical shell, the three components
having common tangents where they meet
7.2.3
Kloepper type
torispherical end for which R/De = 1,0 and r/De = 0,1
7.2.4
Korbbogen type
torispherical end for which R/De = 0,8 and r/De = 0,154
7.2.5
ellipsoidal end
dished end made on a truly ellipsoidal former
UNI EN 13445-3:2021
35
EN 13445-3:2021 (E)
Issue 1 (2021-05)
7.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in Clause 4.
De is the outside diameter of shell;
Di is the inside diameter of shell;
Dm is the mean diameter of shell;
r
is the inside radius of curvature of a knuckle.
7.4 Cylindrical and spherical shells
7.4.1 Conditions of applicability
The rules in 7.4.2 and 7.4.3 are valid for e/De not greater than 0,16. The rules for spheres apply also to
spherical parts of shells, hemispherical ends, the central zones of torispherical ends, and that part of a sphere
used to join a cone and a cylinder (a knuckle of r/Di = 0,5).
NOTE 1
The rules in 7.4.2 and 7.4.3 may be used for larger ratios if accompanied by a detailed fatigue analysis.
NOTE 2
The thickness given by this section is a minimum. Thickness may have to be increased at junctions with
other components, or to provide additional reinforcement at nozzles or openings, or to carry non-pressure loads.
7.4.2 Cylindrical shells
The required thickness shall be calculated from one of the following two formulae:
e 
P  Di
2f  z  P
(7.4-1)
or
e 
P De
2f  z  P
(7.4-2)
For a given geometry:
P max
NOTE
36

2f  z  e a
Dm
(7.4-3)
For application of this formula to different load cases, see 3.16, Note 1.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
7.4.3 Spherical shells
The required thickness shall be calculated from one of the following two formulae.
e 
P  Di
4f  z  P
(7.4-4)
or
e 
P De
4f  z  P
(7.4-5)
For a given geometry:
P max
NOTE

4f  z  e a
Dm
(7.4-6)
For application of this formula to different load cases, see 3.16, Note 1.
7.5 Dished ends
7.5.1 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to or modify those in 7.3.
De is the outside diameter of the cylindrical flange;
Di is the inside diameter of the cylindrical flange;
eb is required thickness of knuckle to avoid plastic buckling;
es is required thickness of end to limit membrane stress in central part;
ey is required thickness of knuckle to avoid axisymmetric yielding;
fb is design stress for buckling formula;
hi is inside height of end measured from the tangent line;
K is shape factor for an ellipsoidal end as defined in Formula (7.5-18);
N is a parameter defined by Formula (7.5-12);
R is inside spherical radius of central part of torispherical end;
X is ratio of knuckle inside radius to shell inside diameter;
Y is a parameter defined by Formula (7.5-9);
Z is a parameter defined by Formula (7.5-10);
ß is a factor given by Figures 7.5-1 and 7.5-2 or by the procedure in 7.5.3.5.
UNI EN 13445-3:2021
37
EN 13445-3:2021 (E)
Issue 1 (2021-05)
7.5.2 Hemispherical ends
The required thickness of a hemispherical end is given by the formulae in 7.4.3. The mean radius of the end
shall be nominally the same as that of the cylinder to which it is welded. The thickness of the cylinder up to the
tangent line shall be kept at or above the minimum for the cylinder in accordance with to 7.4.2.
7.5.3 Torispherical ends
7.5.3.1
Conditions of applicability
The following requirements are limited in application to ends for which all the following conditions are met:
r  0,2 Di
r  0,06Di
r  2e
e  0,08 De
ea  0,001 De
R  De
7.5.3.2
Design
The required thickness e shall be the greatest of es, ey and eb, where:
es 
ey 
P R
(7.5-1)
2f  z  0,5 P
  P  0,75 R  0,2 D i 
(7.5-2)
f
where
ß is found from Figure 7.5-1 or the procedure in 7.5.3.5, replacing e by ey.
and
eb
 P D 
i
  0,75 R  0,2 D i  


111 f b  r 

0,825
 1 



  1,5


(7.5-3)
where
fb 
R p 0 ,2 / T
1,5
(7.5-4)
except for cold spun seamless austenitic stainless steel, where:
1,6 R
fb 
38
p 0 ,2 /T
1,5
(7.5-5)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
At test conditions the value 1,5 in the formulae for fb shall be replaced by 1,05.
NOTE 1
For stainless steel ends that are not cold spun, fb will be less than f.
NOTE 2
The 1,6 factor for cold spun ends takes account of strain hardening.
NOTE 3
It is not necessary to calculate eb if ey > 0,005Di.
NOTE 4
The inside height of a torispherical end is given by
hi  R 
R
 D i / 2    R  D i /2  2 r

Figure 7.5-1 — Parameter  for torispherical end – Design
7.5.3.3
Rating
For a given geometry Pmax shall be the least of Ps, Py and Pb, where:
P
P
s
y


2f  z  e a
R  0,5e
(7.5-6)
a
f  ea
(7.5-7)
 (0,75 R  0,2 D i )
where
ß is found from Figure 7.5-2 or the procedure in 7.5.3.5, replacing e by ea.


ea

P b  111 f b 
 0,75 R  0,2 D 
ι 

NOTE 1
1,5
 r 


D 
 i 
0,825
(7.5-8)
For application of the above Formulae to different load cases, see 3.16, Note 1.
UNI EN 13445-3:2021
39
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 2
It is not necessary to calculate Pb if ea > 0,005Di.
Figure 7.5-2 — Parameter ß for torispherical end - rating
7.5.3.4
Exceptions
It is permissible to reduce the thickness of the spherical part of the end to the value es over a circular area that
shall not come closer to the knuckle than the distance
R e
, as shown in Figure 7.5-3.
Any straight cylindrical flange shall meet the requirements of 7.4.2 for a cylinder, if its length is greater than
0,2
Di  e
. When the length is equal or smaller than
0,2
Di  e
, it may be the same thickness as required for
the knuckle.
40
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
7.5.3.5
Formulae for calculation of factor 
Figure 7.5-3 — Geometry of torispherical end
Y = min(e/R ; 0,04)
Z  log
10
(7.5-9)
1 / Y 
(7.5-10)
X = r/Di
(7.5-11)
N  1,006
1

{6,2  (90 Y )
4
(7.5-12)
}
For X = 0,06

0,06
 N
 0,3635Z
3
 2,2124Z
2
 3,2937Z
 1,8873

(7.5-13)
For 0,06 < X < 0,1

  25 (0,1  X)  0,06  (X  0,06)  0,1

(7.5-14)
For X = 0,1

0 ,1
 N (  0 ,1 8 3 3 Z
3
 1, 0 3 8 3 Z
2
 1, 2 9 4 3 Z  0 ,8 3 7 )
(7.5-15)
For 0,1 < X < 0,2

  1 0 ( 0 ,2  X ) 
0 ,1
 ( X  0 ,1)  0 , 2
(7.5-16)

For X = 0,2

0 ,2
 m ax
 0 ,9 5 ( 0 ,5 6  1,9 4 Y
 8 2 ,5 Y
2
) ; 0 ,5

(7.5-17)
NOTE
When used in 7.5.3.2 the above formulae for ß lead to an iterative calculation. A computer procedure is
recommended.
7.5.4 Ellipsoidal ends
These requirements apply only to ends for which 1,7 < K < 2,2.
K = Di/(2h i)
UNI EN 13445-3:2021
(7.5-18)
41
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Ellipsoidal ends shall be designed as nominally equivalent torispherical ends with:
r  D i   0,5/ K   0,08

(7.5-19)
and
R  D i (0 ,4 4 K  0 ,0 2 )
(7.5-20)
7.6 Cones and conical ends
7.6.1 Conditions of applicability
Requirements are given in 7.6.4 to 7.6.8 for right circular cones and cone/cylinder intersections where the cone
and the cylinder are on the same axis of rotation. Requirements for offset cones are given in 7.6.9.
The requirements do not apply to:
c) cones for which the half angle at the apex of the cone is greater that 75°;
d) cones for which;
e a  cos(  )
Dc
(7.6-1)
 0,001;
e) short cones joining a jacket to a shell.
Limits on the minimum distance from other major discontinuities are given in individual clauses.
7.6.2 Specific definitions
The following definition applies in addition to those in 7.2.
7.6.2.1
junction between the cylinder and the cone
intersection of the mid-thickness lines of cylinder and cone, extended if necessary where there is a
knuckle (see Figure 7.6-1 and Figure 7.6-2 for examples at the large end)
Figure 7.6-1 — Geometry of cone/cylinder intersection without knuckle — Large end
42
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 7.6-2 — Geometry of cone/cylinder intersection with knuckle — Large end
7.6.3 Specific symbols and abbreviations
The following symbols and abbreviations are in addition to or modify those in 7.3.
Dc
is the mean diameter of the cylinder at the junction with the cone;
De
is the outside diameter of the cone;
Di
is the inside diameter of the cone;
DK
is a diameter given by Formula (7.6-8);
Dm
is the mean diameter of the cone;
econ
is required thickness of cone as determined in 7.6.4;
econ,a
the analysis thickness of the conical shell;
ecyl
is required thickness of cylinder as determined in 7.4.2;
ej
is a required or analysis thickness at a junction at the large end of a cone;
e1
is required thickness of cylinder at junction;
e1a
is analysis reinforcing thickness in cylinder;
e2
is required thickness of cone and knuckle at junction;
e2a
is analysis reinforcing thickness in cone;
f
is the nominal design stress. In the design of junctions to 7.6.6 to 7.6.9 it is the lowest of the values
for the individual component parts;
l1
is length along cylinder;
l2
length along cone at large or small end;
r
is the knuckle radius;

is the semi angle of cone at apex (degrees);

is a factor defined in 7.6.6;
H
is a factor defined in 7.6.8;

is a factor defined in 7.6.7;
UNI EN 13445-3:2021
43
EN 13445-3:2021 (E)
Issue 1 (2021-05)

is a factor defined in 7.6.7;

is a factor defined in 7.6.8.
7.6.4 Conical shells
The required thickness at any point along the length of a cone shall be calculated from one of the following two
formulae:
e con

e con

P Di

2f  z  P
1
(7.6-2)
cos(  )
or
P De

2f  z  P
1
(7.6-3)
cos(  )
where
Di and De are at the point under consideration.
For a given geometry:
P max 
2 f  z  e con, a  cos(  )
(7.6-4)
Dm
where
Dm is at the point under consideration.
NOTE
For application of the above Formulae to different load cases, see 3.16, Note 1.
At the large end of a cone attached to a cylinder it is permissible to make the following substitutions:
Di = DK
(7.6-5)
De = DK + 2e2 cos()
(7.6-6)
Dm = (Di + De)/2
(7.6-7)
where
D K  D c  e 1  2 r 1  cos(  )  l 2 sin(  )
(7.6-8)
NOTE 1
The thickness given by this section is a minimum. Thickness may have to be increased at junctions with
other components, or to provide reinforcement at nozzles or openings, or to carry non-pressure loads.
NOTE 2
Since the thickness calculated above is the minimum allowable at that point along the cone, it is
permissible to build a cone from plates of different thickness provided that at every point the minimum is achieved.
7.6.5 Junctions - general
The requirements of 7.6.6, 7.6.7 and 7.6.8 apply when the junction is more than 2l1 along the cylinder and 2l2
along the cone from any other junction or major discontinuity, such as another cone/cylinder junction or a
flange, where:
44
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
l1 
D
c
(7.6-9)
 e1
Dc  e2
l2 
cos 
(7.6-10)

7.6.6 Junction between the large end of a cone and a cylinder without a knuckle
7.6.6.1
Conditions of applicability
The requirements of 7.6.6.2 and 7.6.6.3 apply provided that the following condition is satisfied: the joint is a
butt weld where the inside and outside surfaces merge smoothly with the adjacent cone and cylinder without
local reduction in thickness.
NOTE
Specific NDT rules apply in EN 13445-5:2021EN 13445-5:2021 when the design is such that the thickness
at the weld does not exceed 1,4ej.
7.6.6.2
Design
The required thickness e1 of the cylinder adjacent to the junction is the greater of ecyl and ej where ej shall be
determined by the following procedure:
Assume a value of ej and calculate:
 
e
j

1
Dc
3
e
tan (  )

j
1  1/
 0,15
cos(  )
P Dc  
2f
(7.6-11)
(7.6-12)
The thickness given by Formula (7.6-12) is an acceptable thickness if not less than the value assumed.
NOTE
The minimum required value for ej can be obtained by iterative application of this procedure, until
Formula (7.6-12) gives the same value as that assumed.
 can also be read from the graph in Figure 7.6-3.
This thickness shall be maintained for a distance of at least 1,4l1 from the junction along the cylinder.
UNI EN 13445-3:2021
45
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 7.6-3 — Values of coefficient  for cone/cylinder intersection without knuckle
The required thickness e2 of the cone adjacent to the junction is the greater of econ and ej. This thickness shall
be maintained for a distance of at least 1,4l2 from the junction along the cone, see Figure 7.6-1.
It is permissible to redistribute the reinforcement in the following way, provided that the minimum thicknesses
given by 7.4.2 and 7.6.4 continue to be met.
The thickness for the cylinder may be increased near the junction and reduced further away provided that the
cross-sectional area of metal provided by the cylinder within a distance 1,4l1 from the junction is not less than
1,4e1l 1. In addition, the thickness of the cone may be increased near the junction and reduced further away
provided that the cross-sectional area of metal provided by the cone within a distance 1,4l2 from the junction is
not less than 1,4e2l 2.
7.6.6.3
Rating
The maximum permissible pressure for a given geometry shall be determined as follows:
a) apply Formula (7.4-3) to cylinder;
b) apply Formula (7.6-4) to the cone;
c) determine the analysis reinforcing thickness e1a of the cylinder at the junction;
d) determine the analysis reinforcing thickness e2a of the cone at the junction;
e) apply Formula (7.6-4) with thickness e2a and diameter Dm;
f)
46
find ej, the lesser of e1a and e2a;
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
g) calculate  from Formula (7.6-11), then,
P max
2f  e j

 Dc
(7.6-13)
h) the maximum permissible pressure is the lowest of the pressures determined in a), b), e) and g).
NOTE
The following procedure may be used to find the analysis reinforcing thickness at c) or d) above:
1) Assume e1a (the initial choice should be the thickness at the junction).
2) Calculate
l
1
 1,4
Dc  e
1a
(7.6-14)
3) If the thickness is constant within the distance l1 then e1a is confirmed.
4) If not, calculate the metal area A1 within the distance l1 from the junction.
5) Obtain a better estimate by.
(7.6-15)
e 1a  A1 l1
6) The answer is acceptable if it is not greater than assumed in 1).
7) If the answer is unacceptable, return to 1).
8) Use a similar procedure to find e2a making.
l 2  1,4
D c  e 2a
cos 

(7.6-16)
7.6.7 Junction between the large end of a cone and a cylinder with a knuckle
7.6.7.1
Conditions of applicability
This sub-clause applies provided that all the following conditions are satisfied:
a) the knuckle is of toroidal form and merges smoothly with the adjacent cone and cylinder, and;
b) the inside radius of curvature of the knuckle, r < 0,3 Dc.
NOTE
This clause does not prescribe a lower limit to the radius of curvature of the knuckle.
7.6.7.2
Design
The value of ej shall be determined by the following procedure:
Assume a value of ej and calculate:
UNI EN 13445-3:2021
47
EN 13445-3:2021 (E)
Issue 1 (2021-05)
 
 
1
Dc
3
e
1  1/
j
0,028 r
Dc e
 1
tan(  )

(7.6-17)


1  1/
j
cos  α 
(7.6-18)

0,2 

1,2  1 


ej 
 0,15
cos(  )


(7.6-19)
P Dc  
2 f
(7.6-20)
The thickness given by Formula (7.6-20) is an acceptable thickness for the knuckle if not less than the value
assumed.
NOTE
The minimum required value for ej can be obtained by iterative application of this procedure, until
Formula (7.6-20) gives the same value as that assumed.
The required thickness e1 of the cylinder adjacent to the junction is the greater of ecyl and ej.
This thickness shall be maintained for a distance of at least 1,4l1 from the junction and 0,5l1 from the
knuckle/cylinder tangent line along the cylinder.
The required thickness e2 of the knuckle and the cone adjacent to the junction is the greater of econ and ej. This
thickness shall be maintained for a distance of at least 1,4l2 from the junction and 0,7l2 from the cone/knuckle
tangent line along the cone.
7.6.7.3
Rating
The maximum permissible pressure for a given geometry shall be determined as follows:
a) Determine e1a, the analysis thicknesses for the cylinder next to the knuckle, and e2a, the analysis
thickness for the knuckle and the adjacent part of the cone;
b) Check that the limitations of 7.6.7.1 are met;
c) Apply Formula (7.4-3) to the cylinder with ea = e1a ;
d) Apply Formula (7.6-4) to the cone with econ,a = e2a ;
e) Find ej, the lesser of e1a and e2a ;
f)
Find  and  from Formulae (7.6-17) and (7.6-19), then
P max

2f    e j
 D
(7.6-21)
c
g) The maximum permissible pressure is the lowest of the pressures determined in c), d) and f).
7.6.8 Junction between the small end of a cone and a cylinder
7.6.8.1
Conditions of applicability
The requirements of 7.6.8.2 and 7.6.8.3 apply provided that all the following conditions are satisfied:
48
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) the required thickness of the cylinder e1 is maintained for a distance l1 and that of the cone e2 is
maintained for a distance l2 from the junction (see Figure 7.6-4); and
b) the thicknesses meet the requirements of 7.4.2 and 7.6.4.
Figure 7.6-4 — Geometry of cone/cylinder intersection: small end
7.6.8.2
Design
Required thicknesses e1 and e2 shall be determined by the following procedure:
Assume values of e1 and e2:
s 
e2
(7.6-22)
e1
when s < 1
s
  s
1 s

cos(  )
2
2
(7.6-23)
when s  1
 1
 H  0,4
 1 s
2


 2cos   
(7.6-24)
s
Dc
e1

tan 


 0,5
(7.6-25)
If
P 
2f  z  e1
Dc  
H
UNI EN 13445-3:2021
(7.6-26)
49
EN 13445-3:2021 (E)
Issue 1 (2021-05)
then e1 and e2 are acceptable. If not, repeat with increased values of e1 and/or e2.
NOTE
The above procedure does not provide values for e1 and e2 independently. Any values may be selected to
suit the needs of the design, for example to obtain a favourable value of l1 or l2.
Provided that the requirements of 7.4.2 and 7.6.4 continue to be met, it is permissible to modify a design
according to the above rule in one of the following ways:
a) Where e1 = e2 a knuckle of the same thickness may be included. l1 and l2 continue to be measured
from the junction (i.e. the point where the centre lines of cone and cylinder meet).
b) The thickness of the cylinder may be increased near the junction and reduced further away
provided that the cross-sectional area of metal provided by the cylinder within a distance l1 from
the junction is not less than l1 e1. In addition, the thickness of the cone may be increased near the
junction and reduced further away provided that the cross-sectional area of metal provided by the
cone within a distance l2 from the junction is not less than l2e2.
7.6.8.3
Rating
The maximum permissible pressure for a given geometry and for normal operating load cases shall be:
P max

2f  z  e1
(7.6-27)
Dc  H
H is found from Formulae (7.6-22) to (7.6-25) using e1a and e2a in place of e1 and e2 .
NOTE 1
The procedure for finding e1a and e2a is as provided in the note to 7.6.6.3.
NOTE 2
Analysis thicknesses may exceed the required thickness without leading to any increase in l1 or l2.
7.6.9 Offset cones
This requirement applies to offset cones between two cylinders (see Figure 7.6-5). The cylinders shall have
parallel centre lines offset from each other by a distance no greater than the difference of their radii. A
required thickness shall be calculated in accordance with 7.6.6 for the junction at the large end. A required
thickness shall be calculated in accordance with 7.6.8 for the junction at the small end. The greater of these
shall apply to the whole cone. The angle () shall be taken as the greatest angle between cone and cylinder.
50
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1 Offset of axis
Figure 7.6-5 — Offset cone
7.7 Nozzles which encroach into the knuckle region
7.7.1 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in 7.5.1:
A
is a parameter defined by Formula (7.7-4) or (7.7-8);
A1
is a parameter defined by Formula (7.7-12) or (7.7-16);
B
is a parameter defined by Formula (7.7-5) or (7.7-9);
B1
is a parameter defined by Formula (7.7-13) or (7.7-17);
K
is the weakening factor due to presence of nozzle given by (7.7-10);
di
is the inside diameter of the nozzle;
X
is a parameter defined by Formula (7.7-11) or (7.7-15);
V
is a parameter defined by Formula (7.7-3) or (7.7-7).
7.7.2 Conditions of applicability
In this sub-clause requirements are given for increasing the thickness of a dished end to compensate for
nozzles which are not entirely within the central area of the head as defined in 9.7.2.4 and are therefore not
covered by Clause 9.
The requirements are limited in application to Kloepper and Korbbogen ends for which:
di/D e  0,6
(7.7-1)
and
di
e
a
 6,7
(7.7-2)
De
UNI EN 13445-3:2021
51
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The nozzle centre line shall lie in the same plane as the centre line of the vessel. The nozzle centre line shall lie
between normal to the wall of the end and parallel to the vessel centre line. The location of the nozzle shall be
such that it does not cross the tangent line between knuckle and cylinder. Nozzles parallel to the vessel centre
line and with outside diameter in line with the outside diameter of the vessel are included in these
requirements.
The requirements of 7.7 may also be applied to ellipsoidal ends for which the aspect ratio K  2. The thickness
of such an ellipsoidal end with a nozzle intruding into the knuckle region shall be as for a Korbbogen end of the
same diameter.
The increased thickness required by this clause applies to the whole knuckle region. Welded-on compensation
is not permitted. The thickness of the crown may be reduced provided that the requirements of 7.5.3.4 are met
and reinforcement for nozzles in the crown region meets the requirements of clause 9.
When the distance between the edge of the nozzle where it meets the knuckle and the knuckle/cylinder
tan, line is less than 2 ,5 e a  r (measured along the surface) the validity of the method is in doubt. Unless
the design is supported by special analysis or extensive experience, the design pressure shall be
multiplied by two in such cases, or in a rating the allowable pressure shall be halved.
7.7.3 Design
For Kloepper type end:

V = log10  1 000

P 

f 
(7.7-3)
A = max (0,5; 0,264 + 0,938V - 0,592V 2 + 0,14V 3)
(7.7-4)
B = min (4,2; 4,9 - 2,165V + 0,151V 2)
(7.7-5)

k
 max

d
d
 A  B i ; 1  0,3 B i

De
De





(7.7-6)
For Korbbogen type end:

P 

f 
V = log10  1 000
(7.7-7)

A = 0,54 + 0,41V - 0,044V 3
(7.7-8)
B = 7,77 - 4,53V + 0,744V 2
(7.7-9)

k
 max

d
d
 A  B i ; 1  0,5 B i

De
De





(7.7-10)
Replace P by Pk in Formula (7.5-2) and in Figure 7.5-1 to arrive at the required thickness. The substitution
shall be made before the calculation of  in 7.5.3.5. Formulae (7.5-1) and (7.5-3) continue to apply without
modification.
NOTE
The graphs of Figure 7.7-1 and Figure 7.7-2 are based on the above procedure and give
e f
P R
as a function
of P/f and di/ D e.
52
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 7.7-1 — Design ratio for Kloepper ends
UNI EN 13445-3:2021
53
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 7.7-2 — Design ratio for Korbbogen end
7.7.4 Rating
To determine the maximum permissible pressure corresponding to a given geometry (rating) a trial and error
procedure may be adopted. Alternatively the following procedure provides an approximate and always
conservative estimate of k.
For Kloepper type end:
X = log

ea
 1000
10 
De





(7.7-11)
A1 = 1,07 max(0,71 - X; 0,19X + 0,45)


B 1 = 1,02  min  ( 3  5 X );



54
k
 max

(7.7-12)
1
0,241  0,116

d
d
 A 1  B 1 i ; 1  0,3 B 1 i

De
De





X
 0,26

3
 


 
(7.7-13)
(7.7-14)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For Korbbogen type end:
X = log

e
 1 000 a

10
De





(7.7-15)
1
A1 =
 0,0053
1,136
 De


 di




(7.7-16)
0,8
B1 = (8,87 - 4,35X + 0,19X 3)

di

De
β k  max  (1  0,1
Replace  by
  k



)  A1  B1
(7.7-17)
di 
De

d
d
 ; (1  1,1 i )  1  0,5 B 1 i


De 
De





(7.7-18)
in Formula (7.5-7). Formulae (7.5-6) and (7.5-8) continue to apply without modification.
7.7.5 Multiple nozzles which encroach into the knuckle region
The requirements for multiple nozzles in Clause 9 apply also to nozzles designed to these requirements if the
ligament between adjacent nozzles is entirely within the central area of radius 0,4De in the end, as shown in
Figure 9.5-4. If the connecting line between adjacent nozzles is not entirely within the central area, the
ligament shall not be less than half the sum of the nozzle bores.
8 Shells under external pressure
8.1 Purpose
This clause provides requirements for the design of shells under external pressure loading. They apply to
stiffened and unstiffened cylinders and cones, spheres and dished ends.
Where other significant loadings are present, additional strengthening shall be provided by increasing either
the shell thickness or the stiffening. The rules apply also in the creep range, only under the conditions given in
Clause 19 and under the assumption that shape deviation during creep will not exceed deviations stated in EN
13445-4:2021.
8.2 Specific definitions
The following definitions apply in addition to those in clause 3.
8.2.1
nominal elastic limit
elastic limit applied in this clause for design under external pressure
8.2.2
heavy stiffener
circumferential stiffener, designated as heavy by the designer, to which particular requirements in this
clause apply
8.2.3
light stiffener
circumferential stiffener, designated as ‘light’ by the designer, to which particular requirements in this
clause apply
UNI EN 13445-3:2021
55
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.2.4
interstiffener collapse
collapse of a section of cylinder between two stiffening rings, or between a stiffening ring and a vessel end
8.2.5
overall collapse
collapse of a section of cylinder which includes a light or heavy stiffener
8.2.6
plane of substantial support
vessel end or a plane dividing a vessel into two parts, each of which is treated separately for external
pressure design purposes
8.2.7
safety factor
ratio of the lower bound expected collapse pressure to the calculation pressure
8.2.8
stiffener tripping
sideways twisting of a stiffener about its point of connection to the shell
8.3 Specific symbols and definitions
The following specific symbols and abbreviations apply in addition to those in Clause 4.
a
length of shell covered by heating/cooling coil, see Figures 8.5-11 and 8.5-12
Ae
is cross-sectional area of stiffener and effective length of shell, see Formula (8.5.3-30);
Af
is the cross-sectional area of the flange of a stiffener;
Am
is the modified area of a stiffener, see Formula (8.5.3-17);
As
is the cross-sectional area of stiffener;
Aw
is the cross-sectional area of web;
B
is a parameter in the interstiffener collapse calculation, see Formula (8.5.3-18);
C
is a coefficient in the stiffener tripping calculation, see Formulae (8.5.3-50) and (8.5.3-51);
CG s
indicates the position of the centroid of a stiffener;
CG c
indicates the centroid of the stiffener plus the effective length of shell;
d
is the distance to the extremity of a stiffener, see Formula (8.5.3-40);
d
is radial height of stiffener between flanges, see Figures 8.5-14, 8.5-15, 8.5-16 and 8.5-17;
56
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
ef
is the thickness of the flange of a stiffener;
e
is the thickness of the web of a stiffener;
w
G
is a parameter in the interstiffener collapse calculation, see Formula (8.5.3-22);
h, h ', h "
are external heights of dished ends, see Figures 8.5.1 and 8.5.2;
Ie
is the second moment of area of the composite cross-section of the stiffener and effective length
of shell acting with it (Le) about an axis parallel to the axis of the cylinder passing through the
centroid of the combined section, see Formula (8.5.3-26);
I est
is the estimated second moment of area of a stiffener;
If
is the second moment of area of the flange about its centroïd;
Is
is the second moment of area of the stiffener cross-section about the axis passing through the
centroid parallel to the cylinder axis;
Iw
is the second moment of area of web about its centroïd;
L
is the unsupported length of the shell;
L cyl
is the cylinder length between tangent lines;
Lcon
is the axial length of a cone, see Figure 8.5-2;
Le
is the effective length of shell acting with a light stiffener, see Formula (8.5.3-34);
L eH
is the effective length of shell acting with a heavy stiffener given in 8.5.3.7;
is the distance between heavy stiffeners, see Table 8.5-1;
LH
L 'H , L " H , 
are individual lengths between heavy stiffeners, see Figure 8.5-7;
Ls
is mean length of the two bays of shell adjacent to a light stiffener, see Table 8.5-1;
L sH
is mean length of the two bays of shell adjacent to a heavy stiffener, see Table 8.5-1;
L 's , L " s , 
N
are individual lengths between light stiffeners, see Figures 8.5-6 and 8.5-8;
is a parameter in the interstiffener collapse calculation, see Formula (8.5.3-21) and Table 8.52;
n
is the number of circumferential waves for a stiffened cylinder;
n cyl
is the number of circumferential waves for an unstiffened part of a cylinder, see 8.5.2.2;
UNI EN 13445-3:2021
57
EN 13445-3:2021 (E)
Issue 1 (2021-05)
P
is the required external design pressure
PC
is the design pressure in a heating/cooling channel, as used in 8.5.3.5
Pg
is the theoretical elastic instability pressure of a stiffener on a cylinder, see Formula (8.5.3-24)
or on a cone, see Formula (8.6.4-1);
PH
Pm
is the theoretical elastic instability pressure for a heavy stiffener, see Formula (8.5.3-42);
is the theoretical elastic instability pressure for collapse of a perfect cylindrical, conical or
spherical shell, see Formulae (8.5.2-5), (8.6.3-2) and (8.7.1-2);
is the calculated lower bound collapse pressure obtained from Figure 8.5-5;
Pr
is the pressure at which mean circumferential stress in a cylindrical or conical shell midway
Py
between stiffeners, or in a spherical shell, reaches yield point, see Formulae (8.5.2-4), (8.6.3-1)
and (8.7.1-1);
P ys
is the pressure causing circumferential yield in a stiffener on a cylinder, see
Formula (8.5.3-38), or on a cone, see Formula (8.6.4-6);
is the mean radius of a cylindrical or spherical shell, or mean crown radius of a torispherical
end;
R
R
f
is the radius to the part of the stiffener furthest from the shell (see Figures 8.5-14 to 8.5-17);
Rs
is the radius of the centroid of the stiffener cross-section;
R p 0 , 2 / T ,s
is the 0,2 % proof strength at temperature T for a stiffener;
ri
is the radius of the point on the stiffener web closest to the shell about which rotation is
assumed in stiffener tripping (see Figures 8.5-14 to 8.5-17);
S
is the safety factor applied in this clause, see Formula (8.4.4-1);
Sf
factor depending on method of fabrication of stiffener – Formulae (8.5.3-32) and (8.5.3-33);
u
parameter used in calculation of
wi
is the total width of stiffener i in contact with the shell, see Formula (8.5.3-39) and (see
Figures 8.5-14 to 8.5-17);
wf
is the projecting width of flange of stiffener (see Figures 8.5-14 to 8.5-17);
w' i , w ' ' i
are part widths of stiffener i in contact with the shell (see Figure 8.5-8);
X
is a parameter in the calculation for overall collapse, see Formula (8.5.3-27);
e
X eH
58
L e , see Formulae
(8.5.3-36)
is a parameter in the calculation for overall collapse, see Formula (8.5.3-44);
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Y1 ,Y 2 ,Y 3
are coefficients used in calculation of

is the semi-angle of a cone at its apex (degrees) (see Figure 8.5-2);

is either obtained from Figure 8.5-13 or calculated from Formula (8.5.3-25);

is a parameter in the design of stiffeners, see Formulae (8.5.3-19) and (8.5.3-20);

is the mean elastic circumferential strain at collapse, see 8.5.2.2;
'
is the modified mean elastic circumferential strain at collapse for a conical shell;

is a parameter depending on stiffener location, see Formulae (8.5.3-28) and (8.5.3-29);
 e ,  es
are the nominal elastic limits for shell and stiffener respectively, see 8.4;

is the maximum stress in a heavy stiffener, see Formula (8.5.3-47);
H
is instability stress for sideways tripping of a stiffener, see Formulae (8.5.3-49) and (8.5.3-54);
i

L e , see 8.5.3.6.3;
is the maximum stress in a light stiffener, see Formulae (8.5.3-37) and (8.6.4-5).
s
8.4 General
8.4.1 The thickness of a component under external pressure shall be not less than that required by this
standard under the same pressure applied internally, with a joint efficiency of 1,0.
8.4.2 For shells made in non-austenitic steels, excluding ferritic, martensitic and precipitation hardened
stainless steels in material group 7 and austenitic ferritic stainless steels in material group 10, the nominal
elastic limit shall be given by:

e
 R p 0 ,2 / T
(8.4.2-1)
and for stiffeners in the same material by:
 es  R p 0 , 2 / T ,s
(8.4.2-2)
8.4.3 For shells made in austenitic steels, ferritic, martensitic and precipitation hardened stainless steels
and austenitic ferritic stainless steels, the nominal elastic limit shall be given by:

e

R p 0 ,2 / T
1,25
(8.4.3-1)
and for stiffeners in the same material by:

NOTE
es

R p 0 , 2 / T ,s
1,25
(8.4.3-2)
If the value of Rp0,2 is unavailable a safe estimate is Rp1,0/1,3.
UNI EN 13445-3:2021
59
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.4.4
The minimum safety factor which applies throughout this clause is given by:
For design conditions
S = 1,5
(8.4.4-1)
For testing conditions
S= 1,1
(8.4.4-2)
8.5 Cylindrical shells
8.5.1 Circularity limits
8.5.1.1
Circularity tolerance
The requirements of 8.5.2 and 8.5.3 apply to cylinders that are circular to within 0,5 % on radius (i.e. 0,005R)
measured from the true centre. The tolerance shall appear on the vessel drawing
Methods for verifying the shape of vessels are given in Annex D. A procedure to establish the true centre of a
set of radius measurements, and hence to determine the departure from the true circle of a cylinder, is
described in Annex E.
It is permissible to relax the tolerance if excess thickness is provided. This matter is covered in 8.5.1.2.
8.5.1.2
Circularity tolerance for cylinders with excess thickness
Where the allowable pressure P r / S determined in 8.5.2.2 is greater than the design pressure, then the
required tolerance for the cylinder may be increased to
Tolerance  0 , 005
Pr
(8.5.1-1)
P S
For stiffeners, Formula (8.5.3-37) shall be satisfied with the desired increased tolerance inserted in place of
0,005.
8.5.1.3
Allowable pressure when circularity exceeds 0,5 % tolerance
Annex F gives a procedure by which the allowable pressure may be calculated for cylinders which are found
after manufacture to exceed the 0,5 % circularity tolerance.
NOTE
In practice it is found that in most cases where the circularity tolerance on a cylinder is not met, the
application of Annex F will demonstrate that the actual shape is acceptable, However this should not to be assumed
without following the procedure of Annex F.
Application of Annex F is not required when circularity tolerance complies with Formula 8.5.1-1.
8.5.2 Unstiffened cylinders
8.5.2.1
Unsupported length
In Figure 8.5-1,
L
is given by:
L  L c y l  0 ,4 h ' + 0 ,4 h "
60
(8.5.2-1)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 8.5-1 — Cylinder with heads
In Figure 8.5-2,
L
is given by:
— when   30° :
(8.5.2-2)
L  L c y l  0 ,4 h
— when  < 30° :
(8.5.2-3)
L  L c y l  0 ,4 h  L c o n
NOTE
For cone/cylinder intersections see 8.6.5.
Figure 8.5-2 — Cylinder with head and cone
8.5.2.2
Cylinder thickness
The thickness of a cylinder shall not be less than that determined by the following procedure:
a) Select a value for
Py 
and calculate
Py
as follows;
 e  ea
(8.5.2-4)
R
b) Calculate
Pm 
ea
Pm
E  ea  
R
UNI EN 13445-3:2021
from the following formula using the same assumed value for
ea :
(8.5.2-5)
61
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where
E is the value of the modulus of elasticity at the calculation temperature;
NOTE 1
Calculation temperature is defined in 3.5 and explained in 5.3.11.
NOTE 2
Values of E as a function of the temperature are found in Annex O.4.

is either obtained from Figure 8.5-3 or calculated from:
1
 
n
2
cyl
 1 
Z
2
2








2
1
n2

 c y l  1
2


 Z

2
ea

12 R
2
1   
2
n
2
cyl
 1  Z
2

2








(8.5.2-6)
where
n cyl
Z 
is an integer obtained from Figure 8.5-4 or calculated to minimise the value of Pm ;
  R
(8.5.2-7)
L
in which L is determined according to 8.5.2.1.
NOTE
Figure 8.5-3 is plotted from Formula (8.5.2-6).
c) Calculate
Pm
Py
and determine
Pr
Py
from curve 1) in Figure 8.5-5.
The following shall be satisfied:
(8.5.2-8)
P  Pr / S
If
Pr
62
is too small, the thickness shall be increased or stiffening provided, and the procedure repeated.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 8.5-3 – Values of 
The value of
n cyl
corresponding to the closest line shall be taken but in case of doubt both values of
n cyl
shall
be considered.
UNI EN 13445-3:2021
63
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 8.5-4 — Values of
64
n cyl
for which
Pm
is a minimum
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1 - Cylinders and cones
Pm/Py
0
0,25
0,5
0,75
1,0
1,25
1,5
1,75
2,0
2,25
2,5
2,75
3
3,25
3,5
Pr/Py
0
0,125
0,251
0,375
0,5
0,605
0,68
0,72
0,755
0,78
0,803
0,822
0,836
0,849
0,861
Pm/Py
3,75
4,0
4,25
4,5
4,75
5,0
5,25
5,5
5,75
6,0
6,25
6,5
6,75
> 7,0
Pr/Py
0,87
0,879
0,887
0,896
0,905
0,914
0,917
0,923
0,929
0,935
0,941
0,947
0,953
0,959
2 - Spheres and dished ends
Pm / P y
0
0,5
1
1,5
2
2,5
3,0
3,5
4
4,5
5,0
5,5
6
> 6,5
Pr / P y
0
0,09
0,18
0,255
0,324
0,386
0,435
0,479
0,51
0,533
0,548
0,565
0,567
0,57
versus
P m /P y
Figure 8.5-5 — Values of
UNI EN 13445-3:2021
P r /P y
65
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.5.3 Stiffened cylinders
8.5.3.1
Introduction
8.5.3 provides a procedure to determine whether a cylinder with specified stiffeners can support the design
external pressure. All stiffeners shall be designated as either ‘heavy’ or ‘light’. It is permissible not to consider
small circumferential rings as stiffeners.
NOTE
A ‘heavy’ stiffener is usually a girth flange or other major component, but it may be a particularly large
conventional stiffener. A light stiffener is usually a ring (flat bar), tee, angle or I-section. In most practical cases
there will be a number of similar stiffeners uniformly distributed along the cylinder. It is then most economical to
designate all stiffeners as ‘light’ since the calculation of overall collapse pressure takes account of the resistance of
the shell to that mode of failure, but to designate them all as ‘heavy’ leads to a much simpler calculation.
8.5.3.2
Unsupported length
The unsupported lengths of a cylinder with stiffeners shall be in accordance with Table 8.5-1. The dimensions
are shown in Figures 8.5-6, 8.5-7 and 8.5-8.
Table 8.5-1 — Definition of cylinder length
Cylinder with light stiffeners
For each bay separately

'
''
Cylinder with light and heavy stiffeners
For each bay separately

L  L s  w 1  0 ,4 h '
(8.5.3-1)
or


'
''
''
'
''
(8.5.3-4)
'''
'
''
(8.5.3-5)
L  L s  w 1  0 ,4 h '
(8.5.3-3)
or
''
'
''
L  Ls  w 1  w 2
(8.5.3-2)
L  Ls  w 1  w 2
or
L  Ls  w 2  w 3
For each light stiffener separately

'
''

L s  L s  0 ,4 h '  L s / 2
For each light stiffener separately
(8.5.3-6)
or

'

''
''

L s  L s  0 ,4 h '  L s / 2
(8.5.3-8)
or

''
'''

Ls  Ls  Ls / 2
For purpose of evaluating
L H  L c y l  0 ,4 h '  0 ,4 h "
(8.5.3-7)

'''

Ls  Ls  Ls / 2
(8.5.3-9)
For purpose of evaluating
(8.5.3-10)

'
(8.5.3-11)
''
(8.5.3-12)
L H  L H  0 ,4 h '
or
LH  LH
For each heavy stiffener

'

''
''

L sH  L H  0 , 4 h '  L H / 2
(8.5.3-13)
or
'''

L sH  L H  L H / 2
66
(8.5.3-14)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 8.5-6 — Cylinder with light stiffeners
Figure 8.5-7 — Cylinder with light and heavy stiffeners
Figure 8.5-8 — Dimensional details
Where flanges act as heavy stiffeners, the shaded area shall be determined as shown in Figure 8.5-9 a). Point
‘A’ shall be positioned as shown in Figure 8.5-9 b) and w determined.
As
of one flange shall be calculated from the shaded area minus
The combined
As
and
UNI EN 13445-3:2021
Le
e a e w  L e 
.
of both flanges shall be taken when evaluating their adequacy as stiffeners.
67
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Definition of shaded area
b) Location of A
Figure 8.5-9 — Flanges as heavy stiffeners
8.5.3.3
Design of stiffeners
When stiffeners take the form of purpose-built rings encompassing the shell, such rings may be located
internally, externally or partly internally and partly externally to the vessel. Rings may also combine process
duties, such as tray support in fractionating columns, with resisting external pressure. They shall meet the
requirements of 8.5.3 and be adequate for the process loading.
Where the stiffening ring has a space between it and the shell, the length of the unsupported shell shall not
exceed:
v e s s e l c irc u m fe re n c e
4 n cyl
See Figure 8.5-10.
Where crevice corrosion can occur, intermittent welds shall not be used for the attachment of such rings to the
shell.
NOTE
An initial approximate size for a ring stiffener may be obtained using 10 % of the area of the shell
between the stiffeners.
Figure 8.5-10 — Internal stiffening ring where this is not in complete contact with the shell
68
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.5.3.4
Interstiffener collapse
Each section of a stiffened cylinder shall be checked for interstiffener collapse. The procedure is similar to that
in 8.5.2.2 for unstiffened cylinders but L is determined from Table 8.5-1 depending on whether the cylinder
has light stiffeners or a combination of light and heavy stiffeners:
a) Calculate
Py 

 ea
1  
R
NOTE 1
e
as follows:
Py
G
(8.5.3-15)

The approximation   0 is safe as it under-estimates the pressure.
in which
 
 

Am 1  
2

 Am
 wi  ea
 1 
(8.5.3-16)
B
where
R2
Am  
R2
 s
B 

A
 s

2 ea  N

 Am
 w  ea
0 , 25
(8.5.3-19)
R  ea
from which, if
 
(8.5.3-18)

3 1    
2
 
(8.5.3-17)
  0,3
1, 28
(8.5.3-20)
R  ea
N 
cosh
sinh
 L  
 L  
cos
 L 
(8.5.3-21)
sin  L 
and
G 

 L 
 L 
 L 
 L  
2  sinh 
 cos 
  cosh 
 sin 
 
 2 
 2 
 2 
 2  

sinh
 L  
then
sin  L 
may be used.
NOTE 2
If
NOTE 3
Table 8.5-2 may be used to evaluate G and N.
L  3
b) Calculate
R  ea
Pm
UNI EN 13445-3:2021
G  0
(8.5.3-22)
as in 8.5.2.2 b) continuing to take L from Table 8.5-1.
69
EN 13445-3:2021 (E)
Issue 1 (2021-05)
c) Determine
Pr
as in 8.5.2.2 c) and check that Formula (8.5.2-8) is satisfied.
Table 8.5-2 — Values of G and N which may be assumed
G
  L
N
G
  L
N
0
1,000
0
3,2
0,411
1,090
0,2
1,000
0,100
3,4
0,335
1,085
0,4
1,000
0,200
3,6
0,264
1,077
0,6
0,999
0,300
3,8
0,200
1,066
0,8
0,996
0,400
4,0
0,144
1,054
1,0
0,990
0,497
4,2
0,095
1,042
1,2
0,979
0,593
4,4
0,054
1,032
1,4
0,961
0,685
4,6
0,019
1,023
1,6
0,935
0,772
4,7
0,004
1,019
1,8
0,899
0,851
(4,73)
0,000
1,018
2,0
0,852
0,921
4,8
0,000
1,015
2,2
0,795
0,979
5,0
0,000
1,009
2,4
0,728
1,025
5,2
0,000
1,005
2,6
0,653
1,058
5,4
0,000
1,001
2,8
0,573
1,078
5,5
0,000
1,000
3,0
0,492
1,088
> 5,5
0,000
1,000
8.5.3.5
Heating/cooling channels
This subclause gives requirements for the thickness of a cylinder to which circumferentially orientated heating
or cooling channels are attached. Such channels are also known as hemi-coils or limpet coils. Two typical forms
of construction are shown in Figures 8.5-11 and 8.5-12.
The cylinder thickness required to carry the pressure in the channels is given by :
e  a
Pc
3f
(8.5.3-23)
where a is as shown in the Figures 8.5-11 and 8.5-12.
The cylinder shall also meet the requirements of 7.4.2 (internal pressure), 8.5.3.6 or 8.5.3.7 (external pressure),
ignoring the pressure in the channels. The channels may be considered as stiffeners against external pressure.
NOTE
70
Formula (8.5.3-23) does not include pressure P since that is carried by a membrane load in the cylinder.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 8.5-11  Heating/cooling channels (hemi-coil)
Figure 8.5-12 — Heating/cooling channels (overlapping construction)
8.5.3.6
Design of light stiffeners
8.5.3.6.1
General
To resist overall collapse, the design of light stiffeners shall be in accordance with the procedures in
Subclauses 8.5.3.6.2, 8.5.3.6.3 and 8.5.3.6.4.
8.5.3.6.2
Design against elastic instability
Pg
Calculate
E  ea  
Pg 
where

for n = 2 to n = 6 using:
R

n
2
1
3
R  Ls
1

1
n 2  1 
2


NOTE
and
(8.5.3-24)
E  Ie
is either obtained from Figure 8.5-13, or calculated from:
 
Ls

 R

 L
 H




2




2


2  LH 
n 
  1


 R 


2
(8.5.3-25)
Figure 8.5-13 is plotted from Formula (8.5.3-25).
LH
are obtained from Table 8.5-1.
UNI EN 13445-3:2021
71
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 8.5-13 — Values of 
3
Ie 
ea  Le
3
 ea

 I s  As
  R  Rs 
 2



2
 Ae  X
2
e
(8.5.3-26)
in which
72
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
X
e






e2
 a
 2


ea
L  A
  R  R
s 
 e
 2

s
 


 


Ae
(8.5.3-27)
where for internal stiffeners:
(8.5.3-28)
  1
and for external stiffeners:
Le
  1
(8.5.3-29)
Ae = As  ea  Le
(8.5.3-30)
is determined from 8.5.3.6.3.
For n = 2, 3, 4, 5 and 6:
Pg
P 
(8.5.3-31)
Sf S
where for fabricated or hot-formed stiffeners (i.e. with low residual stresses):
(8.5.3-32)
S f  1, 20
and for cold bent stiffeners (i.e. with high residual stresses):
S
f
(8.5.3-33)
 1,33
If Formula (8.5.3-31) is not met, additional light stiffening or heavy stiffening shall be provided, or the shell
thickness increased.
8.5.3.6.3
Determination of
Le
The following formula shall be used to obtain Le when 0,001095 ≤ ea/R ≤ 0,0346. When ea/R > 0,0346 then Le is
obtained using the formula with the actual value of Ls/R, but with ea/R = 0,0346.
Y1
Le / R 
Y3  x 
ea / R
1  Y2  x
(8.5.3-34)
2
where
2 ea 
x  n 

 R 
(8.5.3-35)
Ls
u 
R
(8.5.3-36)
ea
R
The values of Y1, Y2 and Y3 are given in Table 8.5-3.
UNI EN 13445-3:2021
73
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 8.5-3 — Parameters for calculation of Le
For u =
Y1 =
Y2 =
u1
u/(1/1,098+0,03u3)
0
1<u<2,2
u-1
2,2u2,9
1,2
2,9<u<4,1
1,2+1,642/u
4,1u<5
1,556+0,183/u

s
0,6(1-0,27u)u²
0,75+1,0/u
0,65+1,5/u
5u
8.5.3.6.4
Y3 =
Maximum stresses in the stiffeners
shall be calculated as follows:

s
 P 
 S Sf 
 P
ys

es


2

E  d 0 , 005 n  1 P  S  S f


R  Pg  P  S  S f 

(8.5.3-37)
where
P ys 

R
es
2


Am
f
1 
2 N  ea
  

wi  ea 
1  

2  

 ea  R





(8.5.3-38)
where
Am
is given by Formula (8.5.3-17);

is given by Formula (8.5.3-19);
N
is given by Formula (8.5.3-21) or Table 8.5-2;
and for each stiffener:
(8.5.3-39)
w i  w' i  w " i
and
 
d  max    R  R f   X

 
74
e

ea 
; X
2 
e



Sf
is given by Formula (8.5.3-32) or (8.5.3-33);
Pg
is given by Formula (8.5.3-24).
(8.5.3-40)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Throughout the calculation:
— lengths
—
Le
L, L s
shall be in accordance with Table 8.5-1;
is obtained from 8.5.3.6.3 for each value of n.
For n = 2, 3, 4, 5 and 6:
0  
 
s
(8.5.3-41)
es
Additional stiffening, heavier stiffening or an increased shell thickness shall be provided if Formula (8.5.3-41) is
not satisfied.
NOTE
The simplification A m  0 is always permissible but will result in a larger stiffener section.
8.5.3.7
Design of heavy stiffeners
8.5.3.7.1
Assessment of collapse pressure
For each heavy stiffener, calculate:
PH 
where
3
R
3
(8.5.3-42)
E  I eH
 L sH
is in accordance with Table 8.5-1;
L sH
3
I eH 
e a  L eH
3
 I s  As
 ea

  R  Rs 
 2



2
 Ae  X
(8.5.3-43)
2
eH
where
L eH
is determined from Formula (8.5.3-34) with
2
e a  L eH
X
2

eH

ea
 As 
  R  R s 

 2
L s  L sH
in Formula (8.5.3-36);
(8.5.3-44)
Ae
is from Formula (8.5.3-28) or (8.5.3-29);

(8.5.3-45)
A e  A s  e a  L eH
For each heavy stiffener, it is required that:
PH
P 
(8.5.3-46)
Sf  S
where S f is given by Formula (8.5.3-32) or (8.5.3-33).
8.5.3.7.2
Assessment of maximum stress
Calculate 
H

H
as follows:
 S  Sf
P   es
P ys
UNI EN 13445-3:2021

E  d  0 ,015 P  S  S f
R  PH  P  S  S f

(8.5.3-47)
75
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where
NOTE

H
is given by Formula (8.5.3-38)
P ys
This is the same formula as that for 
s
in light stiffener design but with n = 2.
shall meet the requirement:
0  H  
(8.5.3-48)
es
Additional stiffening, heavier stiffening or an increased shell thickness shall be provided if Formula (8.5.3-48) is
not satisfied.
8.5.3.8
Stiffener tripping
8.5.3.8.1
a)
For a stiffener other than flat bar
 i shall meet the requirement:
 Pys 
 
 i  E  C 

 P 
(8.5.3-49)
es
For stiffeners shown in Figures 8.5-14, 8.5-15 and 8.5-17, C shall be calculated as follows:
3
C =
ri
6d
d ew  8 ef w
2
 e w  12 e f  w
f
3
f
2
d  ef
(8.5.3-50)

and for the stiffener shown in Figure 8.5-16, C is:
3
C =
ri
6 d
ef  w f
2
 e w  6 ef  w f 2 d  ef

 4d  ew  3w f  e f 
 

d  ew  3w f  e f 


(8.5.3-51)
Figure 8.5-14 — External I-shaped stiffener
76
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 8.5-15 — External T-shaped stiffener
Figure 8.5-16 — External angle stiffener
Figure 8.5-17 — Internal T-shaped stiffener
b) If the stiffener is flanged at the edge remote from vessel shell, the stiffener proportions shall
conform to the following:
d
ew

 max  1,1


E

; 0 ,67
es
E  Pys 

 es  P 

(8.5.3-52)
E  Pys 

 es  P 

(8.5.3-53)
or
wf
ef

 max  0,5


UNI EN 13445-3:2021
E

es
; 0 ,32
77
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.5.3.8.2

i

4
For a flat bar stiffener
P 
(8.5.3-54)
es
P ys
i
shall be obtained from Table 8.5-4 for internal stiffeners or from Table 8.5-5 for external stiffeners, using the
value of n c y l from Figure 8.5-4.
Table 8.5-4 — Values of  i / E  d/e
d/R
 2 for internal flat bar stiffeners
w
0,01
0,02
0,04
0,06
0,08
0,10
0,12
0,14
0,16
0,18
0,20
2
0,0119
0,0236
0,0466
0,0691
0,0913
0,114
0,135
0,157 0,180 0,202 0,225
3
0,0239
0,0461
0,0865
0,123
0,156
0,187
0,217
0,247 0,276 0,305 0,334
4
0,0395
0,0734
0,130
0,176
0,216
0,252
0,286
0,319 0,353 0,386 0,421
5
0,0577
0,103
0,171
0,223
0,266
0,304
0,341
0,378 0,416 0,456 0,498
6
0,0778
0,132
0,208
0,262
0,306
0,347
0,387
0,428 0,472 0,517 0,570
7
0,0981
0,160
0,240
0,294
0,340
0,382
0,427
0,474 0,527 0,580 0,643
8
0,119
0,186
0,268
0,322
0,369
0,415
0,465
0,517 0,580 0,647 0,725
9
0,139
0,210
0,290
0,345
0,394
0,445
0,502
0,565 0,638 0,720 0,812
10
0,158
0,231
0,310
0,365
0,417
0,474
0,536
0,614 0,696 0,792 0,903
11
0,176
0,249
0,328
0,383
0,440
0,502
0,575
0,662 0,758 0,874 1,010
12
0,193
0,266
0,343
0,400
0,461
0,531
0,614
0,715 0,831 0,966 1,121
13
0,209
0,280
0,356
0,416
0,483
0,560
0,657
0,768 0,903 1,058
-
14
0,224
0,293
0,368
0,431
0,502
0,594
0,700
0,831 0,981
-
-
15
0,237
0,304
0,379
0,446
0,527
0,628
0,749
0,894 1,068
-
-
16
0,249
0,314
0,389
0,461
0,551
0,662
0,797
0,961
-
-
-
17
0,260
0,324
0,399
0,476
0,575
0,696
0,850
1,034
-
-
-
18
0,270
0,332
0,409
0,493
0,599
0,734
0,903
1,106
-
-
-
19
0,279
0,339
0,418
0,507
0,623
0,773
0,961
-
-
-
-
20
0,287
0,346
0,427
0,522
0,652
0,816
1,019
-
-
-
-
n cyl
NOTE 1
Since
( i /E )
d
/ ew
 is limited to a maximum value of 1,14, values of the expression should not be
2
extrapolated beyond that value.
NOTE 2
For intermediate values of d / R, use (decimal) logarithmic interpolation.
EXAMPLE
78
For
n cyl  2
z  lg
0 ,0 4 6 6  

 d
i
/ E
/ ew

2

lg
 10
, the value of  i / E   d / e w
0 ,0 6 9 1 
z
lg

2
is required for d / R  0 ,0 5 then:
 0 , 0 5  0 ,0 4 

 0 , 0 6  0 ,0 4 
0 ,0 4 6 6   
 0 .0 5 6 7
UNI EN 13445-3:2021
0,0257
0,0466
0,0768
0,120
0,183
0,279
0,438
0,736
1,49*
3
4
5
6
7
8
9
10
11
0,998
0,541
0,331
0,211
0,136
0,0860
0,0517
0,0284
0,0132
0,011
1,42*
0,676
0,390
0,242
0,153
0,0955
0,0570
0,0311
0,0144
0,012
1,49*
0,648
0,356
0,211
0,126
0,0734
0,0374
0,0180
0,015
1,92*
0,677
0,340
0,187
0,103
0,0537
0,0241
0,02
1,48*
0,537
0,263
0,137
0,0687
0,0303
0,025
0,881
0,361
( i / E ) ( d / ew)2 is limited to a maximum value of 1,14.
For intermediate values of d / R use logarithmic interpolation.
NOTE 2
NOTE 3
UNI EN 13445-3:2021
Buckling cannot occur for n > 10, d / R > 0.01 under external pressure.
NOTE 1
1,44*
0,679
0,268
0,119
0,0846
0,175
0,0492
0,04
0,0366
0,03
*These values are provided to enable intermediate values to be interpolated.
0,012
0,01
2
ncyl
d/R
0,965
0,326
0,138
0,0557
0,045
1,46*
0,395
0,157
0,0622
0,05
0,581
0,201
0,0755
0,06
0,10
1,44*
0,310 0,462
0,103 0,133
0,08
Table 8.5-5 — Values of (i / E) (d / ew)2 for external flat bar stiffeners
0,695
0,164
0,12
1,10
0,198
0,14
0,18
0,20
1,99*
0,236 0,277 0,324
0,16
79
EN 13445-3:2021 (E)
Issue 1 (2021-05)
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.6 Conical shell
8.6.1 General
This subclause provides requirements for the thickness of a conical shell with  75°.
Tolerances shall be as for cylindrical shells – see 8.5.1
NOTE
The procedure is similar to that for cylindrical shells.
8.6.2 Additional notation specific to cones
The following symbols and abbreviations apply in addition to those in 8.3.
d'
is distance to the external extremity of a stiffener, see Formula (8.6.4-8);
e
is the minimum thickness over the total cone length;
I 'e
is second moment of area of the combined shell and stiffener, see Formula (8.6.4-2);
I ' e,i
is the combined second moment area of stiffener i and shell at axial distance Xi from the small
end of the cone and taking values for ea separately for each bay, see Formulae (8.6.4-2) and
(8.6.4-14);
L ' e, L" e
are the effective lengths of shell adjacent to a stiffener, see Figure 8.6-1;
NY
is the number of bays between light stiffeners in length LH;
Ri
is the mean radius of the thinnest section of a cone measured in the plane of stiffener i, see
Figure 8.6-6;
Rmax
is the maximum radius of conical shell for a check on interstiffener collapse, see Figures 8.6-2,
8.6-3 and 8.6-6;
R max
is the maximum radius of conical shell for a check of overall collapse, see Figures 8.6-4 and 8.6.-5;
Rn
is the mean radius of conical shell, for a check on interstiffener collapse, see Figures 8.6-2, 8.6-3
and 8.6-6;
Rn
is the mean radius of conical shell for a check of overall collapse, see Figures 8.6-4 and 8.6.-5;
Xw
is the distance from the centroid of the web to the centroid of the combined stiffener and shell,
see Figure 8.6-1;
Xf
is the distance from the centroid of the flange to the centroid of the combined stiffener and shell,
see Figure 8.6-1;
X s, X" s
are the distances from the centroid of the combined stiffener and shell to the centroid of the
effective shell sections adjacent to the stiffener, see Figure 8.6-1;
Xi
is the axial pitch of stiffener i, see Figure 8.6-6;
1
is the maximum hoop stress at the junction without reinforcement;
80
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
2
s the maximum hoop stress in the cylinder, see Formula (8.6.5-1).
8.6.3 Interstiffener collapse
The following procedure shall be used for the design of cones in accordance with Figure 8.6-2 to guard
against interstiffener collapse:
a) Estimate a value for ea and calculate
Py 
ea 
e
cos 
(8.6.3-1)
R max
This is the same as Formula (8.5.3-15) for Py , substituting ea cos for ea , Rmax for R and taking  = 0 .
NOTE
b) Calculate
Pm 
E e a  cos
3

(8.6.3-2)
Rn
 shall be determined from Figure 8.5-3 using
L
2 R n cos 
in place of
L
2R
and
2 R n cos 
in place of
ea
2R
ea
Rn and Rmax shall be as defined in Figures 8.6-2 to 8.6-6.
NOTE
Formula (8.6.3-2) for Pm is the same as Formula (8.5.2-5) substituting ea cos for ea , Rn cos2
4
c os  for  ; L cos for L.
R; 
c) Calculate Pm and determine Pr from curve 1 in Figure 8.5-5.
The calculation pressure shall meet the requirement:
P 
P
r
(8.6.3-3)
S
If Formula (8.6.3-3) is not met, the thickness shall be increased or the spacing between the stiffeners
reduced.
Figure 8.6-1 — Structural members
UNI EN 13445-3:2021
81
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.6.4 Overall collapse of conical shell and spacing
8.6.4.1
Constant shell thickness, stiffener size and spacing
8.6.4.1.1
General
The requirements for stiffening ring proportions to resist stiffener tripping, given for cylinders in
Subclause 8.5.3.8, apply without modification.
Internal stiffeners on cones are not covered by these requirements.
8.6.4.1.2
Light stiffeners
The design of light stiffeners on cones of constant thickness, as shown in Figure 8.6-1, follows the method for
light stiffeners on cylinders in 8.5.3.6 with the following modifications:
Pg 
E  e a   cos
3


n
Rn
2

 1 E  l ' e cos 
R
3
max
(8.6.4-1)
 Ls
where  is determined from Figure 8.5-13 or Formula (8.5.3-25) with R replaced by R n cos  .
R
n
and R
shall be as defined in Figures 8.6-4 and 8.6-5.
max
l 'e  A f  X
2
f
 Aw  X
2
w
 e a  L 'e
 
2


2  ea  L"e
 X ' s  
2



 ea
2
 X " s  l f  l w  

 12
 e3 
L"e 
 L 'e
2
a 

cos  
 

 12 
2 
 2


L ' e and L " e
x  n
2

 sin

2

 L 'e
  
  2




3
 L"e
 
 2
3 

 
 

(8.6.4-2)
shall be derived from 8.5.3.6.3 with:


R



 cos  
ea
i
(8.6.4-3)
Ls
Ri
u 
ea
Ri
(8.6.4-4)
cos 
where Ri is the mean shell radius measured at stiffener i.
To calculate the maximum stress in the stiffeners use :

s
 P 
es
 S Sf 
 P
ys

  E d'
  
 R
  max
 0 ,005 ( n 2  1) P  S  S
f





P
P
S
S
(
)
g
f

(8.6.4-5)
where
82
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
P ys




 es  e a  R f cos 
Am
1 


2
w
N




i
R max (1   / 2 )
 2
e a  cos  


 
 cos 

cos 
  1, 28
R
i
(8.6.4-7)
 ea
ef
d' X f 
8.6.4.1.3
(8.6.4-6)
(8.6.4-8)
2
Heavy stiffeners
The design of heavy stiffeners on cones of constant thickness, as shown in Figure 8.6-1 (where L'e and L''e
are replaced by L'eH and L''eH respectively), follows the method for heavy stiffeners on cylinders in 8.5.3.7
with the following modifications:
PH 
3 E  I ' eH cos 
R
R
3
max
(8.6.4-9)
 L sH
shall be as defined in Figures 8.6-4 and 8.6-5.
max
L sH is in accordance with Table 8.5-1.
I ' eH  A f  X
2
f
 Aw  X
e3 
 L ' eH
2
a 
cos  
 
 12 
 2


L ' eH and L " eH

2
w
 e a  L ' eH
 
2

 e a  L " eH

2
( X ' s )  


2


L " eH 

2

 ea 

2
 sin
( X " s )  I f  I w  



 12 

2

 L ' eH 


 2 

  
2
 L " eH
 
2

(8.6.4-10)
shall be derived from 8.5.3.6.3 with:

ea
2
x  n 

 R i  cos 




(8.6.4-11)
Ls
Ri
u 
ea
Ri
(8.6.4-12)
cos 
and L s replaced by L sH .
To calculate the maximum stress in the stiffeners use :

H
 P 
es
 S Sf 

P ys

UNI EN 13445-3:2021
 E  d'

  



 R max
 0 ,015 P  S  S
f

 (P  P  S  S )
H
f

(8.6.4-13)
83




3




EN 13445-3:2021 (E)
Issue 1 (2021-05)
where
P ys
8.6.4.2
is given by Formula (8.6.4-6).
Varying shell thickness, stiffener size or spacing
The minimum shell thickness for any length between planes of substantial support shall be determined using
the procedure given in 8.6.3.
The requirements for stiffening ring proportions shall apply without modification.
For the design of light stiffeners, either of varying size or spacing or on cones of varying thickness, as shown
in Figure 8.6-6, it is permissible to use the method of assessment for stiffened cylinders with formulae of
8.6.3 with any of the following.
a) Where the stiffener pitch and size is constant use the minimum thickness anywhere along the
length of the section under consideration in calculating P g and P y ;
b) Consider each stiffener separately using the appropriate minimum shell thickness and
the two half bays on either side of the stiffener and   0 ;
c) Consider each stiffener separately using the appropriate minimum thickness and
two half bays on either side of the stiffener.
Where
n  2
Pg 
calculate
E  e   cos
Rn
3
Pe

, as in b) and where

2 E  cos  n
2
n  2
 1
LH
i N Y

with
R n cos 
for
for the
use the following formula:
I ' e, i  sin

2
X i 

 LC 

(8.6.4-14)
3
Ri
i0
where shall be determined from Figure 8.5-13 with
R m ax
R max
LH
2 R
n
cos 
instead of
LH
2R
or from Formula (8.5.3-25)
instead of R.
8.6.5 Cone-cylinder intersections
8.6.5.1
Planes of substantial support
Where there is no knuckle, the intersection between a cone and a cylinder (at both large and small ends) is a
plane of substantial support if   30  and if n c y l (the mode number for the minimum buckling pressure
obtained from Figure 8.5-4, or found when applying formula 8.5.3-24 when light stiffeners are present) does
not equal 2 for either cone or cylinder.
When the above conditions are not met (either
  30 
or
n cyl
= 2), the distance L between planes of
substantial support is the sum of the effective unsupported length(s) of the cylinder or cylinders plus the
axial length of the cone. The thickness of the cone and the small cylinder shall not be less than the cylinder
thickness required by 8.5.3.4 and if there are light stiffeners they shall be applied at the pitch and size
determined in 8.6.3.1 to the cone and small cylinder as well as to the large cylinder.
84
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.6.5.2
Reinforcement of small end intersection
Reinforcement in the form of additional thickening and/or local stiffening shall be provided if necessary to
keep the maximum local hoop stress at the small end of the cone within acceptable limits, using the
following procedure.
Calculate the maximum hoop stress in the cylinder:

2

P  R 1    G

Calculate the maximum hoop stress
NOTE
(8.6.5-1)
e

1
at the junction without reinforcement, that is with thickness
No simple formula is available for the calculation of 
1
ea
.
and a stress analysis technique is required.
If  1   2 then no reinforcement is required. If reinforcement is required then increase the thickness of
either cone or cylinder or both or introduce additional material such as a ring stiffener or a transition piece
such that  1 when re-calculated is less than or equal to  2 .
Figures 8.6-2 — Unstiffened cone between stiffening rings
UNI EN 13445-3:2021
85
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 8.6-3 — Unstiffened cone between junctions with cylinders
Figures 8.6-4 — Stiffened conical shell with light and heavy stiffeners
86
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figures 8.6-5 — Stiffened conical shell with light stiffeners only
Figure 8.6-6 — Stiffener conical shell with varying thickness and varying stiffener pitch (see
8.6.4.2)
UNI EN 13445-3:2021
87
EN 13445-3:2021 (E)
Issue 1 (2021-05)
8.7 Spherical shells
8.7.1 Design procedure
The design thickness shall be determined by the following procedure:
a) Assume a value for
Py 
2
e
ea
and calculate:
 ea
(8.7.1-1)
R
b) Calculate
as follows:
Pm
2
Pm 
1 , 21 E  e a
R
c) Calculate
P 
If
Pr
(8.7.1-2)
2
Pm
Py
and determine
Pr
Py
from Figure 8.5-5 curve 2.
Pr
(8.7.1-3)
S
is less than required, the value of
ea
shall be increased and the procedure repeated.
8.7.2 Permissible shape deviations
The method of 8.7.1 applies only to spheres that are spherical to within 1 % on radius and in which the
radius of curvature based on an arc length of 2 , 4 e a  R max does not exceed the nominal value by more
than 30 %.
For some applications this criterion for applicability can be too stringent owing to difficulties of manufacture
and measurement. In such cases it is permissible to divide the pressure obtained from the above procedure
by the factor
 R max


 1,3 R




2
where
R m ax
is the maximum local radius of curvature either measured or estimated
conservatively.
Methods for verifying the shape of spheres are given in Annex D.6. The maximum local radius of curvature
shall appear on the vessel drawing
8.8 Vessel ends
8.8.1 Hemispherical ends
Hemispherical ends shall be designed as for spherical shells.
8.8.2 Torispherical ends
Torispherical ends shall be designed as spherical shells of mean radius R equal to the external dishing or
crown radius.
88
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
In carrying out the internal pressure calculation for a dished end, as required by 7.5.3, the factor N in the
formula for  (see Formula (7.5-12)) shall be given the value 1,0. The graphs in Figures 7.5-1 and 7.5-2 shall
not be applied.
8.8.3 Ellipsoidal ends
Ends of semi-ellipsoidal form as defined in 7.2.5 shall be designed as spherical shells of mean radius R equal
to the maximum radius of the crown:
2
R  D e /( 4 h )
(8.8.3-1)
with De as defined in 7.5.1 and h as defined in 8.3.
9 Openings in shells
9.1 Purpose
The design method specified in this clause is applicable to circular, elliptical or obround openings in dished
ends or cylindrical, conical or spherical shells under internal or external pressure.
This clause is applicable to openings, nozzles and reinforcing plates in dished ends which are completely
located inside the central area limited by a radius equal to 0,4De as shown in Figure 9.5-4. For different
locations (i.e. nozzles in knuckle regions) the relevant design rules are given in Clause 7.
Design for non-pressure loads is covered by Clause 16.
9.2 Specific definitions
The following definitions apply in addition to those in Clause 3.
9.2.1
ligament check
evaluation of the reinforcement between two adjacent openings
9.2.2
opening
through penetration of the shell which may or may not be fitted with a reinforcing plate, a reinforcing
ring or a nozzle
9.2.2.1
obround opening
an opening with an obround shape, given by two semicircles connected by two parallel straight lines
9.2.3
overall check
evaluation of the reinforcement in the cross-section including the walls on each side of each opening
and the lengths of adjacent shell
9.2.4
reinforcement
loaded cross-sectional area of metal considered to provide resistance to the pressure at an opening
UNI EN 13445-3:2021
89
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.2.5
reinforced opening
opening where the reinforcement includes a contribution from the shell, from a nozzle, a reinforcing
plate or a reinforcing ring
9.2.6
reinforcing plate
plate which is fillet welded to the shell and contributes to the reinforcement
9.2.7
reinforcing ring
set-in ring which contributes to the reinforcement
9.2.8
set-in nozzle
nozzle which passes through the shell and is welded to it on the inside and outside of the shell (see
Figure 9.4-8)
9.2.9
set-on nozzle
nozzle which is welded only to the outside of the shell (see Figure 9.4-7)
9.2.10
shell
cylinder, sphere, cone or dished end
9.2.11
shell discontinuity
junction between any two of the following: cylinder, cylinder on a different axis, cone, dished head,
spherical end, flange or flat head
9.2.12
small opening
isolated opening which satisfies the condition of Formula (9.5-18)
9.3 Specific symbols and abbreviations
The following symbols, subscripts and abbreviations apply in addition to those in Clause 4.
9.3.1 Subscripts
The following subscripts apply to the symbols listed in 9.3.2.
a refers to the analysis thickness of a component;
b refers to a nozzle or branch;
c refers to the mean value of a dimension;
e refers to the outside or external dimension;
i refers to the inside or internal dimension;
L refers to a ligament check;
90
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
O refers to an overall check;
o refers to a possible maximum or minimum value; among different values;
p refers to a reinforcing plate;
r refers to a reinforcing ring;
s refers to the shell;
w refers to the area of fillet weld which may be taken in account for reinforcement;
 refers to additional pressure loaded area for an oblique nozzle connection;
1 refers to the first of two adjacent openings;
2 refers to the second of two adjacent openings.
UNI EN 13445-3:2021
91
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.3.2 Symbols
Symbol
a
a1 , a2
a’1 , a’2
Af
AfLs
AfOs
Afw
Ap
ApLs
ApOs
Ap
d
deb
dib
dip
der
dir
dix
Dc
De
Di
e1
e2
eb
ea,b
ea,m
ec,s
Description
Unit
Distance taken along the mid-thickness of the shell between the centre of an
opening and the external edge of a set-in nozzle or ring; or, if no nozzle or ring
is present or if the nozzle is set-on, a is the distance between the centre of the
hole and its bore.
Values of a on the ligament side of the opening (Figures 9.6-2 and 9.6-3).
Values of a on the opposite side of the opening to the ligament (see Figure 9.65).
Stress loaded cross-sectional area effective as reinforcement.
Af of the shell contained along the length Lb (see Figures 9.6-1 to 9.6-4).
Af of the shell contained along the length Lb1 (see Figures 9.6-5 to 9.6-6).
Cross-sectional area of fillet weld between nozzle (or plate) and shell
(see 9.5.2.3.3 and Figures 9.4-4 and 9.5-1).
Pressure loaded area.
Ap of the shell for the length Lb (see Figures 9.6-1 to 9.6-4).
Ap of the shell for the length Lb1 (see Figures 9.6-5 to 9.6-6).
Additional pressure loaded area for oblique nozzle connection, function of
angle  (see Figures 9.5-1 to 9.5-3).
Diameter (or maximum width) of an opening on shell without nozzle.
External diameter of a nozzle fitted in a shell.
Internal diameter of a nozzle fitted in a shell.
Internal diameter of a reinforcing plate.
External diameter of a reinforcing ring.
Internal diameter of a reinforcing ring.
Internal diameter of extruded opening.
Mean diameter of a cylindrical shell at the junction with another component.
External diameter of a cylindrical or spherical shell, the cylindrical part of a
torispherical or an elliptical dished end, a conical shell at the centre of an
opening.
Internal diameter of a cylindrical or spherical shell, the cylindrical part of a
torispherical or an elliptical dished end, a conical shell at the centre of an
opening.
Minimum required thickness of a cylindrical shell at the junction with another
component (see Figures 9.7-6 and 9.7-10).
Minimum required thickness of a conical shell at the junction with a cylindrical
shell (see Figures 9.7-6 and 9.7-10).
Effective thickness of nozzle (or mean thickness within the external length lbo or
internal length lbio) taken into account for reinforcement calculation.
Analysis thickness of nozzle (or mean analysis thickness within the length lb
external or internal by the shell).
Average thickness along the length lo for reinforcing rings (see Formula (9.548))
Assumed shell thickness of shell wall (see Formula (9.5-2) for checking of
reinforcement of an opening. The thickness may be assumed by designer between
the minimum required shell thickness e and the shell analysis thickness ea,s. This
assumed thickness shall then be used consistently in all requirements.
mm
mm
mm
mm2
mm2
mm2
mm2
mm2
mm2
mm2
mm2
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
NOTE
For ec,s the shell analysis thickness may be used always, but sometimes it
may be advantageous to use a smaller assumed value to obtain smaller distances from
adjacent shell discontinuities.
92
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Symbol
ep
ea,p
er
ea,r
ea,s
e's
fb
fp
fs
h
k
lb
l'b
lbi
l’bi
lbo
lcyl
lcon
ln
lo
lp
lpi
l’p
lr
l’r
ls
l’s
lso
Lb
Lb1
ris
Description
Unit
Effective thickness of reinforcing plate taken into account for reinforcement
calculation.
Analysis thickness of reinforcing plate.
Effective thickness of reinforcing ring taken into account for reinforcement
calculation.
Analysis thickness of reinforcing ring.
Analysis thickness of shell wall or mean analysis thickness within the length l's
and excluding the thickness of the reinforcing pad if fitted.
Length of penetration of nozzle into shell wall for set-in nozzles with partial
penetration.
Nominal design stress of the nozzle material.
Nominal design stress of the reinforcing plate material.
Nominal design stress of shell material.
Inside height of a dished end, excluding cylindrical skirt.
Reduction factor for lso (used for overall check in 9.6.4).
Length of nozzle extending outside the shell.
Effective length of nozzle outside the shell for reinforcement
Length of nozzle extending inside the shell (i.e.: protruding nozzle)
Effective length of nozzle inside the shell for reinforcement
Maximum length of nozzle outside the shell for reinforcement
Length of cylindrical shell given by Formula (9.7-3) and used in the strength
assessment of a junction (see Figure 9.7-6) between a cylinder and:
— the small end of a conical shell with same axis;
— a spherical shell convex towards the cylinder;
— a cylindrical shell with convergent axis.
Length of conical shell given by Formula (9.7-7) and used in the strength
assessment of a junction between the small end of a cone and a cylindrical shell,
(see Figure 9.7-6).
Distance between the centre line of a shell butt-weld and the centre of an
opening near or crossing the butt-weld.
Maximum length of ring and shell wall in reinforcing rings for reinforcement
Width of reinforcing plate.
Width of reinforcing plate between two adjacent openings (Figure 9.6-5).
mm
Effective width of reinforcing plate for reinforcement.
Width of reinforcing ring.
Effective width of reinforcing ring for reinforcement.
Length of shell, from the edge of an opening or from the external diameter of a
nozzle, to a shell discontinuity.
Effective length of shell for opening reinforcement.
Maximum length of shell contributing to opening reinforcement, taken on the
mean surface of the shell wall.
Centre-to-centre distance between two openings or nozzles taken on the mean
surface of the shell (see Figure 9.6-2).
Length of cross sectional area of shell including the whole section of two
adjacent openings taken on the surface of the shell.
Inside radius of curvature of the shell at the opening centre.
UNI EN 13445-3:2021
mm
mm
mm
mm
mm
MPa
MPa
MPa
mm
_
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
mm
93
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Symbol
R
w
wmin
wp



e


Description
Unit
Inside radius of a hemispherical end or of the crown of a torispherical end.
Distance between an opening and a shell discontinuity (see Figures 9.7-1 to 9.711).
Required minimum value for w.
Minimum value for w which has no influence on ls from shell discontinuities
Half apex angle of a conical shell.
For a nozzle having a longitudinal weld, angle between the plane containing the
nozzle axis and the longitudinal weld line, and the plane containing the nozzle
axis and the shell generatrix passing through the center of the opening.
Obliquity angle in the longitudinal or transversal cross-section, measured
between the normal to the wall at the opening centre and the projection of the
nozzle axis on the considered cross-section.
Projection of  in the plane in which Lb lies for ligament check of multiple
openings.
Angle between the centre-to-centre line of two openings or nozzles and the
generatrix of a cylindrical or conical shell (0°    90°) (see Figure 9.6-1).
- for isolated openings, angle between shell generatrix and axis of major
diameter
- for adjacent openings, angle between the plane containing the opening
centres and the axis of major diameter.
mm
mm
mm
mm
degrees
degrees
degrees
radians
degrees
degrees
9.4 General
9.4.1 A shell containing an opening shall be adequately reinforced in the area adjacent to the opening.
This is to compensate for the reduction of the pressure bearing section. The reinforcement shall be
obtained by one of the following methods:
a) increasing the wall thickness of the shell above that required for an unpierced shell (see
Figures 9.4-1 and 9.4-2);
b) using a reinforcing plate (see Figures 9.4-3 and 9.4-4);
c) using a reinforcing ring (see Figures 9.4-5 and 9.4-6);
d) increasing the wall thickness of the nozzle (see Figures 9.4-7 and 9.4-8) above that required for
the membrane pressure stress;
e) using a combination of the above (see Figures 9.4-9 to 9.4-13).
9.4.2 The dimensions of the reinforcement area at an opening shall be assumed and the design shall be
verified by the method laid down in the following subclauses.
The method is based on ensuring that the reactive force provided by the material is greater than, or equal
to, the load from the pressure. The former is the sum of the product of the average membrane stress in each
component and its stress loaded cross-sectional area (see Figures 9.4-1 to 9.4-13). The latter is the sum of
the product of the pressure and the pressure loaded cross-sectional areas. If the reinforcement is
insufficient, it shall be increased and the calculation repeated.
Reinforcement and strength may vary around the axis of an opening. Reinforcement shall be shown to be
sufficient in all planes.
94
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.4.3 The design method is applicable when the opening is located at a minimum distance from a shell
discontinuity. Rules for determining this minimum distance are given in 9.7.
9.4.4 Elliptical or obround openings
Elliptical or obround openings resulting from a circular nozzle oblique to the shell wall shall be calculated
according to 9.5.2.4.5.
For all other elliptical or obround openings the ratio between the major and minor diameter shall not exceed
2.
9.4.4.1 Elliptical or obround openings reinforced by increased shell wall thickness, reinforcing
plate or reinforcing ring (see 9.4.1 a), b) or c) )
In cylindrical or conical shells the diameter d of the opening for reinforcing calculations shall be taken:
— along the generatrix of the shell for isolated openings
— in the plane containing the centres of the openings
In spherical shells and dished ends the diameter d of the opening shall be taken:
— along the largest dimension of the bore (major axis) for isolated openings
— in the plane containing the centres of the openings
9.4.4.2 Openings reinforced by elliptical or obround nozzles normal to the shell wall (see
9.4.1.d)
In cylindrical or conical shells the diameter d of the opening shall be calculated as follows:
2
d  d min  ( sin
 
d max
d min

( d min  d max )
2  d min
 cos
2
 )
(9.4-1)
where dmin and dmax are the minor and major diameter of the opening,
and  is :
— for isolated openings, the angle between the shell generatrix passing through the centre of the
opening and the axis of the major diameter.
— for adjacent openings, and for each of the two openings, the angle between the shortest line lying
on the surface of the shell passing through the centres of the two openings, and the line resulting on
the shell from the intersection of the plane defined by the nozzle axis and the axis of the major
diameter of any nozzle cross section under consideration.
In spherical shells and dished ends the diameter d of the opening shall be calculated as follows:
d  d max  (
d min  d max
2  d min
)
(9.4-2)
where dmin and dmax are defined above.
UNI EN 13445-3:2021
95
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The diameter for the calculation of value lbo in Formula (9.5-75) is defined in 9.5.2.4.4.1.
NOTE
For nozzles with elliptical or obround cross-section the pressure produces not only membrane
stresses, but also bending stresses in the circumferential direction. Thus the attached shell wall on one side and
the attached flange or circular pipe on the other side have to support the nozzle if its wall thickness has been
determined using only membrane stresses. The nozzle loads the shell and it is possible that the diameter which
applies for the elliptical or obround nozzle is larger than the major axis.
9.4.4.3
For elliptical or obround nozzles not normal to the shell wall 9.4.4.2 is not applicable,
therefore 9.4.4.1 shall be used without contribution of nozzle wall for reinforcing calculations.
9.4.5 Limitations on diameter
9.4.5.1
Shell reinforced openings
Shell reinforced openings without a nozzle shall satisfy the following condition:
d
2 r is
9.4.5.2
(9.4-3)
 0,5
Openings with reinforcing plates
Where an opening is fitted with a reinforcing plate, with or without the presence of a nozzle, the condition
of the Formula (9.4-3) shall be satisfied.
Reinforcing plates are normally situated on the external surface of the shell, but they may be situated also
on the internal surface or on both surfaces.
In case of high mean wall temperature for the shell (more than 250 °C) or in the presence of severe
temperature gradients through the shell, the use of reinforcing plates shall be avoided; if it is necessary then
the material of the reinforcing plate shall be of the same quality of shell material, and special measures and
warnings shall be taken to avoid thermal stress concentrations.
9.4.5.3
Openings in dished ends
For openings in hemispherical ends and dished ends, the ratio d / De shall not exceed 0,6. Therefore, if the
opening is reinforced by a nozzle or a reinforcing ring dib / De and dir / De shall not exceed 0,6.
9.4.5.4
Openings with nozzles
For openings in cylindrical shells reinforced by nozzles the ratio dib / (2ris) shall not exceed 1.0 (see
Figures 9.4-14 and 9.4-15).
9.4.6 Effective thickness for nozzles
9.4.6.1 in fatigue applications where fatigue is assessed using Clause 17 and if the opening is a
critical area (as defined in 17.2)
The ratio eb/ea,s shall not exceed the value taken from the graph in Figure 9.4-14 and the value of eb shall
never exceed the value of ea,b. Nozzle thickness in excess of that calculated using Figure 9.4-14 shall not be
included in the reinforcement calculation.
96
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Furthermore the ratio ea,b/ea,s shall not exceed the value taken from the graph in Figure 9.4-15.
NOTE 1
eb is the effective thickness of the nozzle, to be used for the verification of the reinforcement; ea,b is the
analysis thickness of this nozzle; the ratio eb/ea,s limits the contribution of the nozzle to the resistance of the
opening; the ratio ea,b/ea,s limits the analysis thickness of the nozzle, and thus its manufacturing thickness, in order
to limit the stresses which can occur due to great thickness differences and to avoid the fatigue problems which
can result.
NOTE 2
When fatigue is assessed using Clause 18, no limitation to the thickness ratio is necessary because in
that case more accurate stresses are used for fatigue calculations.
9.4.6.2
range)
in creep applications (i.e.: when the calculation temperature is situated in the creep
The effective thickness eb may be taken equal to the analysis thickness ea,b of the nozzle.
However the ratio ea,b/ea,s shall not exceed the value taken from the graph in Figure 9.4-15.
9.4.6.3 in applications without creep and without fatigue assessment using Clause 17 (i.e.:
when the calculation temperature is situated out of the creep range and the opening is not a
critical area as defined in 17.2)
The effective thickness eb may be taken equal to the analysis thickness ea,b of the nozzle and no limitations
apply to the ratio ea,b/ea,s .
9.4.7
Nozzles to shell connections
Nozzles are usually of the following forms: welded (set-in, set-on, protruding nozzles) or extruded or
screwed.
For welded nozzles the cross sectional area of the nozzle can always be taken in account for reinforcement
of the opening, provided weld dimensions are in accordance with Tables A-6 and A-8 of Annex A of this
standard.
For nozzles extruded from the shell the cross sectional area of the nozzle shall be taken in account for
reinforcement provided the requirements of 9.5.2.4.4.2 are applied.
For screwed nozzles the cross sectional area of the nozzle shall not be taken in account for reinforcement of
the opening.
9.4.8 Distance between a nozzle and a shell butt-weld
The distance between the centre line of a shell butt-weld (longitudinal or circumferential) and the centre of
an opening shall be either less than dib / 6 or greater than the value ln given by:
ln = min (0,5 deb + 2ea,s ; 0,5 deb + 40)
UNI EN 13445-3:2021
(9.4-4)
97
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.4-1 — Cylindrical shell with isolated opening and increased wall thickness
Figure 9.4-2 — Spherical shell or dished end with isolated opening and increased wall thickness
Figure 9.4-3 — Cylindrical shell with isolated opening and reinforcing plate
98
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.4-4 —Spherical shell or dished end with isolated opening and reinforcing plate
Figure 9.4-5 — Cylindrical shell with isolated opening and reinforcing ring, with external blind
flange B
UNI EN 13445-3:2021
99
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.4.6— Spherical shell or dished end with isolated opening and reinforcing ring, with
internal blind flange B
Figure 9.4-7 — Cylindrical shell with isolated opening and set-on nozzle
100
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.4-8 — Spherical shell or dished end with isolated opening and set-in nozzle
Figure 9.4-9 — Cylindrical shell with isolated opening, increased wall thickness and set-in nozzle
UNI EN 13445-3:2021
101
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
The various lengths and areas shown for the case of a nozzle with a reinforcing plate in a sphere also
applies to the case of a nozzle with a reinforcing plate in a cylinder.
Figure 9.4-10 — Spherical shell or dished end with isolated opening and shell, nozzle and
reinforcing plate
102
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.4-11 — Cylindrical shell with isolated opening and a butt-weld nozzle (see X) or an
extruded shell (see Y)
Figure 9.4-12 — Spherical shell or dished end with isolated opening extruded from the shell,
with internal blind flange B
UNI EN 13445-3:2021
103
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.4-13 — Conical shell with isolated opening. Combined reinforcement from shell and
nozzle
104
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
dib
2ּris
Figure 9.4-14 — Limitation of effective thickness ratio for nozzles, for the calculation
Figure 9.4-15 — Limitation of actual thickness ratio for nozzles, for the manufacturing
9.5 Isolated openings
9.5.1 Limitations
An opening is considered isolated if the following condition is satisfied:
Lb  a1 + a2 + lso1 + lso2
(9.5-1)
where
UNI EN 13445-3:2021
105
d
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a1 and a2 are shown in Figures 9.6-1 to 4, and lso1 and lso2 are calculated according to
l so 
(9.5-2)
( 2 r is  e c ,s )  e c ,s
where
ec,s is the assumed shell thickness to be taken as is explained in 9.3.2 ; normally the value of shell analysis
thickness ea,s may be taken, but this may be conservative and sometimes it may be advantageous to use a
smaller assumed value for ec,s to obtain smaller minimum distances from adjacent shell discontinuities;
ris is given by
— for cylindrical or spherical shells
r is 
De
2
(9.5-3)
 e a, s
— for hemispherical or torispherical ends
ris = R
(9.5-4)
— for elliptical ends
2
r is 
0,44 D i
2h
(9.5-5)
 0,02 D i
— for conical shells
r is 
De
2 cos 
(9.5-6)
 e a, s
9.5.2 Reinforcement rules
9.5.2.1
9.5.2.1.1
General formula and its derivates
The general formula for the reinforcement of an isolated opening is given by
(Afs + Afw) ( fs - 0,5P) + Afp (fop - 0,5P) + Afb (fob - 0,5P)  P (Aps + Apb + 0,5 Ap)
(9.5-7)
where
fob = min (fs ; fb)
(9.5-8)
fop = min (fs ; fp)
(9.5-9)
Where a reinforcing ring is fitted, Afr and Apr shall be substituted for Afb and Apb .
9.5.2.1.2 For all reinforced openings except small openings and those reinforced by a ring, the
Formula (9.5-7) applies; in particular:
a) Where either fb or fp is not greater than fs, the reinforcement shall be determined from
Formula (9.5-7)
and Pmax shall be obtained as follows
106
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
( Af
P max

( Ap
s
+ Ap
b
s
+ Af
)f
w
+ 0,5Ap
+ Af
s
b
 f ob + Af
) + 0,5 ( Af

s
+ Af
 f op
p
w
+ Af
b
+ Af
p
)
(9.5-10)
b) Where fb and fp are both greater than fs, the reinforcement shall be determined from
(Afs + Afw + Afp + Afb)  (fs - 0,5P)  P (Aps + Apb + 0,5Ap)
P max

9.5.2.1.3
( Af
( Ap
s
 Ap
b
s
 Af
 Af b  Af p )  f
w
 0,5 Ap  )  0,5( Af
s
 Af
s
w
 Af b  Af p )
(9.5-11)
(9.5-12)
For an opening with a reinforcing ring:
a) where fr is less than fs, the following shall apply
(Afs + Afw)  ( fs - 0,5P) + Afr  (for - 0,5P)  P (Aps + Apr + 0,5Ap)
(9.5-13)
and Pmax is given by
P max

( Af
( Ap
s
+ Ap
r
s
+ Af
w
+ 0,5 Ap
)f

s
+ Af r  f or
) + 0,5( Af
s
+ Af
w
+ Af r )
(9.5-14)
where for is given by
for = min (fs ; fr)
(9.5-15)
b) where fr is greater than or equal to fs, the following shall apply
(Afs + Afw + Afr)  ( fs - 0,5P)  P (Aps + Apr + 0,5Ap)
(9.5-16)
and Pmax is given by
P max

( Af
( Ap
s
+ Ap
r
s
+ Af
+ 0,5 Ap
w

+ Af r )  f
s
) + 0,5( Af
s
+ Af
w
+ Af r )
(9.5-17)
NOTE
Note 1.
For application of Formulae (9.5-10), (9.5-12), (9.5-14) and (9.5-17) to different load cases, see 3.16,
9.5.2.2
Small opening
A small opening is one which satisfies the following condition
d  0,15
(2 r
is
 e
c, s
)e
c, s
(9.5-18)
Where a small opening lies beyond the distance wp defined in 9.7.3, no reinforcement check is necessary.
Where it lies within this distance, the reinforcement shall be in accordance with Formula (9.5-7) or (9.5-11)
as appropriate. However the distance w between small opening and shell discontinuity shall respect the
minimum value wmin as required in 9.7.1.
UNI EN 13445-3:2021
107
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.5.2.3
General requirements for reinforcement
9.5.2.3.1
Reinforcing pads
For cases where a reinforcing pad contributes to the reinforcement (see Figures 9.4-3, 9.4-4, 9.4-10):
— reinforcing plates shall be fitted in close contact with the shell.
— the width of a reinforcing plate l'p to be considered as contributing to reinforcement is given by
'
(9.5-19)
l p  min( l so ; l p )
— the value of ep used for the calculation of Afp shall not exceed the following
e
p
(9.5-20)
 min( e a , p ; e c , s )
furthermore the analysis thickness of the reinforcing pad shall meet the following condition
ea,p  1.5 ea,s
(9.5-21)
— ea,p and lp are dimensions of reinforcing pads used in formulae for openings that may be reinforced
also by reinforcing pads; if reinforcing pad is not present then the values ea,p and lp shall be put
equal to zero. If the reinforcing pad is contributing to reinforcement then, for all cases:
'
Af p  l p  e p
9.5.2.3.2
(9.5-22)
Joint coefficient
9.5.2.3.2.1
Opening intersecting with a shell governing weld
If an opening intersects with a shell governing weld (see definition in 5.6), the value fs in Formula (9.57,11,13 and 16) for the shell material shall be replaced by fs∙z, where z is the joint coefficient of the shell.
9.5.2.3.2.2
Nozzle with a longitudinal weld
If a nozzle has a longitudinal weld having a weld joint factor z, the value fb for the nozzle material shall be
as defined in
replaced by fbz except for openings in cylindrical or conical shells if the angle
Subclause 9.3.2 is greater than 45°.
9.5.2.3.2.3
Reinforcing pad with a weld
If a reinforcing pad has a weld having a weld joint factor z, the value fp for the pad material shall be
replaced by fp  z except for openings in cylindrical or conical shells if the angle between the pad weld and
the shell generatrix is greater than 45°.
9.5.2.3.3
Fillet weld areas for compensation
For all cases:
— Afw is the area of any welds connecting together the different components (shell to nozzle, shell to
reinforcing ring or reinforcing plate) which is located within length l’s on the shell (see 9.5.2.4.2)
and lengths l’b and l’bi on the nozzle (see 9.5.2.4.4.1). Areas of welds already included in other areas,
e.g. Afs, Afr, Afp or Afb, shall be omitted from Afw (see Figures 9.4-6 and 9.4-10).
108
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.5.2.4
Pressure loaded cross-sectional areas Ap and stress loaded cross-sectional areas Af
9.5.2.4.1
General
With reference to the general formulae and its derivates of 9.5.2.1 the stress loaded and pressure loaded
cross-sectional areas shall be calculated by different formulae depending on different cases of shells and
different cases of nozzles.
In presence of reinforcing pads the cross sectional area Afp shall be calculated according to 9.5.2.3.1.
For fillet weld areas participating to the reinforcement the cross sectional area Afw shall be evaluated
according to 9.5.2.3.3.
For additional pressure loaded cross sectional area
9.5.2.4.2
pads
Ap 
due to the obliquity of a nozzle, see 9.5.2.4.5
Shells with openings without nozzle or reinforcing ring, with or without reinforcing
9.5.2.4.2.1
On cylindrical shell, longitudinal cross-section
With reference to Figures 9.4-1 and 9.4-3 the values useful for compensation of opening shall be calculated
as follows:
d
a 
2
(9.5-23)
De
r is 
2
l so 
 e a ,s
(( D e  2 e a , s )  e c , s )  e c , s
'
l s  min( l so ; l s )
(9.5-25)
(9.5-26)
'
Ap
Af
(9.5-24)
s
 ris ( l s  a )  a  ( e a , s  e a , p )
(9.5-27)
'
s
 ls  ec ,s
(9.5-28)
If the closure of the opening is located inside the shell (as in Figure 9.4-2 ), then:
Ap
'
s
 ris ( l s  a )
(9.5-29)
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.2.2
On conical shell, longitudinal cross-section
With reference to Figure 9.4-13 the values useful for compensation of opening shall be calculated as follows:
a 
d
2
UNI EN 13445-3:2021
(9.5-30)
109
EN 13445-3:2021 (E)
Issue 1 (2021-05)
ris 
De
 e a ,s
2 cos 
l so 
((
De
(9.5-31)
 2 ea ,s )  ec ,s )  ec ,s
cos 
(9.5-32)
'
l s  min( l so ; l s )
Af
Ap
(9.5-33)
'
 l s  e c ,s
s
(9.5-34)
'
s
'
 0 , 5  ( l s  a )  ( 2 ris  ( l s  a ) tan  )  a  ( e a , s  e a , p )
(9.5-35)
If the closure of the opening is located inside the ring, then:
Ap
'
s
'
(9.5-36)
 0 , 5  ( l s  a )  ( 2 ris  ( l s  a ) tan  )
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.2.3
On spherical shell, dished end, cylindrical and conical shell, transverse section
With reference to Figure 9.4-2 and 9.4-4, in the following formulae the formulae of ris shall be those of
Formulae (9.5-3) to (9.5-6) of 9.5-1.
l so 
(9.5-37)
( 2 r is  e c , s )  e c , s
l s  min( l so ; l s )
(9.5-38)
r ms  ( r is  0 , 5  e a , s )
(9.5-39)
'
 
d
(9.5-40)
2  r ms
a  r ms  arcsin 
(9.5-41)
'
Ap
Af
s
 0 ,5 
2
r is

ls  a
0 , 5  e a , s  r is
(9.5-42)
 a  (e a ,s  e a , p )
(9.5-43)
'
s
 l s  e c ,s
If the closure of the opening is located inside the shell, then
'
Ap
2
s
 0 , 5  r is 
ls  a
(9.5-44)
0 , 5  e a , s  r is
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
110
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.5.2.4.3
Shells with openings without nozzle, reinforced by reinforcing rings
This applies only when rings of the set-in welded type in accordance with Figures 9.4-5 and 9.4-6 are used,
and the effective thickness of reinforcing ring for reinforcement calculation er shall be:
e r  min( e a , r ; max( 3 e c , s ; 3 l r ))
(9.5-45)
NOTE
The design described here does not cover tightness issue. Additional calculation may be necessary. See
Annex G for opening with flange in sphere (Figure G.3-7 b))
Considering ring plus shell as a shell wall of variable thickness starting from the bore of reinforcing ring (see
Figures 9.4-5 and 9.4-6), the maximum length lo of ring plus shell from the bore contributing to opening
reinforcement is given by:
lo 
(9.5-46)
( 2 r is  e a , m )  e a , m
(9.5-47)
l o  l r  (l o  l r )
where ea,m is the average thickness (obtained considering er and ec,s and by iterative calculation) along the
length lo :
e a ,m  e c ,s  ( e r  e c ,s ) 
lr
lo
(9.5-48)
with
lr
lo
(9.5-49)
1
If the width of reinforcing ring lr is greater than lo for reinforcement calculation shall be put lr = lo .
Therefore the effective length l's of shell for calculation of Aps and Afs is:
'
l s  min( l s ; ( l o  l r ))
9.5.2.4.3.1
(9.5-50)
Reinforcing ring on cylindrical shell, longitudinal cross-section
With reference to Figure 9.4-5 the values useful for compensation of opening shall be calculated as follows:
a 
r is 
lo 
d ir
(9.5-51)
2
De
2
 e a ,s
(( D e  2 e a , s )  e a , m )  e a , m
UNI EN 13445-3:2021
(9.5-52)
(9.5-53)
111
EN 13445-3:2021 (E)
Issue 1 (2021-05)
'
Af
s
 ls  ec ,s
(9.5-54)
Af
r
 lr  er
(9.5-55)
De
Ap s  (
'
 e a, s )  (l s  l r  a )  e a,r  a
2
(9.5-56)
If the closure of the opening is located inside the ring, then
Ap
 (
s
De
9.5.2.4.3.2
(9.5-57)
'
 e a ,s )  (l s  l r  a )
2
Reinforcing ring on conical shell, longitudinal cross-section
With reference to Figures 9.4-5 and 9.4-13 the values useful for compensation of opening shall be calculated
as follows:
d ir
a 
(9.5-58)
2
De
ris 
lo 
((
(9.5-59)
 e a ,s
2 cos 
De
 2 e a ,s )  e a ,m )  e a ,m
cos 
'
(9.5-60)
Af
s
 ls  ec ,s
(9.5-61)
Af
r
 lr  er
(9.5-62)
'
'
Ap s  0 ,5  ( l s  l r  a )  ( 2 ris  ( l s  l r  a ) tan  )  e a , r  a
(9.5-63)
If the closure of the opening is located inside the ring, then :
Ap
'
s
'
 0 , 5  ( l s  l r  a )  ( 2 ris  ( l s  l r  a ) tan  )
(9.5-64)
9.5.2.4.3.3
Reinforcing ring on spherical shell, dished end, cylindrical and conical shell,
transverse section
With reference to Figure 9.4-6, in the following formulae the formulae of ris shall be those of Formulae (9.53) to (9.5-6) of 9.5-1.
r ms  ( r is  0 , 5  e a , s )

r

d er
2  r ms
d er  d ir  2 l r
112
(9.5-65)
(9.5-66)
(9.5-67)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a r  r ms  arcsin  r
lo 
9.5-68)
(9.5-69)
( 2 r is  e a , m )  e a , m
d ir
 
2  r ms
(9.5-70)
a  r ms  arcsin 
(9.5-71)
'
ls  ar
2
 e a,r  a
(9.5-72)
Ap
s
 0 ,5  r is 
Af
s
 l s  e c ,s
(9.5-73)
Af
r
 lr  er
(9.5-74)
0 ,5  e a , s  r is
'
If the closure of the opening is located inside the ring, then:
'
Ap
ls  ar
2
 0 ,5  ris 
s
9.5.2.4.4
0 ,5  e a , s  r is
(9.5-75)
Nozzles normal to the shell, with or without reinforcing pads
9.5.2.4.4.1
General
This paragraph refers to Figures 9.4-7 to 9.4-13.
For a set-on nozzle (see Figure 9.4-7) or set-in nozzle (see Figure 9.4-8), the length of the nozzle contributing
to the reinforcement shall not be greater than lbo calculated as follows:

l bo
 d eb
 eb
 eb
(9.5-76)
For the calculation of value lbo the diameter deb of nozzles with elliptical or obround cross section shall be
taken along the smallest dimension of the bore.
For protruding nozzles (see Figures 9.4-8 to 9.4-10 ):
l'bi = min (lbi ; 0,5lbo)
(9.5-77)
For a set-in nozzle:
Afb = eb  (l’b + l’bi + e's)
Af
'
s
 ls  ec ,s
(9.5-78)
(9.5-79)
For a set-on nozzle:
Afb = ebl’b
Af
'
s
 (l s  e b )  e c ,s
UNI EN 13445-3:2021
(9.5-80)
(9.5-81)
113
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where:
l’b = min (lbo ; lb )
(9.5-82)
'
(9.5-83)
l s  min( l so ; l s )
e's is the length of penetration (full or partial) of set-in nozzle into shell wall, but not greater than ea,s.
For both set-in and set-on nozzles:
Apb = 0,5dib( l'b + ea,s )
(9.5-84)
If a reinforcing pad is also contributing to reinforcement then:
App = 0
(9.5-85)
Afp = epl’p
(9.5-86)
l’p = min (lso ; lp )
(9.5-87)
ep = min (ea,p ; ec,s)
(9.5-88)
with
Furthermore the analysis thickness of the reinforcing pad shall meet the following condition:
ea,p  1.5 ea,s
9.5.2.4.4.2
(9.5-89)
Extruded nozzles
For a nozzle extruded from the shell see Figures 9.4-11 shape Y and 9.4-12. Both Afs and Afb shall be
multiplied by 0,9 to compensate for thinning during manufacturing, if minimum or actual thickness of
extruded part is not known.
For butt-welded nozzles as in Figure 9.4-11 shape X and extruded nozzles as in Figure 9.4-11 shape Y and
Figure 9.4-12 the pressure loaded areas Ap and stress loaded cross-sectional areas Af of nozzles shall be
calculated by a suitable method.
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.4.3
Nozzle in cylindrical shell, longitudinal cross-section
With reference to Figures 9.4-7 and 9.4-9 the values useful for compensation of opening shall be calculated
as follows:
a 
r is 
l so 
'
d eb
(9.5-90)
2
De
2
 e a ,s
(( D e  2 e a , s )  e c , s )  e c , s
l s  min( l so ; l s )
114
(9.5-91)
(9.5-92)
(9.5-93)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Ap
'
s
 ris  ( l s  a )
(9.5-94)
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.4.4
Nozzle in conical shell, longitudinal cross-section
With reference to Figure 9.4-13 the values useful for compensation of opening shall be calculated as follows:
d eb
a 
(9.5-95)
2
ris 
De
l so 
((
(9.5-96)
 e a ,s
2 cos 
De
 2 ea ,s )  ec ,s )  ec ,s
cos 
(9.5-98)
'
l s  min( l so ; l s )
Ap
'
s
(9.5-97)
'
 0 , 5  ( l s  a )  ( 2 ris  ( l s  a ) tan  )
(9.5-99)
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.4.5
section
Nozzle in spherical shell, dished end, cylindrical and conical shell, transverse
With reference to Figures 9.4-8 and 9.4-10, in the following formulae the formulae of ris shall be those of
Formulae (9.5-3) to (9.5-6) of 9.5-1.
l so 
( 2 r is  e c , s )  e c , s
(9.5-100)
l s  min( l so ; l s )
(9.5-101)
r ms  ( r is  0 , 5  e a , s )
(9.5-102)
'
 
d eb
(9.5-103)
2  r ms
a  r ms  arcsin 
(9.5-104)
'
Ap
s
 0 ,5 
2
r is

ls  a
0 , 5  e a , s  r is
(9.5-105)
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
UNI EN 13445-3:2021
115
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.5.2.4.5
Nozzles oblique to the shell, with or without reinforcing pads
9.5.2.4.5.1
General
This paragraph refers to Figures 9.5-1, 9.5-2 and 9.5-3.
For the oblique nozzles in all cases:
—
is the additional area due to the obliquity of the nozzle; its value is equal to zero when the
Ap 
nozzle is normal (φ = 0) to the shell (see Figures 9.5-1 and 9.5-3).
9.5.2.4.5.2
General for cylindrical and conical shells
Where a nozzle is oblique in the transverse cross-section (see Figure 9.5-2), and
following value,

 < arcsin (1-)
does not exceed the
(9.5-106)
Where
d
 
2 ( r is

eb
(9.5-107)
0,5 e a, s )
the reinforcement shall be checked on both the longitudinal and transverse cross-sections. For the check on
longitudinal cross-section,  shall be taken equal to zero.
Where the axis of the nozzle is oblique in the longitudinal cross-section (see Figure 9.5-1) and  does not
exceed 60°, the reinforcement shall be checked on the longitudinal cross-section only.
The reinforcement shall always be calculated on the side where there is an acute angle between the nozzle
wall and the shell wall.
The value of distance a shall be calculated as given below:
i)
for cylindrical and conical shells, in the longitudinal cross-section
a  0,5 
d eb
(9.5-108)
cos 
ii) for cylindrical and conical shells in the transverse cross-section
a  0 , 5 r ms  arcsin

 sin    arcsin

 sin 

(9.5-109)
with
r ms  ( r is  0 , 5  e a , s )
 
116
d eb
2  r ms
(9.5-110)
(9.5-111)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The additional area due to the obliquity of the nozzle shall be determined as given below:
Ap  
d
2
ib
(9.5-112)
 tan 
2
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.5.3
Oblique nozzle in cylindrical shell, longitudinal cross-section
With reference to Figure 9.5-1 the values useful for compensation of opening shall be calculated as follows:
'
(9.5-113)
Ap s  ris  ( l s  a )
with
calculated according to 9.5.2.4.5.2.
a
The values of ris , lso , l's shall be calculated with the same formulae and the same conditions of paragraph
9.5.2.4.4.3.
The values of lbo , l'bi , e's , Afb , Afs , Apb , App , Afp and ep shall be calculated with the same formulae and the
same conditions of 9.5.2.4.4.1.
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.5.4
Oblique nozzle in conical shell, longitudinal cross-section
With reference to Figures 9.5-1 and 9.4.13 the values useful for compensation of opening shall be calculated
as follows:
'
'
Ap s  0 ,5  ( l s  a )  ( 2 ris  ( l s  a ) tan  )
with
(9.5-114)
calculated according to 9.5.2.4.5.2
a
NOTE
This applies even if the actual direction of the nozzle axis would involve a reduced value of Aps on the
side of the nozzle where the reinforcement is calculated. Formula of Aps should be used in both cases: where the
nozzle axis is inclined along the generatrix of the cone in one direction or in the other direction.
The values of ris , lso , l's shall be calculated with the same formulae and the same conditions of 9.5.2.4.4.4.
The values of lbo , l'bi , e's , Afb , Afs , Apb , App , Afp and ep shall be calculated with the same formulae and the
same conditions of 9.5.2.4.4.1.
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.5.5
Oblique nozzle in cylindrical and conical shell, transverse section
With reference to Figure 9.5-2 the values useful for compensation of opening shall be calculated as follows:
'
Ap
with
2
s
 0 ,5  r is 
a
ls  a
0 ,5  e a , s  r is
(9.5-115)
calculated according paragraph 9.5.2.4.5.2
The values of ris , lso , l's shall be calculated with the same formulae and the same conditions of paragraph
9.5.2.4.4.5.
UNI EN 13445-3:2021
117
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The values of lbo , l'bi , e's , Afb , Afs , Apb , App , Afp and ep shall be calculated with the same formulae and the
same conditions of paragraph 9.5.2.4.4.1.
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
9.5.2.4.5.6
General for oblique nozzles in spherical shells and dished ends
The following applies to nozzles on spherical shells and spherical portions of dished ends and also on
elliptical ends (see Figure 9.5-3) having an axis which is oblique to radial direction of the sphere or to local
radial direction of the elliptical head, and forming an angle with it limited by:
 < arcsin (1- )
(9.5-116)
with
 
d eb
(9.5-117)
2  r ms
(9.5-118)
r ms  ( r is  0 , 5  e a , s )
With reference to Figure 9.5-3, in the following formulae the formulae of ris shall be those of Formulae (9.53) to (9.5-6) of 9.5-1.
The reinforcement shall be calculated on the plane defined by the nozzle axis and the sphere radius passing
through the nozzle centre. The calculation shall be made considering only the areas located on the side of
the nozzle where there is an acute angle between the wall of the nozzle and the surface of the sphere, with
the exception that l’s shall be calculated on both sides of the nozzle, and the smaller value shall be taken.
For spherical shells and dished ends the value of a is given by:
a  0 , 5 r ms  arcsin

 sin    arcsin

 sin 

(9.5-119)
with
(9.5-120)
r ms  ( r is  0 , 5  e a , s )
 
d eb
(9.5-121)
2  r ms
The additional area due to the obliquity of the nozzle shall be determined by the following:
Ap  
d
2
ib
(9.5-122)
 tan 
2
With reference to Figure 9.5-3 the values useful for compensation of opening shall be calculated as follows:
'
Ap
with
2
s
a
 0 ,5  r is 
ls  a
0 ,5  e a , s  r is
(9.5-123)
calculated according to this paragraph 9.5.2.4.5.6
The values of ris , lso , l's shall be calculated with the same formulae and the same conditions of 9.5.2.4.4.5.
118
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The values of lbo , l'bi , e's , Afs , Afb , Apb , App , Afp and ep shall be calculated with the same formulae and the
same conditions of 9.5.2.4.4.1.
For adequate reinforcement either Formula (9.5-7) or (9.5-11), as appropriate, shall be satisfied.
Figure 9.5-1 — Cylindrical shell with nozzle oblique in the longitudinal cross section
UNI EN 13445-3:2021
119
Figure 9.5-2 — Cylindrical shell with nozzle oblique in the transverse cross section
120
1 Figure 9.5-2
Cylindrical shell with nozzle oblique in the transverse cross section
EN 13445-3:2021 (E)
Issue 1 (2021-05)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.5-3 — Spherical shell with a non radial nozzle
Figure 9.5-4 — Position of openings, nozzles and reinforcing plates in dished ends
UNI EN 13445-3:2021
121
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.6 Multiple openings
9.6.1 Adjacent openings
This subclause provides a ligament check (in 9.6.3) and an overall check (in 9.6.4). These are used as follows.
If the centre-to-centre distance Lb of two adjacent openings (see Figures 9.6-1 and 9.6-3) does not satisfy
Formula (9.5-1), a ligament check shall be carried out in accordance with 9.6.3, unless all the conditions
given in 9.6.2 are met. If the ligament check is not met, an overall check shall be made. If the ligament check
is met, no overall check is required.
No ligament between the nozzles shall be smaller than
max (3 e a,s ; 0,2
(2 r is  e c,s )  e c,s
(9.6-1)
where
ris is the mean of the shell radii at the centres of two adjacent nozzles (e.g. a conical shell).
The requirements of 9.5 for isolated openings shall in all cases be satisfied.
9.6.2 Conditions under which a ligament check is not required
If all the following conditions are met, a ligament check is not required:
a) the sum of the nozzle diameters (or maximum widths) meets the following
(d 1  d
2
 ..  d n )  0,2
(2 r
is
 e
c, s
)e
(9.6-2)
c, s
b) the nozzles are totally located within a circle having a diameter dc given by
d
c
 2
(2 r
is
 e
c, s
)e
(9.6-3)
c, s
c) the nozzles are isolated from any other opening or discontinuity outside that circle;
9.6.3 Ligament check of adjacent openings
9.6.3.1
General
The ligament check is satisfied if the following formula is met (see Figures 9.6-1 to 9.6-4)
(AfLs + Afw)( fs -0,5P) + Afb1 ( fob1 - 0,5P) + Afp1 ( fop1 -0,5P)+ Afb2 ( fob2-0,5P) +
+ Afp2 ( fop2-0,5P) > P (ApLs+ Apb1+ 0,5 Ap1+ Apb2 + 0,5 Ap2)
(9.6-4)
Where a reinforcing ring is fitted, Afr and Apr shall be substituted for Afb and Apb.
In this formula areas AfLs and ApLs of the shell are specified in 9.6.3.2.2 and 9.6.3.2.3.
122
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For groups of openings, the ligament check shall be carried out for each pair of adjacent openings.
9.6.3.2
Openings in cylindrical and conical shells
9.6.3.2.1 For two adjacent openings in cylindrical and conical shells (see Figures 9.6-1 to 9.6-2),
Formula (9.6-4) shall be satisfied in the plane normal to the shell and containing the centres of the
openings. ApLs and AfLs are given in 9.6.3.2.2 and 9.6.3.2.3 respectively.
9.6.3.2.2
For cylindrical shells, ApLs is given by
2
Ap
Ls

0 ,5 r is  L b  ( 1  cos  )
(9.6-5)
r is  0 ,5 e a, s  sin 
where
ris is given by Formula (9.5-3).
For conical shells, ApLs is given by
Ap
Ls

0,25
 r is1
 r is2

2
 L b  1  cos 

r is1  r is2  e a, s  sin 
(9.6-6)
where
ris is given by Formula (9.5-6).
In all cases,  is as shown in Figure 9.6-1 and Lb is as shown in Figures 9.6-1 to 9.6-6.
9.6.3.2.3
AfLs is given by
AfLs = (Lb - a1 - a2 )  ec,s
(9.6-7)
where distances a1 and a2 along Lb are given by the following (see Figures 9.6-1 and 9.6-2)
a) in cases with = 0° (i.e. where the nozzles lie on the axis of the vessel)
a 
0,5 d
(9.6-8)
eb
cos 
e
b) in cases with
 0° where
— the oblique nozzle is inclined towards the adjacent opening
a = ros  [arcsin (  + sin e ) - e ]
(9.6-9)
— the oblique nozzle is inclined away from the adjacent opening
a = ros  [ e+ arcsin (  - sin e )]
UNI EN 13445-3:2021
(9.6-10)
123
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where
r is
r os 
 
2
sin 
(9.6-11)
 0,5 e a, s
d eb
(9.6-12)
2 r os
and arcsin is in radians.
For adjacent oblique nozzles lying on the same generatrix the nozzle axes shall be projected on the plane
containing the centres of each opening and the axis of the shell.
The value of Ap1 and Ap2 shall be calculated according to 9.5.2.4.5.2.
9.6.3.3
Openings in spherical shells and dished ends
In the case of two adjacent normal openings (see Figure 9.6-3), Formula (9.6-4) shall be satisfied in the plane
normal to the shell and containing the centres of the two openings.
For this purpose, the distances a1 and a2 and the areas ApLs and AfLs shall be calculated according to formulae
of 9.6.3 for cylindrical shells and with angle equal to 90°.
For adjacent oblique nozzles (see Figure 9.6-4), the nozzle axes shall be projected onto the plane containing
the normals to the shell at the centre of each opening. The value of Ap1 and Ap2 shall be calculated
according to 9.5.2.4.5.6.
9.6.3.4
Adjacent openings in regular hole pattern
Adjacent openings are in a regular hole pattern when not less than 3 nozzles lie on the same line
(circumferential or longitudinal at angle  to the generatrix for cylindrical or conical shells, and in any
direction for spherical shells and dished ends) No other openings shall be located near each of these
adjacent openings at a distance less than 2lso .
When holes are drilled in a regular hole pattern, the design methods given in the water-tube boiler standard
(see EN 12952) may be used.
9.6.3.4.1 If adjacent openings on a regular hole pattern have the same value of internal diameter dib
and the same distance Lb between them, having nozzles normal to shell with same dimensions and
with value of fb not less than fs of shell, the following conditions may be applied for reinforcement
evaluation.
Taking into consideration the length n x Lb occupied by the holes, the general Formula (9.6-4) is simplified as
follows:
n  Af
Ls
 ( f s  0 ,5 P )  n  2 Af b ( f s  0 ,5 P )  P  n  ( Ap
Ls
 2 Ap
b
)
(9.6-13)
where
124
AfLs = ec,s ( Lb - dib )
(9.6-14)
Afb = lbo ea,b
(9.6-15)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Apb = 0,5dib lbo
(9.6-16)
ApLs is defined in 9.6.3 for different types of shell and different values of 
for conical shell
ri 
r i 1  r in
(9.6-17)
2
Therefore the following conditions apply for the reinforcement of the adjacent openings drilled in a regular
hole pattern:
e c , s  ( L b  d ib )  2  e a , b  l bo 
P
( f s  0 ,5 P )
 ( Ap
Ls
 d ib  l bo )
(9.6-18)
9.6.4 Overall check of adjacent openings
If the ligament check is not satisfied, an overall check shall be made extending the calculation to a larger
cross-sectional area which includes both the walls of each nozzle and the adjacent sections of the shell (see
Figures 9.6-5 and 9.6-6). The following conditions shall be satisfied:
a) Lb + a’1 + a’2 < 2 (lso1 + lso2)
(9.6-19)
where a’1 and a’2 are taken in the direction opposite to the ligament;
b) Formula (9.6-4) is satisfied with the term in the right hand side multiplied by 0,85;
c) no other opening is adjacent to the two openings under consideration;
d) neither of the two openings is close to a discontinuity (see 9.7.2).
A further calculation of reinforcement shall be carried out considering the whole section of the shell within
the length Lb1,
Where
Lb1 = Lb + a’1 + a’2 + k  lso1 + k  lso2
(9.6-20)
Lb is as defined in 9.5.1 and the value of k is given by:
k  2 
L b  a '1  a ' 2
l so1  l so2
(9.6-21)
If k is greater than 1, it shall be put equal to 1.
The following condition shall be fulfilled (see Figures 9.6-5 and 9.6-6)
(AfOs +Afw)(fs- 0,5P)+ 2Afb1 (fob1-0,5P)+ 2Afb2(fob2-0,5P)+Afpo1 (fop1-0,5P) +
+ Afpo2 (fop2-0,5P) + Afp i (fopi-0,5P) > P (ApOs+2Apb1+ Ap1+2Apb2+ Ap2)
(9.6-22)
where
ApOs and the distances a1 and a2 , a'1 and a'2 are calculated like ApLs in accordance with 9.6.3 with Lb1
instead of Lb and with ris defined in Formulae (9.5-3 to 9.5-6);
UNI EN 13445-3:2021
125
EN 13445-3:2021 (E)
Issue 1 (2021-05)
AfOs = (Lb1 - a1 - a2 - a’1 - a’2)ec,s
(9.6-23)
Afw is the total of weld areas inside Lb1;
— for each nozzle Afb, Apb and Ap are calculated in accordance with 9.5.2.4.4 and 9.5.2.4.5;
— for reinforcing plate outside Lb
Afpo = ep  l’p
(9.6-24)
l’p = min (lp ; klso)
(9.6-25)
— for reinforcing plate between nozzles and inside Lb
126
Afpi = ep  Lbp
(9.6-26)
Lbp = min ( lp ; (Lb - al - a2) )
(9.6-27)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1) direction of the generatrix
NOTE
The cross section shown in this figure illustrate the case when  = 0
Figure 9.6-1 — Ligament check of adjacent nozzles normal to a cylindrical shell
UNI EN 13445-3:2021
127
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
The cross section shown in this figure illustrate the case when  = 0
Figure 9.6-2 — Ligament check of adjacent oblique nozzles in a conical shell
128
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.6-3 — Ligament check of adjacent nozzles normal to a spherical shell
UNI EN 13445-3:2021
129
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.6-4 — Ligament check of adjacent oblique nozzles in a spherical shell
130
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.6-5 — Overall check of adjacent nozzles in a cylindrical shell
UNI EN 13445-3:2021
131
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.6-6 — Overall check of adjacent nozzles in a spherical shell or dished end
132
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
9.7 Openings close to a shell discontinuity
9.7.1 Two limits are applied for the permissible distance w (see Figures 9.7-1 to 9.7-11) between an
opening and a shell discontinuity:
a) openings shall not lie at a distance w (see Figures 9.7-1 to 9.7-11) less than a minimum value wmin
from a discontinuity as given by 9.7.2.1;
b) if an opening lies within wp from a discontinuity, the length of shell ls available for opening
reinforcement shall be reduced, as given by 9.7.3.
9.7.2 Rules regarding wmin
9.7.2.1
Openings in cylindrical shells
a) On a cylindrical shell connected to dished or hemispherical end, the large diameter of a conical
shell, a flat end, a tubesheet or any type of flange, the distance w, as shown in Figures 9.7-1 to 3
and 9.7-5, shall satisfy the following condition
w > wmin = max
( 0 ,2 ( 2 r is  e c ,s )  e c ,s ; 3 e a ,s )
(9.7-1)
b) On a cylindrical shell connected to the small diameter of a conical shell, a spherical shell convex
towards the cylinder or another cylindrical shell on a different axis, the distance w, as shown in
Figures 9.7-6 to 8, shall satisfy the condition
w > wmin = lcyl
(9.7-2)
where
lcyl =
(9.7-3)
D c  e1
c) On a cylindrical shell connected to expansion joint, the distance w, as shown in Figure 9.7-4, shall
satisfy the condition
w > wmin = 0,5lcyl
9.7.2.2
(9.7-4)
Openings in conical shells
a) On a conical shell connected at its larger diameter with a cylindrical shell on the same axis, the
distance w, as shown on Figure 9.7-9, shall satisfy the following condition
w > wmin = max

 0 ,2


D c  e c, s
cos 

; 3 e a, s 


(9.7-5)
where Dc is the mean diameter of the cylindrical shell, ea,s is the thickness of the conical shell and 
is its half apex angle.
b) On a conical shell connected at its smaller diameter with a cylindrical shell having the same axis,
the distance w, as shown in Figure 9.7-10, shall satisfy the following condition
w > wmin = lcon
UNI EN 13445-3:2021
(9.7-6)
133
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where
Dc e2
lcon =
9.7.2.3
(9.7-7)
cos 
Openings in domed and bolted ends
For openings in domed and bolted ends, the distance w of the edge of the opening from the flange, taken as
shown in Figure 9.7-11, shall satisfy the following condition
w > wmin = max
9.7.2.4
(9.7-8)
( 0 ,2 ( 2 r is  e c ,s )  e c ,s ; 3 e a ,s )
Openings in elliptical and torispherical ends
For dished ends the value w is the distance along the meridian between edge of the opening (outside
diameter of nozzle or pad) and the point on the dished end which is determined by the distance of De/10
shown in Figure 9.5-4 (i.e. the distance wmin = 0 ). In case the value of w limited as above is not sufficient to
reinforce the opening, it is allowed to calculate the reinforcement taking into account the full value of ls,
provided the thickness of the end complies with 7.7, considering the opening as encroaching into the
knuckle region.
9.7.2.5
Openings in hemispherical ends
On a hemispherical end connected to a cylindrical shell, a flange or a tubesheet, the distance w shall satisfy
the following condition:

w  w min  max 0 ,2
2 r is
 e c, s   e c, s ; 3 e a, s

(9.7-9)
9.7.3 Rules regarding wp
When the distance w of an opening from a discontinuity, as shown in Figures 9.7-1 to 11, is lower than the
value wp defined in a), b), c) as below, the shell length ls available for reinforcement to take in account for
Formula (9.5-26) and others similar is reduced to the following values:
a) for discontinuities indicated in 9.7.2.1 (a), 9.7.2.2 (a), 9.7.2.3, 9.7.2.4 and 9.7.2.5.
w < wp = lso
(9.7-10)
ls = w
(9.7-11)
b) for discontinuities indicated in 9.7.2.1 (b) and (c)
w < wp = lso + wmin
(9.7-12)
ls = w - wmin
(9.7-13)
c) for discontinuities indicated in 9.7.2.2.(b)
134
w < wp = lso + lcon
(9.7-14)
ls = w - lcon
(9.7-15)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.7-1 — Opening in a cylindrical shell, close to the junction with a domed end
Figure 9.7-2 — Opening in a cylindrical shell, close to the junction with the larger diameter of a conical
reducer
UNI EN 13445-3:2021
135
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.7-3 — Opening in a cylindrical shell, close to the junction with a flat end or a tubesheet
Figure 9.7-4 — Opening in a cylindrical shell, close to the junction with an expansion bellow
136
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.7-5 — Opening in a cylindrical shell, close to the junction with a flange
Figure 9.7-6 — Opening in a cylindrical shell, close to the junction with the smaller diameter of a
conical reducer
UNI EN 13445-3:2021
137
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.7-7 — Opening in a cylindrical shell, close to the junction with a spherical shell
Figure 9.7-8 — Opening in a cylindrical shell close to the junction with another cylindrical shell
having a different axis
138
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.7-9 — Opening in a conical shell, close to the junction with a cylindrical shell at its large
end
Figure 9.7-10 — Opening in a conical shell, close to the junction with a cylindrical shell at its
small end
UNI EN 13445-3:2021
139
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 9.7-11 — Opening in a domed and bolted end close to the junction with the flange
10 Flat ends
10.1 Purpose
10.1.1 This clause specifies methods for determining the thickness of circular and non-circular
unstayed flat ends under pressure and for providing adequate reinforcement for openings fitted in such
ends. Loads other than pressure are not considered.
NOTE 1
For welded flat ends, the method takes into account the stresses caused by the junction forces and
moments. For bolted flat ends, the method takes into account the stresses caused by the forces and moments due
to the flange and bolting.
NOTE 2
For the design of vessels of rectangular cross-section, refer to Clause 15.
10.1.2 Stayed plates, i.e. plates supported by braces, stay bars or stay tubes, are not considered in this
clause.
NOTE
Stayed plates may be calculated using the formulae and methods of the European Standard for Shell
Boilers (see EN 12953) with the nominal design stresses of this standard.
These rules do not apply to heat exchanger tubesheets, which are covered by Clause 13.
10.1.3 These rules do not apply to self-sealing covers, i.e. to covers where compression of the gasket is
obtained through the action of internal pressure and which are equipped with a bolting-up device.
140
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
10.2 Specific definitions
The following specific definitions apply in addition to those in Clauses 3 and 11.
10.2.1
flat end
unstayed flat plate of generally constant thickness, connected to a shell by either welding or bolting, not
supported by stays or stay-tubes, not strengthened by beams, and supported only at its periphery so
that it is subject predominantly to bending
10.2.2
hub
cylindrical or conical projection on a flat end provided so that the end may be butt welded to a
cylindrical shell (see Figure 10.4-1)
10.2.3
relief groove
peripheral groove in a flat end to be butt welded to a cylindrical shell (see Figure 10.4-3)
10.2.4
annular plate
flat end of annular form, connected to one cylindrical shell at its outside diameter and another at its
inside diameter, and subject predominantly to bending and not shear
UNI EN 13445-3:2021
141
EN 13445-3:2021 (E)
Issue 1 (2021-05)
10.3 Specific symbols and abbreviations
The following symbols apply in addition to those in Clauses 4 and 11.
A
is the nozzle reinforcement area, see 10.6.2.2;
a’
is the smaller width dimension in a rectangular, elliptical or obround end;
b’
is the greater width dimension in a rectangular, elliptical or obround end;
C1, C2 are the shape factors for calculation of circular flat ends;
C3, C4 are the shape factors for calculation of flat ends of non-circular shape;
c
is the mean distance between the gasket reaction and the bolt pitch circle diameter;
Deq
is the equivalent diameter of an end with a hub, see Figure 10.4-1;
DF
is the diameter of the flat part of an end with a tapered hub, see Figure 10.4-1;
Di
is the inside diameter of the cylindrical shell welded to a flat end. When the thickness of the
cylindrical shell adjacent to the shell is not constant, see Figure 10.4-1b), Di is the inside diameter to the
equivalent cylinder of mean thickness es;
DX
is the inside diameter of an annular plate;
DY
is the outside diameter of an annular plate;
d
is the diameter of an opening, the equivalent diameter of a nozzle, the mean diameter of two
openings or the mean equivalent diameter of two nozzles;
di
is the nozzle inside diameter;
de
is the nozzle outside diameter;
e1
is the required thickness for the flange extension on a flat end;
eab
is the analysis thickness of the external section of a nozzle, see Figure 10.6-3;
e’ab
is the analysis thickness of the internal protrusion of a nozzle, see Figure 10.6-4;
eaf
is the analysis thickness of an end with a hub;
eb
is the required thickness of the nozzle cylinder for pressure loading;
eo
is the required thickness of an unpierced end, in the design of a pierced end;
er
is the required thickness under a relief groove, see Figure 10.4-3;
es
is the analysis thickness of a uniform cylindrical shell, or the equivalent thickness of a tapered
cylindrical shell, adjacent to a flat end;
fA
is the material nominal design stress at ambient temperature;
fb
is the nominal design stress at calculation temperature of the nozzle;
142
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
fmin
is the lower of the nominal design stresses f of the end and fs of the shell;
fs
is the nominal design stress at calculation temperature of the shell;
h
is the smallest distance between the centre of an opening and the inside of the shell, see
Figure 10.6-1;
hw
is the distance between the external wall of an end with a relief groove and the weld on the shell
(see Figure 10.4-3);
j
is determined from the position of an opening, see 10.6.2.1;
k
is the distance between the centres of two openings, see Figure 10.6-2;
l
is the external length of a nozzle effective for reinforcement;
l’
is the internal length on a protruding nozzle effective for reinforcement, see Figure 10.6-3;
is the length of cylindrical shell, as shown in Figures 10.4-1 to 10.4-3, which contributes to the
lcyl
strength of the flat end (all types of flat ends) and of the end-to-shell junction (ends welded directly to the
shell);
n
is the number of bolts in a flat end of non circular shape;
r
is the inside radius of a hub, see Figure 10.4-1;
rd
is the inside radius of the relief groove, see Figure 10.4 -3;
tB
is the mean bolt pitch in a bolted flat end;
Y1
is the calculation coefficient for opening reinforcement, see Formula (10.6-3);
Y2
is the calculation coefficient for opening reinforcement, see Formula (10.6-4);

is the Poisson’s ratio of the material for the end.
10.4 Unpierced circular flat ends welded to cylindrical shells
10.4.1 General
The requirements of 10.4.2 to 10.4.5 apply to the following types of unpierced, circular flat end:
— with a hub, see Figure 10.4-1;
—
welded directly to the shell, see Figure 10.4-2;
— with a relief groove, see Figure 10.4-3.
10.4.2 Limitations
10.4.2.1 The length lcyl (see Figures 10.4-1 to 10.4.-3) shall not contain another junction between the
shell and an end, tubesheet, flange or other shell.
10.4.2.2
For an end with a hub, the following conditions shall apply:
a) the inside radius of the hub shall meet the following: r  es and r  1,3 eaf;
UNI EN 13445-3:2021
143
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) the hub and adjacent cylinder may be offset, but their wall centre-lines shall not be offset by an
amount which is greater than the difference between their nominal thicknesses;
c) a taper hub shall have a slope not exceeding 1:3;
d) where the thickness of the cylindrical shell adjacent to the flat end is uniform (see Figure 10.41(a)), lcyl shall be calculated as follows:
l cyl  0 ,5
(10.4-1)
( D i  e s )e s
e) where the thickness of the cylindrical shell adjacent to the flat end is tapered (see Figure 10.41(b)), a value of lcyl shall be assumed and the mean thickness over that length calculated. This
thickness shall be inserted into Formula (10.4.1) and the required value of lcyl calculated. If lcyl
required is greater than the assumed value, the calculation shall be repeated using a larger
assumed value.
Flat ends which do not meet these conditions shall be treated as ends welded directly to the shell.
10.4.2.3
l cyl 
10.4.2.4
For a flat end welded directly to the shell (see Figure 10.4-2), lcyl is given by:
(10.4-2)
( D i  e s )e s
For a flat end with a relief groove (see Figure 10.4-3), the following conditions shall apply:
a) lcyl is also given by Formula (10.4-2);
b) radius rd shall be at least equal to 0,25es or 5 mm, whichever is greater;
c) the centre of the radius shall lie within the thickness of the flat end and not outside it, and the
distance hw of the end-to-shell weld to the outside surface of the end shall be greater than (e –
2 mm), see Figure 10.4-3.
10.4.3 Flat ends with a hub
The minimum required thickness for a flat end with a hub is given by:
e  C 1  D eq
P
(10.4-3)
f
When the distance from the inside surface of the flat portion of the end to the end-to-shell weld is larger
than lcyl + r, the coefficient C1 is given by Figure 10.4-4 or by :

C 1  MAX   0 , 40825

A1
Di  es  
e s 


 ,  0 , 299  1  1,7
Di
D i 
 

(10.4-4)
where:
es


A 1  B 1 1  B 1

2 D i  e s  

144
(10.4-5)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B1  1 
es
3f 

P  Di  es



2

Di
3 

16  D i  e s



4
P
f
2

3  2 D i  e s e s
4
D i  e s 
(10.4-6)
3
When this distance is lower than lcyl + r , then the coefficient C1 is still given by Figure 10.4-4 but using P/f
instead of P/fmin .
For a uniform thickness shell per Figure 10.4-1 a),
D
eq
(10.4-7)
 Di  r
For a tapered shell per Figure 10.4-1 b),
D eq 
D i
 DF

(10.4-8)
2
The following condition shall be met:
(10.4-9)
e af  e
10.4.4 Flat ends welded directly to the shell
10.4.4.1 The minimum required thickness for the end is given, for a normal operating case, by the
greatest of the following:
 
e  max   C 1  D i

 

 , C 2 Di


f 

P 
P
f min
 


 
(10.4-10)
where
f m in  m in
f ;
(10.4-11)
fs 
C1 is given:
— either by Figure 10.4-4
— or by Formula (10.4-4) calculated with the A1 value derived from Formulae (10.4-5) and (10.46) using fmin instead of f.
C2 is given by Figure 10.4-5.
Instead of reading C2 on Figure 10.4-5, the term
C 2  Di
P
f min
may also be calculated directly by means of the
method given in 10.4.6
NOTE
The Formula (10.4-10) is valid only for values of P/f up to 0,1 (see Figures 10.4-4 and 10.4-5). For
values of P/f below 0,01 the value of 0,01 may be taken. For values of P/f above 0,1, it is recommended to use
design by analysis, see Annex B or C.
When C2 is less than 0,30, only the first term of Formula (10.4-10) shall be considered.
10.4.4.2 For an exceptional operating case and for a hydrostatic testing case the calculation of e shall
take into account only the first term of Formula (10.4-10):
UNI EN 13445-3:2021
145
EN 13445-3:2021 (E)
Issue 1 (2021-05)
P
e  C1 Di
(10.4-12)
f
10.4.4.3 In Formulae (10.4-10) to (10.4-12), f, fs and P shall be understood as generic symbols valid
for all types of load cases (normal, exceptional, testing) and having the following meaning:
— for a normal operating case, f is fd,
fs
is
(fd )s
and P is Pd;
— or an exceptional operating case, f is fexp,
fs
— for an hydrostatic testing case, f is ftest,
is (ftest)s and P is Ptest.
fs
is (fexp)s and P is Pexp;
10.4.4.4 For a normal operating case, the minimum required thickness of the end may alternatively
be calculated using Formula (10.4-12) instead of Formula (10.4-10), provided a simplified assessment
of the fatigue life of the flat end to shell junction is performed according to Clause 17. In performing this
assessment:
— the following stress index value shall be used :
 P max,
1
P
 max,
2
  3 




(10.4-13)
where
Pmax,1
is the maximum permissible pressure derived from Formula (10.4-12) for the analysis
thickness ea;
Pmax,2
is the maximum permissible pressure derived from Formula (10.4-10) for the same
thickness ea.
NOTE 1
The iterative calculations which are necessary to determine Pmax,1 and Pmax,2 may be avoided by
replacing Formula (10.4-13) with the following more conservative one:
C
  3  2
 C1




2
f
(10.4-14)
f min
where
C1 and C2 are the values determined for the calculation pressure P.
— for calculation of the pseudo elastic stress range   with Formula (17.6-1), the value to be given to
the maximum permissible pressure Pmax shall be Pmax,1.
NOTE 2
The iterative calculations which are necessary to determine Pmax,1 may be avoided by replacing Pmax,1
with the calculation pressure P, which will lead to a more conservative result.
— the relevant plasticity correction shall be applied to

, as required by 17.6.1.3.
— the fatigue class corresponding to the weld detail actually used for the flat end to shell junction
shall be considered, as provided by Clause 17 (see Table 17-4).
146
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— for vessels of testing group 4, a NDE of the flat end to shell welded joint shall be performed
according to the requirements of testing group 3a or 3b, as relevant (see Table 6.6.2-1 in EN 134455:2021).
10.4.5 Flat ends with a relief groove
The minimum required thickness for a flat end with a relief groove shall be determined using the same rules
as given in 10.4.4 for flat ends without relief groove.
The minimum required thickness at the bottom of the groove is given by:

 fs  
e r  MAX  e s ; e s 


 f 
(10.4-15)
a) Uniform thickness shell
b) Tapered shell
Figure 10.4-1 — Circular flat ends with a hub
Figure 10.4-2 — Circular flat ends welded directly to the shell (refer to Annex A for acceptable
weld details)
UNI EN 13445-3:2021
147
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 10.4-3 — Circular flat ends with a relief groove
Figure 10.4-4 — Values of coefficient C1
NOTE 1
Where P/fmin is lower than the value corresponding to the point of intersection between the es/Di curve
and the bottom curve (dotted line), C1 is the value defined by the horizontal line passing through this point.
NOTE 2
148
There are cases where P/f shall be used instead of P/fmin , see 10.4.3.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 10.4-5 — Values of coefficient C2
10.4.6 Direct calculation of the term with coefficient C2 in formula 10.4-10
d) calculate successively the following quantities :
g 
Di
Di  es
4
H 
J 
12
3 f min
(10.4-16)
1
2
es

Di  es
(10.4-17)
2

P
U 
 
Di
4  Di  es  es
 1
(10.4-18)
2 2   g
3
f1  2 g
2
1   2 
 g
(10.4-19)
4
 3 U  Di
 2J
A  
 4 e
s

UNI EN 13445-3:2021
(10.4-20)


 1     1  1  





es

Di  es 
(10.4-21)
149
EN 13445-3:2021 (E)
Issue 1 (2021-05)
 3 U Di

 J  H

es
8


B  

2

3
2

2    g  g  H

Di  es
es
3
3
 2J
F  
U g 
f1
es
Di  es
16
8

3
G  
f1  2 J
 8

(10.4-22)

 H

2
 3 2    g  g
es
Di  es
2


  H

 


es

 D  e
i
s

(10.4-24)
B
a 
(10.4-25)
A
F
b 
(10.4-26)
A
G
c 
(10.4-27)
A
N 
Q 
K 
b

3
c
2
(10.4-23)

N
3
Q
2
a
2
(10.4-28)
9
a b
6

a
3
(10.4-29)
27
(10.4-30)
3
If Q  0 :
S 
If Q < 0 :
S  
Q
3
1 
Q
1  K 
1 
1/2
1  K 

1/2
(10.4-31)

(10.4-32)
e) The value of the term with coefficient C2 in Formula (10.4-10) is given by :
C
2
 Di
P
f min
N
 D i  e s  
 S
 S 
a 

3 
(10.4-33)
10.5 Unpierced bolted circular flat ends
10.5.1 General
10.5.1.1 The procedures specified in 10.5.2 and 10.5.3 determine the thickness of bolted circular flat
ends without openings. They apply to flat ends with the following types of gasket:
a) narrow-face gasket (see Figures 10.5-1, 1 to 4);
b) full-face gasket (see Figure 10.5-2).
10.5.1.2 The thickness of the flanged extension, see Figures 10.5-1 2 to 4 and Figure 10.5-2, may be
smaller than e, but shall meet the requirements of either 10.5.2.2 or 10.5.3.2 as appropriate.
150
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
10.5.2 Flat end with a narrow-face gasket
10.5.2.1
e  max
The minimum thickness within the gasket shall be determined by:
e A ; e P 
(10.5-1)
where
eA 
eP 
C
F
CF
3( C  G )  W

 f
 G
 A
 3 3  ν 
G

32

 max







2d
b
2




 P
G

 3C F 
 2 b  m  C  G 
 4

 f


tB

; 1
6 e 1, a



m  0 ,5

(10.5-2)
(10.5-3)
(10.5-4)
In the above formulae e1,a is the analysis thickness for the flanged extension, while db is the bolt outside
diameter, C is the bolt pitch circle, m is the gasket factor, G is the gasket reaction diameter, b is the effective
gasket width and W is the design bolt load for assembly conditions as defined in Clause 11.
NOTE
Formulae (10.5-2) and (10.5-3) apply to the assembly and operating conditions respectively.
Formula (10.5-3) also applies to testing conditions with P replaced by PT and f by ftest
10.5.2.2
The minimum thickness for the flanged extension is given by:

e1  m a x e A ; eP1

(10.5-5)
where
eA is given by Formula (10.5-2) and:
eP1 
P
G

3 CF 
 2 b  m  C  G 
f
 4

(10.5-6)
NOTE
Formulae (10.5-2) and (10.5-6) apply to the assembly and operating conditions respectively.
Formula (10.5-6) also applies to testing conditions with P replaced by PT and f by ftest
UNI EN 13445-3:2021
151
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 10.5-1 — Bolted circular flat ends with a narrow-face gasket
1) plane face
2) raised face
3) tongued joint
4) grooved joint
Figure 10.5-2 — Bolted circular flat end with a full-face gasket
152
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
10.5.3 Flat end with a full-face gasket
10.5.3.1
The minimum thickness for a flat end with a full-face gasket is given by:
e  0 ,4 1C
NOTE
10.5.3.2
P
(10.5-7)
f
C is the bolt pitch circle diameter as defined in Clause 11.
The minimum thickness for the flanged extension is given by:
(10.5-8)
e 1  0 ,8 e
The reduced thickness of the flanged extension shall be limited to an area whose internal diameter is not
smaller than 0,7 C.
10.5.4 Flat ends with unequally spaced bolts
Circular flat ends with unequally spaced bolts can be calculated as circular flat ends with equally spaced bolts
provided all the calculations are made considering an equivalent bolt number nEQ obtained from the
following formula:
n EQ 
 C
t Bmax
(10.5.-9)
where tBmax is the maximum bolt pitch, to be used also in Formula (10.5-4) in place of tB. The equivalent bolt
number nEQ need not to be an integer.
10.6 Pierced circular flat ends
10.6.1 General
10.6.1.1 These requirements of 10.6.2 apply to the reinforcement of single or multiple openings in
circular flat ends which are either bolted or welded to the shell. The openings may be in any location on
the flat end (see Figure 10.6-1).
NOTE
flat end.
An opening may be either a hole in the flat end with a bolted connection to a flange or a nozzle in the
10.6.1.2 Blind threaded bolt holes drilled around openings fitted to standard pipe flanges do not
need reinforcement provided that:
— the bore of the opening does not exceed that of the standard pipe flange;
— the thickness of the material under the bolt hole is at least 50 % of the bolt diameter.
10.6.1.3 These requirements are applicable to circular openings or nozzles, provided the opening
diameter is smaller than 50 % of the shell inside diameter Di for welded ends or 50 % of the gasket
reaction diameter (G or C) for bolted ends.
10.6.2 Flat end thickness
10.6.2.1 A pierced circular flat end shall satisfy the conditions specified in 10.4 or 10.5 as
appropriate and in addition its thickness shall not be less than that given below.
UNI EN 13445-3:2021
153
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For flat ends welded to the shell (see Figures 10.4-1 to 10.4-3),


e  m a x  (Y 1  e o ) ;



 C 1  Y2  D i


P 



f 

(10.6-1)
For bolted flat ends (see Figures 10.5-1 and 10.5-2),
(10.6-2)
e  Y 2 e o
In Formulae (10.6-1) and (10.6-2), eo is the required thickness of the unpierced flat end calculated according
to 10.4 or 10.5 as appropriate, and Y1 and Y2 are obtained as follows:


j


Y 1  m in  2 ; 3

j

d




Y2 
j
(10.6-3)
(10.6-4)
j  d
For single isolated openings (see Figure 10.6-1):
—
d is the diameter of an opening or equivalent diameter of a nozzle from 10.6.2.2.
—
j is equal to:
2h for Formula (10.6-3)
Di for Formula (10.6-4) for a welded end with no hub,
Deq for Formula (10.6-4) for a welded end with a hub,
G for Formula (10.6-4) for a bolted end.
For a pair of openings (see Figure 10.6-2):
—
d is the (arithmetic) mean of the diameters of the openings or the mean equivalent diameter of the
nozzles from 10.6.2.2.
—
j equals k, the distance between the centres of the openings.
Where there are multiple openings, each opening shall be checked as an isolated opening and every pair of
openings shall be checked. Alternatively, it is allowed to replace the check of the pair of openings by a check
of a single fictitious opening having a diameter which inscribes the other two, provided a simplified
assessment of the fatigue life of the ligament is performed according to Clause 17.
In performing this assessment:
— the pseudo elastic stress range in the ligament shall be taken as equal to :
 C Y  D
1
2
i
  2 

e

a




2
 P
(10.6-5)
where Y2 shall be calculated considering the mean diameter (or the mean equivalent diameter) of the
two openings.
154
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— the relevant plasticity correction shall be applied to

, as required by 17.6.1.3.
— for openings fitted with nozzles, the lowest fatigue class corresponding to the weld details actually
used for the nozzle to flat end junctions shall be considered, as provided by Clause 17 (see
Table 17-4), while for openings without nozzles the fatigue curve for unwelded details shall be
used, as provided by the same Clause 17.
— for vessels of testing group 4, a NDE of the nozzle to flat end welded joints shall be performed
according to the requirements of testing group 3a or 3b, as relevant (see Table 6.6.2-1 in EN 134455:2021).
10.6.2.2
When the opening has a nozzle, the equivalent diameter shall be given by:
— for set-on nozzles:
2A'
d  di 
(10.6-6)
e
— for set-in nozzles:
d  de 
2A'
(10.6-7)
e
where

fb 

f 
A '  min  A ; A

(10.6-8)
A is the total area of the reinforcement in mm2, as defined in Figures 10.6-3 and 10.6 -4.
eb is the required thickness of the nozzle cylinder for pressure loading from 7.4.2.
l  0,8
d i
 e ab
l '  0,8
d i
 e ' ab
 e ab
 e ' ab
(10.6-9)
(10.6-10)
When Formulae (10.6-6) and (10.6-7) give a value of the equivalent diameter which is negative, further
calculation in accordance with 10.6.2.1 is not required.
UNI EN 13445-3:2021
155
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 10.6-1 — Single opening in a flat end
Figure 10.6-2 — Pair of openings in a flat end
156
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 10.6-3 — Set-on nozzle in a flat end
Figure 10.6-4 — Set-in nozzle in a flat end
UNI EN 13445-3:2021
157
EN 13445-3:2021 (E)
Issue 1 (2021-05)
10.7 Flat ends of non-circular or annular shape
10.7.1 General
These requirements apply to welded or bolted flat ends of non-circular or annular shape. It is assumed that
the form of the wall (rectangular, square, elliptical, obround or annular) is regular and that the flat end is
uniformly supported at its edge.
NOTE
The calculation procedure for non-circular flat ends in 10.7 is similar to that used for circular flat ends
in 10.4 and 10.5. However, it is empirical and may be very conservative. Methods based on stress analysis should
be considered.
10.7.2 Unpierced rectangular, elliptical or obround flat ends
10.7.2.1
The minimum thickness of an unpierced rectangular, elliptical or obround flat end shall be:
P
e  C 3  a'
(10.7-1)
f
where C3 is obtained:
— for welded flat ends from Figure 10.7-1;
— for bolted flat ends with a full-face gasket from Figure 10.7-2 for rectangular ends, and from
Figure 10.7-3 for elliptical or obround ends;
— for bolted flat ends with a narrow-face gasket from:
C
3

C
4
6 W  c

P n t
B
 a'
2
(10.7-2)
where
C4 is obtained from Figure 10.7-4.
10.7.2.2
e
e
NOTE
1
1

The thickness e1 of the flanged extension shall not be less than the following:
6  W c
n t

B
f
(10.7-3)
6  W c
n  t
B
f
(10.7-4)
A
Formulae (10.7.3) and (10.7-4) apply to the operating and assembly conditions respectively.
10.7.3 Unpierced annular plates
Annular plates supported at both edges shall be considered as rectangular ends having:
158
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a' 
DY  DX
(10.7-5)
2
b'  
DY  DX
(10.7-6)
2
10.7.4 Reinforcement of openings in rectangular, elliptical or obround flat ends or annular
plates
For pierced rectangular, elliptical or obround flat ends or annular plates, the minimum thickness shall be:
e C
3
Y
2
a '
P
f
(10.7-7)
where Y2 is given by Formula (10.6-4), and all the dimensions specified in this formula shall be determined
with reference to an ideal circular flat end having the maximum diameter which can be inscribed into the
profile of the non circular flat end.
Figure 10.7-1 — Shape factor C3 for welded non-circular flat ends
UNI EN 13445-3:2021
159
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 10.7-2 — Shape factor C3 for bolted rectangular flat end with full-face gasket
160
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 10.7-3 — Shape factor C3 for bolted elliptical or obround flat end with full-face gasket
Figure 10.7-4 — Shape factor C4 for bolted non-circular flat end with narrow-face gasket
UNI EN 13445-3:2021
161
EN 13445-3:2021 (E)
Issue 1 (2021-05)
11 Flanges
11.1 Purpose
This clause gives requirements for the design of circular bolted flange connections. Flanges with full face and
narrow face gaskets, subject to internal and external pressure are included, as are reverse flanges and seal
welded flanges. The requirements provided in this clause are based on the well established Taylor Forge
rules. Reference is made to Annex G which provides a modern alternative for narrow face gasket design.
NOTE
The alternative rules in Annex G are most appropriate when: a) thermal cycling is important, b) bolt
stress is controlled by use of a defined tightening procedure, c) there are significant additional loadings (forces or
moments) or d) leak tightness is of special importance.
11.2 Specific definitions
The following definitions apply in addition to those in Clause 3.
11.2.1
assembly condition
condition applying when the gasket or joint contact surface is seated during assembly of the joint at
ambient temperature and the only loading comes from the bolts
11.2.2
operating condition
condition when the hydrostatic end force due to the design pressure (internal or external) acts on the
flange
11.2.3
narrow face flange
flange in which the gasket is entirely inside the circle enclosed by the bolts and there is no contact
outside the bolt circle
11.2.4
full face flange
flange in which the face contact area, either direct or through a gasket or spacer, extends outside the
circle enclosing the bolts
11.2.5
reverse flange
flange attached at its outside diameter to the shell
11.2.6
shell
pipe, vessel wall or other cylinder which is attached to and supports the flange
11.2.7
lap joint
flange assembly in which the bolt load is transmitted through a loose backing flange onto a stub flange
NOTE
162
The stub flange incorporates the gasket contact face.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
11.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in Clause 4:
A
is the outside diameter of the flange or, where slotted holes extend to outside of flange, the
diameter to bottom of slots;
AB
is the total cross-sectional area of bolts at the section of least bolt diameter;
AB,min
is the total required cross-sectional area of bolts;
A2
is the outside diameter of the contact face between loose and stub flanges in a lap joint, see
Figure 11.5-9 (typical);
B
is inside diameter of flange;
B2
is the inside diameter of the contact face between loose and stub flanges in a lap joint, see
Figure 11.5-9 (typical);
b
is the effective gasket or joint seating width;
b0
is the basic gasket or joint seating width;
C
is the bolt pitch circle diameter;
CF
is the bolt pitch correction factor;
D
is the inside diameter of shell;
db
is bolt outside diameter;
dn
is the bolt nominal diameter;
e
is the minimum flange thickness, measured at the thinnest section;
fB
is the bolt nominal design stress at operating temperature (see 11.4.3);
fB,A
is the bolt nominal design stress at assembly temperature (see 11.4.3);
fH
is the nominal design stress of the hub – see 11.5.4.2;
G
is the diameter of gasket load reaction, as given by requirements in 11.5.2;
G1
is the assumed diameter of load reaction between loose and stub flanges in a lap joint;
g0
is the thickness of hub at small end;
g1
is the thickness of hub at back of flange;
H
is the total hydrostatic end force;
HD
is the hydrostatic end force applied via shell to flange;
UNI EN 13445-3:2021
163
EN 13445-3:2021 (E)
Issue 1 (2021-05)
HG
is the compression load on gasket to ensure tight joint;
HT
is the hydrostatic end force due to pressure on flange face;
h
is the hub length;
hD
is the radial distance from bolt circle to circle on which HD acts;
hG
is the radial distance from gasket load reaction to bolt circle;
hL
is the radial distance from bolt circle to circle on which load reaction acts for the loose flange in a
lap joint;
hT
is the radial distance from bolt circle to circle on which HT acts;
K
is the ratio of the flange diameters – see formulae 11.5-21 and 11.9-13;
k
is stress factor defined in 11.5.4.2;
l0
is a length parameter given by Formula (11.5-22);
M
is the moment exerted on the flange per unit of length, defined in 11.5.4.1;
MA
is the total moment acting upon flange for assembly condition;
Mop
is the total moment acting upon flange for operating condition;
m
is a gasket factor;
Pe
is the external calculation pressure, expressed as a positive number;
W
is the design bolt load for assembly condition;
WA
is the minimum required bolt load for assembly condition;
Wop
is the minimum required bolt load for operating condition;
w
is the contact width of gasket, as limited by gasket width and flange facing;
y
is the minimum gasket or joint seating pressure;
F
is a factor for integral method flange design as given in Figure 11.5-4;
FL
is a factor for loose hubbed flanges as given in Figure 11.5-7;
T
is a factor, given by formula (11.5-23);
U
is a factor, given by formula (11.5-24);
V
is a factor for the integral method, from Figure 11.5-5;
VL
is a factor for loose hubbed flanges, from Figure 11.5-8;
Y
is a factor, given by Formula (11.5-25);

is the nominal gap between the shell and loose flange in a lap joint;
b
is distance between centre lines of adjacent bolts;
164
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)

is a factor defined in 11.5.4.1;
b
is calculated bearing stress in a lap joint;
H
is the calculated longitudinal stress in hub;
r
is the calculated radial stress in flange;

is the calculated tangential stress in flange;

is the hub stress correction factor for integral method flange design as given in Figure 11.5-6.
11.4 General
11.4.1 Introduction
Circular bolted flanged connections, either sealed with a gasket or seal welded, used in the construction of
vessels to this standard shall conform to either:
a) an appropriate European Standard for pipework flanges, and the requirements of 11.4.2; or
b) the requirements for bolted flanged connections specified in this clause; or
c) the alternative rules in Annex G.
Both flanges of a mating pair shall be designed to the same standard or set of requirements. This applies
when one of the pair is a bolted flat end or cover. The requirements for bolted flat ends in Clause 10 and
bolted domed ends in Clause 12 are considered part of the same set of requirements as this clause.
11.4.2 Use of standard flanges without calculation
Flanges that conform to an European Standard for pipework flanges may be used as pressure vessel
components without any calculation, provided all the following conditions are fulfilled:
a) Under normal operating conditions, the calculation pressure does not exceed the rating pressure
given in the tables of the relevant European Standard, for the flange and material under
consideration for the calculation temperature.
b) Under testing conditions or exceptional conditions, the calculation pressure does not exceed
1,5 times the rating pressure given in the same tables, at appropriate temperature.
c) The gasket is one of those permitted by Table 11.4-1 for the relevant PN or Class series.
UNI EN 13445-3:2021
165
EN 13445-3:2021 (E)
Issue 1 (2021-05)
d) The bolts are of a strength category (see Table 11.4-2) at least equal to the minimum required by
Table 11.4-1 as a function of the gasket type used in the connection.
e) The vessel is subjected to loadings of predominantly non-cyclic nature, see 5.4.2.
f)
The difference between mean temperatures of bolts and flange does not exceed 50 C in any
condition.
g) The bolt and flange materials have coefficients of thermal expansion at 20 C that differ by more
than 10 % (e.g. austenitic steel flanges with ferritic steel bolts) but the calculation temperature is
< 120 C, or the bolt and flange materials have coefficients of thermal expansion at 20 °C which do
not differ by more than 10 %.
11.4.3 Bolting
11.4.3.1 Bolts
There shall be at least four bolts.
The bolts shall be equally spaced. Flanges with unequally spaced bolts can be calculated as flanges with
equally spaced bolts provided in all the following subparagraphs the bolt area AB to be used for comparison
with ABmin is decreased in respect of the actual bolt area by replacing the actual bolt number n with an
equivalent bolt number nEQ obtained from the following formula:
n EQ 
 C

(11.4-1)
B max
where δBmax is the maximum bolt pitch; in Formula (11.5-20) the value of δB shall also be replaced by δBmax.
nEQ need not to be an integer.
In the case of small diameter bolts it may be necessary to use torque spanners or other means for
preventing the application of excessive load on the bolt.
Special means may be required to ensure that an adequate preload is obtained when tightening bolts of
nominal diameter greater than 38 mm.
Bolt nominal design stresses for determining the minimum bolt area in 11.5.2 shall be:
— for carbon and other non-austenitic steels, the lesser of Rp0,2/3 measured at design temperature and
Rm/4 measured at room temperature;
— for austenitic stainless steel, Rm/4 measured at design temperature.
11.4.3.2 Nuts
The nuts shall have specifies proof load values not less than the minimum proof load values of the screws on
which they are mounted.
Nuts with standard thread pitch (i.e. coarse pitch) fulfil this requirement if they have :
— a height not less than 0,8dn,
166
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— a yield strength or class of quality not less than that of the screws.
When these conditions are not met, the height of the nuts shall not be less than:
0 ,8 d n 
NOTE
R p, screw
R
R
p, nut
p
is
R p0,2
for non-austenitic steels,
R p1,0
for austenitic steels.
11.4.3.3 Threaded holes
The engagement length of screws in threaded holes of a component shall not be less than:
max

; 0 ,8  d n 



R p, screw
 0 ,8  d
n

R p, component

NOTE
R
p
is
R p0,2
for non-austenitic steels,
R p1,0
for austenitic steels.
Table 11.4-1 — Gaskets for standard flanges
PN
designated
series1)
Class
designated
series1)
2,5 to 16
-
25
40
63
150
-
300
Gasket type
Minimum bolt strength
category required
(see Table 11.4-2)
—
Non-metallic flat gasket with or without jacket
Low strength
—
Non-metallic flat gasket with or without jacket
Low strength
—
—
—
—
Spiral-wound metal with filler
Corrugated metal jacketed with filler
Corrugated metal with or without filler
Non-metallic flat gasket with or without jacket
—
—
—
Spiral-wound metal with filler
Corrugated metal jacketed with filler
Corrugated metal with or without filler
—
—
—
Flat metal jacketed with filler
Grooved or solid flat metal
Non-metallic flat gasket with or without jacket
—
—
—
Spiral-wound metal with filler
Corrugated metal jacketed with filler
Corrugated metal with or without filler
—
—
—
Flat metal jacketed with filler
Grooved or solid flat metal
Metal ring joint
Medium strength
Low strength
Medium strength
High strength
Low strength
Medium strength
High strength
— Non-metallic flat gasket with or without jacket
100
600
—
—
—
—
—
—
Spiral-wound metal with filler
Corrugated metal jacketed with filler
Corrugated metal with or without filler
Flat metal jacketed with filler
Grooved or solid flat metal
Metal ring joint
Medium strength
High strength
1)
The PN (or Class) values presented in this table are restricted to those existing in EN Standards on Steel Flanges, up to PN 100 (or
Class 600).
UNI EN 13445-3:2021
167
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 11.4-2 — Bolt strength categories
R p ,b o lt
Low strength
Medium strength
High strength
1
 1,4
 2,5
R p ,f la n g e
NOTE
Rp is Rp0,2 for non-austenitic steels, Rp1,0 for austenitic steels. If Rp1,0 is not known, use Rp0,2 for both bolt
and flange.
The assembly condition and operating condition are both normal design conditions for the purpose of
determining nominal design stresses.
These allowable stresses may be multiplied by 1,5 for testing or exceptional conditions.
NOTE
These stresses are nominal in so far as they may have to be exceeded in practice to provide against all
conditions that tend to produce a leaking joint. However there is sufficient margin to provide a satisfactory
closure without having to overload or repeatedly tighten the bolts.
11.4.4 Flange construction
A distinction is made between flanges in which the bore of the flange coincides with the bore of the shell (for
example welded joints F1, F2, F3 and F5 as shown in Annex A Table A.7) and those with a fillet weld at the
end of the shell (for example welded joint F4) in which the two bores are different. They are known as
smooth bore (see Figure 11.5-1) and stepped bore (see Figure 11.5-2) respectively.
A further distinction is made between the slip-on hubbed flange (see Figure 11.5-3), in which a forged flange
complete with taper hub is slipped over the shell and welded to it at both ends, and other types of welded
construction.
Any fillet radius between flange and hub or shell shall be not less than 0,25g0 and not less than 5 mm.
Hub flanges shall not be made by machining the hub directly from plate material without special
consideration.
Fillet welds shall not be used for design temperatures above 370 C.
11.4.5 Machining
The bearing surface for the nuts shall be parallel within 1 to the flange face. Any back facing or spot facing
to accomplish this shall not reduce the flange thickness nor the hub thickness below design values. The
diameter of any spot facing shall be not less than the dimension across corners of the nut plus 3 mm. The
radius between the back of the flange and the hub or shell shall be maintained.
The surface finish of the gasket contact face should be in accordance with the gasket manufacturers'
recommendations or be based on experience.
11.4.6 Gaskets
The values of the gasket factors m and y should normally be provided by the gasket manufacturer but
suggested values are given in Annex H.
168
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Suggested minimum values of w, the assembly width, are also given in Annex H.
NOTE
Asbestos containing gaskets are forbidden in most European countries.
11.5 Narrow face gasketed flanges
11.5.1 General
Figure 11.5-1 — Narrow face flange - smooth bore
UNI EN 13445-3:2021
169
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 11.5-2 — Narrow face flange - stepped bore
Figure 11.5-3 — Narrow face flange - slip on hub type
170
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
One of the three following methods of stress calculation shall be applied in 11.5.4. to narrow face flanges
with gaskets or joints under internal pressure, taking account of the exceptions given.
a) Integral method. The integral method shall not be applied to the slip-on hubbed flange or to the
loose flange in a lap joint. The integral design method allows for a taper hub, which may be a
weld; the hub assumed for purposes of calculation shall not have a slope of more than 1:1, i.e. g1 
h + g0.
b) Loose method. The loose method shall only be applied, except for loose flanges in lap joints, if all
of the following requirements are met:
1) go  16 mm;
2) P  2 MPa;
3) B /go  300;
4) operating temperature  370 °C.
c) Loose hubbed flange method. This shall be applied to the slip-on hubbed flange and the loose
hubbed flange in a lap joint.
NOTE 1
In the integral method account is taken of support from the shell and stresses in the shell are
calculated, but in the loose method the flange is assumed to get no support from the shell and shell stresses are
ignored.
NOTE 2
In more unusual shapes of hub it can be necessary to choose values of g1 and h defining a simple taper
hub which fits within the profile of the actual assembly.
NOTE 3
There is no minimum value of h for a slip-on hubbed flange.
NOTE 4
The procedure for calculating the value of M is independent of the design method chosen.
11.5.2 Bolt loads and areas
b0 = w/2
(11.5-1)
except for the ring-joint (see Annex H), for which
b0 = w/8;
(11.5-2)
When b0  6,3 mm,
b = b0
(11.5-3)
When b0 > 6,3 mm,
b
= 2 ,5 2
b0
(11.5-4)
(This expression is valid only with dimensions expressed in millimetres).
When b0 ≤ 6,3 mm, G = mean diameter of gasket contact face,
UNI EN 13445-3:2021
171
EN 13445-3:2021 (E)
Issue 1 (2021-05)
when b0 > 6,3 mm, G = outside diameter of gasket contact face less 2b:

H 
4
 (G
2
(11.5-5)
 P)
HG = 2 G  b  m  P
(11.5-6)
Bolt loads and areas shall be calculated for both the assembly and operating conditions as follows.
a) Assembly condition. The minimum bolt load is given by:
WA = b  G  y
(11.5-7)
NOTE
The minimum bolt loading to achieve a satisfactory joint is a function of the gasket and the effective
gasket area to be seated.
b) Operating condition. The minimum bolt load is given by:
Wop = H + HG
(11.5-8)
The required bolt area AB,min is given by:
A B, min
 max
 W A W op

;
 f
fB
 B, A




(11.5-9)
Bolting shall be chosen so that AB ≥ AB,min
NOTE
Internal pressure tends to part the joint and the bolt load has to maintain sufficient pressure on the
gasket to ensure a tight joint. The minimum bolt load under this condition is a function of design pressure, gasket
material and the effective gasket contact area to be kept tight under pressure. More than one operating condition
may require consideration.
11.5.3 Flange moments
H
D


4
 (B
2
P )
(11.5-10)
H T = H - HD
(11.5-11)
hD = (C - B - g1)/2
(11.5-12)
except for slip-on hubbed and stepped bore flanges for which
hD = (C - B) / 2
(11.5-13)
hG = (C - G) / 2
(11.5-14)
hT = (2C - B - G) / 4
(11.5-15)
W = 0,5 (AB,min + AB) fB,A
(11.5-16)
a) Flange assembly condition. The total flange moment shall be:
M A = W  hG
172
(11.5-17)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) Operating condition. The total flange moment shall be:
Mop = HD  hD + HT  hT + HG  hG
(11.5-18)
For flange pairs having different design conditions, as for example when they trap a tubesheet, bolt loads
shall be calculated at assembly and operating conditions for each flange/gasket combination separately. Wop
and WA shall be taken as the greater of the two calculated values. For the flange for which Wop has the lower
calculated value, the value of HG shall be increased as follows:
HG,new = HG + Wop,max – Wop,min
(11.5-19)
11.5.4 Flange stresses and stress limits
11.5.4.1 Flange stresses
11.5.4.1.1 Flange stresses calculation


CF  m a x 





; 1
b
2 db 
6e
(11.5-20)



m  0 ,5
K = A/B
l0 =
Bg
K

T
(11.5-21)

1  8,55246
2
1,0472
K
 1,9448
1,36136
K


0,66845

K  1

1
Y
log
1  8,55246
2
U 

(11.5-22)
0
10
K
log
2

2

(K )  1
 K
10
(11.5-23)
 1

(K )  1
(11.5-24)
 1 ( K  1)
K
2
log
 5,7169
K
2
10
(K ) 
1



(11.5-25)
Flange stresses shall be determined from the moment, M, as follows:
For the assembly condition,
M  M
CF
A
B
(11.5-26)
For the operating condition,
M  M
CF
op
B
(11.5-27)
a) Integral method
UNI EN 13445-3:2021
173
EN 13445-3:2021 (E)
Issue 1 (2021-05)
F V and  are given by Formulae (11.5-28) to (11.5-30) or are found from Figures 11.5-4 to 11.5-6:
E 6
βF 


C


2

 3 1  v

1/ 4

(11.5-28)
1 
A
3
C
where A, C and E6 are coefficients obtained from formulae in 11.5.4.1.2.
For flanges with cylindrical hub, F = 0,908920.
E4
βν 


31  ν 2 


C


(11.5-29)
1/ 4
1 
A
3
where A, C and E4 are coefficients obtained from formulae in 11.5.4.1.2.
For flanges with cylindrical hub,  V = 0,550103.
 
C 36
(11.5-30)
1 A
where A and C36 are coefficients obtained from formulae in 11.5.4.1.2.
Figure 11.5-4 — Value of  F for  = 0,3 (integral method factor)
174
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 11.5-5 — Value of  v for  = 0,3 (integral method factor)
Figure 11.5-6 — Value of  for  = 0,3 (hub stress correction factor)
UNI EN 13445-3:2021
175
EN 13445-3:2021 (E)
Issue 1 (2021-05)
 
3

e V
 e   F  l0

  l
2
 U  l0  g 0
T
0





(11.5-31)
The longitudinal hub stress:

H
M
=
(11.5-32)
2
g 1
The radial flange stress:

r

(1,333 e  F  l 0 ) M
(11.5-33)
2
e l0
The tangential flange stress:
 
b)
Y M
e
 r
2
K
K
2
 1
2
1
(11.5-34)
Loose method
The tangential flange stress:
 

Y
e
M
(11.5-35)
2
The radial stress in flange and longitudinal stress in hub are

c)
r
 
H
(11.5-36)
 0
Loose hubbed flange method
and  V L are given by Formulae (11.5-37) and (11.5-38) or are found from Figures 11.5-7 and 11.5-8
respectively :
 FL
β FL 
 3  2A   9  5A 
 21  11 A 
3 A
C 18 

  
  C 24 
  C 21 
84

 210   360


 6 


C


2
 3 (1  v ) 
1/4
1 
A
3
(11.5-37)
C
where A, C, C18, C21 and C24 are coefficients obtained from formulae in 11.5.4.1.2.

is the Poisson's ratio
1
β VL 
4


C 24
5
3 1  v

C

3 C 21

2
2



 C 18
1/ 4
1 
A
(11.5-38)
3
where A, C, C18, C21 and C24 are coefficients obtained from formulae in 11.5.4.1.2.
176
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)

is the Poisson's ratio
Figure 11.5-7 — Value of  FL for  = 0,3 (loose hub flange factor)
Figure 11.5-8 — Value of  VL for  = 0,3 (loose hub flange factor)
UNI EN 13445-3:2021
177
EN 13445-3:2021 (E)
Issue 1 (2021-05)

  
e  FL  l 0



T l0
3
e


VL
2
 Ul0g 0




(11.5-39)
The longitudinal hub stress:

M

H
(11.5-40)
2
g 1
The radial flange stress:
(1,333 e   FL  l 0 ) M
 r
 e
2
(11.5-41)
 l0
The tangential flange stress:




M
Y
 
2
e
K
r
K
2
 1
2
1
(11.5-42)
11.5.4.1.2 Coefficients for flange stresses calculations
A

g1
g0
(11.5-43)
1
C  48 ( 1  v
C1 
C2 
C3 
C4 
C5 
C6 
C7 
178
1

3
5
42
 h 

)
l 
 0 
2
4
(11.5-44)
A
(11.5-45)
12

1
210
11
360
1
90
1
120
215
2772
17 A
(11.5-46)
336




A
(11.5-47)
360
59 A
5040
5A
1008
17 A
5040

51 A
1232



1 3A
(11.5-48)
C
(1  A )
3
(11.5-49)
C
1
(11.5-50)
C
 120  225 A  150 A 2  35 A 3
 

14

 1

C

(11.5-51)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C8 
C9 
C 10 
C 11 
C 12 
C 13 
C 14 
C 15 
31
6930
128 A

533

30240
29
3780
31
6048
45045


1
2925

761
831600
197
415800
233
831600
653 A
73920
 42  198 A  243 A 2  91 A 3
 

704
84

1763 A
665280
300300


(11.5-54)
 1

C

(11.5-55)
 88  198 A  156 A 2  42 A 3
 

385

937 A
1663200
103 A
332640
97 A
554400
(11.5-53)
 1

C

 42  72 A  45 A 2  10 A 3
 

84

71 A
(11.5-52)
 1

C

 42  198 A  117 A 2  25 A 3
 

84

3A

 1

C

 66  165 A  132 A 2  35 A 3
 

77

 2  12 A  11 A 2  3 A 3
 

70

 1

C

(11.5-56)
 1

C

(11.5-57)
 2  12 A  17 A 2  7 A 3
 

70

 1

C

(11.5-58)
 6  18 A  15 A 2  4 A 3
 

210

 1

C

(11.5-59)

2
2
2
C 16  C 1 . C 7 . C 12  C 2 . C 8 . C 3  C 3 . C 8 . C 2  C 3 . C 7  C 8 . C 1  C 2 . C 12


2


2



C 17  C 4 . C 7 . C 12  C 2 . C 8 . C 13  C 3 . C 8 . C 9  C 13 . C 7 . C 3  C 8 . C 4  C 12 . C 2 . C 9
(11.5-60)

C 18  C 5 . C 7 . C 12  C 2 . C 8 . C 14  C 3 .C 8 .C 10  C 14 . C 7 .C 3  C 8 . C 5  C 12 . C 2 . C 10

2
C 19  C 6 . C 7 . C 12  C 2 . C 8 . C 15  C 3 . C 8 . C 11  C 15 . C 7 . C 3  C 8 . C 6  C 12 . C 2 . C 11

C 20  C 1 . C 9 . C 12  C
4

. C 8 . C 3  C 3 . C 13 . C 2  C
2
3
1
. C 9  C 13 . C 8 . C 1  C 12 . C
(11.5-61)
C 16

4
1
(11.5-62)
C 16
1
(11.5-63)
C 16
.C 2

1
C 16


2
3
. C 10  C 14 . C 8 . C 1  C 12 C 5 . C 2



2
3
. C 11  C 15 . C 8 . C 1  C 12 . C 6 . C 2

C 21  C 1 . C 10 . C 12  C 5 . C 8 . C 3  C 3 . C 14 . C 2  C
C 22  C 1 . C 11 . C 12  C 6 . C 8 . C 3  C 3 . C 15 . C 2  C
UNI EN 13445-3:2021
1
C 16
1
C 16
(11.5-64)
(11.5-66)
(11.5-67)
179
EN 13445-3:2021 (E)
Issue 1 (2021-05)

C 23  C 1 . C 7 . C 13  C 2 . C 9 . C 3  C
4

.C 8 .C 2  C 3 .C 7 .C 4  C 8 .C 9 .C 1  C




2
2
. C 13
C 24  C 1 . C 7 . C 14  C 2 . C 10 . C 3  C 5 . C 8 . C 2  C 3 . C 7 . C 5  C 8 . C 10 . C 1  C
C 25  C 1 . C 7 . C 15  C 2 . C 11 . C 3  C 6 . C 8 . C 2  C 3 . C 7 . C 6  C 8 . C 11 . C 1  C
C
26
C 
 

 4 
1/ 4
C 28  C 22  C 19 
29
C 
 

 4 
C 
C 30   

 4 
C 31 
C 32 
C 33 
C 34 
3A
2
1
2
5
12
. C 14

. C 15

1
C 16
1
C 16
(11.5-69)
(11.5-70)
1
12
(11.5-72)
 C 19 . C 26
(11.5-73)
(11.5-74)
(11.5-75)
(11.5-76)
 C 17 . C 30
(11.5-77)
 C 19 . C 30
 C 30 . C 28

 C 28 . C 31 . C 29  
 C 32 . C 27 . C 29 
2


 C 18  C 21  C 18 . C 26
C 36  C 28 . C 35 . C 29  C 32 . C 34 . C 29
(11.5-78)
(11.5-79)
(11.5-80)
C 35  C 18 . C 30
180
(11.5-68)
C 16
 C 17 . C 26
3/4
2
1
12
1/ 2
C 26 . C 32
2
2
1
(11.5-71)
C 27  C 20  C 17 
C
2
2


1
C 33
(11.5-81)
C 30 . C 34
 C 26 . C 35
 1
C 37  
 C 34 . C 31 . C 29 
 C 35 . C 27 . C 29 
2
2

 C 33
(11.5-82)
E 1  C 17 . C 36  C 18  C 19 . C 37
(11.5-83)
E 2  C 20 . C 36  C 21  C 22 . C 37
(11.5-84)
E 3  C 23 . C 36  C 24  C 25 . C 37
(11.5-85)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
3  C 37  3 C 36
E4 
12

2 E 3  15 E 2  10 E 1
10
(11.5-86)
3  A 
 21  11 A 
 3  2A 
E 5  E 1
  E2
  E3

6
84




 210

(11.5-87)
A
3A 
1
A
A
1 
 7
 1
E 6  E 5  C 36 



 C 37 


 

36
C 
40
72
120
C 
 120
 60
(11.5-88)
11.5.4.2 Stress limits
The assembly condition and operating condition are both normal design conditions for the purpose of
determining nominal design stresses.
Nominal design stresses f shall be obtained in accordance with Clause 6, except that for austenitic steels as
per 6.5 the nominal design stress for normal operating load cases is given by 6.5.1 a) only, and for testing
load cases by 6.5.2 a).
fH shall be the nominal design stress of the shell except for welding neck or slip-on hubbed construction
where it is the nominal design stress of the flange.
If B ≤ 1 000 mm then k = 1,0.
If B ≥ 2 000 mm then k = 1,333.
For values of B between 1 000 mm and 2 000 mm:
k 
2 
B

1 

3 
2 000 
(11.5-89)
The flange stresses as calculated in 11.5.4.1 shall meet the following requirements:
f ; f H 
k 
H
k 
r
 f
(11.5-91)
k 

 f
(11.5-92)
 1,5 min
0,5 k ( 
H
 
r
0,5 k ( 
H

θ
)  f
)  f
(11.5-90)
(11.5-93)
(11.5-94)
11.5.5 Narrow face flanges subject to external pressure
If the flange is subject to both internal and external pressure it shall be designed for both conditions, except
that external pressure need not be considered where the external calculation pressure Pe is less than the
internal calculation pressure.
The design of flanges for external pressure shall be in accordance with 11.5.4 except that:
a) Pe replaces P;
UNI EN 13445-3:2021
181
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b)
M
 H
op
D
(hD  hG )  H
T
(11.5-95)
(hT  hG )
and
c) Wop = 0
(11.5-96)
NOTE
In the case of external pressure the bolts can be completely loose, leading to Wop = 0. This is a
conservative assumption as any bolt load reduces the net moment on the flange.
Where a flange is being designed for external pressure and is one of a flange pair having different design
conditions, Wop shall be that calculated for the other of the pair and Mop shall be the greater of Mop as
calculated above and WophG.
11.5.6 Lap joints
11.5.6.1 General
In a lap joint the loose flange may have a hub. The stub flange may be attached to the shell in any way
permitted for a bolted flange.
Bolt loads and areas shall meet the requirements of 11.5.2 or 11.6.2 as appropriate, depending on which
method is applied to the stub flange in 11.5.6.2.
The diameter G1 of the load reaction between stub and loose flanges shall be given a value lying between
(A2–) and (B2+).
NOTE
The value given by Formula (11.5-97) should be used unless there is good reason to do otherwise.
G1  (A2  B
2
)/2
(11.5-97)
The area of the contact face between the two flanges shall be given by:
Ac 

min
2
 A
2
 

2
 G 1 ; G 1  B 2  
2
2

2

(11.5-98)
If the diameters A2 and B2 are defined by the same component, as with the stepped flange shown in
Figure 11.5-9,  shall be given the value zero in Formula (11.5-98).
Bearing stress b at the contact face shall be determined for both assembly and operating conditions using
the following formula:

182
b

W op
Ac
or

b

W
Ac
(11.5-99)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 11.5-9 — Stepped loose flange
The bearing stress shall not exceed 1,5 times the lower nominal design stress of the two flanges.
11.5.6.2 Stub flange
The stub flange shall take one of the forms listed in 11.4.4 and either the narrow face (see 11.5) or full face
(see 11.6) method shall be applied.
NOTE
When G1 is greater than the outside diameter of the gasket then the full face method is inapplicable.
Even when G1 is less than the outside diameter of the gasket the narrow face method is applicable though possibly
less economic.
The stub flange shall meet the requirements for a flange loaded directly by the bolts as given in 11.5.4 or
11.6, except that the bolt load is assumed to be imposed at diameter G1, which therefore replaces C in the
calculation at the moment arms hD, hG and hT. The diameter of the bolt holes, dh, required in 11.6, shall be
taken as zero.
11.5.6.3 Loose flange
See Figures 11.5-10 and 11.5-11.
h L  C  G 1  /2
(11.5-100)
The moment arm on the loose flange for all components of load shall be hL so that:
M
op
NOTE
M
 W
op
 hL
(11.5-101)
For external pressure, Wop = 0 – see 11.5.5.
A
 W  hL
(11.5-102)
The loose flange stresses and stress limits shall meet the requirements of 11.5.4.
UNI EN 13445-3:2021
183
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figures 11.5-10 — Lap type joint; loose flange with hub
Figures 11.5-11 — Lap type joint; loose flange without hub
184
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
11.5.7 Split ring flanges
It is permissible to split the loose flange in a lap joint across the diameter to make it readily removable from
the nozzle neck or vessel. The design shall be in accordance with 11.5.6.3 modified as follows.
When the flange consists of a single split ring, it shall be designed as if it were a solid flange (without splits),
using 200 % of the moment Mop and/or MA required in 11.5.6.3.
When the flange consists of two split rings, each ring shall be designed as if it were a solid flange (without
splits), using 75 % of the moment required in 11.5.6.3. The pair of rings shall be assembled so that the splits
in one ring are 90° from the splits in the other ring. The splits shall be located midway between bolt holes.
11.6 Full face flanges with soft ring type gaskets
Figure 11.6-1 — Full face flange (soft gasket)
11.6.1 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in 11.3:
UNI EN 13445-3:2021
185
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
See Figure 11.6-1 for an illustration of the various dimensions.
A1
is inside diameter of gasket contact face;
b'
is the effective assembly width;
2b”
is the effective gasket pressure width, taken as 5 mm;
b' 0
is the basic assembly width effective under initial tightening up;
dh
is diameter of bolt holes;
G
is the diameter at location of gasket load reaction;
G0
is outside diameter of gasket or outside diameter of flange, whichever is less;
H
is the total hydrostatic end force;
HG
is compression load on gasket to ensure tight joint;
HR is the balancing reaction force outside bolt circle in opposition to moments due to loads inside bolt
circle;
hR
is radial distance from bolt circle to circle on which HR acts;
hT
is radial distance from bolt circle to circle on which HT acts;
hG
is radial distance from bolt circle to circle on which HG acts;
MR
is balancing radial moment in flange along line of bolt holes;
n
is number of bolts;
b
is bolt spacing.
11.6.2 Bolt loads and areas
2b” is given the value 5 mm
b'0 = min (G0 - C ; C - A1 )
(11.6-1)
b' =
(11.6-2)
b o
4
(This expression is valid only with dimensions expressed in millimetres);
G = C - (dh + 2b”)
H 

HD 
 (C  d
4

4
B
2
H T = H - HD
186
h
P
)
(11.6-3)
2
P
(11.6-4)
(11.6-5)
(11.6-6)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
H G  2 b "   G  m  P
(11.6-7)
hD = (C-B-g1)/2
(11.6-8)
hT = (C + dh + 2b” - B) /4
(11.6-9)
hG = (dh + 2b”) / 2
(11.6-10)
hR = (G0 - C + dh) / 4
(11.6-11)
M R  H D  hD  H T  hT  H G  hG
(11.6-12)
H
R

M
(11.6-13)
R
hR
Bolt areas shall be calculated in accordance with 11.5.2, taking:
  C  b ' y
W
A
W
op
 H  H
G
(11.6-14)
(11.6-15)
 HR
11.6.3 Flange design
The flange thickness shall be not less than the greatest value of e from the following three formulae:
e 
e 
6M
R
f  C - nd
m
 0,5
h

 E /200000 
(11.6-16)

0,25

(
b
 2d b )
6
(11.6-17)
where
E is expressed in MPa.
e 
( A 1  2 g 1 )P
(11.6-18)
2f
Where two flanges of different internal diameters, both designed to the rules of 11.6.4, are to be bolted
together to make a joint, the following additional requirements apply:
a) the value of MR to be used for both flanges shall be that calculated with the smaller internal
diameter;
b) the thickness of the flange with the smaller bore shall be not less than:
e =
3 M
1
 M
2
  A
 B
  f  B A  B


(11.6-19)
where
UNI EN 13445-3:2021
187
EN 13445-3:2021 (E)
Issue 1 (2021-05)
M1 and M2 are the values of MR calculated for the two flanges.
11.6.4 Full face flanges subject to external pressure
If the flange is subject to both internal and external pressure it shall be designed for both conditions, except
that external pressure need not be considered where the external calculation pressure is less than the
internal.
The design of flanges for external pressure shall be in accordance with 11.6 except that:
a) Pe replaces P;
b) Formula (11.6-17) does not apply;
c) Wop = 0.
11.7 Seal welded flanges
Seal welded flanges (as shown in Figure 11.7-1) shall be designed in accordance with 11.5, except that:
a) only the operating condition is to be considered;
b) G = DL, the inside diameter of seal weld lip, as shown in Figure 11.7-1;
c) HG = 0;
d) flange thickness e shall be determined as the mean thickness of the flange.
Figure 11.7-1 — Seal welded flange
11.8 Reverse narrow face flanges
11.8.1 Internal pressure
Reverse flanges with narrow face gaskets (see Figures 11.8-1 and 11.8-2) under internal pressure shall be
designed in accordance with 11.5 with the following modifications.
188
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The limits on g0 and B/g0 to the application of the loose method of calculation do not apply.
The following symbols and abbreviations are in addition to or modify those in 11.3:
A
is the inside diameter of the flange;
B
is the outside diameter of the flange;
HT
is the net pressure load on the flange faces.
Figures 11.8-1 — Reverse narrow face flange
UNI EN 13445-3:2021
189
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figures 11.8-2 — Reverse narrow face flange; slip in type
The following formulae replace the formulae in 11.5 for the given variables:
HD = /4 P D2
(11.8-1)
H T = HD - H
(11.8-2)
hD = (B - C - g1) / 2
(11.8-3)
except for slip-in type flange with fillet weld (so that B = D), when
hD = (B - C) / 2
(11.8-4)
hT = (2C - G - D) / 4
(11.8-5)
Mop = HT  hT + HD  hD
(11.8-6)
M = (MA or Mop) CF / A
(11.8-7)
K = B/A
(11.8-8)
The sign of hT, which may be negative, has to be respected.
190
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
The moment due to gasket reaction is taken as zero for the operating condition. This is a conservative
assumption since any gasket load reduces the moment in the flange.
11.8.2 External pressure
Reverse flanges with narrow face gaskets under external pressure shall be designed in accordance with
11.8.1 modified by 11.5.5, except that Formula (11.5-5) is replaced by:
Mop = HD (hD  hG)  HT (hG  hT)
(11.8-9)
11.9 Reverse full face flanges
11.9.1 General
The design method shall be in accordance with either 11.9.2 or 11.9.3; both are equally valid. For both
design methods gaskets and bolting loads at the assembly condition shall be in accordance with 11.6.
NOTE
Two alternative design methods are provided for reverse full face flanges. The first follows the
approach of 11.5 at the operating condition and assumes resistance to rotation comes from the flange itself; the
second follows 11.6 and requires a larger bolt area.
11.9.2 Design following method of 11.5
NOTE
See Figure 11.9-1 for an illustration of the loads and dimensions.
Design for the operating condition shall be in accordance with 11.5 with the following modifications.
The following symbols and abbreviations are in addition to or modify those in 11.3.
A
is inside diameter of flange;
A1
is inside diameter of gasket contact face;
B
is outside diameter of flange;
HS
is the hydrostatic end force due to pressure on exposed flange face;
hS
is the radial distance from bolt circle to circle on which HS acts.
UNI EN 13445-3:2021
191
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 11.9-1 — Reverse full face flange design to 11.9.2
The following additional formulae apply:
w = (C - A1) / 2
(11.9-1)
HS = HD - /4 P A12
(11.9-2)
hS = (2C - D - A1 ) / 4
(11.9-3)
The following formulae replace the formulae in 11.5 for the given variable:
H 

4
 P C  d h
2
(11.9-4)
HD = /4 P D2
(11.9-5)
HG = 2b C m P
(11.9-6)
HT = (H - HD + HS) / 2
(11.9-7)
hD = (B - g1 - C) / 2
(11.9-8)
except for the slip-in type flange (BD) for which,
hD = (B - C) / 2
192
(11.9-9)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
hT = (2C + dh - 2A1 ) / 6
(11.9-10)
Mop = HD hD - HT hT + HS hS
(11.9-11)
M = Mop CF / A
(11.9-12)
K=B/A
(11.9-13)
The sign of hS, which may be negative, shall be respected.
NOTE
The moment due to gasket reaction is taken as zero for the operating condition since this assumption
gives higher stresses.
11.9.3 Design following method of 11.6
NOTE
See Figure 11.9-2 for an illustration of loads and dimensions.
The rules in 11.9.3 shall only be used for reverse flanges where the mating component is a tubesheet or flat
plate.
Design for the operating condition shall be in accordance with 11.6 with the following modifications.
The following symbols and abbreviations are in addition to or modify those in 11.3:
A
is inside diameter of flange;
A1
is inside diameter of gasket contact face;
B
is outside diameter of flange;
UNI EN 13445-3:2021
193
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 11.9-2 — Reverse full face flange design to 11.9.3
HC
is the pressure force on the flange face outside the bolt circle diameter;
hC
is radial distance from bolt circle to circle on which HC acts;
The following additional formulae apply (see symbols in Figure 11.9-2):
HC = HD – /4 P C 2
(11.9-14)
hC = (D - C) / 4
(11.9-15)
The following formulae replace the formulae in 11.6 for the given variable:
HD = /4 P D 2
(11.9-16)
hD = (B - C - g1 ) / 2
(11.9-17)
M R = H D hD - H C hC
(11.9-18)
Wop = HD - HC + HR
(11.9-19)
194
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
hR = (C-A1+dh)/4
(11.9-20)
11.10 Full face flanges with metal to metal contact
11.10.1 General
NOTE
See Figure 11.10-1 for an illustration of loads and dimensions.
The requirements of 11.10.2 shall be applied when there is metal to metal contact both inside and outside
the bolt circle before the bolts are tightened with more than a small amount of preload and the seal is
provided by an O-ring or equivalent.
Manufacturing procedures and tolerances shall ensure that the flange is not dished in such a way as to give
initial contact outside bolt circle.
NOTE 1
The rules are conservative where initial contact is at the bore.
NOTE 2
It is assumed that a self-sealing gasket is used approximately in line with the wall of the attached pipe
or vessel and that the assembly load and any axial load from the seal may be neglected.
11.10.2 Specific symbols and abbreviations
The following symbols and abbreviations are in addition to those in 11.3:
G
HR
is mean diameter of gasket;
is the balancing reaction force outside bolt circle in opposition to moments due to loads inside
bolt circle;
hR
is radial distance from bolt circle to circle on which HR acts;
MR
is balancing radial moment in flange along line of bolt holes;
n
is number of bolts.
UNI EN 13445-3:2021
195
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 11.10-1 — Flange with full face metal to metal contact and O-ring seal
196
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
11.10.3 Design
The following requirements apply where the flange is to be bolted to an identical flange or to a flat cover.
Bolt loads shall be calculated in accordance with 11.5.2 taking:
hR = (A - C) / 2
M
R
 H
D
H
R
 M
R
 hD  H
(11.10-1)
T
(11.10-2)
 hT
(11.10-3)
/h R
WA = 0
W
op
(11.10-4)
= H H
(11.10-5)
R
The flange thickness shall be not less than:
e 
6M
(11.10-6)
R
f  C  n  d h

where dh is the diameter of bore holes.
Where two flanges of different internal diameters, both designed to the rules of this clause, are to be bolted
together to make a joint, the following additional requirements apply:
a) value of MR to be used for both flanges shall be that calculated for the smaller internal diameter;
b) the thickness of the flange with the smaller bore shall be not less than:
e =
3 M 1 - M 2  A + B

 f  B A - B 
(11.10-7)
where M1 and M2 are the values of MR calculated for the two flanges.
UNI EN 13445-3:2021
197
EN 13445-3:2021 (E)
Issue 1 (2021-05)
12 Bolted domed ends
12.1 Purpose
This clause specifies requirements for the design of bolted domed ends, with either full face or narrow face
gaskets, and with the dome either convex or concave to pressure. The rules provided in this clause for the
narrow face gasket design are well established but Annex G provides a modern alternative - see NOTE 1
of 11.1.
12.2 Specific definitions
The following definition applies in addition to those in 11.2.
12.2.1
bolted domed end
cover or blind flange consisting of a flange and a dome of constant radius of curvature
12.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in 11.3:
a
is distance from top of flange to the mid-thickness line of the dome where it meets the flange;
eD
is required thickness of spherical dome section;
fD
is design stress for dome section;
Hr
is radial component of membrane force developed in dome, acting at edge of flange;
hr
is the axial distance from mid-surface of dome section at edge to center of flange ring cross-section, as given
by Formula (12.5-3);
R
is inside radius of curvature of dome.
12.4 General
Relevant parts of 11.4 also apply to flanges designed in accordance with Clause 12.
12.5 Bolted domed ends with narrow face gaskets
12.5.1
NOTE
Dome concave to pressure
See Figure 12-1 for an illustration of loads and dimensions.
Bolt loads and areas and gasket loads shall be calculated in accordance with 11.5.2.
The required thickness of the spherical dome section shall be:
198
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
5P  R
eD =
(12.5-1)
6 fD
Moments and moment arms shall be calculated in accordance with 11.5.3, except that Formula (11.5-18)
shall be replaced by Formula (12.5-4).
H
r
=H
D

4R
2
 B
2
(12.5-2)
B
(12.5-3)
h r  e /2  a
Figure 12-1 — Bolted domed end with narrow face gasket
The moment on the flange in the operating condition is:
M
op
 H D  hD  H
G
 hG  H
T
 hT  H
r
 hr
(12.5-4)
The assembly condition and operating condition are both design conditions for the purpose of determining
nominal design stresses.
The absolute value of Mop shall be used in Formula (12.5-6).
The following conditions shall be checked:
UNI EN 13445-3:2021
199
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) the thickness shall be such that e ≥ 2eD;
b) the stress at the assembly condition is:
3M
A
A

A
 B CF
 B
B
e
2
(12.5-5)
 f
c) the stress in the operating condition is:
H
r

B  e  3M

12.5.2
A
op
A
- B B  e
 B C F
2
(12.5-6)
 f
Dome convex to pressure
The required thickness of the spherical dome shall be the greater of the thicknesses from 12.5.1 and
Clause 8.
Design of the flange shall be in accordance with 12.5.1 except that:
M op  H D  h D  h G

H T h T  h G

(12.5-7)
H r  hr
12.6 Bolted domed ends with full face joints
12.6.1
NOTE
Bolted domed ends with full face joints concave to pressure
see Figure 12-2 for an illustration of loads and dimensions.
The rules in 12.6 shall only be applied to domed and bolted ends that are bolted to a tubesheet.
The following procedure shall apply to bolted domed ends with soft full face gaskets concave to pressure:
a) Apply the rules of 12.5.1 to the spherical dome;
b) Calculate HD, hD, HT, hT, HG and hG using 11.6; eq (11.6-8) shall be computed using g1=0;
c) Calculate Hr and hr using 12.5.1;
d) Calculate:
M R  H D  hD  H G  hG  H T  hT  H r  hr
(12.6-1)
e) Complete the calculation for both bolt loads and flange design according to 11.6; Formula (11.618) shall be computed using g1=0;
f)
Increase the thickness e if necessary so that:
H
NOTE
200
r
 f  e A  B  2d h

(12.6-2)
The limitation on Hr ensures that the flange ring hoop stress is not excessive.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 12-2 — Bolted domed end with full face gasket
12.6.2
Bolted domed ends with full face joints convex to pressure
The following requirements apply to bolted domed ends with full face joints convex to pressure:
a) the requirements of 11.6.4;
b) for the spherical dome, 12.5.2;
c) Formula (12.6-2).
UNI EN 13445-3:2021
201
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13 Heat Exchanger Tubesheets
13.1 Purpose
This clause provides rules for tubesheet heat exchangers of the three following types:
a) U-tube tubesheet heat exchangers, see Figure 13.1-1a, covered in 13.4;
b) Fixed tubesheet heat exchangers, see Figure 13.1-1b, covered in 13.5;
c) Floating tubesheet heat exchangers, see Figure 13.1-1c, covered in 13.6.
The rules provided in this clause are based on the classical elastic theory of thin shells, assuming that the
tubesheet rests on an elastic foundation created by the tubes. Reference is made to Annex J which provides
an alternative method based on limit load analysis.
NOTE
This alternative method may be used instead of the classical method, especially when the heat
exchanger considered is outside the field of application of the classical method.
13.2 Specific definitions
The following definitions are in addition to those in Clause 3.
13.2.1
U-tube tubesheet heat exchanger
heat exchanger with one tubesheet attached to the shell and channel (see Figure 13.2-1a)
13.2.2
Fixed tubesheet heat exchanger
heat exchanger with two tubesheets, each attached to the shell and channel (see Figure 13.2-1b)
13.2.3
floating tubesheet heat exchanger
heat exchanger with two tubesheets (see Figure 13.2-1c):
— a stationary tubesheet (item 2') attached to the shell and channel,
— a floating tubesheet (item 2") which can move axially.
13.2.4
gasketed tubesheet
tubesheet attached to the shell and/or channel by bolting
13.2.5
integral tubesheet
tubesheet attached to the shell and/or channel by welding
13.3 Specific symbols and abbreviations
Specific symbols are defined in the following relevant subclauses.
202
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(1 )
(1) Configurations of tubesheet – shell – channel connections are detailed in 13.4.1.
a) U-tube heat exchanger
(1 )
(1 )
(1) Configurations of tubesheet – shell – channel connections are detailed in 13.5.1.
b) Fixed tubesheet heat exchanger
(1 )
(1 )
(1) Configurations of tubesheet – shell – channel connections are detailed in 13.6.1.
c) Floating head heat exchanger
Figure 13.1-1 — Three types of tubesheet heat exchangers
UNI EN 13445-3:2021
203
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) U-tube tubesheet heat exchanger
b) Fixed tubesheet heat exchanger
c) Floating tubesheet heat exchanger
Key
1
2
2'
2"
3
4
5
6
Stationary Head-Channel
Fixed Tubesheet
Stationary Tubesheet
Floating Tubesheet
Tubes
Shell
Shell Flange
Shell Cover Flange
7
8
9
10
11
12
13
Expansion Bellows
Floating Head Cover
Floating Head Flange
Floating Head Backing Device
Baffles or Support Plates
Longitudinal Baffle
Pass Partition
Figure 13.2-1 — Terminology of heat exchanger components
204
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.4 U-tube tubesheet heat exchangers
13.4.1 Scope
a) This clause provides rules for the design of U-tube heat exchangers that have one tubesheet
attached to the shell and channel and connected to a U-tube bundle, as shown in Figure 13.4.1-1.
(1) Configuration a, b, c, d, e or f (see Figure 13.4.1-2)
Figure 13.4.1-1 — Typical U-tube tubesheet heat exchanger
b) The tubesheet may have one of the six configurations shown in Figure 13.4.1-2:
— configuration a:
tubesheet integral with shell and channel;
—
configuration b: tubesheet integral with shell and gasketed with channel, extended as a flange;
—
configuration c: tubesheet integral with shell and gasketed with channel, not extended as a
flange;
— configuration d:
tubesheet gasketed with shell and channel, extended as a flange or not;
—
configuration e: tubesheet gasketed with shell and integral with channel, extended as a flange;
—
configuration f: tubesheet gasketed with shell and integral with channel, not extended as a
flange.
Configuration d covers the cases where the tubesheet is (see Figure 13.4.1-3):
— not extended as a flange (configuration d1);
— extended as a flange (configuration d2).
c) 13.4.2 to 13.4.6 apply to configuration a (where the tubesheet is integral) and to configurations b,
c, d, e, f where the gasketed tubesheet has a narrow gasket.
Subclause 13.4.7 outlines how to use these rules for configurations b', d', e' where the gasketed
tubesheet has a full face gasket.
UNI EN 13445-3:2021
205
EN 13445-3:2021 (E)
Issue 1 (2021-05)
c) Configuration c
a) Configuration a
b) Configuration b
Tubesheet integral with
shell and channel
Tubesheet integral with shell
and gasketed with channel,
extended as a flange
Tubesheet integral with shell
and gasketed with channel,
not extended as a flange
d) Configuration d
e) Configuration e
f) Configuration f
Tubesheet gasketed with
shell and channel, extented
as a flange or not
Tubesheet gasketed with
shell and integral with
channel, extended as a flange
Tubesheet gasketed with
shell and integral with
channel, not extended as a
flange
Figure 13.4.1-2 — U-tube tubesheet configurations
a) Configuration d1
b) Configuration d2
Tubesheet not extended as a flange
Tubesheet extended
as a flange
Figure 13.4.1-3 — Various types of configuration d (tubesheet gasketed both sides)
206
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.4.2 Conditions of applicability
13.4.2.1 Tubesheet
The tubesheet shall comply with the following conditions of applicability.
a) The tubesheet shall be flat, circular and of uniform thickness.
b) A local reduction of thickness at the periphery of the tubesheet for a gasket groove or a relief
groove is permitted, provided that the remaining analysis thickness, e a , p , is at least equal to
0,8 times the assumed thickness, e , of the tubesheet (see Figure 13.4.2-1):
(13.4.2-1)
e a, p  0 , 8 e
The radius shall be not less than 5 mm and not less than 20 % of the adjacent shell thickness. The
requirement for the remaining analysis thickness given above shall apply only if the ratio of the outside
diameter to inside diameter of the adjacent shell is larger than 1,2.
a) Configuration a
b) Configuration b and e
c) Configuration d
d) Configuration c and f
Figure 13.4.2-1  Local reduction of thickness at tubesheet periphery
c) When the tubesheet is extended as a flange, the flange extension thickness shall be calculated
according to:
 13.10 if the gasket is narrow (configurations b, d2, e);
 13.11 if the gasket is full face (configurations b',
d
'
2
, e').
d) Unless satisfactory experience has been demonstrated with thinner tubesheets, the following
conditions shall be met when the tubes are expanded into the tubesheet:
— when
dt
UNI EN 13445-3:2021
 25 mm:
207
EN 13445-3:2021 (E)
Issue 1 (2021-05)
ea 
0,75
(13.4.2-2)
dt
— when 25 mm 
ea 
(13.4.2-3)
dt
 40 mm:
25 mm
(13.4.2-4)
— when 40 mm 
ea 
 30 mm:
22 mm
— when 30 mm 
ea 
dt
dt
 50 mm:
30 mm
(13.4.2-5)
e) The tubesheet shall be uniformly perforated over a nominally circular area of diameter D o , in
either equilateral triangular or square pattern. However, untubed lanes for pass partitions are
permitted, provided that the distance between adjacent tube rows U L (see Figure 13.7.3-1) is
such that:
(13.4.2-6)
UL  4 p
where
p is the tube pitch.
13.4.2.2 Tubes
a) The tubes shall be of uniform nominal thickness and diameter over their straight length, and
same material;
b) They shall be rigidly attached to the tubesheet.
13.4.2.3 Shell and channel
Shell and channel shall be cylindrical at their junction to the tubesheet.
13.4.2.4 Loading
Tube-side pressure
Pt
and shell-side pressure
Ps
are assumed to be uniform in each circuit.
Other loadings, such as weight or pressure drop, are not considered.
13.4.3 Symbols
All moments in this clause are moments per unit length [Nmm/mm].
A
C
Dc
Ds
208
is the outside diameter of tubesheet;
is the bolt circle diameter;
is the inside channel diameter (see Figure 13.4.1-1);
is the inside shell diameter (see Figure 13.4.1-1);
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Do
dt
E
E
c
E
s
*
E
e
ec
es
F
f
fc
fs
G1
Gc
Gs
'
is the diameter of the perforated tubesheet area, given by Formula (13.7.5-1);
is the nominal outside diameter of tubes (see Figure 13.7.3-3);
is the elastic modulus of tubesheet material at design temperature;
is the elastic modulus of channel material at design temperature;
is the elastic modulus of shell material at design temperature;
is the effective elastic modulus of the tubesheet at design temperature, see 13.7;
is the assumed thickness of the tubesheet (see Figure 13.7.3-3);
is the channel thickness (see Figure 13.4.1-1);
is the shell thickness (see Figure 13.4.1-1);
is a coefficient given in 13.4.4.3d;
is the nominal design stress of tubesheet material at design temperature;
is the nominal design stress of channel material at design temperature;
is the nominal design stress of shell material at design temperature;
is the diameter of the midpoint of contact face between flange and tubesheet, given by
Formula (11.5-97);
is the diameter of channel gasket load reaction (see Clause 11);
is the diameter of shell gasket load reaction (see Clause 11);
is the effective depth of tube-side pass partition groove, see 13.7;
hg
K
kc
ks
M
o
M
P
M
Pc
is the tubesheet diameter ratio given by Formula (13.4.4-6);
is the edge moment per unit length required to rotate the channel edge through unit angle, given by
Table 13.4.4-1;
is the edge moment per unit length required to rotate the shell edge through unit angle, given by
Table 13.4.4-1;
is the moment [Nmm/mm] acting at centre of tubesheet, given by Formula (13.4.5-7);
is the moment [Nmm/mm] acting at periphery of tubesheet, given by Formula (13.4.5-6);
is the moment [Nmm/mm] acting on the unperforated tubesheet rim due to pressure in the integral
channel, given by Table 13.4.4-1;
UNI EN 13445-3:2021
209
EN 13445-3:2021 (E)
Issue 1 (2021-05)
M
Ps
M
TS
M*
Ps
is the moment [Nmm/mm] acting on the unperforated tubesheet rim due to pressure in the
integral shell, given by Table 13.4.4-1;
is the moment [Nmm/mm] due to pressures P s and P t acting on the unperforated tubesheet rim,
given by Formula (13.4.4-5);
is the moment [Nmm/mm] acting on the unperforated tubesheet rim (see 13.4.5.1);
is the shell-side calculation pressure. In case of vacuum, this shall be taken as negative;
'
is the shell-side calculation pressure coefficient, given by Table 13.4.4-1;
is the tube-side calculation pressure. In case of vacuum, this shall be taken as negative;
Ps
Pt
'
Pt
W
max
W
c
W
s

c

s
c
s


*
c
s
is the tube-side calculation pressure coefficient, given by Table 13.4.4-1;
is the maximum flange design bolt load for the assembly condition, given by
Formula (13.4.4-11);
is the channel flange design bolt load for the assembly condition (see 13.4.4.3);
is the shell flange design bolt load for the assembly condition (see 13.4.4.3);
is the coefficient given by Table 13.4.4-1;
is the coefficient given by Table 13.4.4-1;
is the coefficient given by Table 13.4.4-1;
is the coefficient given by Table 13.4.4-1;
is the basic ligament efficiency of the tubesheet (see 13.7);
is the effective ligament efficiency of the tubesheet (see 13.7);
is the Poisson's ratio of channel material;
is the Poisson's ratio of shell material;

is the effective Poisson's ratio of tubesheet (see 13.7);
is the channel diameter ratio, given by Formula (13.4.4-3) and (13.4.4-4);
is the shell diameter ratio, given by Formula (13.4.4-1) and (13.4.4-2);
is the calculated stress in a component.
Subscripts:
b
for bending;

*
c
s
210
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
c
eq
m
p
s
t
for channel;
for equivalent;
for membrane;
for periphery;
for shell;
for tubes;
No subscript is used for the tubesheet.
13.4.4 Design considerations
13.4.4.1 Loading conditions
The various loading conditions to be considered shall include the normal operating conditions, the start-up
conditions, the shut-down conditions, the upset and the pressure test conditions, which may govern the
design of the tubesheets.
For each of these conditions the following loading cases shall be considered:
— loading case 1 :
Tube-side pressure
Pt
acting only
Ps
 0 ;
— loading case 2 :
Shell-side pressure
Ps
acting only
P t
 0;
— loading case 3 :
Tube-side pressure
Pt
and shell-side pressure
Ps
acting simultaneously.
This loading case 3 shall always be considered if vacuum exists on one side.
If loading cases 1 and 2 cannot occur in service, the design may be based on loading case 3 only.
13.4.4.2 Design conditions
a) The design shall be performed in the corroded condition, except for the tubes for which the
nominal outside diameter d t and the nominal thickness e t shall be used;
b) As the calculation procedure is iterative, a value e shall be assumed for the tubesheet thickness to
calculate and check that the maximum stresses in tubesheet, shell and channel are within the
maximum permissible stresses. An initial assumed tubesheet thickness not less than that given by
the following formula is recommended:
e 
Do
4 μ 0,8 f

Ps  Pt
Two cases are possible:
— If the calculated stress of the component is within the permissible stress, the calculations may be
repeated using a lower thickness of the component until the calculated stress is equal to the
permissible stress in order to obtain the minimum required thickness.
— If the calculated stress of the component exceeds the permissible stress, the calculations shall be
repeated with a higher thickness of the component (or modifying other parameters) until the
calculated stress is within the permissible stress.
UNI EN 13445-3:2021
211
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.4.4.3 Determination of intermediate coefficients
a) Effective elastic constants of tubesheet. From 13.7 calculate:
— The diameter of the perforated tubesheet area,
— The basic ligament efficiency,
Do

— The effective ligament efficiency,

*
— The effective elastic modulus, E *
— The Poisson's ratio,  *
Values of

*
, E * ,  * shall be determined for the assumed tubesheet thickness, e.
b) Diameter ratios
— Ratio
s
 s and
c
and moment
M
TS
:
for shell:
— configurations a, b, c:
s 
Ds
(13.4.4-1)
Do
— configurations d, e, f:
s 
Gs
(13.4.4-2)
Do
— Ratio
for channel:
c
— configurations a, e, f:
c 
Dc
(13.4.4-3)
Do
— configurations b, c, d:
c 
Gc
(13.4.4-4)
Do

Moment M TS due to pressures P s and P t acting on the unperforated tubesheet rim:
M

2
TS
Do
16
 
s



 
 1  s  1 P s    c  1  c  1 P t
2
2
(13.4.4-5)
c) Integral shell and/or channel coefficients and moments M Ps and/or M Pc acting on the tubesheet,
due to pressure in the integral shell and/or channel (see Table 13.4.4-1).
212
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 13.4.4-1 ― Coefficients for integral shell and/or channel
Integral shell (configurations a, b, c)
4
s 
k
s
'
Ps 
M
Ps
D s
 
s 

2
12 1   s

es
2 e

2
s

 

s

2

e 
2




c 

Ds
E
ks 
es
s
1 
s
'
 Ps
e 
Pt 
s
 P s'
M
Pc
2
c
12 1  
D c
kc  
2
s
8
s
c 

2
s

k s 


3 Ds
 
4
3
s
6 1
2 

 es   es
E
s
Integral channel (configurations a, e, f)
 ec  ec
E

c
3
c
ec
6 1
3 Dc
2 e
2 


2
c

k c 


2
c

 

c
2

e 
2




2
c

Dc
E
c
ec
 c kc 
c
1 
8

 Pt
e 
c
 P t'
NOTE
These coefficients do not apply when the shell (configurations d, e, f) or the channel (configurations b,
c, d) are gasketed with the tubesheet.
d) Diameter ratio K for tubesheet and coefficient F:
— Diameter ratio K:
K 
A
…(13.4.4-6)
Do
— Coefficient F:
— configuration a:
F 
1 *
E *
 s
  c  E ln K

(13.4.4-7)
— configurations b and c:
F 
1 *
E *
 s
 E ln K

(13.4.4-8)
— configuration d:
F 
1 *
E *
UNI EN 13445-3:2021
E
ln K

(13.4.4-9)
213
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— configurations e and f:
F 
1 *
E *
 c
 E ln K

(13.4.4-10)
e) Flange design bolt loads acting on the gasketed tubesheet:
— Configurations d2, e, f:
W
s
shall be calculated from Formula (11.5-16) of Clause 11;
— Configurations b, c, d2:
W
c
shall be calculated from Formula (11.5-16) of Clause 11.
For configuration d1 (tubesheet not extended as a flange), the flange design bolt load is given by:
W max
 max
W s  ; W c 
…(13.4.4-11)
13.4.5 Tubesheet design
13.4.5.1 Determination of maximum bending moments in the tubesheet
13.4.5.1.1 Moment M * acting on the unperforated tubesheet rim
— For configuration a:
M
*
 M
TS
(13.4.5-1)
 M Pc  M Ps
— For configuration b:
M
*
 M TS  M Ps 
W c C  G c

(13.4.5-2)
2  Do
— For configuration c:
M
*
 M TS  M Ps 
W c G 1  G c

(13.4.5-3)
2  Do
— For configuration d:
— configuration d1:
M
*
 M TS 
W max G c  G s 
(13.4.5-4)
2  Do
— configuration d2:
M
*
 M TS 
W s C  G s   W c C  G c
2  Do

(13.4.5-5)
— For configuration e:
M
214
*
 M TS  M Pc 
W s C  G s 
2  Do
(13.4.5-6)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— For configuration f:
M
*
13.4.5.1.2 Moment
2
*
M
M
p
Do

32

M
acting at periphery of tubesheet
p

(13.4.5-8)
1 F
2
0
(13.4.5-7)
2  Do
F P s  P t
13.4.5.1.3 Moment
M
W s G 1  G s 
 M TS  M Pc 
 M
p

M
acting at centre of tubesheet
0
3    P
Do
*
64
s
 Pt

(13.4.5-9)
13.4.5.1.4 Maximum bending moment acting on the tubesheet
M  max
M
; M
p
0

(13.4.5-10)
13.4.5.2 Bending stress in tubesheet
a)
The maximum radial bending stress in the tubesheet is given by:
6 M
 

*
(13.4.5-11)
e  h 
'
g
2
b) For each of the loading cases considered, the bending tubesheet stress

shall not exceed 2 f :
(13.4.5-12)
  2f
13.4.5.3 Shear stress in tubesheet
a)
The maximum shear stress in the tubesheet is given by:
1 


 4  

  
 Do

 e

 P s  P t

(13.4.5-13)
b) For each of the loading cases considered, the shear tubesheet stress

shall not exceed 0,8 f :
(13.4.5-14)
  0 ,8 f
13.4.6 Design of shell and channel at their junction with the tubesheet
This subclause applies only to configurations a, b, c, e, f:
13.4.6.1 Determination of stresses in shell (configurations a, b, c)
The shell shall have a uniform thickness
UNI EN 13445-3:2021
es
for a minimum length
ls
adjacent to the tubesheet, given by:
215
EN 13445-3:2021 (E)
Issue 1 (2021-05)
D s
l s  1, 4
a)
 es es
(13.4.6-1)
The axial membrane stress is given by:
2


s, m
Ds
4 e s D s  e s

(13.4.6-2)
Ps
b) The axial bending stress is given by:

6

s, b
e
2
s
*

Do 
1
'
k s  s Ps  3


2
E *

e 

2
 M
e 


s
2
Do

p

 P t  


P s
32
(13.4.6-3)
c) The equivalent stress in the shell, at its junction to the tubesheet, is given by:

 max
s, eq

s, m

s, b
 Ps ; 
 
s, m
s, b

(13
13.4.6.2 Determination of stresses in channel (configurations a, e, f)
The channel shall have a uniform thickness
D c
l c  1, 4
a)
ec
for a minimum length
lc
adjacent to the tubesheet, given by:
 ec ec
(13.4.6-5)
The axial membrane stress is given by:
2


c, m
Dc
4 ec
D c
 ec

(13.4.6-6)
Pt
b) The axial bending stress is given by:


c, b
6
2
ec

k c 


'
c
Pt  3
1
E
*
*

Do 

2
e 
c

2
 M
e 

2
p

Do
32
P s

 P t  


(13.4.6-7)
c) The equivalent stress in the shell, at its junction to the tubesheet, is given by:

c, eq
 max

c, m

c, b
 Pt ; 
c, m
 
c, b

(13.4.6-8)
13.4.6.3 Checking of the shell and channel equivalent stresses
a)
For each of the normal operating loading cases,

s, eq
and

c, eq
, shall be such that:
— For configurations a, b, c:

s, eq
(13.4.6-9)
 1,5 f s
— For configurations a, e, f:

c, eq
b) If
216

(13.4.6-10)
 1,5 f c
s, eq
 1,5 f s
(configurations a, b, c)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
or

c, eq
 1,5 f c
(configurations a, e, f)
the design shall be reconsidered. One or a combination of the following 3 options may be used:
Option 1: increase the assumed tubesheet thickness e and re-design the shell and/or channel according
to 13.4.6. The relevant coefficients of 13.4.4.3 depending on e shall be recalculated as
necessary.
Option 2: increase the integral shell and/or channel thickness as follows:
— configurations a, b, c:
if

s
 1 .5 f s
, increase shell thickness
es
;
— configurations a, e, f:
if

c
 1 .5 f c
, increase shell thickness
ec
;
Re-design the tubesheet according to 13.4.5 and the shell and/or channel according to 13.4.6.
The relevant coefficients of 13.4.4.3 depending on
necessary.
es , Ds
and/or
ec , Dc
shall be recalculated as
Option 3: This option shall only be used if:
—

s
 3 fs
(configurations a, b, c).
—

c
 3 fc
(configurations a, e, f).
Perform a simplified elastic-plastic calculation by using a reduced elastic modulus for the
integral shell and/or channel to reflect the anticipated load shift resulting from plastic action at
the integral shell and/or channel – to – tubesheet junction. This may result in a higher
tubesheet bending stress .
Replace:
—
—
E
E
s
c
by E
by E
1,5 f s
s

s, eq
1,5 f c
c

'
and recalculate k s ,  s , P s and M Ps (configurations a, b, c).
'
and recalculate k c ,  c , P t and M Pc (configurations a, e, f).
c, eq
Recalculate the tubesheet bending stress
— If   2 f :
complete.

according to 13.4.5.2.
the assumed tubesheet thicknes e is acceptable and the design is
the assumed tubesheet thickness is not acceptable and the design shall
— If   2 f :
be reconsidered by using option 1 or 2.
UNI EN 13445-3:2021
217
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.4.7 Treatment of configurations with a full face gasket
13.4.7.1 Scope
This subclause applies to the following configurations where the tubesheet is gasketed with the shell and/or
channel with a full face gasket (see Figure 13.4.7-1):
— Configuration b': tubesheet integral with shell and gasketed with channel.
— Configuration d': tubesheet gasketed with shell and channel.
— Configuration e': tubesheet gasketed with shell and integral with channel.
(1)
(2)
(1)
(2)
Configuration b'
(1)
Configuration d'
(2)
Configuration e'
Key
(1) Channel
(2) Shell
Figure 13.4.7-1 — Tubesheet extended as a flange with a full face gasket
(Configurations b', d', e')
Configuration d' covers the cases where the tubesheet is (see Figure 13.4.7-2):
— Not extended as a flange (configuration
— Extended as a flange (configuration
a) Tubesheet not extended as a flange
(Configuration
'
d1
)
d
'
2
'
d1
).
).
b) Tubesheet extended as a flange
(Configuration
d
'
2
)
Figure 13.4.7-2 — Various types of configuration d'
218
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.4.7.2 Conditions of applicability
The conditions of applicability given in 13.4.2 apply, considering the gasketed shell and/or channel as
integral with the tubesheet.
13.4.7.3 Design rule
The design shall be performed according to 13.4.4 to 13.4.6, with the following modifications:
a) The shell, when gasketed with the tubesheet (configurations d', e'), shall be considered as integral
with the tubesheet, using for k s :
k
s

1
2


s
E

3
s
6 1 -
es
2
s
(13.4.7-1)

b) The channel, when gasketed with the tubesheet (configurations b', d'), shall be considered as
integral with the tubesheet, using for k c :
kc 
1
2


c
E

3
c
6 1 -
ec
2
c
(13.4.7-2)

13.5 Fixed tubesheet heat exchangers
13.5.1 Scope
a) This subclause provides rules for the design of fixed tubesheet heat exchangers that have two
tubesheets attached to the shell and channel and connected to a bundle of straight tubes, as
shown in Figure 13.5.1-1.
The shell may be fitted with an expansion bellows.
(1) Configurations a, b, c, or d (see Figure 13.5.1-2)
Figure 13.5.1-1  Typical fixed tubesheet heat exchanger
UNI EN 13445-3:2021
219
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) The tubesheets may have one of the four configurations shown in Figure 13.5.1-2:
— configuration a:
tubesheet integral with shell and channel.
—
configuration b:
flange.
tubesheet integral with shell and gasketed with channel, extended as a
—
configuration c:
tubesheet integral with shell and gasketed with channel, not extended as a
flange.
— configuration d:
tubesheet gasketed with shell and channel, not extended as a flange.
c) 13.5.2 to 13.5.9 apply to configuration a (where the tubesheet is integral) and to configurations b,
c and d where the gasketed tubesheet has a narrow gasket.
13.5.10 outlines how to use these rules for configuration b' and d' where the gasketed tubesheet
has a full face gasket.
13.5.9 enables to cover shell having a different thickness, or a different material, adjacent to the
tubesheet when integral with the tubesheet (configurations a, b, c).
a) Configuration a
b) Configuration b
Tubesheet integral with shell and channel
Tubesheet integral with shell and gasketed
with channel, extended as a flange
c) Configuration c
d) Configuration d
Tubesheet integral with shell and gasketed
with channel, not extended as a flange
Tubesheet gasketed with shell and channel,
not extended as a flange
Figure 13.5.1-2  Fixed tubesheet configurations
220
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.5.2 Conditions of applicability
13.5.2.1 Tubesheets
The tubesheets shall comply with the following conditions of applicability:
a) The two tubesheets shall be flat, circular and identical (i.e. same uniform thickness, same
material, same connection with shell and channel);
b) A local reduction of thickness at the periphery of the tubesheet for a gasket groove or a relief
groove is permitted, provided that the remaining analysis thickness, e a, p , is at least equal to
0,8 times the assumed thickness, e, of the tubesheet (see Figure 13.5.2-1):
(13.5.2-1)
e a, p  0 , 8 e
The radius shall be not less than 5 mm and not less than 20 % of the adjacent shell thickness. The
requirement for the remaining analysis thickness given above shall apply only if the ratio of the outside
diameter to inside diameter of the adjacent shell is larger than 1,2.
a) Configuration a
b) Configuration b
c) Configuration c
d) Configuration d
Figure 13.5.2-1  Local reduction of thickness at tubesheet periphery
c) When the tubesheets are extended as a flange, the flange extension thickness, shall be calculated
according to:
— 13.10 if the gasket is narrow (configuration b),
— 13.11 if the gasket is full face (configuration b').
d) Unless satisfactory experience has been demonstrated with thinner tubesheets, the following
conditions shall be met when the tubes are expanded into the tubesheet:
— when
dt
UNI EN 13445-3:2021
 25 mm:
221
EN 13445-3:2021 (E)
Issue 1 (2021-05)
ea 
0,75
dt
(13.5.2-2)
— when 25 mm 
ea 
(13.5.2-3)
dt
 40 mm:
25 mm
(13.5.2-4)
— when 40 mm 
ea 
 30 mm:
22 mm
— when 30 mm 
ea 
dt
dt
 50 mm:
30 mm
(13.5.2-5)
e) The tubesheets shall be uniformly perforated over a nominally circular area of diameter
either equilateral triangular or square pattern.
Do ,
in
— Unperforated diametral rows are permitted for pass partitions provided that the distance
between adjacent rows U L (see Figure 13.7.3-1) is such that:
(13.5.2-6)
UL  4 p
where p is the tube pitch.
f) An unperforated annular ring is permitted provided that:
(13.5.2-7)
D o  0 ,85 D e
13.5.2.2 Tubes
a) The tubes shall be straight and identical (i.e. same uniform thickness, same material and same
diameter).
b) They shall be rigidly attached to the tubesheets.
13.5.2.3 Shell
a) The shell shall be cylindrical, and of uniform thickness and diameter (however, when integral
with the tubesheets – configurations a, b and c – the thickness of the shell adjacent to the
tubesheets may be increased as shown in Figure 13.5.9-1).
For configurations a, b and c, the shell shall have a thickness es, for a minimum length ls adjacent to the
tubesheet, given by:
l s  1, 4
D s
 es  es
(13.5.2-8)
The effective shell lengths (l1,l'1) adjacent to the tubesheets are measured as shown in Figure 13.5.9-1.
Welds are allowed on these lengths. See 9.7.2.1 if the shell has an opening close to the tubesheets.
222
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) The shell may be fitted with an expansion bellows provided that the extremities of the bellows
are located at a distance from the tubesheets at least equal to 1, 4 D s  e s   e s .
13.5.2.4 Channel
a) The inside diameters
Ds
and
Dc
of the shell and channel shall be such that:
— for configuration a:
(13.5.2-9)
0 ,9 D s  D c  1,1 D s
— for configurations b and c:
(13.5.2-10)
0 ,9 D s  G c  1,2 D s
— for configuration d:
(13.5.2-11)
0 ,9 G s  G c  1,1 G s
b) When the channels are integral with the tubesheets (configuration a), they shall be cylindrical
and of constant thickness ec, for a minimum length lc adjacent to the tubesheets, given by:
l c  1, 4
D c
 ec  ec
(13.5.2-12)
The effective channel lengths adjacent to the tubesheets are measured as explained in 13.5.2.3 a). Welds
are allowed on these lengths. See 9.7.2.1 if the shell has an opening close to the tubesheets.
13.5.2.5 Loading
This clause covers heat exchangers subjected to:
— Tube-side pressure
Pt
and shell-side pressure
— Loads resulting from the thermal expansion

Ps
, which are assumed to be uniform in each circuit.
.
Other loadings, such as weight or pressure drop, are not considered.
13.5.3 Symbols
Dc
De
is the inside channel diameter (see Figure 13.5.1-1);
is the effective diameter of tubesheet, given by Formulae (13.5.4-1) to (13.5.4-4);
DJ
is the inside diameter of expansion bellows convolutions (this diameter DJ corresponds to diameter Di in
Ds
Figure 14.1-1);
is the inside shell diameter (see Figure 13.5.1-1);
is the equivalent diameter of outer tube limit circle, given by Formula (13.7.5-1);
Do
D
dt
*
is the equivalent bending rigidity of tubesheet, given by Formula (13.7.9-1);
is the nominal outside diameter of tubes (see Figure 13.7.3-3);
UNI EN 13445-3:2021
223
EN 13445-3:2021 (E)
Issue 1 (2021-05)
E
E
c
E
s
E
t
*
E
e
ec
es
et
Fi
Fq
f
is the elastic modulus of tubesheet material at design temperature;
is the elastic modulus of channel material at design temperature;
is the elastic modulus of shell material at design temperature;
is the elastic modulus of tube material at design temperature;
is the effective elastic modulus of the tubesheet at design temperature, see 13.7;
is the tubesheet thickness (see Figure 13.7.3-3);
is the channel thickness (see Figure 13.5.1-1);
is the shell thickness (see Figure 13.5.1-1);
is the nominal tube wall thickness (see Figure 13.7.3-3);
is a coefficient given as a function of X, for different values of Z (see Figures 13.5.6-1 and 2);
is a coefficient given as a function of X, for different values of Z (see Figures 13.5.4-1 and 2);
f t, bk
is the nominal design stress of tubesheet material at design temperature;
is the nominal design stress of channel material at design temperature;
is the nominal design stress of shell material at design temperature;
is the nominal design stress of tube material at design temperature;
is the maximum permissible buckling stress of the tubes;
f t, j
is the maximum permissible tube to tubesheet joint stress;
Gc
is the diameter of channel gasket load reaction (see Clause 11);
is the diameter of shell gasket load reaction (see Clause 11);
is the coefficient given as a function of X, for different values of Z (see Figures 13.5.5-1 and 2);
is the effective depth of tube-side pass partition groove, see 13.7;
fc
fs
ft
Gs
H
'
hg
J
is the ratio of expansion bellows to shell axial rigidity, given by Formula (13.5.4-11);
J = 1.0 if there is no expansion bellows;
KJ
is the axial rigidity of expansion bellows (see Clause 14);
K
s
224
is the shell axial rigidity, given by Formula (13.5.4-8);
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
K
s, t
K
t
K
w
kc
ks
L
Lt
N
t
Pe
Ps
Pt
T s, m
is the ratio of shell to tube-bundle axial rigidity, given by Formula (13.5.4-9);
is the tube axial rigidity, given by Formula (13.5.4-7);
is the modulus of the elastic foundation equivalent to the tube-bundle, given by
Formula (13.5.4-10);
is the edge moment per unit length required to rotate the channel edge through unit angle, given
by Formula (13.5.4-15);
is the edge moment per unit length required to rotate the shell edge through unit angle, given by
Formula (13.5.4-13);
is the tube length between inner tubesheet faces, given by Formula (13.5.4-4);
is the tube length between outer tubesheet faces (see Figure 13.5.1-1);
is the number of tubes;
is the effective pressure acting on tubesheet, given by Formula (13.5.4-18);
is the shell-side calculation pressure. In case of vacuum, this shall be taken as negative;
is the tube-side calculation pressure. In case of vacuum, this shall be taken as negative;
is the mean shell metal temperature along shell length, in °C;
T t, m
is the mean tube metal temperature along tube length, in °C;
w
is the height of the expansion bellows (see Clause 14);
J
X
xs
xt
Z

s ,m

t,m



*
is the tube-bundle to tubesheet rigidity factor, given by Formula (13.5.4-12);
is the tubesheet drilling coefficient on shell-side, given by Formula (13.5.4-5);
is the tubesheet drilling coefficient on tube-side, given by Formula (13.5.4-6);
is the tubesheet edge restraint coefficient due to shell and channel, given by
Formula (13.5.4-17);
is the mean thermal expansion coefficient of shell material at temperature T s, m ;
is the mean thermal expansion coefficient of tube material at temperature T t, m ;
is the axial differential thermal expansion between tubes and shell, given by
Formula (13.5.4-19);
is the basic ligament efficiency of the tubesheet (see 13.7);
is the effective ligament efficiency of the tubesheet (see 13.7);
UNI EN 13445-3:2021
225
EN 13445-3:2021 (E)
Issue 1 (2021-05)
is the Poisson's ratio of channel material;
is the Poisson's ratio of shell material;
is the Poisson's ratio of tube material;
c
s


t
is the effective Poisson's ratio of tubesheets (see 13.7);
is the calculated stress in a component;
is the calculated shear stress in a component.
*


Subscripts:
b
for bending;
c
for channel;
eq
for equivalent;
J
for expansion bellows;
m
for membrane;
p
for periphery;
s
for shell;
t
for tubes;
No subscript is used for the tubesheet.
13.5.4 Design considerations
13.5.4.1 Loading conditions
It is necessary to evaluate all the anticipated loading conditions to ensure that the worst load combination is
considered in the design.
NOTE
It is generally not possible to determine, by observation, the most severe condition of coincident
pressures P t and P s and thermal expansion  .
The various loading conditions to be considered shall include the normal operating conditions, the start-up
conditions, the shut-down conditions, the upset and the pressure test conditions, which may govern the
design of the main components of the heat exchanger (i.e. tubesheets, tubes, shell, channel).
For each of these conditions the following loading cases shall be considered to determine the effective
pressure P e to be used in the design formulas:
— loading case 1: Tube-side pressure
Pt
acting only  P s
 0  , without thermal expansion    0  .
— loading case 2: Shell-side pressure
Ps
acting only  P t
 0  , without thermal expansion    0  .
— loading case 3: Tube-side pressure P t and shell-side pressure
thermal expansion    0  .
Ps
acting simultaneously, without
— loading case 4:
Thermal expansion

acting only  P t
 0 , Ps  0  .
— loading case 5:
Tube-side pressure
Pt
acting only  P s
 0  , with thermal expansion 
226
.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— loading case 6:
Shell-side pressure
Ps
acting only  P t
— loading case 7: Tube-side P t and shell-side
expansion  .
Ps
 0  , with thermal expansion 
.
pressures acting simultaneously, with thermal
If loading cases 1, 2, 5, 6 cannot occur in service, the design may be based on loading cases 3, 4 and 7 only.
For pressure test conditions, only the loading cases where
  0
shall be studied (cases 1, 2 and 3).
See Annex I for more details on the loading cases to be studied.
13.5.4.2 Design conditions
a) The design shall be performed in the corroded condition, except for the tubes for which the
nominal outside diameter d t and the nominal thickness e t shall be used.
b) As the calculation procedure is iterative, a value e shall be assumed for the tubesheet thickness to
calculate and check that the maximum stresses in tubesheets, tubes, shell and channel are within
the maximum permissible stresses. Two cases are possible:
— If the calculated stress of the component is within the permissible stress, the calculations may
be repeated using a lower thickness of the component until the calculated stress is equal to the
permissible stress in order to obtain the minimum required thickness.
— If the calculated stress of the component exceeds the permissible stress, the calculations shall
be repeated using a higher thickness of the component (or modifying other parameters), untill
the calculated stress is within the permissible stress.
When tubesheets are integral with the shell (configurations a, b, c), an alternative solution is to increase the
shell thickness adjacent to the tubesheet, as detailed in 13.5.9.
NOTE
The designer should note that any increase or decrease of thickness in a component will modify the
stresses not only in this component, but also in other components.
c) Because any increase of tubesheet thickness may lead to overstresses in tubes, shell or channel, a
final check shall be performed, using in the formulae the analysis thicknesses of tubesheets,
tubes, shell and channel.
13.5.4.3 Determination of intermediate coefficients
a) Effective elastic constants of tubesheet. From 13.7, calculate:
— The diameter of the perforated tubesheet area,
UNI EN 13445-3:2021
Do
227
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— The basic ligament efficiency,

— The effective ligament efficiency,

*
— The effective elastic modulus, E *
—
The Poisson's ratio,  *
Values of
, E * ,  * shall be determined for the assumed tubesheet thickness, e.
*

b) Effective tubesheet diameter
— For configuration a:
De 
Ds  Dc
(13.5.4-1)
2
— For configurations b and c:
De 
Ds  Gc
(13.5.4-2)
2
— For configuration d:
De 
Gs  Gc
(13.5.4-3)
2
c) Effective tube length:
(13.5.4-4)
L  Lt  2 e
d) Tubesheet drilling coefficients:
xs  1 N
xt  1 N
2
t
 dt

D
 e




t
d



 2 et 


De

t
(13.5.4-5)
2
(13.5.4-6)
e) Axial rigidities:
Kt 
Ks 
K s ,t 
228
 e t  d t  e t   E t
L
 e s  D s  e s   E s
L
Ks
N
t
K
(13.5.4-7)
(13.5.4-8)
(13.5.4-9)
t
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
K

w
8 Nt K
(13.5.4-10)
t
2
π De
1
J 
1 
(13.5.4-11)
Ks
KJ
f) Tube-bundle to tubesheet rigidity ratio:
Kw 
X  

*
 D 
0 , 25
De

(13.5.4-12)
2
g) Bending rigidities
— For shell:
— configurations a, b, c:
2 E s  e s
ks 
12 1   
0 , 75
2
s
2 ,5
 D s  e s

(13.5.4-13)
0 ,5
— configuration d:
(13.5.4-14)
ks  0
— For channel:
— configuration a:
kc 
2 E c  e c
12 1   
2
0 , 75
c

2 ,5
 D c  ec

(13.5.4-15)
0 ,5
— configurations b, c, d:
(13.5.4-16)
kc  0
h) Tubesheet edge restraint factor due to shell and channel:
ks  kc
Z 
K w 
NOTE
0 ,2 5
 
 D
*
(13.5.4-17)
0 ,7 5
for low values of Z (close to 0):
the tubesheet is essentially simply supported;
for high values of Z (higher than 5):
the tubesheet is essentially clamped.
13.5.4.4 Effective pressure
Pe
The effective pressure accounting for the pressures
UNI EN 13445-3:2021
Pt
and
Ps
and thermal expansion, is given by:
229
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Pe 


J K
1 J K
J K
1 J K
J K
1 J K
s,t
s,t
s,t
s,t
 Fq
s,t
s,t
 Fq
 Fq

 xs  2


 xt  2

t
t
 1  x s  
 1  x t  
2
K
1
J K
s,t
s

s,t
1 J
2 J K

s,t
D J
 2w
J
2
Ds
2
2
 Ds 
  Ps


  Pt

 Kw 

 
 2 
(13.5.4-18)
where
 
  t, m  T t, m
 20  C   
s, m
 T s, m  20  C
  L
(13.5.4-19)
13.5.5 Tubesheet design
13.5.5.1 Bending stress
a) The maximum radial bending stress in the tubesheet is given by:
 1,5 F
m
  
*

 
Fm 




 D
e


e  h'
g





2
(13.5.5-1)
 Pe
1
(13.5.5-2)
6 H
NOTE
The minimum tubesheet bending stress is obtained when Z value is close to 0,52. This value can be
achieved by modifying the shell or channel thickness nearby the tubesheet (see 13.5.9).
b) The calculated stress

shall be checked against the permissible stress as follows.
1) When the tubesheet is extended as a flange (configuration b):
— For each of the loading cases considered, the tubesheet stress  due to pressures ( P t and
acting only (i.e. calculated using   0 in Pe ) shall not exceed 1,5 f :

 1,5 f
Ps
)
(13.5.5-3)
— For each of the normal operating loading cases considered, the tubesheet stress  due to
pressures ( P t and Ps ) and thermal expansion    acting simultaneously shall not exceed 2,25 f
:
  2 ,2 5 f
(13.5.5-4)
— The flange extension thickness shall be calculated according to:
— 13.10 if the gasket is narrow,
— 13.11 if the gasket is full face.
230
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
2) When the tubesheet is not extended as a flange (configurations a, c and d):
— For each of the loading cases considered, the tubesheet stress  due to pressures ( P t and
acting only (i.e. calculated using   0 in Pe ) shall not exceed 2 f :
Ps
)
(13.5.5-5)
  2 f
— For each of the normal operating loading cases considered, the tubesheet stress  due to
pressures ( P t and Ps ) and thermal expansion    acting simultaneously shall not exceed 3 f :
(13.5.5-6)
  3 f
c) If the above conditions are not fulfilled, assume a larger value of tubesheet thickness e and repeat
the calculations.
If the tubesheet is integral with the shell or channel (configurations a, b, c) it is also possible to increase
the thickness of these two components nearby the tubesheet, as explained in 13.5.9, especially if Z is
close to 0,5.
13.5.5.2 Shear stress
a) The maximum shear stress in the tubesheet is given by:
 1 


 4 
  
 Do
 
 e

  P e

(13.5.5-7)
b) For each of the loading cases, considered the shear stress  shall not exceed 0,8 f :
(13.5.5-8)
  0 ,8 f
13.5.6 Tube design
13.5.6.1 Axial membrane stress
a) The maximum axial stress in the tubes is given by:
— For the outer tube row:

t, o

1
xt  xs
 P
s
 x s  P t  x t  - P e  Fq

(13.5.6-1)
— For the inner tube rows:

t,i

1
xt  xs
  Ps
 x s  P t  x t  - P e  Fi

(13.5.6-2)
b) For each of the loading cases considered, the absolute value of these stresses shall not exceed the
maximum permissible tube-to-tubesheet joint stress f t, j , given in 13.8:

t,o
 f t, j
UNI EN 13445-3:2021
(13.5.6-3)
231
EN 13445-3:2021 (E)
Issue 1 (2021-05)

t, i
 f t, j
(13.5.6-4)
c) For each of the loading cases for which  t, o or  t, i are negative (tubes in compression), the
absolute value of these stresses shall not exceed the maximum permissible buckling stress limit
f t, bk of the tubes, given in 13.9:

t,o

t,i
(13.5.6-5)
 f t,b k
(13.5.6-6)
 f t,b k
13.5.6.2 Equivalent stress
a) The maximum equivalent stress in the tubes is given by:

t, eq
 max

t, i

t, 
; 
t, i

t, r
; 
t, 

t, r
; 
t, o

t, 
; 
t, o

t, r

(13.5.6-7)
where

t, 
is the mean circumferential stress in the tubes:

t, 


t,r
is the mean radial stress in the tubes:

t,r
 
P t  d t  2 e t   Ps  d t
(13.5.6-8)
2 et
P t  Ps
(13
2
b) For each of the loading cases considered, the equivalent stress
acting only (i.e. calculated using

t, eq
  0 in P e
t, eq
ft
t, e q
due to pressures
P t and P s
:
(13.5.6-10)
 ft
— For each of the loading cases where

) shall not exceed

  0
, the equivalent stress 
t, e q
shall not exceed 1,5
ft
:
(13.5.6-11)
 1,5 f t
13.5.7 Shell design
13.5.7.1 Shell design far from tubesheets
13.5.7.1.1 Axial membrane stress
a) The axial membrane stress in the shell is given by:
2

232
s, m

Ds
4 e s D s  e s

 P t  P e

(13.5.7-1)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) For each of the loading cases for which  s , m is negative (shell in compression), its absolute value
shall not exceed the permissible buckling stress of the shell, f s, bk :

s ,m
(13.5.7-2)
 f s ,b k
where
f s ,b k  K 
es E
4
D s
(13.5.7-3)
s
 es

where
K = 1,0
for normal operating conditions.
K = 1,35
for exceptional operating conditions and pressure test conditions.
13.5.7.1.2 Equivalent stress
a)
The maximum equivalent stress is given by:

s,eq
 m ax


s ,m
 
s ,
;

s ,m
 
s ,r

;
s ,
 
s ,r

(13.5.7-4)
where
is the mean circumferential stress in the shell

s ,

s ,

s ,r
is the mean radial stress in the shell:

s ,r
 

Ps  D s
(13.5.7-5)
2 es
Ps
(13.5.7-6)
2
b) For each of the loading cases considered, the equivalent stress
acting only (i.e. calculated using

s, eq
  0
s, eq
Pe
) shall not exceed
s,eq
due to pressure
P t and P s
fs :
(13.5.7-7)
 fs
c) For each of the loading cases where

in

  0
,

s,eq
shall not exceed 1,5
fs :
 1,5 f s
(13.5.7-8)
13.5.7.2 Shell design at its junction with the tubesheets
This subclause applies only when the shell is integral with the tubesheets (configurations a, b, c).
UNI EN 13445-3:2021
233
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.5.7.2.1 Axial bending stress
The maximum axial bending stress in the shell at its junction with the tubesheet is given by:

s, b

ks
ks  kc

1
I1
 De

2 e
s





2
(13.5.7-9)
 Pe
where
*
 

2
1  

 F q ,     1 
I1  H   

X  Z

  X  Z







(13.5.7-10)
where
H
and
F q, 
are the values of coefficients H and
Fq
for
Z  
(see Figures 13.5.5-1 and 13.5.4-1).
13.5.7.2.2 Equivalent stress
a)
The maximum equivalent stress in the shell at its junction with the tubesheets is given by:

s , e q ,1
 m ax


s ,m
 
s ,b
 Ps ; 
s ,m
 
s ,b

(13.5.7-11)
where

s, m
is given by Formula (13.5.7.-1)
b) For each of the normal operating loading cases considered,


s , e q ,1
shall not exceed
3 fs
(13.5.7-12)
 3 fs
s, eq,1
:
NOTE
If this condition is not fulfilled, an option is to increase the thickness of the shell adjacent to the
tubesheets, as explained in 13.5.9.
13.5.8 Channel design at its junction with the tubesheet
This subclause applies only when the channel is integral with the tubesheet (configuration a).
13.5.8.1 Axial membrane stress
The axial membrane stress in the channel is given by:
2

234
c ,m

Dc
4 ec
D c
 ec

 Pt
(13.5.8-1)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.5.8.2 Axial bending stress
The maximum axial bending stress in the channel at its junction with the tubesheet is given by:

c, b

kc

ks  kc
1
I1
 De

2 e
c





2
(13.5.8-2)
Pe
where
II
is given by Formula (13.5.7-10).
13.5.8.3 Equivalent stress
a)
The maximum equivalent stress in the channel at its junction with the tubesheet is given by:

c , e q ,1
 m ax


c ,m
 
c ,b
 Pt ; 
c ,m
 
c ,b

b) For each of the normal operating loading cases considered,

c, eq,1
(13.5.8-3)

c , e q ,1
shall not exceed
3 fc
:
 3 fc
(13.5.8-4)
13.5.9 Shell with different thickness or different material adjacent to the tubesheet
13.5.9.1 Purpose
This subclause describes how to use the rules of 13.5 when the shell has a different thickness and/or
different material adjacent to the tubesheets (see Figure 13.5.9-1) in order to:
— fulfil the stress conditions relative to tubesheet, shell, or channel when these components are
overstressed;
— decrease the tubesheet thickness;
— modify the edge restraint factor Z, so as to get a value close to 0,52, which will minimise the
bending stress  in the tubesheet. This leads to an optimum design of the tubesheet thickness if
iterative calculations are performed using formulae of 13.5.5.1;
— solve the problem of incompatible shell and tubesheet materials.
13.5.9.2
Conditions of applicability
This subclause applies only when the shell is integral with the tubesheet (configurations a, b, c).
This clause shall be applied in addition to Clauses 13.5.1 to 13.5.8.
The shell portions adjacent to the tubesheets shall have the same diameter, the same uniform thickness and
the same material.
UNI EN 13445-3:2021
235
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Their lengths
l1
'
and
D s
l s,1  1, 4
l1
, which may be different, shall be at least equal to:
 e s,1   e s,1
(13.5.9-1)
(2)
(1)
(1)
Key
(1) Configuration a, b or c
(2) Slope < 1/3
Figure 13.5.9-1  Shell with increased thickness adjacent to the tubesheets
13.5.9.3 Additional symbols
The following symbols are in addition to those in 13.5.3.
E s,1
is the elastic modulus of shell material adjacent to tubesheets at design temperature;
e s,1
is the thickness of shell adjacent to tubesheets;
f s,1
is the nominal design stress of the shell material adjacent to the tubesheets;
l1
,
l '1
K
*
s
is the equivalent axial rigidity of the shell, given by Formula (13.5.9-2);

s , m ,1
is the mean thermal expansion coefficient of shell material adjacent to tubesheets at temperature
are the lengths of shell of thickness
T s, m

e s,1
adjacent to tubesheets (see Figure 13.5.9-1);
;
*
is the axial differential thermal expansion between tubes and shell, given by Formula (13.5.9-3).
13.5.9.4 Design calculations
The calculations shall be performed according to 13.5.4 to 13.5.8, accounting for the following modifications:
a)
In Formula (13.5.4-11) giving J and Formula (13.5.4-9) giving
K
*
s

 D s  e s
L  l1 es  E
236
'
l1
s
K s, t
, replace
K
s
by
K
*
s
, where:

'

l1 + l1
e s,1  E
s,1
(13.5.9-2)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) In Formula (13.5.4-13) giving
—
es
by
e s ,1
—
Es
by
E s ,1 .
,
c) In Formula (13.5.4-8) giving

*
k s , replace:
Pe
, replace
 T t, m  20  C   t, m  L  T s, m  20  C
d) In 13.5.7.2 replace
es
by
e s,1
and
fs

by
  s, m
by

*
L  l
, where:
'
1

 l 1   s, m,1
l
'
1
 l1

(13.5.9-3)
f s,1
13.5.10 Treatment of configurations with a full face gasket
13.5.10.1 Scope
This subclause applies to the following configurations where the tubesheet is gasketed with the shell and/or
channel with a full face gasket (see Figure 13.5.10-1):
— Configuration b': tubesheet integral with shell and gasketed with channel;
— Configuration d': tubesheet gasketed with shell and channel, not extended as a flange.
Configuration b'
Configuration d'
Figure 13.5.10-1  Tubesheet with a full face gasket (configurations b', d')
13.5.10.2 Conditions of applicability
The conditions of applicability given in 13.5.2 apply, considering the gasketed shell and/or channel as
integral with the tubesheet.
13.5.10.3 Design rule
The design shall be performed according to 13.5.4 to 13.5.8, with the following modifications in 13.5.4.3 g:
a)
The shell, when gasketed with the tubesheet (configuration d') shall be considered as integral
with the tubesheet, using for k s :
ks 
1
2 E
2
12 1   
UNI EN 13445-3:2021
2
s
2,5
s
 es
0 , 75
D s
 es
 0 ,5
(13.5.10-1)
237
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) The channel, when gasketed with the tubesheet (configurations b', d') shall be considered as
integral with the tubesheet, using for k c :
kc 
1
2 E
2
12 1   
2
c
2,5
c
 ec
0 , 75
D c
 ec
 0 ,5
(13.5.10-2)
13.5.9 is not applicable.
238
UNI EN 13445-3:2021
UNI EN 13445-3:2021
(2) For X  5 : see Figure 13.5.4-2
(1) For X  5
Key
(2)
(1)
Figure 13.5.4-1  Curves for determination of coefficient
Fq
for
0  X  20

239
EN 13445-3:2021 (E)
Issue 1 (2021-05)
240
Values of coefficients
Fq
Figure 13.5.4-2  Curves for determination of coefficient
for X < 5 are given by Table 13.5.4-1
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Fq
for
0 X 5
UNI EN 13445-3:2021
UNI EN 13445-3:2021
(1) For X > 5
(2) For X < 5 :see Figure 13.5.5-2
(2)
(1)
Figure 13.5.5-1  Curves for determination of coefficient H for
0  X  20

241
EN 13445-3:2021 (E)
Issue 1 (2021-05)
242
EN 13445-3:2021 (E)
Issue 1 (2021-05)
UNI EN 13445-3:2021
UNI EN 13445-3:2021
Figure 13.5.5-2  Curves for determination of coefficient H for
Values of coefficient H for X < 5 are given by Table 13.5.5-1
0 X 5
243
EN 13445-3:2021 (E)
Issue 1 (2021-05)
244
Values of coefficient
Fi
(2)
(1)
Fi    i  X   i
Figure 13.5.6-1  Curves for determination of coefficient
for X < 13 are given by Table 13.5.6-1
(2) For X  5 : see Figure 13.5.6-2
(1) For X > 13
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Fi
for
0  X  20
UNI EN 13445-3:2021
Fi
Figure 13.5.6-2  Curves for determination of coefficient
for X < 5 are given by Table 13.5.6-1
UNI EN 13445-3:2021
Values of coefficient
Fi
for
0 X 5
245
EN 13445-3:2021 (E)
Issue 1 (2021-05)
246
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 13.5.4-1  Values of coefficient
Fq
for X < 5
UNI EN 13445-3:2021

UNI EN 13445-3:2021
Table 13.5.5-1  Values of coefficient H for X < 5

247
EN 13445-3:2021 (E)
Issue 1 (2021-05)
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 13.5.6-1  Values of coefficient
Fi
for
X  13

248
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.6 Floating tubesheet heat exchangers
13.6.1
a)
Scope
This clause provides rules for the design of floating tubesheet heat exchangers that have two
tubesheets connected by a bundle of straight tubes, as shown in Figure 13.6.1-1:
— one stationary tubesheet attached to the shell and channel;
— one floating tubesheet.
Three types of heat exchangers are considered (see Figure 13.6.1-1):
— immersed floating head;
— externally sealed floating head,
— internally sealed floating tubesheet.
Immersed and externally floating types are covered in 13.6.1b to 13.6.9. Internally sealed type is
covered in 13.6.10.
b) The stationary tubesheet may have one of the six configurations shown in Figure 13.6.1-2:
—
configuration a:
tubesheet integral with shell and channel.
—
configuration b:
tubesheet integral with shell and gasketed with channel, extended as a
flange.
—
configuration c:
tubesheet integral with shell and gasketed with channel, not extended as
a flange.
—
configuration d:
tubesheet gasketed with shell and channel, not extended as a flange.
—
configuration e:
tubesheet gasketed with shell and integral with channel, extended as a
flange.
—
configuration f:
tubesheet gasketed with shell and integral with channel, not extended as
a flange.
The floating tubesheet may have one of the 3 configurations shown in Figure 13.6.1-3:
— configuration A:
tubesheet integral;
— configuration B:
tubesheet gasketed, extended as a flange;
— configuration C:
tubesheet gasketed, not extended as a flange.
c) 13.6.2 to 13.6.8 apply to configuration a (where the stationary tubesheet is integral) and to
configurations b, c, d, e, f, where the gasketed tubesheet has a narrow gasket.
13.6.9 outlines how to use these rules for configurations b', d', e' where the gasketed tubesheet has
a full face gasket.
UNI EN 13445-3:2021
249
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(1)
(1) Stationary tubesheet, configuration a, b, c, d, e or f
a)
(2) Floating tubesheet, configuration A, B, or C
Floating tubesheet exchanger with an immersed floating head
(1)
(1) Stationary tubesheet, configuration a, b, c, d, e or f
b)
(2)
(2)
(2) Floating tubesheet, configuration C
Floating tubesheet exchanger with an externally sealed floating head
(1)
(1) Stationary tubesheet, configuration a, b, c, d, e or f
c)
Floating tubesheet exchanger with an internally sealed floating tubesheet
Figure 13.6.1-1 ― Typical floating tubesheet heat exchangers
250
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Configuration a
b) Configuration b
c) Configuration c
Tubesheet integral with
shell and channel
Tubesheet integral with shell
and gasketed with channel,
extended as a flange
Tubesheet integral with shell
and gasketed with channel, not
extended as a flange
d) Configuration d
e) Configuration e
Tubesheet gasketed with
shell and channel, not
extended as a flange
Tubesheet gasketed with
shell and integral with
channel, extended as a flange
f) Configuration f
Tubesheet gasketed with
shell and integral with
channel, not extended as a
flange
Figure 13.6.1-2 — Stationary tubesheet configurations
UNI EN 13445-3:2021
251
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Configuration A: Tubesheet integral
b) Configuration B: Tubesheet gasketed, extended as a flange
c) Configuration C: Tubesheet gasketed, not extended as a flange
Figure 13.6.1-3 ― Floating tubesheet configurations
13.6.2
13.6.2.1
Conditions of applicability
Tubesheets
The tubesheets shall comply with the following conditions of applicability:
a) The two tubesheets shall be flat, circular, of same uniform thickness and same material;
b) The effective tubesheet diameters of the stationary tubesheet,
diameter, D e, f , shall be such that:
De
, and floating tubesheet
0 , 9 D e  D e, f  1 ,1 D e
where the effective diameter
D e, f
is (see Figure 13.6.2-2):
— for configurations B and C: the gasket load reaction diameter of the floating tubesheet:
252
D e, f  G f
;
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— for configuration A: the inside diameter
D e, f  D f ;
Df
of the channel attached to the floating tubesheet:
c) A local reduction of thickness at the periphery of the tubesheet for a gasket groove or a relief
groove is permitted, provided that the remaining analysis thickness, e a, p , is at least equal to 0,8
times the assumed thickness, e, of the tubesheet (see Figures 13.6.2-1 and 2):
(13.6.2-1)
e a, p  0 , 8 e
The radius shall be not less than 5 mm and not less than 20 % of the adjacent shell thickness. The
requirement for the remaining analysis thickness given above shall apply only if the ratio of the outside
diameter to inside diameter of the adjacent shell is larger than 1,2.
a) Configuration a
b) Configurations b and e
c) Configuration d
d) Configurations c and f
Figure 13.6.2-1 — Local reduction of thickness at stationary tubesheet periphery
UNI EN 13445-3:2021
253
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Configuration A
b) Configuration B
c) Configuration C
Figure 13.6.2-2 — Local reduction of thickness at floating tubesheet periphery
d) When the tubesheets are extended as a flange, the flange extension thickness, shall be calculated
according to:
— 13.10 if the gasket is narrow (configurations b, d, e)
— 13.11 if the gasket is full face (configurations b', d', e')
e) Unless satisfactory experience has been demonstrated with thinner tubesheets, the following
conditions shall be met when the tubes are expanded into the tubesheet:
— when
ea 
dt
 25 mm:
0,75 d t
— when 25 mm 
ea 
f)
 30 mm:
(13.6.2-3)
dt
 40 mm:
25 mm
— when 40 mm 
ea 
dt
22 mm
— when 30 mm 
ea 
(13.6.2-2)
(13.6.2-4)
dt
 50 mm:
30 mm
(13.6.2-5)
The tubesheets shall be uniformly perforated over a nominally circular area of diameter
either equilateral triangular or square pattern.
Do
, in
Unperforated diametral rows are permitted for pass partitions provided that the distance between
254
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
adjacent rows
UL
(see Figure 13.7.3-1) is such that:
(13.6.2-6)
UL  4p
where p is the tube pitch.
g) An unperforated annular ring is permitted provided that:
(13.6.2-7)
D o  0 , 85 D e
13.6.2.2
Tubes
a) The tubes shall be straight and identical (i.e. same uniform thickness, same material and same
diameter).
b) They shall be rigidly attached to the tubesheets.
13.6.2.3
Shell
a) The shell shall be cylindrical at its junction with the tubesheet.
b) The shell shall be cylindrical, and of uniform thickness and diameter.
For configurations a, b and c, the shell shall have a thickness es, for a minimum length ls adjacent to the
tubesheet, given by:
l s  1, 4
D s
(13.6.2-8)
 es  es
The effective shell length (l1) adjacent to the stationery tubesheet is measured as shown in Figure 13.5.9-1.
Welds are allowed on these lengths. See 9.7.2.1 if the shell has an opening close to the tubesheets.
13.6.2.4
Channel
a) The channel shall be cylindrical at its junction with the tubesheet.
b) The diameters
Ds
,
Gs
and
Dc
,
Gc
of the shell and channel shall be such that:
— for configuration a:
0 , 9 D s  D c  1 ,1 D s
(13.6.2-9)
— for configurations b and c:
0 , 9 D s  G c  1 ,2 D s
(13.6.2-10)
— for configuration d:
0 , 9 G s  G c  1 ,1 G s
(13.6.2-11)
— for configurations e and f:
0 , 9 G s  D c  1 ,1 G s
UNI EN 13445-3:2021
(13.6.2-12)
255
EN 13445-3:2021 (E)
Issue 1 (2021-05)
c) When integral with the stationary tubesheet (configurations a, e, f), the channel shall have a
thickness ec, for a minimum length lc adjacent to the stationery tubesheet, given by:
l c  1, 4
D c
 ec
(13.6.2-13)
 ec
The effective channel length adjacent to the stationery tubesheet is measured as explained in 13.5.2.3
a). Welds are allowed on these lengths. See 9.7.2.1 if the shell has an opening close to the tubesheets.
13.6.2.5
Loading
Tube-side pressure
Pt
and shell-side pressure
Ps
, are assumed to be uniform in each circuit.
Other loadings, such as weight or pressure drop, are not considered.
13.6.3
Symbols
Dc
is the inside channel diameter;
De
is the effective diameter of stationary tubesheet, given by 13.6.4-3b;
Ds
is the inside shell diameter;
Do
is the equivalent diameter of the outer tube limit circle, given by Formula (13.7.5-1);
*
D
is the equivalent bending rigidity of stationary tubesheet, given by Formula (13.7.9-1);
dt
is the nominal outside diameter of tubes (see Figure 13.7.3-3);
E
is the elastic modulus of tubesheet material at design temperature;
Ec
is the elastic modulus of channel material at design temperature;
Es
is the elastic modulus of shell material at design temperature;
Et
is the elastic modulus of tube material at design temperature;
E
*
is the effective elastic modulus of the tubesheet at design temperature, see 13.7;
e
is the thickness of the stationary tubesheet (see Figure 13.7.3-3);
ec
is the channel thickness;
es
is the shell thickness;
et
is the nominal tube wall thickness (see Figure 13.7.3-3);
256
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Fi
is a coefficient given by curves as a function of X, for different values of Z (see Figures 13.5.6-1 and 2);
Fm
is a coefficient given by Formula (13.6.5-2);
Fq
is a coefficient given by curves as a function of X, for different values of Z (see Figures 13.5.4-1 and 2);
f
is the nominal design stress of tubesheet material at design temperature;
fc
is the nominal design stress of channel material at design temperature;
fs
is the nominal design stress of shell material at design temperature;
ft
is the nominal design stress of tube material at design temperature;
Gc
is the diameter of channel gasket load reaction (see Clause 11);
Gs
is the diameter of shell gasket load reaction (see Clause 11);
H
is the coefficient given by curves as a function of X, for different values of Z (see Figures 13.5.5-1
and 2);
'
is the effective depth of tube-side pass partition groove, see 13.7;
hg
K
t
is the tube axial rigidity, given by Formula (13.6.4-7);
K
w
is the modulus of the elastic foundation equivalent to the tube-bundle, given by Formula (13.6.4-8);
kc
is the edge moment per unit length required to rotate the channel edge through unit angle, given by
Formula (13.6.4-11);
ks
is the edge moment per unit length required to rotate the shell edge through unit angle, given by
Formula (13.6.4-10);
L
is the tube length between inner tubesheet faces, given by Formula (13.6.4-4);
Lt
is the tube length between outer tubesheet faces;
Nt
is the number of tubes;
Pe
is the effective pressure acting on tubesheet, given by Formula (13.6.4-13) and Formula (13.6.4-14);
Ps
is the shell-side calculation pressure. In case of vacuum, this shall be taken as negative;
UNI EN 13445-3:2021
257
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Pt
is the tube-side calculation pressure. In case of vacuum, this shall be taken as negative;
X
is the tube-bundle to tubesheet rigidity factor, given by Formula (13.6.4-9);
xs
is the tubesheet drilling coefficient on shell-side, given by Formula (13.6.4-5);
xt
is the tubesheet drilling coefficient on tube-side, given by Formula (13.6.4-6);
Z
is the tube edge restraint coefficient due to shell and channel, given by Formula (13.6.4-12);

is the basic ligament efficiency of the tubesheet (see 13.7);
*

is the effective ligament efficiency of the tubesheet (see 13.7);
c
is the Poisson's ratio of channel material;
s
is the Poisson's ratio of shell material;

is the Poisson's ratio of tube material;

t
*
is the effective Poisson's ratio of tubesheet (see 13.7);

is the calculated stress in a component;

is the calculated shear stress in a component.
Subscripts:
b
for bending;
c
for channel;
eq
for equivalent;
m
for membrane;
p
for periphery;
s
for shell;
t
for tubes;
No subscript is used for the tubesheet.
258
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.6.4
Design considerations
13.6.4.1
Loading conditions - Design pressure
The various loading conditions to be considered shall include the normal operating conditions, the start-up
conditions, the shut-down conditions, the upset and the pressure test conditions which may govern the
design of the main components of the heat exchanger (i.e. tubesheets, tubes, shell, channel).
For each of these conditions it is necessary to account for the following loading cases to determine the
effective pressure P e (see 13.6.4.4) to be used in the design formulas:
— loading case 1 :
Tube-side pressure
Pt
acting only  Ps
 0;
— loading case 2 :
Shell-side pressure
Ps
acting only  P t
 0;
— loading case 3 :
Tube-side pressure
Pt
and shell-side pressure
Ps
acting simultaneously.
This loading case shall be always considered if vacuum exists on one side.
If loading cases 1 or 2 cannot occur in service, the design may be based on loading case 3 only.
13.6.4.2 Design conditions
a) The design shall be performed for corroded condition, except for the tubes for which the nominal
outside diameter d t and the nominal thickness e t shall be used;
b) The calculations shall be performed for the stationary tubesheet. The floating tubesheet shall
have same thickness as the stationary tubesheet;
c) As the calculation procedure is iterative, a value e must be assumed for the stationary tubesheet
thickness to calculate and check that the maximum stresses in tubesheets and tubes are within
the maximum permissible stresses. An initial assumed tubesheet thickness not less than that
given by the following formula is recommended:
e 
Do
4 μ  0 ,8 f

Pe
Two cases are possible:
— If the calculated stress of the component is within the permissible stress, the calculations may
be repeated using a lower thickness of the component until the calculated stress is equal to the
permissible stress in order to obtain the minimum required thickness.
— If the calculated stress of the component exceeds the permissible stress, the calculations shall
be repeated with a higher thickness of the component (or modifying other parameters) until
the calculated stress is within the permissible stress.
NOTE
The designer should note that any increase or decrease of thickness in a component will modify the
stresses not only in this component, but also in other components.
UNI EN 13445-3:2021
259
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.6.4.3
Determination of intermediate factors
a) Effective elastic constants of tubesheet. From 13.7, calculate:
— The diameter of the perforated tubesheet area,
— The basic ligament efficiency,
Do

— The effective ligament efficiency,

*
*
— The effective elastic modulus, E
— The Poisson's ratio,  *
Values of

*
*
, E ,  * shall be determined for the assumed tubesheet thickness, e.
b) Effective tubesheet diameter
— For configuration a:
De 
Ds  Dc
(13.6.4-1)
2
— For configurations b and c:
De 
Ds  Gc
(13.6.4-2)
2
— For configuration d:
De 
Gs  Gc
(13.6.4-3)
2
— For configurations e and f:
De 
Dc  Gs
2
c) Effective tube length:
(13.6.4-4)
L  Lt  2 e
d) Tubesheet drilling coefficients:
xs
 dt
 1 Nt 
D
 e
xt  1  N
260
t




 d



2
(13.6.4-5)
t
 2 et 


De

2
(13.6.4-6)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
e) Axial rigidities:
 e t  d t  e t   E t
Kt 
K
f)
8 N

w
(13.6.4-7)
L
t
K
(13.6.4-8)
t
2
 De
Tube-bundle to tubesheet rigidity ratio:



Kw
X  
*
 D
0 , 25
De

(13.6.4-9)
2
g) Bending rigidities:
— For shell:
— configurations a, b, c:
ks 
2 E s  e s


12 1  
2
s

0 ,7 5

2 ,5
 D s  e s

0 ,5

0 ,5
(13.6.4-10)
— configurations d, e, f:
ks  0
— For channel:
— configurations a, e, f:
kc 
2 E c  e c
 
12 1  
—
2
c

0 ,7 5

2 ,5
 D c  e c
(13.6.4-11)
configurations b, c, d:
kc  0
h) Tubesheet edge restraint factor due to shell and channel:
ks  kc
Z 
K w 
NOTE
0 ,2 5
 
 D
*
for low values of Z (close to 0)
:
for high values of Z (higher than 5) :
UNI EN 13445-3:2021
(13.6.4-12)
0 ,7 5
the tubesheet is essentially simply supported;
the tubesheet is essentially clamped.
261
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.6.4.4
Effective pressure
The effective pressure
Pe
Pe
due to pressures
Pt
and
Ps
acting on the stationary tubesheet is given by:
— For immersed floating head heat exchanger:
(13.6.4-13)
Pe  Ps  Pt
— For externally sealed floating head heat exchanger:
(13.6.4-14)
Pe   P t
13.6.5
Tubesheet design
13.6.5.1
Bending stress
a) The maximum radial bending stress in the tubesheet is given by:
 1,5 F
m
σ  
*

μ

Fm 
NOTE




 D
e

 e  h'
g





2
(13.6.5-1)
 Pe
1
(13.6.5-2)
6 H
The minimum tubesheet bending stress is obtained when Z value is close to 0,52.
b) For each of the loading cases considered, the bending tubesheet stress  shall not exceed:
— 2 f for stationary tubesheet configurations a, c, d, f coupled with floating tubesheet
configurations A or C (where neither the stationary nor the floating tubesheet are extended as
a flange):
(13.6.5-3)
  2 f
— 1,5 f for other configurations (where either the stationary or the floating tubesheet are
extended as a flange):
(13.6.5-4)
  1,5 f
The flange extension thickness shall be calculated according to:
— 13.10 if the gasket is narrow,
— 13.11 if the gasket is full face.
13.6.5.2
Shear stress
a) The maximum shear stress in the tubesheet is given by:
1 


4
  

  
262
D
o

 e


P
e


(13.6.5-5)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) For each of the loading cases considered, the shear stress  shall not exceed 0,8 f:
(13.6.5-6)
  0 ,8 f
13.6.6
Tube design
13.6.6.1
Axial membrane stress
a) The maximum axial stress in the tubes is given by:
— For the outer tube row:


t, o
1
xt  xs
 P s

 x s  Pt  x t   Pe  Fq
(13.6.6-1)
— For the inner tube rows:

t, i
1

xt  xs
 P s
 x s  Pt  x t   Pe  Fi
(13.6.6-2)

b) For each of the loading cases considered, the absolute value of these stresses shall not exceed the
maximum permissible tube-to-tubesheet joint stress limit, f t, j , given in 13.8:

t,o

t,i
(13.6.6-3)
 f t, j
(13.6.6-4)
 f t, j
c) For each of the loading cases for which

t, o
or

t, i
are negative, the absolute value of these stresses
shall not exceed the maximum permissible buckling stress limit

t,o

t,i
f t, bk
(13.6.6-5)
 f t,b k
(13.6.6-6)
 f t,b k
13.6.6.2
of the tubes, given in 13.9:
Equivalent stress
a) The maximum equivalent stress in the tubes is given by:

t, eq
 max

t, i
 
t, 
; 
t, i
 
t, r
; 
t, 
 
t, r
; 
t, o
 
t, 
; 
t, o
 
t, r

(13.6.6-7)
where:

t, 

t, 
is the mean circumferential stress in the tubes:

Pt
d t
UNI EN 13445-3:2021
 2 e t   Ps  d t
2 et
(13.6.6-8)
263
EN 13445-3:2021 (E)
Issue 1 (2021-05)

t, r
is the mean radial stress in the tubes:

t,r
 
P t  Ps
(13.6.6-9)
2
b) For each of the loading cases considered, the equivalent stress

t, eq
shall not exceed
ft
:
(13.6.6-10)
 ft
t, e q
13.6.7

Shell design at its junction with the stationary tubesheet
This subclause applies only when the shell is integral with the stationary tubesheet (configurations a, b, c).
13.6.7.1
Axial membrane stress
The axial membrane stress in the shell is given by:
2


s, m
13.6.7.2
Ds
4 e s D s  e s

 P t  P e

(13.6.7-1)
Axial bending stress
The maximum axial bending stress in the shell at its junction with the stationary tubesheet is given by:

s, b

ks
ks  kc

1
I1
 De

2 e
s





2
(13.6.7-2)
 Pe
where
*
 

2
1  

 F q ,     1 
I1  H   

X  Z

  X  Z
where
H
13.6.7.3
a)

and
F q, 
 
 

 
(13.6.7-3)
are the values of coefficients H and
Fq
for
Z 
Equivalent stress
The maximum equivalent stress in the shell at its junction with the stationary tubesheet is given
by:

s, eq
 max

s, m
 
s, b
 Ps ; 
s, m
 
s, b

b) For each of the normal operating loading cases considered,

264
(see Figures 13.5.5-1 and 13.5.4-1).
s, eq
 3 fs
(13.6.7-4)

s, eq
shall not exceed
3 fs :
(13.6.7-5)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.6.8
Channel design at its junction with the stationary tubesheet
This subclause applies only when the channel is integral with the stationary tubesheet (configurations a, e, f).
13.6.8.1
Axial membrane stress
The axial membrane stress in the channel is given by:
2


c ,m
13.6.8.2
Dc
4 ec
D c
 ec

(13.6.8-1)
 Pt
Axial bending stress
The maximum axial bending stress in the channel at its junction with the stationary tubesheet is given by:

c, b

kc
ks  kc

1
I1
 De

2e
c





2
(13.6.8-2)
Pe
where
*
 

2
1  

 F q ,     1 
I1  H   

X  Z

  X  Z
H
where
13.6.8.3
a)

and
F q, 







(13.6.8-3)
are the values of coefficients H and
Fq
for
Z 
(see Figures 13.5.5-1 and 13.5.4-1).
Equivalent stress
The maximum equivalent stress in the channel at its junction with the stationary tubesheet is
given by:

c, eq
 max

c, m
 
c, b
 Pt ; 
c, m
 
c, b

b) For each of the normal operating loading cases considered,

c, eq
13.6.9
13.6.9.1
(13.6.8-4)

c, eq,1
shall not exceed
3 fc :
(13.6.8-5)
 3 fc
Treatment of configurations with a full face gasket
Scope
This subclause applies to the following configurations where the integral tubesheet is gasketed with the shell
and/or channel with a full face gasket (see Figure 13.6.9-1):
— Configuration b'
tubesheet integral with shell and gasketed with channel;
— Configuration d': tubesheet gasketed with shell and channel, not extended as a flange;
— Configuration e': tubesheet gasketed with shell and integral with channel.
UNI EN 13445-3:2021
265
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Configuration b'
Configuration d'
Configuration e'
Figure 13.6.9-1  Tubesheet with full face gasket
(Configurations b', d', e',)
13.6.9.2
Conditions of applicability
The conditions of applicability given in 13.6.2 apply, considering the gasketed shell and/or channel as
integral with the tubesheet.
13.6.9.3
Design rule
The design shall be performed according to 13.6.3 to 13.6.8, with the following modifications in 13.6.4.3g:
a)
The shell, when gasketed with the stationary tubesheet (configurations d', e') shall be considered
as integral with the tubesheet, using for k s :
ks 
2,5
1
2 E
2
12 1   
2
s
s
 es
0 , 75
D s
 es
 0 ,5
(13.6.9-1)
b) The channel, when gasketed with the stationary tubesheet (configuration b', d') shall be considered
as integral with the tubesheet, using for k c :
kc 
2,5
1
2 E
2
12 1   
2
c
c
 ec
0 , 75
D c
 ec
 0 ,5
(13.6.9-2)
13.6.10 Internally sealed floating tubesheet heat exchanger
13.6.10.1 Scope
This subclause provides rules for the design of internally sealed floating tubesheet heat exchanger (see
Figure 13.6.1-1). This type of heat exchanger has two tubesheets:
— one stationary tubesheet attached to the shell and channel (configurations a, b, c, d, e, f – see
Figure 13.6.1-2);
— one internally sealed floating tubesheet (see Figure 13.6.1-1).
13.6.10.2 Conditions of applicability
— The tubesheets shall comply with conditions 13.6.2.1a, d, e and f.
— The tubes shall comply with conditions 13.6.2.2.
266
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— The shell shall comply with condition 13.6.2.3a.
— The channel shall comply with condition 13.6.2.4a.
— The loading shall comply with condition 13.6.2.5.
13.6.10.3 Tubesheet design
The stationary tubesheet shall have an analysis thickness e a determined from the application of the
conditions 13.6.2.1e, whether the tubes are expanded into the tubesheet or not.
The floating tubesheet shall have the same thickness as the stationary tubesheet.
13.6.10.4 Tube design
The tubes shall be designed according to 13.6.6, using in 13.6.6.1a:

t, o
 
t, i

Ps x s  Pt x t
xt  xs
(13.6.10-1)
13.7 Tubesheet characteristics
13.7.1
Purpose
This subclause provide rules to determine effective depth of tube-side pass partition groove, ligament
efficiencies and effective elastic constants of perforated tubesheets.
13.7.2
Conditions of applicability
a) The tubesheets shall be flat, circular and of uniform thickness.
b) They shall be uniformly perforated over a nominally circular area of diameter
Figure 13.7.3-1), in either equilateral triangular or square pattern (see Figure 13.7.3-4);
Do
(see
c) Unperforated diametrial rows are permitted for pass partitions provided that the distance
between adjacent tube rows, U L (see Figure 13.7.3-1), is such that U L is less than:
UL  4 p
13.7.3
(13.7.2-1)
Symbols
ct
is the tubesheet corrosion allowance on tube-side;
Do
is the equivalent diameter of outer tube limit circle (see Figure 13.7.3-1), given by Formula (13.7.51);
D
*
is the effective bending rigidity of tubesheet at design temperature, given by Formula (13.7.9-1);
dt
is the nominal outside diameter of tubes (see Figure 13.7.3-3);
d*
is the effective tube hole diameter, given by Formula (13.7.7-2);
E
is the elastic modulus of tubesheet material at design temperature;
UNI EN 13445-3:2021
267
EN 13445-3:2021 (E)
Issue 1 (2021-05)
E
t
*
E
is the elastic modulus of tube material at design temperature;
is the effective elastic modulus of perforated tubesheet at design temperature (see Figure 13.7.8-1
and 2);
e
is the tubesheet thickness (see Figure 13.7.3-3);
et
is the nominal tube wall thickness (see Figure 13.7.3-3);
f
is the nominal design stress of tubesheet material at design temperature;
ft
is the nominal design stress of tube material at design temperature;
hg
is the tube side pass partition groove depth (see Figure 13.7.3-2);
'
hg
is the effective tube side pass partition groove depth, given by Formula (13.7.5-2);
l t, x
is the expanded length of tube in tubesheet 0 
p
is the tube pitch;
*
p
l t, x  e  , (see
Figure 13.7.3-3);
is the effective tube pitch, given by Formula (13.7.7-4);
ro
is the radius to outermost tube hole centre (see Figure 13.7.3-1);
S
is the total area of untubed lanes (see Figure 13.7.3-5);
U
L

is the largest centre-to-centre distance between adjacent tube rows (see Figure 13.7.3-1);
is the basic ligament efficiency of perforated tubesheet for shear, given by Formula (13.7.6-1);

*
is the effective ligament efficiency of perforated tubesheet for bending, given by Formula (13.7.7-1);

*
is the effective Poisson's ratio of perforated tubesheet, (see Figure 13.7.8-1 and 2);
is the tube expansion depth ratio 0

13.7.4
   1  , given by Formula (13.7.7-3).
Design considerations
a) Values of  *, E * / E and  * shall be determined for the assumed thickness e of the tubesheet and
for the relevant value of  , which may be chosen as a constant, or calculated from e and l t, x .
b) The present rules apply to usual tube-to-tubesheet welded joint. For other types of joints,
see 13.12.
268
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Do
UL
p
ro
Figure 13.7.3-1  Tubesheet layout
hg
Figure 13.7.3-2  Definition of
Figure 13.7.3-3  Definition of
UNI EN 13445-3:2021
e
hg
l t,x
269
EN 13445-3:2021 (E)
Issue 1 (2021-05)
p
p
p
p
a) Triangular pitch
b) Square pitch
Figure 13.7.3-4  Tube pitch
U
L
UL
S
ro
S
U
ro
L
UL
Figure 13.7.3-5  Determination of area S
13.7.5
a)
Determination of the effective dimensions of the tubesheet
The diameter of the perforated tubesheet area is given by:
(13.7.5-1)
D o  2 ro  d t
b) The effective depth of the tube-side pass partition groove is given by:
'
h g  max
13.7.6
h g

 c t ;  0 ,0 

Determination of the basic ligament efficiency
(13.7.5-2)

for shear
The basic ligament efficiency of the tubesheet to be used in shear formula is given by:
 
270
p  dt
p
(13.7.6-1)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.7.7
Determination of the effective ligament efficiency

*
for bending
The effective ligament efficiency of the tubesheet to be used in bending formula is given by:

*
p

*
 d
p
*
(13.7.7-1)
*
where
— The effective tube hole diameter
d
*
d
 

 E t   ft 

 m a x  d t  2 e t 
       ;
 E   f 


 
*
is given by:
d t


 2 et 


(13.7.7-2)
where
l t, x
 
NOTE
(13.7.7-3)
e

may be
- either chosen as a constant
- or calculated from values of e and l t, x .

p
*
The effective pitch diameter p * is given by:
p

1 4
min
 S  ;  4 D o
(13.7.7-4)
p 
2
 Do
If there is no unperforated diametral row (S = 0):
p
*
 p
If there is only one diametral unperforated lane of width
p
*
L
(see Figure 13.7.3-1):
p

1
13.7.8
U
4U
(13.7.7-5)
L
 Do
Determination of the effective elastic constants
E
*
and  *
The effective elastic constants E * and  * of the tubesheet are given as a function of the effective ligament
efficiency  * , for various values of the ratio e / p :
— for equilateral triangular pattern, by Figure 13.7.8-1 a and b respectively;
— for square pattern,
by Figure 13.7.8-2 a and b respectively.
The thickness e to be used is the assumed tubesheet thickness used in the relevant rule.
UNI EN 13445-3:2021
271
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.7.9
Determination of the effective bending rigidity of the tubesheet
D
*
The effective bending rigidity of the tubesheet is given by:
D
*
E


*
e
3
12 1  
a)
E
*
*2
(13.7.9-1)

(equilateral triangular pattern)
/ E

b)
*
(equilateral triangular pattern)
Polynomial formulae given below can also be used.
NOTE
*
 These coefficients are only valid for 0 ,1    0 ,6 .
 For values of e/p lower
 For values of e/p higher
than 0,1, use e/p = 0,1.
than 2,0, use e/p = 2,0.
c) Equilateral triangular Pattern
e/p
0,10
0,25
0,50
2,00

0,0353
0,0135
0,0054
-0,0029
0,10
0,15
0,25
0,50
1,00
2,00

0
-0,0958
0,8897
0,7439
0,9100
0,9923
0,9966
*
/ E  

0
d) Equilateral triangular Pattern 
e / p
E
0
 
1
 
0
 

1,2502
0,9910
0,5279
0,2126
*
*
1
 1 
2

*2
 
3

*
 
2

1
0,6209
-9,0855
-4,4989
-4,8901
-4,8759
-4,1978
*2


*
 
3

*3
 
4


2
/ E
 
3
0,3604
-1,0498
-4,3657
-6,1730
-0,8683
36,1435
12,5779
12,4325
12,3572
9,0478
E
*3
2
-0,0491
1,0080
3,0461
3,9906
Figure 13.7.8-1  Curves for the determination of
272


*

*4

4
-0,6100
0,0184
1,9435
3,4307
*4
3
2,1099
-59,5425
-14,2092
-12,7039
-13,7214
-7,9955
and
4

4
-1,6831
35,8223
5,7822
4,4298
5,7629
2,2398
(equilateral triangular pattern)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a)
E
*
/ E
(square pattern)
b)

*
(square pattern)
Polynomial formulae given below can also be used.
NOTE
 These coefficients are only valid for 0 ,1 
μ
*
 0 ,6
.
 For values of e/p lower than 0,1, use e/p = 0,1.
 For values of e/p higher than 2,0, use e/p = 2,0.
e) Square Pattern
*
E /E 0 1 

e / p
f)
*
2 

0
*2
3 
*3

1
4 
*4

2

3
4
0,10
0,0676
1,5756
-1,2119
1,7715
-1,2628
0,25
0,0250
1,9251
-3,5230
6,9830
-5,0017
0,50
0,0394
1,3024
-1,1041
2,8714
-2,3994
2,00
0,0372
1,0314
-0,6402
2,6201
-2,1929
Square Pattern 
e/p
*
 

0
 1 
0
*
 
2

*2
 
1
3

*3
 
4


*4
2


3
4
0,10
-0,0791
0,6008
-0,3468
0,4858
-0,3606
0,15
0,3345
-2,8420
10,9709
-15,8994
8,3516
0,25
0,4296
-2,6350
8,6864
-11,5227
5,8544
0,50
0,3636
-0,8057
2,0463
-2,2902
1,1862
1,00
0,3527
-0,2842
0,4354
-0,0901
-0,1590
2,00
0,3341
0,1260
-0,6920
0,6877
-0,0600
*
Figure 13.7.8-2  Curves for the determination of E / E and
UNI EN 13445-3:2021

*
(square pattern)
273
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.8 Maximum permissible tube to tubesheet joint stress
13.8.1
Purpose
This clause provides rules to determine the maximum permissible stress of tube-to-tubesheet joint.
13.8.2
Symbols
at
is the weld throat thickness;
dt
is the nominal outside diameter of tubes (see Figure 13.7.3-3);
et
is the nominal tube wall thickness (see Figure 13.7.3-3);
f
is the nominal design stress of tubesheet material at design temperature;
ft
is the nominal design stress of tube material at design temperature;
l t, x
is the expanded length of tube in tubesheet 0 
f min
is the minimum nominal design stress of tubesheet or tubes material:
f min  min
13.8.3
l t, x  e  , (see
Figure 13.7.3-3).
f  ; f t 
(13.8.2-1)
Determination of maximum permissible tube-to-tubesheet joint stress
The maximum permissible stress of the tube-to-tubesheet joint,
f t, j
, is given by:
a) For welded only joint:

f t, j  min 


a 
 f min  t  ; f t

e t 


(13.8.3-1)


b) For expanded joint:
— with plain holes
  l t, x
f t, j  0 ,5 f min  min  

  d t

 ; 1,6 





(13.8.3-2)
— with one single groove:
f t, j  0 , 6 f min
(13.8.3-3)
— with two or more grooves:
f t, j  0 , 8 f min
274
(13.8.3-4)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
These formulas can also be applied if the expansion is completed by a weld for tightness, provided this
weld is not detrimental to the expanded joint.
c) These values of
f t, j
can be increased up to the value
ft
if the tube-to-tubesheet joining
procedure is approved and checked with pull-out tests.
13.9 Maximum permissible longitudinal compressive stress for tubes
13.9.1
Purpose
This clause provides rules to determine the maximum permissible longitudinal compressive stress in the
tubes of exchangers with a pair of tubesheets joined by a bundle of straight tubes to cover their failure
through elastic instability and buckling under the effect of an axial compressive force and pressures P t and
Ps
.
13.9.2
Symbols
b0
is the tube imperfection factor;
dt
is the nominal outside diameter of tubes (see Figure 13.7.3-3);
E
is the elastic modulus of tube material at design temperature;
t
et
is the nominal tube wall thickness (see Figure 13.7.3-3);
f t, bk
is the maximum permissible buckling stress of tubes;
l t, bk
is the buckling length of tubes;
Ps
is the shell-side calculation pressure. In case of vacuum, this shall be taken as negative;
Pt
is the tube-side calculation pressure. In case of vacuum, this shall be taken as negative;
R p 0,2/T
is the proof strength of tube material at design temperature;
x
is the safety factor on tube buckling;

t, c r
is the Euler critical stress for tubes;

t, p
is the factor for pressure effect on tubes;
Symbols
13.9.3
l 1 , l ' 1 , l 2 , l ' 2 and l 3
are defined on Figure 13.9.3-1.
Determination of maximum permissible buckling stress
a) The buckling length of tubes,
l t, bk
, is given by:
— if some tubes are not supported by any baffle-plate:
l t, bk  0 , 5 L
UNI EN 13445-3:2021
(13.9.3-1)
275
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— if all the tubes are supported by at least one baffle-plate (see Figure 13.9.3-1):
l t,b k  m in
  0 ,5 L  ;
m ax
  0 ,7 l 
;
1
 0 ,7
l '1

;
 0 ,7
l2

;
 0 ,7
l '2

;
l 3   
(13.9.3-2)
b) Calculate:

b 0  0 ,206
t, cr
R p0,2/
T

 1  0 ,2



Rp
t, cr
0,2/ T




(13.9.3-3)
x = 1,1
(13.9.3-4)
d t
2


t, p
t, c r

Ps  d t  P t
2
dt 


2
 Et
2
d t
 2 et
 2 et
2
(13.9.3-5)
2
d t  d t  2 e t 
2

2
(13.9.3-6)
16
l t,b k
c) The maximum permissible buckling stress of tubes,
f t, bk




1
x 

x 




The value of
t, p
Rp

1+
f t, bk
0,2/ T
 1  b
0




 x
 R p 0,2/

t, cr
T
t, p
 x
t, p





2
, is given by:










(13.9.3-7)
must be positive. If a negative value is obtained, the buckling length
reduced as necessary to obtain a positive value for
276
f t, bk
f t, bk
l t, bk
must be
.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Heat exchangers without baffle plate or with one baffle plate not supporting all the tubes of the bundle
b) Heat exchangers with several baffle plates not supporting all the tubes of the bundle
c) Heat exchangers with one or several baffle plates supporting all the tubes of the bundles
Figure 13.9.3-1  Definition of lengths
UNI EN 13445-3:2021
'
'
l1 , l1 , l2 , l2 , l3
277
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.10 Design of tubesheet flange extension with a narrow face gasket
13.10.1 Purpose
This subclause provides rules for the design of tubesheet extension when the tubesheet is extended as a
flange with a narrow gasket, as shown in Figure 13.10.1-1. It applies to configurations b, d 2 (U-tube
tubesheet only) and e.
13.10.2 Conditions of applicability
This subclause applies only if:
— The calculation pressure P is positive (internal pressure).
— The gasket is one of the types covered in clause 11.
—
D ex  G
.
a) Configuration b: stationary
tubesheet gasketed with channel
b) Configuration e: stationary
tubesheet gasketed with shell
c) Configuration d 2 : U-tube
tubesheet gaskted both sides
G  Gc
G  Gs
G  G s or G c
D ex  D s, e
D ex  D c, e
D ex  D o
P  Pt
P  Ps
P  Ps
or
Pt
Figure 13.10.1-1  Tubesheet flange extension
278
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.10.3 Symbols
A
is the outside diameter of tubesheet extension (see Figure 13.10.1-1);
b
is the effective gasket seating width (see Clause 11);
C
is the bolt circle diameter (see Figure 13.10.1-1);
Dc
is the inside channel diameter;
D c, e
is the outside diameter of the channel at its junctions with the tubesheet (usually:
D c, e  D c  2 e c
),
(see Figure 13.10.1-1);
D ex
is the inside diameter of tubesheet extension, given by 13.10.4a;
Do
is the diameter of the perforated tubesheet area, given by Formula (13.7.3-1);
Ds
is the inside shell diameter;
D s, e
is the outside diameter of the shell at its junction with the tubesheet (usually: D s, e
 Ds  2 es
), (see
Figure 13.10.1-1);
ea
is the analysis thickness of tubesheet (see Figure 13.10.4-1);
e a, p
is the analysis thickness at the periphery of tubesheet;
ec
is the channel thickness;
e fl
is the required thickness of tubesheet extension;
e fl, a
is the analysis thickness of tubesheet extension (see Figure 13.10.4-1);
es
is the shell thickness;
f
is the nominal design stress of tubesheet material at design temperature;
fA
is the nominal design stress of the tubesheet material, at assemby temperature;
G
is the diameter of gasket load reaction on shell-side or tube-side (either
Gc
is the diameter of channel gasket load reaction;
Gs
is the diameter of shell gasket load reaction;
M
A
Gs
or
Gc
);
is the total moment acting upon tubesheet for assembly condition, given by Formula (13.10.5-2);
UNI EN 13445-3:2021
279
EN 13445-3:2021 (E)
Issue 1 (2021-05)
M op
is the total moment acting upon tubesheet for operating condition, given by Formula (13.10.5-4);
m
is the gasket factor (see clause 11);
P
is the calculation pressure acting on the tubesheet, see 13.10.2;
Ps
is the shell-side calculation pressure. In case of vacuum, this shall be taken as negative;
Pt
is the tube-side calculation pressure. In case of vacuum, this shall be taken as negative;
W
is the flange design bolt load for the assembly condition (see Clause 11);

is the Poisson's ratio for the tubesheet material.
13.10.4 Design considerations
a) The inside diameter D ex of the tubesheet extension, and the design pressure P are determined as
shown on Figure 13.10.1-1.
b) The calculations shall be performed for each of the loading cases which may govern the design,
including the assembly condition.
c) The analysis tubesheet thickness at its periphery,
thickness of the tubesheet extension
e fl, a
e a, p
, shall be at least equal to the analysis
(see Figure 13.10.4-1):
(13.10.4-1)
e a, p  e fl, a
d) Calculation for configuration
280
d2
shall be performed for tube-side and shell-side.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
e fl,a
e fl,a
e fl,a
a) Flat facing
b) Raised facing
ea
c) Single tongue and groove
e fl, a
e fl,a
d) Double tongue and groove
e) Groove for ring joint
Figure 13.10.4-1  Analysis thicknesses of tubesheet flange extension
UNI EN 13445-3:2021
281
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.10.5 Required thickness of tubesheet flange extension
a) The required thickness for assembly condition,
e fl, A 
12

 A  1  

 D 
  1     ex 
 A 
2




M
e fl, A
, is given by:
(13.10.5-1)
A
fA
where
M
A
 W 
C G
(13.10.5-2)
2
b) The required thickness for operating conditions,
e fl, op 
12

 A  1  


 D
  1     ex 
 A 
2




M
e fl, op
, is given by:
op
(13.10.5-3)
f
where
M
op
 D 2
ex
   
  4
 C  D
 
 
2

ex
G

  


2
 D
4
2
ex
 2 C  D
 
 
4

ex
 G 
C  G  
  2 b  G  m  
  P

 

2

c) The required thickness of the flange tubesheet extension,
e fl  max
e fl
, is given by:
 e fl, A  ; e fl, op  
d) The analysis thickness of the tubesheet extension,
(13.10.5-4)
(13.10.5-5)
e fl, a
, shall be at least equal to
e fl
:
(13.10.5-6)
e fl, a  e fl
13.11 Design of tubesheet flange extension with a full face gasket
13.11.1 Purpose
This subclause provides rules for the design of tubesheet extension when the tubesheet is extended as a
flange with a full face gasket, as shown in Figure 13.11.1-1. It applies to configurations b',
tubesheet only) and e'.
'
d2
(U-tube
13.11.2 Conditions of applicability
This subclause applies only if:
— The calculation pressure P is positive (internal pressure).
— The gasket is one of the types covered in Clause 11.
282
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Configuration b': stationary
tubesheet gasketed with channel
b) Configuration e': stationary
tubesheet gasketed with shell
c) Configuration d '2 : U-tube
tubesheet gasketed both sides
G  Gc
G  Gs
G  G s or G c
P  Pt
P  Ps
P  Ps
or
Pt
Figure 13.11.1-1  Tubesheet flange extension
13.11.3 Symbols
B
is the inside diameter of tubesheet flange extension (see Figure 13.11.1-1);
2 b"
is the effective gasket pressure width (see 11.6);
C
is the bolt circle diameter (see Figure 13.11.1-1);
db
is the bold outside diameter;
dh
is the diameter of bolt holes;
ea
is the analysis thickness of tubesheet;
e fl
is the required thickness of tubesheet extension, given by Formula (13.11.5-1);
e fl, a
is the analysis thickness of tubesheet extension (see Figure 13.11.4-1);
f
is the nominal design stress of tubesheet material at design temperature;
G
is the diameter of gasket load reaction on shell-side or tube-side (either
Gc
is the diameter of channel gasket load reaction;
Gs
is the diameter of shell gasket load reaction;
UNI EN 13445-3:2021
Gs
or
Gc
);
283
EN 13445-3:2021 (E)
Issue 1 (2021-05)
g1
M
is the thickness of hub at back of flange (see 11.3);
is the total moment acting upon tubesheet for operating condition, given by Formula (13.11.5-2);
r
m
is the gasket factor (see Clause 11);
n
is the number of bolts;
P
is the calculation pressure acting on the tubesheet, see 13.11.2;
Ps
is the shell-side calculation pressure. In case of vacuum, this shall be taken as negative;
Pt
is the tube-side calculation pressure. In case of vacuum, this shall be taken as negative.
13.11.4 Design considerations
a) The calculations shall be performed for each of the loading cases, which may govern the design.
b) The analysis tubesheet thickness at its periphery,
thickness of the tubesheet extension
e fl, a
e a, p
, shall be at least equal to the analysis
(see Figure 13.11.4-1):
(13.11.4-1)
e a, p  e fl, a
c) Calculation for configuration
d2
shall be performed for tube-side and shell-side.
e fl, a
Figure 13.11.4-1  Analysis thickness of tubesheet flange extension
13.11.5 Required thickness of tubesheet flange extension
The required thickness of tubesheet flange extension is given by:
e fl 
6 M

(13.11.5-1)
r
C - n dh f
where
M
284
r

  


B2

 4





C  B  g1
 
2

 G
  

 
2
 B
4
2

 2C  B  G 
C  G 

   2 b " G  m  
  P

4
2


 
 

(13.11.5-2)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.12 Special tube-to-tubesheet welded joints
13.12.1 Purpose
This subclause explains how to apply the rules of 13.7 when the type of tube-to-tubesheet welded joint is
different from the current type covered in 13.7.
This subclause covers the following types of tube-to-tubesheet welded joints:
— tubes welded to the outer tubesheet face with machined grooves (see 13.12.3);
— tubes joined by fillet weld to the inner tubesheet face as follows:
— tubes inserted into the tubesheet with machined grooves (see 13.12.4);
— tubes partially inserted into the tubesheet (see 13.12.5);
— tubes joined by butt weld to the inner tubesheet face having:
— hubs (see 13.12.6);
— machined grooves (see 13.12.7).
13.12.2 Additional symbols
The following symbols are in addition to those in 13.7.3
d
is the tube hole diameter;
hw
is the depth of tube weld groove.
13.12.3 Tubes welded to the outer tubesheet face with machined grooves
a) The tubesheet thickness shall be measured from the root of the tube weld groove (see
Figure 13.12.3-1).
b) The effective depth
'
h g  max
h g
'
hg

of the pass partition groove, if any, is given by the following relation:
 c t  h w , 0 

(13.12.3-1)
hw
e
Figure 13.12.3-1 — Tube welded to the outer tubesheet face with machined grooves
UNI EN 13445-3:2021
285
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.12.4 Inserted tubes welded to the inner tubesheet face with machined grooves
The tubesheet thickness shall be measured from the root of the tube weld groove (see Figure 13.12.4-1).
e
hw
Figure 13.12.4-1 — Inserted tube welded to the inner tubesheet face having machined grooves
13.12.5 Partially inserted tubes welded to the inner tubesheet face
a) The diameter
Do
of the perforated area of the tubesheet is given by the following formula:
(13.12.5-1)
D o  2 ro  d
b) The basic ligament efficiency
 

p  d
(13.12.5-2)
p
c) The effective ligament efficiency
* 
of the tubesheet is given by:
 *
of the tubesheet is given by:
p *  d
(13.12.5-3)
p *
d
d t  2 et  d  d t
Figure 13.12.5-1 — Partially inserted tubes welded to the inner tubesheet face
286
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.12.6 Tubes butt welded to the inner tubesheet face with hubs
a) The diameter
Do
of the perforated area of the tubesheet is given by the following formula:
(13.12.6-1)
D o  2 ro  d
b) The basic ligament efficiency
 

p  d
(13.12.6-2)
p
c) The effective ligament efficiency
* 
of the tubesheet is given by the following formula:
 *
of the tubesheet is given by the following formula:
p *  d
p *
(13.12.6-3)
Figure 13.12.6-1 — Tube butt welded to the inner tubesheet face with hub
UNI EN 13445-3:2021
287
EN 13445-3:2021 (E)
Issue 1 (2021-05)
13.12.7 Tubes butt welded to the inner tubesheet face with machined grooves
a) The tubesheet thickness shall be measured from the root of the tube weld groove (see
Figure 13.12.7-1).
e
hw
Figure 13.12.7-1 — Tubes butt welded to the inner tubesheet face with machined groove
b) requirements a), b) and c) of 13.12.6 apply.
14 Expansion bellows
14.1 Purpose
This clause provides design rules for expansion bellows consisting of a single or multiple convolutions of the
three following types:
a) unreinforced U-shaped bellows (see Figure 14.1-1a);
b) reinforced U-shaped bellows (see Figure 14.1-1b);
c) toroidal bellows (see Figure 14.1-1c);
subject to internal or external pressure and cyclic displacement.
Such bellows are intended to be installed on pressure vessels, especially tubesheet heat exchangers, in order
to provide adequate flexibility for thermal expansion, whilst ensuring a safe design against internal pressure.
NOTE
The attention of the designer is drawn to the fact that the design of expansion bellows is complex
because these strength and flexibility requirements are generally conflicting. Clause K.1 gives detailed information
on this issue.
If erosion or vibration is considered to be a concern due to the velocity of the medium conveyed, the use of
an internal sleeve should be considered.
14.2 Specific definitions
The following terms and definitions apply in addition to those in Clause 3.
288
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.2.1
expansion bellows
flexible element consisting of one or more convolutions and the end tangents
14.2.2
convolution
the flexible unit of an expansion bellows (see Figure 14.1-1)
14.2.3
end tangents
the straight unconvoluted portions at the ends of a bellows (see Figure 14.1-1)
14.2.4
collar
cylinder attached to the end tangent to reinforce it (see Figure 14.1-1)
14.2.5
reinforcing and equalizing rings
devices that are tightly fitted into the roots of the convolutions in order to reinforce the bellows against
internal pressure
Reinforcing rings are fabricated from tubing or round bars. Equalizing rings are approximately "T" shaped in
cross section and their primary purpose is to limit the total equivalent axial displacement range.
(1) convolution
(2') end tangent with collar
(2) end tangent without collar
(3) reinforcing collar
a) Unreinforced U-shaped bellows
UNI EN 13445-3:2021
289
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(1) convolution
(4) end equalizing ring
(2) end tangent
(5) equalizing ring
(3) reinforcing collar
(6) reinforcing rings
b) Reinforced U-shaped bellows
Key
(1) convolution
(2) renforcing collar
c) Toroidal bellows
Figure 14.1-1 — Three types of expansion bellows
14.3 Specific symbols and abbreviations
The following symbols apply in addition to those listed in clause 4.
A
is the cross sectional metal area of one convolution, given by Formula (14.5.2-7) or (14.6.3-7);
Cp,Cf,Cd
are coefficients used for U-shaped convolutions, see Figures 14.5.2-1, 2 and 3;
C 1 and C
Dc
290
2
are coefficients given by Formulae (14.5.2-8) and (14.5.2-9) or (14.6.3-8) and (14.6.3-9), used to
determine the coefficients C p , C f , C d ;
is the mean diameter of collar, given by Formula (14.5.2-2) or (14.6.3-2) or (14.7.3-2);
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Di
is the inside diameter of bellows convolution and end tangents, see Figure 14.1-1;
Dm
is the mean diameter of bellows convolution, given by Formula (14.5.2-3) or (14.6.3-3)
or (14.7.3-3);
Eb
is the modulus of elasticity of bellows material at design temperature;
Ec
is the modulus of elasticity of collar material at design temperature;
Eo
is the modulus of elasticity of bellows material at room temperature;
e
is the bellows nominal thickness, given by Formula (14.5.2-1) or (14.6.3-1) or (14.7.3-1);
For single ply bellows:
e
 ep
;
ec
is the collar thickness, see Figure 14.1-1;
ep
is the nominal thickness of one ply;
e
*
*
ep
is the bellows thickness, corrected for thinning during forming, given by Formula (14.5.2-5)
or (14.6.3-5) or (14.7.3-5);
is the thickness of one ply, corrected for thinning during forming, given by Formula (14.5.2-4)
or (14.6.3-4) or (14.7.3-4);
f
is the nominal design stress of bellows material at design temperature;
fc
is the nominal design stress of collar material at design temperature;
Kb
is the bellows axial rigidity, given by Formula (14.5.7-1, 14.6.8-1 or 14.7.8-1);
k
is the factor considering the stiffening effect of the attachment weld and the end convolution on
the pressure capacity of the end tangent, given by Formula (14.5.2-6) or (14.6.3-6);
Lc
is the collar length, see Figure 14.1-1;
UNI EN 13445-3:2021
291
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Lt
is the end tangent length, see Figure 14.1-1;
N
is the number of convolutions;
N alw
is the allowable number of fatigue cycles;
N
is the specified number of fatigue cycles;
spe
np
is the number of plies;
P
is the calculation pressure;
q
is the convolution pitch, given by Formula (14.5.2-10);
ri
is the internal radius of torus at the crest and root of U-shaped convolutions, see Figure 14.5.11;
sd
is the strain caused by deformation during manufacturing, see 14.5.2.2;
w
is the convolution height, see Figure 14.1-1;

is the in-plane instability stress interaction factor, given by Formula (14.5.2-12);

is the in-plane stress instability stress ratio, given by Formula (14.5.2-11);
q
is the total equivalent axial displacement range per convolution, given by 14.10.5;
b
is the Poisson's ratio of the bellows material;
 P 
is a stress depending on P;
  q 
is a stress depending on

is the total stress range due to cyclic displacement;
eq
q
;
Main subscripts:
b
for bellows
c
for collar
m
for membrane or meridional
p
for ply
r
for reinforced
t
for end tangent

for circumferential
No subscript is used for the bellows convolutions.
292
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.4 Conditions of applicability
14.4.1 Geometry
14.4.1.1 An expansion bellows comprises one or more identical convolutions. Each convolution is
axisymmetric.
14.4.1.2
Each convolution may have one or more plies of equal thickness and made of same material.
14.4.1.3 Bellows including a cylindrical end tangent of length Lt, with or without collar (see
Figure 14.1-1): if the thickness of the tangent is less than the cylindrical shell to which the bellows is
welded, Lt shall be such that:
L t  L c  0 ,5
e Di
In this formula, Lc = 0 if the bellow is without collar.
14.4.1.4
The number of plies shall be such that:
np  5
14.4.2 Loading
This clause provides rules for bellows subjected to constant internal pressure, and cyclic axial displacements.
In addition:
— bellows subjected to lateral or angular displacement, shall be calculated as per 14.10,
— specific rules are given to cover external pressure (see 14.5.5),
— other loads (e.g. weight, vibration, wind, or thermal shock) shall be given special consideration.
14.4.3 Temperature
This clause applies only at material temperatures below the creep range, as stated in the relevant European
material standard. In the absence of such specification:
— design temperature shall be less than 500 °C for austenitic steel and similar materials quoted
in 14.5.6.3.2,
— design temperature shall be less than 380 °C for ferritic steel.
14.4.4 Materials
These rules apply to ferritic steel, austenitic steel and nickel-chromium-iron, nickel-iron-chromium alloys.
14.4.5 Welding seams
Expansion bellows may include one or several longitudinal welds. U-shaped unreinforced bellows may also
have circumferential welds (see 14.5.9).
The circumferential attachment welds of single and multi-ply expansion bellows shall be designed according
to the sketches given in Table 14.4.5-1.
UNI EN 13445-3:2021
293
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 14.4.5-1 — Typical bellows attachment welds
Weld type
General design
N°
A
Increased neck
1.1
1)
1.2
outside lap joint/filled weld
1)
Variants (combinations of A to D are permitted)
B
C
D
assisting collar
Reinforcing collar
Single
double
2) 3)
inside lap joints/fillet weld
2.1
outside lap joint/groove weld
2.2
inside lap joint/groove weld
3.0
4)
4)
4.1
butt weld
5)
radial edge weld (inside or outside)
4.2
axial edge weld (inside or outside)
Fittings and reinforcing collars opposite to the pressure bearing side of the bellows shall have a radius or a bevel at the edge in contact with the
bellows and tangent.
NOTE
These sketches are not exhaustive. Other configurations can be used, provided they lead to an equivalent level of safety.
1) In the case of fillet welds, the weld thickness "a“ shall fulfil following formula:
a  0 ,7 e
s
where es is the nominal thickness of the connecting shell.
2) A reinforcing collar is advisable, if the cylindrical end tangent of bellows Lt exceeds:
L t  0 ,5 e s D i
3) The reinforcing collar shall be fixed axially by welding or mechanical devices.
4) In the case of butt welds, special tools are necessary for welding of multi-ply bellows.
5) The diameter of the weld shall not exceed the mean diameter of bellows Dm by more than 20 % of the convolution height w.
294
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.4.6 Installation
The expansion bellows shall be provided with bars or other suitable members for maintaining the proper
overall length dimension during shipment and installation. Bellows shall not be extended, compressed,
rotated, or laterally offset to accommodate connecting parts which are not properly aligned, unless the
design considers such movements.
In all vessels with expansion bellows, the hydrostatic end force caused by pressure and/or the bellows spring
force shall be resisted by adequate restraint elements (e.g. exchanger tubes or shell, external restraints,
anchors). The stress in these elements shall not exceed the nominal design stress at the design temperature.
14.5 U-shaped unreinforced bellows
14.5.1 General
14.5.1.1 Scope
This subclause applies to two types of unreinforced bellows having nominally U-shaped convolutions:
— Those shown in Figure 14.5.1-1 are generally manufactured by a forming process (e.g. hydraulic
forming, roll forming) without any circumferential welding in the convolutions. This type of bellows
is covered by subclauses 14.5.2 to 14.5.7.
— Those shown in Figure 14.5.8-1 are of single ply construction where the convolutions have
circumferential welds at their roots and crests. This type of bellows shall comply with the
additional requirements of 14.5.8.
Each convolution consists of a sidewall and two tori of nearly the same radius (at the crest and root of the
convolution), in the neutral position, so that the convolution profile presents a smooth geometrical shape as
shown in Figure 14.5.1-1.
Key
(1) end tangent without reinforcing collar
(3) convolution root
(2) end tangent with reinforcing collar
(4) convolution crest
Figure 14.5.1-1 — U-shaped unreinforced bellows
14.5.1.2 Conditions of applicability
The following conditions of applicability apply in addition to those listed in 14.4.
UNI EN 13445-3:2021
295
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) A variation of 10 % between the crest convolution radius r ic and the root convolution radius
is permitted (see Figure 14.5.1 -2 for definitions of r ic and r ir ).
r ir
b) The torus radius shall be such that:
ri  3 e p
,
where
ri 
r ic  r ir
.
2
c) The off-set angle of the sidewalls, , in the neutral position shall be such that:
 15     15
degrees (see Figure 14.5.1-2).
d) The convolution height shall be such that:
w 
Di
3
.
Figure 14.5.1-2 — Possible configuration shapes in the neutral position
14.5.2 Determination of intermediate quantities
14.5.2.1 General
The following formulae are used in the determination of the intermediate factors.
e  np  ep
(14.5.2-1)
D c  D i  2 e  ec
(14.5.2-2)
Dm  Di  w  e
(14.5.2-3)
*
ep  ep
e
296
*
Di
Dm
*
 np  ep
(14.5.2-4)
(14.5.2-5)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)

k  min 




 1,5



; 1,0


Lt
Di  ep





   2 
 *
 q  2 w e
 2 

A  
C1 
(14.5.2-7)
q
(14.5.2-8)
2 w
q
C2 
(14.5.2-9)
*
Dm  ep
2 ,2
(14.5.2-10)
q  4ri  2e
NOTE
δ 
Where 
(14.5.2-6)
Formula (14.5.2-10) applies in the case of parallel walls. Otherwise, the actual pitch has to be used.
σ m ,b
(14.5.2-11)
3 σ θ ,I
m, b
and 
  1  2
2

θ, I
are defined in 14.5.3.3.
1  2 
2
 4
4

(14.5.2-12)
For coefficient Cp, Cf and Cd, see Figures 14.5.2-1 to 14.5.2-3.
UNI EN 13445-3:2021
297
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
Clause K.2 gives polynomial approximations for these curves.
Figure 14.5.2-1 — Coefficient
298
C
p
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
Clause K.2 gives polynomial approximations for these curves.
Figure 14.5.2-2 — Coefficient
UNI EN 13445-3:2021
C
f
299
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
Clause K.2 gives polynomial approximations for these curves.
Figure 14.5.2-3 — Coefficient
300
Cd
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.5.2.2 Determination of strain caused by deformation
The maximum true strain caused by deformation for bellows is given by:
s d  1, 0 4
2
sθ
 sb
(14.5.2-13)
2
The circumferential true strain caused by deformation sc depends on the forming process. For the common
forming processes the following formulas shall be used:
— for hydraulic or similar processes where the forming is performed 100 % to the outside of the
initial cylinder:

w 
s θ  ln  1  2

Di 

(14.5.2-14)
— for roll forming processes with 50 % forming to the inside and 50 % to the outside of the initial
cylinder:
S θ  1n (1 
w
Di
(14.5.2-15)
)
— for half-convolutions manufactured from ring plates by roller bending or other methods, where the
maximum strain occurs at the inner crest:



 1   2 ri  e p


 2

s θ   ln  1 
D i  ep





(14.5.2-16)




The bending component of the true strain caused by deformation sb is independent of the forming process
and given by:


ep
s b  ln 1 

2 ri  e p 


(14.5.2-17)
14.5.3 Stresses due to internal pressure
14.5.3.1 End tangent
The circumferential membrane stress due to pressure:
σ θ , t P  
1
2 e  D i
D i  e  2
 eLt E b
Lt E b  k
 ec  D c  Lc  E c  k
P
(14.5.3-1)
shall comply with:

 ,t
P 
 f
UNI EN 13445-3:2021
301
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.5.3.2 Collar
The circumferential membrane stress due to pressure:
2
Dc Lt E c  k
1
σ θ ,c P  
2 e  D i  e   L t  E b  e c  D c  L c  E c  k
P
(14.5.3-2)
shall comply with:

P  
 ,c
fc
14.5.3.3 Bellows convolutions
a) The circumferential membrane stress due to pressure:
— For end convolutions
σ
θ ,E
1
P  

2
q  D m  L t D i  e 
*
A  e
 Lt
P
(14.5.3-3)
shall comply with:

P 
 ,E
 f
— For intermediate convolutions
  , l P  
1
2
q  Dm

A
(14.5.3-4)
P
shall comply with:

 ,I
P 
 f
b) The meridional membrane stress due to pressure is given by:

m, m
w
P  
2 e
*
(14.5.3-5)
P
c) The meridional bending stress due to pressure is given by:

m, b
P  
1
2 np
 w 


e* 
 p 
2
Cp P
(14.5.3-6)
d) The meridional membrane and bending stresses shall comply with:

m, m
P  

m, b
P  
K
f
f
(14.5.3-7)
where:
K
302
f
 3 ,0
for as-formed bellows (with cold work)
(14.5.3-8)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
K
f
 1,5
for annealed bellows (without cold work)
(14.5.3-9)
14.5.4 Instability due to internal pressure
14.5.4.1 Column instability
The allowable internal design pressure to avoid column instability, Ps,c , is given by:
Ps, c  0 , 34
Kb
(14.5.4-1)
Nq
The internal pressure P shall not exceed
P s, c
:
P  P s, c
14.5.4.2 In-plane instability
The allowable internal design pressure to avoid in-plane instability, Ps ,i , is given by:
P s, i  (   2 )
AR
Dmq
*
(14.5.4-2)
e

where Re* is the effective proof stress at design temperature of bellows material in the as-formed or
annealed condition.
In absence of values for Re* in material standards, the following values shall be used for austenitic steel:
*
for as-formed bellows (with cold work)
(14.5.4-3)
*
for annealed bellows (without cold work)
(14.5.4-4)
e)
R e  K d R p 1,0 / T
f)
R e  0 ,75 R p 1,0 / T
where
R p 1, 0 / T
Kd
K
is the yield stress at 1 % at design temperature, as defined in clause 4;
is the bellows cold-work factor, given by:
d
1  5  s d
 
2 ,0

si s d  0 . 2
(14.5.4-5)
si s d  0 , 2
For non-austenitic steel: Re* = Rp 0,2/t
The internal pressure P shall not exceed
P s, i
:
P  Ps,i
UNI EN 13445-3:2021
303
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.5.5 External pressure design
14.5.5.1 Stresses due to external pressure
The rules of 14.5.3 shall be applied taking P as the absolute value of the external pressure.
NOTE
When the expansion bellows is submitted to vacuum, the design shall be performed assuming that only
the internal ply resists the pressure. The pressure stress formulae of 14.5.3 shall be applied with
np  1
.
14.5.5.2 Instability due to external pressure
The design shall be performed according to the rules of Clause 8 by replacing the bellows with an equivalent
cylinder, using:
— an equivalent outside diameter
D eq
given by:
(14.5.5-1)
D eq  D i  w  2 e eq
— an equivalent thickness
e eq 
3

12 1  
2
 I
e eq
given by:
xx
(14.5.5-2)
q
where I xx is the moment of inertia of one convolution cross section relative to the axis passing by the center
of gravity and parallel to the axis of the bellows (see Figure 14.5.5-1).
NOTE
If L t  0 , then Ixx is given by:

 2 w  q 3
2
*
I xx  e  
 0 , 4 q  w  0 ,2 q  
48


(14.5.5-3)
The portion of cylindrical shell shall be taken between the two closest stiffening rings adjacent to the
bellows.
Figure 14.5.5-1  Dimensions to determine
304
I xx
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.5.6 Fatigue evaluation
14.5.6.1 Calculation of stresses due to the total equivalent axial displacement range q of each
convolution
a)
Meridional membrane stress:
σ
Δ q  
m, m
 
*
E
b
 ep
2w
3
C
2
(14.5.6-1)
 Δq
f
b) Meridional bending stress:
*

m, b
 q  
5 E b  ep
2
3 w
Cd
(14.5.6-2)
 q
14.5.6.2 Calculation of the total stress range due to cyclic displacement
σ
eq
 0 ,7  σ
m, m
P  
σ
m, b
P   σ m, m  Δ q  
σ
m, b
(14.5.6-3)
 Δ q 
14.5.6.3 Calculation of the allowable number of cycles
14.5.6.3.1 General
The specified number of cycles
N
spe
shall be stated as consideration of the anticipated number of cycles
expected to occur during the operating life of the bellows. The allowable number of cycles
calculated in this subclause, shall be at least equal to N s p e : N a lw  N s p e .
N alw
, as
The allowable number of cycles given by the following formulae includes a reasonable safety margin (factor
3 on cycles and 1,25 on stresses) and represents the maximum number of cycles for the operating condition
considered.
Therefore an additional safety factor should not be applied: an overly conservative estimate of cycles can
necessitate a greater number of convolutions and result in a bellows more prone to instability.
If the bellows is submitted to different cycles of displacement, such as those produced by start-up or
shutdown, their cumulative damage shall be calculated using Miner's rule for cumulative fatigue (see 18.5.6).
NOTE
Use of specific fatigue curves established by a manufacturer will be covered later and specific
requirements to be applied will be set-up in Annex K.3.
14.5.6.3.2 Austenitic steel and other similar materials
This following formula applies to as-formed bellows made of austenitic steel, nickel-chromium-iron and
nickel-iron-chromium alloys.
The allowable number of cycles is given by (see Figure 14.5.6-1):
— If
E
0
E
b
σ
eq
 1080
UNI EN 13445-3:2021
MPa:
305
EN 13445-3:2021 (E)
Issue 1 (2021-05)






9283 , 3


 E0 


,
372
3
eq
 Eb



where
— If

eq
E
0
E
b
σ
3 ,4
(14.5.6-4)
is expressed in MPa.
eq
 1080
MPa:


10259, 4
 
 E0   297,9
eq
 E
 b
N a lw
where

— If
E
0
E
b
eq
σ






3,4
14.5.6-5)
is expressed in MPa.
eq
 297 ,9
MPa:
N a lw
 10
6
cycles shall be used.
The curve and the formulae are only valid for:
306
370
 N
alw
 10
6
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
X
number of cycles N
Y
σeq in MPa
Figure 14.5.6-1 — Fatigue curve at room temperature (Eb=E0)
for unreinforced as-formed bellows
UNI EN 13445-3:2021
307
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.5.6.3.3 Ferritic steel
The fatigue design curves of 18.10 or 18.11, as appropriate, shall be used.
14.5.7 Axial rigidity
The theoretical axial rigidity of a bellows comprising N convolutions may be evaluated by the following
formula:
K
b

F
N  Δq


π
2 1 ν
2
b

Eb 
np
N
Dm
where F is the applied axial force and
e*
p

 w

N  q




3

1
(14.5.7-1)
Cf
the corresponding axial displacement of the bellows.
This formula is valid only in the elastic range.
NOTE
Outside this range lower values can be used, based on manufacturer's experience or representative
test results (see K.1).
14.5.8 U-shaped convolutions circumferentially welded at their crest or root
14.5.8.1 Scope
This subclause applies to unreinforced U-shaped bellows of single ply fabricated from two symmetrical halfconvolutions joined by a circumferential butt weld:
— either directly (Figure 14.5.8-1a);
— or by means of a cylindrical shell (Figure 14.5.8-1b);
— or by means of a straight part obtained by forming (Figure 14.5.8-1c).
Each of the half-convolutions may be of one single seamless element (Figures 14.5.8-1a and 14.5.8-1b), or
formed from several elements joined by meridional butt welding (Figure 14.5.8-1d).
308
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
(1) circumferential welds
(2) meridional welds
Figure 14.5.8-1 — Circumferential welds in U-shaped expansion bellows
14.5.8.2 Design
Rules of 14.5.1 to 14.5.7 apply with the following additional requirements.
a) The two half convolutions may have a short cylindrical part, of length m i at the root and m e at
the crest (see Figure 14.5.8-2), in order to facilitate the welding. The length m i or m e shall
comply with:
m i  0 ,2
Dm  e
m
e
 0 ,2
Dm  e
Figure 14.5.8-2 — Convolutions with a cylindrical part
UNI EN 13445-3:2021
309
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) In 14.5.3.3, Formulae (14.5.3-3) and (14.5.3-4) giving
formulae:


 ,E
 ,l
P 
P 


1

2
1
2
q
 m
i
Dm
 m
*
A  e

q
c) In 14.5.6.2 :
 m
i
Dm
 m
A  e

eq
*
e
 w  L t  m i / 2   D i  e 
m e
e
 Lt  m i / 2
 w  m i  D i  e 
m e
 m
i


 ,E
P 
and

 ,I
P 
are replaced by
P
(14.5.8-1)
P
(14.5.8-2)
obtained from Formula (14.5.6-3) shall be multiplied by a coefficient 2.
14.6 U-shaped reinforced bellows
14.6.1 Purpose
This subclause applies to bellows that have nominally U-shaped convolutions with rings to reinforce the
bellows against internal pressure.
Each convolution consists of a sidewall and two tori of the same radius (at the crest and root of the
convolution), in the neutral position, so that the convolution profile presents a smooth geometrical shape as
shown in Figure 14.6.1-1.
Key
(1) convolution
(3) reinforcing collar
(5) equalizing ring
(2) end tangent
(4) end equalizing ring
(6) reinforcing rings
Figure 14.6.1-1 — U-shaped reinforced bellows
310
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The following symbols apply in addition to those listed in Clause 4 and 14.3.
Af
is the cross sectional metal area of one reinforcing fastener, see Figure 14.6.1-1;
Ar
is the cross sectional metal area of one bellows reinforcing ring member, see Figure 14.6.1-1;
Cr
is the convolution height factor for reinforced bellows, given by Formula 14.6.3-11;
Ef
is the modulus of elasticity of reinforcing fastener material at design temperature;
Er
is the modulus of elasticity of reinforcing ring member material at design temperature;
H
is the resultant total internal pressure force acting on the bellows and reinforcement, given by
Formula (14.6.3-12);
ff
is the allowable stress of reinforcing fastener material at design temperature;
fr
is the allowable stress of reinforcing ring member material at design temperature;
R
is the ratio of the internal pressure force resisted by the bellows on the internal pressure force
resisted by the reinforcement, given by Formula (14.6.4-3).
14.6.2 Conditions of applicability
The following conditions of applicability apply in addition to those listed in 14.4.
a) A variation of 10 % between the crest convolution radius ric and the root convolution radius rir
shall be permitted (see Figure 14.5.1-2 for definitions of ric and rir).
b) The torus radius shall be such that:
ri  3 e p
where
ri 
r ic  r ir
2
.
c) The off-set angle of the sidewalls, , in the neutral position shall be such that:
 15     15
degrees (see Figure 14.5.1-2).
d) The convolution height shall be such that:
w 
Di
3
.
14.6.3 Determination of intermediate quantities
The following formulae are used in the determination of the intermediate factors.
e  np ep
D c  D i  2 e  ec
Dm  Di  w  e
UNI EN 13445-3:2021
(14.6.3-1)
(14.6.3-2)
(14.6.3-3)
311
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Di
*
ep  ep
Dm
*
(14.6.3-4)
*
e  np ep
(14.6.3-5)




k  m in
A  e
C1 
C2 
*


Lt

 1 ,5
D iep


 ;


 1 ,0 




2 w  (   2 )( 2 ri  e ) 
(14.6.3-6)
(14.6.3-7)
2 ri  e
w
(14.6.3-8)
2 ri  e
1, 1
*
D m ep
(14.6.3-9)
q  4 ri  2 e
(14.6.3-10)
100


C r  0, 3  

1,5
1
0
4
8
P
3
2
0



2
(14.6.3-11)
where P is expressed in MPa
H  PDm q
R1 
R2 
(14.6.3-12)
AEb
Ar E r
(14.6.3-13)
A E b  Lf
Dm 



D m  Af E f
Ar E r 
(14.6.3-14)
14.6.4 Stresses due to internal pressure
14.6.4.1 End tangent
The circumferential membrane stress due to pressure:
2

θ ,t

 Di  e  Lt Ebk
1 
P
P  
2  e  D i  e  L t E b  ec D c Lc E c k 


(14.6.4-1)
shall comply with:
 θ ,t  P   f
312
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.6.4.2 Collar
The circumferential membrane stress due to pressure:

θ ,c
P
2

Dc Lt E ck
1 


P
2  e  D i  e  L t E b  ec D c Lc E c k 
(14.6.4-2)
shall comply with:

θ ,c
P 
fc
14.6.4.3 Bellows convolutions
e) The circumferential membrane stress due to pressure:
θ




H
R



2A R  1




(14.6.4-3)
shall comply with:  θ  f 
where
R  R1 for integral reinforcing ring members, given by Formula (14.6.3-12);
R  R2 for reinforcing ring members joined by fasteners, given by Formula (14.6.3-13).
NOTE
In the case of reinforcing members that are made in sections, and joined by fasteners in tension, this
formula assumes that the structure used to retain the fastener does not bend in order to permit the reinforcing
member to expand diametrically. In addition, the end reinforcing members must be restrained against the
longitudinal annular pressure load of the bellows.
f)
The meridional membrane stress due to pressure is given by:
 m, m ( P )  0 , 85
(w  C r q )
2e
*
(14.6.4-4)
P
g) The meridional bending stress due to pressure is given by:
2

(P) 
m ,b
0,85  w  C r q 
*

 C
2np
ep


p
P
(14.6.4.-5)
h) The meridional membrane and bending stresses shall comply with:

m ,m
 P    m ,b  P  
Kf f
(14.6.4.-6)
where
Kf  3,0 for as-formed bellows (with cold work);
Kf  1,5 for annealed bellows (without cold work).
UNI EN 13445-3:2021
313
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.6.4.4 Reinforcing ring member
The circumferential membrane stress due to pressure

'
θ, r




H
1
(P ) 


2 Ar
R 1

 1


(14.6.4-7)
shall comply with:
'
 θ, r
(P)  fr
NOTE
In the case of equalizing rings, this formula provides only the simple membrane stress and does not
include the bending stress caused by the eccentric fastener location. Elastic analysis and/or actual tests can be
used to determine these stresses.
14.6.4.5 Reinforcing fastener
The membrane stress due to pressure:

"
θ, f




H
1
(P ) 


2A f
R 1

 2


(14.6.4.-8)
shall comply with:
  , f P  f
"
f
14.6.5 Instability due to internal pressure
14.6.5.1 Column instability
The allowable internal design pressure to avoid column instability, Ps,c , is given by:
Ps, c  0 , 3
 Kb
(14.6.5-1)
Nq
The internal pressure P shall not exceed
P s, c
:
P  Ps,c
14.6.5.2 In-plane instability
Reinforced bellows are not subject to in-plane instability.
314
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.6.6 External pressure design
14.6.6.1 Stresses due to external pressure
The rules of 14.5.3 that relate to unreinforced bellows shall be applied, taking P as the absolute value of the
external pressure.
When the expansion bellows is submitted to vacuum, the design shall assume that only the internal ply
resists the pressure. The pressure stress formulae of 14.5.3 shall be applied with np = 1.
14.6.6.2 Instability due to external pressure
The circumferential instability of a reinforced bellows shall be calculated in the same manner as for
unreinforced bellows. See 14.5.5.2.
14.6.7 Fatigue evaluation
14.6.7.1 Calculation of stresses due to the total equivalent axial displacement range q of each
convolution
The following formulae are used to determine the stresses due to the total equivalent axial displacement
range of q of each convolution.
i)
The meridional membrane stress, 

j)
( q ) 
m, m
Eb
*
(e p )
2 (w  C rq)
3
m ,b
  q  , is given by:
2
Cf
(14.6.7-1)
q
The meridional bending stress, 

m ,n
m ,b
  q  , is given by:
*

E b ep
5 
 q
q   
2
3 w  C q C 
r
d 

(14.6.7-2)
14.6.7.2 Calculation of the total stress range due to cyclic displacement
The total stress range due to cyclic displacement, 

eq
 0 , 7  
m ,m
eq
, is given by:
 P    m ,b  P      m ,m   q    m ,b   q  
(14.6.7-3)
14.6.7.3 Calculation of the allowable number of cycles
14.6.7.3.1 General
k) The specified number of cycles N spe shall be stated as a consideration of the anticipated number
of cycles expected to occur during the operating life of the bellows. The allowable number of
cycles N alw , as derived in this subclause, shall be at least equal to N s p e : N a lw  N s p e .
UNI EN 13445-3:2021
315
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The allowable number of cycles given by the following formulas includes a reasonable safety
margin (factor 3 on cycles and 1,25 on stresses) and represents the maximum number of cycles for
the operating condition considered. Therefore an additional safety factor should not be applied: an
overly conservative estimate of cycles could necessitate a greater number of convolutions and
result in a bellows that is more prone to instability.
l)
If the bellows is submitted to different cycles of displacement, such as those produced by start-up
or shutdown, their cumulative damage shall be calculated using Miner's rule for cumulative
fatigue (see 18.5.6).
m) Use of specific fatigue curves established by a manufacturer will be covered later and specific
requirements to be applied will be set-up in Annex K.3 (in course of consideration by
CEN/TC 54/WG C).
14.6.7.3.2 Austenitic steel and other similar materials
This subclause applies to as-formed bellows made of austenitic steel, nickel-chromium-iron and nickel-ironchromium alloys.
The allowable number of cycles are given by the following formulae (see Figure 14.6.7-1):
— if
E0
Eb
N a lw

eq


24452, 5
 
 E 0   2 8 8, 2
eq
 E
 b
where 
— if
E0
Eb
N a lw

eq
E0
Eb
eq

eq






2 ,9
(14.6.7-4)
is expressed in MPa;
 6 3 0 ,4 MPa:


2 8 5 7 1, 9
 
 E0   230, 6
eq
 E
 b
where 
— if
 6 3 0 , 4 MPa:
eq






2 ,9
(14.6.7-5)
is expressed in MPa;
 2 3 0 , 6 MPa:
N a lw
 10
6
cycles shall be used.
The curve and the formulae are only valid for:
10
316
2
 N
alw
 10
6
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.6.7.3.3 Ferritic steel
The fatigue design curves of 18.10 or 18.11, as appropriate, shall be used.
14.6.8 Axial rigidity
The theoretical axial rigidity of a bellows comprising N convolutions may be evaluated by the following
formula:
K
b


 
2
 2  1  v b
3

 n

 1
ep
p

EbDm 

  N
  w  C r q   C f
(14.6.8-1)
This formula is valid only in the elastic range.
NOTE
Outside this range lower values can be used, based on manufacturer's experience or representative
test results (see K.1).
UNI EN 13445-3:2021
317
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
X
Number of cycles N
Y
σeq in MPa
Figure 14.6.7-1 — Fatigue curve at room temperature (E=E0) for reinforced as-formed bellows
318
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.7 Toroidal bellows
14.7.1 Purpose
This subclause applies to bellows that have toroidal convolutions. Each convolution consists of a torus of
radius r, as shown in Figure 14.7.1-1.
Key
(1) convolution
(2) reinforcing collar
Figure 14.7.1-1 — Toroidal bellows
The following symbols apply in addition to those listed in 14.3.
Ac
is the cross sectional metal area of all reinforcement collars for toroidal bellows;
B1, B2, B3
are coefficients given by Table 14.7.3-1;
r
is the mean radius of toroidal bellows convolution.
14.7.2 Conditions of applicability
The general conditions of applicability listed in 14.4 apply.
14.7.3 Determination of intermediate quantities
The following formulae are used in the determination of the intermediate quantities.
e  np ep
(14.7.3-1)
D c  D i  2 e  ec
Dm  Di  w  e
(14.7.3-3)
Di
*
ep  ep
*
(14.7.3-2)
Dm
(14.7.3-4)
*
e  np ep
UNI EN 13445-3:2021
(14.7.3-5)
319
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 14.7.3-1 — Coefficients B1, B2, B3
6 , 61 r
2
Dm ep 
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
B1
B2
B3
1,0
1,1
1,4
2,0
2,8
3,6
4,6
5,7
6,8
8,0
9,2
10,6
12,0
13,2
14,7
16,0
17,4
18,9
20,3
21,9
23,3
1,0
1,0
1,0
1,0
1,0
1,0
1,1
1,2
1,4
1,5
1,6
1,7
1,8
2,0
2,1
2,2
2,3
2,4
2,6
2,7
2,8
1,0
1,1
1,3
1,5
1,9
2,3
2,8
3,3
3,8
4,4
4,9
5,4
5,9
6,4
6,9
7,4
7,9
8,5
9,0
9,5
10,0
14.7.4 Stresses due to internal pressure
14.7.4.1 End tangent
The circumferential membrane stress due to pressure:
2

P
θ ,t 
 Di  e  Lw E b
1 


2  e  D i  e  L w E b  D c E c Ac


P

(14.7.4-1)
shall comply with:
 θ ,t
P 
ft
14.7.4.2 Collar
The circumferential membrane stress due to pressure:

P
θ ,c 
1 

2 e

P
 D i  e  L w E b  D c E c Ac 
2
D c Lw E c
(14.7.4-2)
shall comply with:
320
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
 θ ,c  P   f c
14.7.4.3 Bellows convolutions
The following formulae are used to determine the bellows convolutions:
n) The circumferential membrane stress due to pressure:

θ
r
P 
2e
*
(14.7.4-3)
P
shall comply with:
 P  f
o) The meridionial membrane stress due to pressure:

m ,m
P

r  Dm  r 
P
* 
e  Dm  2r 
(14.7.4-4)
shall comply with:

m ,m
P 
f
14.7.5 Instability due to internal pressure
14.7.5.1 Column instability
The allowable internal design pressure to avoid column instability, Ps,c , is given by:
Ps ,c  0 , 1 5
 Kb
(14.7.5-1)
Nr
The internal pressure P shall not exceed
P s, c
:
P  P s, c
14.7.5.2 In-plane instability
Toroidal bellows are not subject to in-plane instability
14.7.6 External pressure design
14.7.6.1 Stresses due to external pressure
The rules of 14.7.4 shall be applied, taking P as the absolute value of the external pressure and using Ac in
the formulae.
When the expansion bellows is submitted to vacuum, the design shall assume that only the internal ply
resists the pressure. The pressure stress formulae of 14.7.4. shall be applied with np = 1.
UNI EN 13445-3:2021
321
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.7.6.2 Instability due to external pressure
Instability due to external pressure is not covered by the present rules.
14.7.7 Fatigue evaluation
14.7.7.1 Calculation of stresses due to the total equivalent axial displacement range q of each
convolution
The following formulae are used to determine the stresses due to the total equivalent axial displacement
range of q of each convolution.
p) The meridional membrane stress,  m ,m   q  , is given by:
E b  ep
*

m ,m
q  

2
34, 3 r
B1
3
(14.7.7-1)
q
q) The meridional bending stress, 
m ,b
  q  , is given by:
*

q 
m ,b 

E b ep B 2
5, 7 2 r
2
(14.7.7-2)
q
14.7.7.2 Calculation of the total stress range due to cyclic displacement
The total stress range due to cyclic displacement, 
eq
, is given by:
 e q  3  m ,m  P    m ,m   q    m ,b   q 
(14.7.7-3)
14.7.7.3 Calculation of the allowable number of cycles
14.7.7.3.1 General
r)
The specified number of cycles N spe shall be stated as a consideration of the anticipated number
of cycles expected to occur during the operating life of the bellows. The allowable number of
cycles N alw , as derived in this subclause, shall be at least equal to N s p e : N a lw  N s p e .
The allowable number of cycles given by the following formulae includes a reasonable safety
margin (factor 3 on cycles and 1,25 on stresses) and represents the maximum number of cycles for
the operating condition considered. Therefore an additional safety factor should not be applied: an
overly conservative estimate of cycles could necessitate a greater number of convolutions and
result in a bellows that is more prone to instability.
s)
If the bellows is submitted to different cycles of displacement, such as those produced by start-up
or shutdown, their cumulative damage shall be calculated using Miner's rule for cumulative
fatigue (see 18.5.6).
t)
Use of specific fatigue curves established by a manufacturer will be covered later and specific
requirements to be applied will be set-up in Annex K.3 (in course of consideration by
CEN/TC 54/WG C).
322
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.7.7.3.2 Austenitic steel and other similar materials
This subclause applies to as-formed bellows made of austenitic steel, nickel-chromium-iron and nickel-ironchromium alloys.
The allowable number of cycles are given by the following formulae (see Figure 14.7.7-1):
— if
E0
Eb

eq


11309, 4
 
 E 0   2 8 8, 2
eq
 E
 b
N a lw
where 
— if
E0
Eb

eq
eq
where 
E0
Eb

eq






3,25
(14.7.7-4)
is expressed in MPa;
 7 6 1 ,6 MPa:


12686, 3
 
 E 0   230, 6
eq
 E
 b
N a lw
— if
 7 6 1, 6 MPa:
eq






3,25
(14.7.7-5)
is expressed in MPa;
 2 3 0 , 6 MPa:
N a lw
 10
6
cycles shall be used.
The curve and the formula are only valid for:
10
2
 N alw  10
6
14.7.7.3.3 Ferritic steel
The fatigue design curves of 18.10 or 18.11, as appropriate, shall be used.
14.7.8 Axial rigidity
The theoretical axial rigidity of a bellows comprising N convolutions may be evaluated by the following
formula:
K
b

1
 
1 2 1  

2
b
 n 
p

 EbDm
   N 
*
3
 ep 

 B3


 r 
(14.7.8-1)
This formula is valid only in the elastic range.
UNI EN 13445-3:2021
323
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
Lower values for theoretical axial rigidity can be used outside this range, based on manufacturer's
experience or representative test results (see K.1).
Key
X
Number of cycles N
Y
σeq in MPa
Figure 14.7.7-1 — Fatigue curve at room temperature (E=E0) for toroidal as-formed bellows
324
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.8 Fabrication
14.8.1 Forming of the bellows
14.8.1.1 General
Different forming processes may be applied.
— Bellows as shown in Figure 14.1-1 shall be manufactured by cold forming (e.g. hydraulic and
similar processes, or roll forming).
— Bellows as shown in Figure 14.5.8-2 (half-convolutions) shall be manufactured by cold or hot roller
bending or other methods.
The forming processes used shall ensure a smooth profile free from scores, scratches or other stress raising
defects, and shall not affect the bellows resistance to corrosion.
14.8.1.2 Limitations for the forming process
The amount of forming given by the true strain of deformation sd according to Formula (14.5.2-13) shall
normally be limited to the true strain of rupture sr reduced by a factor kr:
s r  k r ln  1  A 5 / 1 0 0 
sd  sr
where
A5 is the percentage elongation at rupture, using a gauge length of five times the diameter;
kr is given by Table 14.8.1-1.
Table 14.8.1-1 — Safety factor kr
Material
Ply thickness
ep
Safety factor
kr
e p  0 ,7 mm
0,9
e p > 0 ,7 mm
0,8
all
0,5
Austenitica
ferriticb
a
See Clause 2
b Materials with A5  20 % and
UNI EN 13445-3:2021
R e,
T
Rm
 0 , 66
325
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.8.2 Heat treatment
Annealing of bellows after forming is not required if the limits according to 14.8.1.2 are met.
If there are exceptional cases, such as:
— a brittle fracture;
— corrosion; or
— if the limits of 14.8.1.2 have been exceeded;
where annealing is required, it shall be carried out in an inert atmosphere after the forming processes have
been completed.
14.8.3 Tolerances
14.8.3.1 General
This subclause deals with the tolerances that influence the main characteristics of a bellows (such as
pressure resistance, spring rate, fatigue and installation).
Dimensional tolerances of bellows convolutions depend on the tolerances of the base materials used, and on
the manufacturing processes. They are the responsibility of the expansion joint manufacturer.
14.8.3.2 U-shaped convolutions without circumferential welds
14.8.3.2.1 Ply thickness ep
The tolerance on the ply thickness, ep, is directly related to the nominal thickness, tN, of the material used for
the manufacture of the bellows.
The tolerances of the nominal thickness of the material, like strip, sheet, or plate, shall be in accordance with
Table 14.8.3.2.1-1:
Table 14.8.3.2.1-1 — Tolerances on wall thickness tN
EN 10258
tN
Limit deviations
EN 10259
tN
Limit deviations
≤ 0.4 mm
(F) Reduced
≤ 0.5 mm
(S) Special
> 0.4 mm
Normal
> 0.5 mm
Normal
14.8.3.2.2 Convolution height w
The tolerance on the convolution height w shall not be greater than ± 5 % for ep up to 0,5 mm, and ± 8 % for
ep greater 0,5 mm.
326
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.8.3.3 U-shaped convolutions with circumferential welds at their crest or root
14.8.3.3.1 Ply thickness ep
The tolerance of the nominal thickness of the plate material shall either be in accordance with EN 10259,
Normal, or shall not be greater than ± 6 % of tN if other standards are used. If the tolerance is greater than
± 6 % of tN, the actual mean thickness of the plate material shall be taken into account for the calculation.
14.8.3.3.2 Convolution height w
The tolerance on the convolution height w shall not be greater than ± 8 %.
14.8.3.3.3 Bellows tangent
The tolerance on the convolution bellows tangent shall be in accordance with the related pipe ends.
14.8.3.4 Toroidal bellows
To be defined later.
14.9 Inspection and testing
14.9.1 General
The following requirements are in addition to those of EN 13445-5:2021.
14.9.2 Non destructive examination
14.9.2.1 Circumferential attachment welds
Circumferential attachment welds shall comply with the requirements of Part 5. Lapped joints shall be
subjected to a magnetic particle, or dye penetrant, examination in accordance with requirements of EN
13445-5:2021 and to a 100 % leak test (see EN 13445-5:2021, Annex D).
The circumferential attachment welds of expansion bellows shall be designed and tested according to testing
groups 1, 2 or 3 (see EN 13445-5:2021, 6.6.1.1). The testing group selected for the attachment welds may be
different from the testing group used for the other parts of the vessel.
14.9.2.2 Convolutions welds
14.9.2.2.1 Circumferential welds at root or crest of convolutions
This subclause deals with convolutions circumferentially welded at their crest and/or root as covered
in 14.5.9.
Circumferential weld joints of convolutions shall be subjected to 100 % non-destructive examination in
accordance with requirements of EN 13445-5:2021.
14.9.2.2.2 Longitudinal welds
This clause applies to bellows manufactured out of cylinders that are convoluted after longitudinal butt
welding.
UNI EN 13445-3:2021
327
EN 13445-3:2021 (E)
Issue 1 (2021-05)
These longitudinal butt welds shall be subjected to:
— 100 % visual examination before forming the convolutions of the bellows;
— non-destructive examination in accordance with Table 14.9.2-1 after forming the convolutions of
the bellows.
For bellows fabricated in series, at least 10 % of the bellows, but not less than one, shall be subjected to nondestructive examination. Samples shall be taken throughout the production run during manufacture.
Table 14.9.2-1 — Non-destructive examination for longitudinal butt welds of bellows without
circumferential welds
Bellows forming method
Hydraulic, elastomer forming
or similar method
ep
mm
DN
Single ply
Multiply
Single ply
Multiply
≤ 1,5
—
—
PTa
outside
PTa
tight ply
> 1,5
PTa
outside
—
PTa
outside
PTa
tight ply
≤ ep, max
—
—
PTa
outside
PTa
tight ply
> ep, max
PT
outside
PTa
tight ply
PT
outside
PTa
tight ply
≤ 300
> 300
e p , max
Rolling
 min
 0 ,087
D
i
 ;  4 mm  
PT=Penetrant Testing
a The test shall be performed on the longitudinal welds at the outside crest and the inside root of the
convolutions, to the maximum extent possible considering physical accessibility.
14.9.2.3 Radiographic examination
When radiographic examination is performed, the requirements of EN 13445-5:2021, 6.6.3.2 apply, with the
following modifications to EN 13445-5:2021, Table 6.6.4-1:
— gas porosity and pores:
— maximum pore diameter: 0 , 4 e p ;
— maximum number of pores: 5 per 100 mm;
— elongated cavity: not permitted;
— inclusion: not permitted;
— lack of fusion and lack of penetration: not permitted;
— maximum undercut for short imperfections:
328
0 ,1 e p
.·A smooth transition is required;
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— shrinkage groove for short imperfections:
0 ,1 e p
.·A smooth transition is required.
14.9.3 Pressure test
Expansion bellows shall be tested in accordance with EN 13445-5:2021, 10.2.3.
However, the designer shall consider the possibility of instability of the bellows due to internal pressure if
the test pressure exceeds:
Pt,s  1,5 Max (Ps,c) ; (Ps,i)
(14.9.3-1)
where Ps,c and Ps,i shall be calculated at room temperature.
In this case, the designer shall either:
u) specify special precautions to be taken during the test; or
v) redesign the bellows to satisfy the test condition.
NOTE
For reinforced and toroidal bellows, use Ps ,i  0 in Formula (14.9.3-1).
14.9.4 Leak test
When a leak test is performed, EN 13445-5:2021, Annex D applies.
14.10 Bellows subjected to axial, lateral or angular displacements
14.10.1 General
The purpose of this subclause is to determine the equivalent axial displacement of an expansion bellows
subjected at its ends to:
— an axial displacement from the neutral position: x in extension (x > 0), or in compression (x < 0);
— a lateral deflection from the neutral position:
y (y > 0);
— an angular rotation from the neutral position:
  > 0).
14.10.2 Axial displacement
When the ends of the bellows are subjected to an axial displacement x (see Figure 14.10.2-1), the equivalent
axial displacement per convolution is given by:
q x 
1
N
(14.10.2-1)
x
Where x shall be taken: - positive for extension(x > 0)
- negative for compression
(x < 0)
Values of x in extension and compression may be different.
The corresponding axial force
Fx  K b  x
UNI EN 13445-3:2021
Fx
applied to the ends of the bellows is given by:
(14.10.2-2)
329
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
(1) initial length
Figure 14.10.2-1 — Bellows subjected to an axial displacement x
14.10.3 Lateral deflection
When the ends of the bellows are subjected to a lateral deflection y (see Figure 14.10.3-1), the maximum
equivalent axial displacement per convolution is given by:
q
y
3 Dm

N N  q + x 
(14.10.3-1)
y
where
y shall be taken positive.
The corresponding lateral force
Fy 
3 K
2
N
330
y

3K
applied to the ends of the bellows is given by:
2
b
 Dm
 q + x
2
(14.10.3-2)
 y
The corresponding moment
M
Fy
M
y
applied to the ends of the bellows is given by:
2
b
 Dm
4 N  q + x 
 y
(14.10.3-3)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
(1) initial length
Figure 14.10.3-1 — Bellows subjected to a lateral deflection y
14.10.4 Angular rotation
When the ends of the bellows are subjected to an angular rotation  (see Figure 14.10.4-1), the equivalent
axial displacement per convolution is given by:
q 
Dm
2N
(14.10.4-1)

where  ,expressed in radian, shall be taken positive.
The corresponding moment
M
θ

K
M
applied to the ends of the bellows is given by:
2
b
Dm
8
θ
(14.10.4-2)
Figure 14.10.4-1 — Bellows subjected to an angular rotation 
UNI EN 13445-3:2021
331
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.10.5 Total equivalent axial displacement range per convolution
14.10.5.1 Equivalent axial displacement per convolution
The equivalent axial displacement per convolution, in extension or compression, is given by:
q
e
 q
x
 q
y
 q
(extended convolution)
(14.10.5-1)
q
c
 q
x
 q
y
 q
(compressed convolution)
(14.10.5-2)
14.10.5.2 Bellows installed without cold spring
This subclause applies when the bellows is submitted to displacements (see Figure 14.10.5-1):
— from the neutral position  x 0
 0,y
0
 0 ,
0
 0
— to the operating position (x, y, )
The equivalent axial displacement, in extension or compression, of each convolution is given by:
q
e
 q
x
 q
y
 q
(extension)
(14.10.5-3)
q
c
 q
x
 q
y
 q
(compression)
(14.10.5-4)
If x > 0 : first formula controls
If x < 0 : second formula controls
The total equivalent axial displacement range is given by:
 q  max
q e
, q
c
…(14.10.5-5)

Key
(n) neutral position
(1) operating position q
Figure 14.10.5-1 — Cyclic displacements
332
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.10.5.3Bellows installed with cold spring
This sublclause applies when the bellows is submitted to displacements (see Figure 14.10.5-2):
— from an initial position  x 0 , y 0 ,  0  , which is not the neutral position,
 q e,0   q x,0   q y,0   q  , 0
(extension)
(14.10.5-6)
 q c,0   q x,0   q y,0   q  , 0
(compression)
(14.10.5-7)
— to the operating position (x, y, )
 q
x
 q
y
 q
(extension)
(14.10.5-8)
q c  q
x
 q
y
 q
(compression)
(14.10.5-9)
q
e
The total equivalent axial displacement range is given by:
 q  max
 q
e
  q c,0 ,  q c   q
(n) neutral position
e,0

(14.10.5-10)
(0) initial position q0
(1) operating position q
Figure 14.10.5-2 — Cyclic displacements
UNI EN 13445-3:2021
333
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14.10.5.4 Bellows extending between two operating positions
This subclause applies when the bellows is submitted to displacements (see Figure 14.10.5-3):
— from operating position 1  x 1 , y 1 ,  1  ,
 q e,1   q x,1   q y,1   q  ,1
(extension)
(14.10.5-11)
 q c,1   q x,1   q y,1   q  ,1
(compression)
(14.10.5-12)
— to operating position 2  x 2 , y 2 ,  2 
 q e,2   q x,2   q y,2   q  , 2
(extension)
(14.10.5-13)
 q c,2   q x,2   q y,2   q  , 2
(compression)
(14.10.5-14)
The total equivalent axial displacement range is given by:
 q  max
 q
e,2
  q c,1 ,  q c,2   q
e,1

(14.10.5-15)
An initial cold spring (initial position 0) has no effect on the results.
Key
(0) initial position 0
(1) operating position 1
(n) neutral position
(2) operating position 2
Figure 14.10.5-3 — Cyclic displacements
334
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
15 Pressure vessels of rectangular section
15.1 Purpose
This clause specifies requirements for the design of unreinforced and reinforced pressure vessels of
rectangular cross-section. For fatigue, designs shall be checked against Clause 18. Thermal loads or effects
are not considered in this clause.
15.2 Specific definitions
The following terms and definitions apply in addition to those in Clause 3. The governing stresses in this
clause are not structural stress within the meaning of Clause 18.
15.2.1
membrane stress
equivalent uniform stress through the wall of the vessel, see also C.4.4.2
15.2.2
bending stress
equivalent linear distributed stress through the wall of the vessel, see also C.4.4.3
15.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in Clause 4:
a
is the inside corner radius;
A
is the area in vessel’s longitudinal direction without hole between stiffeners or between
stiffener walls;
Ah
is the area A reduced by hole;
Arf
is the required reinforcing area;
A1
is the cross-sectional area of a reinforcing member which is attached to the short side of a
vessel;
A2
is the cross-sectional area of a reinforcing member which is attached to the long side of the
vessel;
Aw1
is cross sectional area of short side stiffener webs at corner;
Aw2
is cross sectional area of long side stiffener webs at corner;
A’
is the area of that part of the composite section above or below the calculation point;
A’web
is the area of the reinforcement web;
b
is the unsupported width of a flat plate between reinforcing elements, see Figure 15.6–1;
bcw
is the weld throat dimension of the continuous weld;
be
is the effective width of a plate in combination with a reinforcing member, see Figure 15.6–1;
bR
is the pitch between centrelines of reinforcing members on a vessel;
bv
is the length of side wall (either h or H);
bw
is the weld throat dimension of the intermittent weld;
UNI EN 13445-3:2021
335
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C
is a shape factor determined from the long and short sides of an unsupported plate between
stiffeners, see Table 15.6–2;
c
is the distance from the neutral axis of a section to the outer fibre of a section and is positive
when inwards;
d
is either the diameter of an opening or the inside diameter of a welded connection if attached
by a full penetration weld;
G
is the shear modulus (by steel appr. E/2.6);
g
is the length of an unsupported span;
gw
is the gap between intermittent welds;
h
is the inside length of the long side;
h1
is the distance between the neutral axes of reinforcing members on the long side;
H
is the inside length of the short side;
H1
is the distance between the neutral axes of reinforcing members on the short side;
I
is the applicable second moment of area;
I1, I2, I3 is the second moment of area per unit width of a plate strip;
I11
is the second moment of area of the combined reinforcing member and plate on the short side
of the vessel;
I21
is the second moment of area of the combined reinforcing member and plate on the long side
of the vessel;
J 1, J 2
is the stress correction factors of short vessels;
j
is the distance from the neutral axis of the centroid of A’;
jweb
is the distance from the neutral axis of the centroid of A`web;
k
is a factor, see Formula (15.5.2–4) or (15.6.5–5);
k1
is factor, see Formula (15.5.3–13);
k2
is factor, see Formula (15.5.3–14);
K3
is a factor for unreinforced vessel to Figure 15.5–1, see Formula (15.5.1.2–12);
Lv
is the length of vessel;
L1
is the half length of the shorter side of vessel (see Figure 15.5–1);
L2
is the half length of the longer side of vessel;
Lx
is the distance from centreline of shorter side plate to calculation point (mid of ligament or
weld seam) in perpendicular direction to vessel axis;
Ly
is the distance from centreline of longer side plate to calculation point (mid of ligament or weld
seam) in perpendicular direction to vessel axis;
lw
is the length of the intermittent weld;
MA
is the bending moment at the middle of the long side in transversal direction of vessel, it is
positive when the outside surface of the vessel (or reinforcement) has compressive stress. It is
expressed as bending moment per unit length (in N·mm/mm);
MBC
is the bending moment in the corner of the vessel;
MD
is the bending moment at the middle of the short side of the vessel;
336
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
MX
is the bending moment at distance Lx;
My
is the bending moment at distance Ly;
N
is factor, see Formula (15.5.3–10);
p
is the hole pitch along the plate length, see Figure 15.5–2;
ps
is the diagonal hole pitch in triangular hole pattern, see Figure 15.5–2;
Q
is the shear force;
S1
is the first moment of area of short side reinforcement cross section at corner in respect to
outside surface of shell plate;
S2
is the first moment of area of long side reinforcement cross section at corner in respect to
outside surface of shell plate;
tw
is the thickness of web;
W
is the elastic section modulus of combined cross section;
Wp
is the plastic section modulus of combined (shell wall +stiffener) cross section:
α
is H / h;
α1
is H1 / h1;
α2
is L2 / L1;
β
is the angle between the line of the holes and the long axis, see Figure 15.5–2;
θ
is an angle indicating position at the corner of a vessel, see Figure 15.5–2;
μ
is ligament efficiency;
σb
is bending stress;
σm
is membrane stress;
ϕ
is a factor, see Formula (15.5.1.2–15);
15.4 General
The formulas given in this subclause shall be used for calculation of the membrane and bending stresses in
unreinforced and reinforced rectangular pressure vessels. The total stress at the point of consideration shall
be taken as the sum of the membrane stress and the bending stress at that location.
For pressure vessels provided with doors a special analysis according either to Annex C or to Annex B shall be
performed to detect any deformation in the door and the edge of the vessel.
Special care should be taken in the choice of gasket for the door.
15.5 Unreinforced vessels
15.5.1 Unreinforced vessels without a stay
15.5.1.1 General
This method applies to vessels of the type shown in Figure 15.5-1. The given formulas are applicable to
vessels with length Lv < 4h. The use of method for shorter vessels is conservative. The walls of short vessels
with length Lv < 2h may be designed acc. to requirements in cl. 15.5.5.
UNI EN 13445-3:2021
337
EN 13445-3:2021 (E)
Issue 1 (2021-05)
It is assumed that the thicknesses of the short and long sides are equal. When they are not, the method
in 15.5.3 shall be used.
15.5.1.2 Unperforated plates
Where the thickness of the smaller side is not the same as the thickness of the longer side, the calculation
method in 15.5.3 shall be used.
For unreinforced vessels conforming to Figure 15.5-1, the membrane stresses are determined from the
following formulas:
at C,

P a  L
 m  C

 m  D

 m  B

 m  A

2

1

(15.5.1.2-1)
e
at D,
 m  C
at B,

P a  L
(15.5.1.2-2)
e
at A,
 m  B
at a corner, e.g. between B and C, it is given by:
 m  B  C

P 
a 
e 
L
2
2
 L
2
1
 

(15.5.1.2-3)
The second moment of area is given by:
I1 = I2 = e3/12
338
(15.5.1.2-4)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 15.5-1 — Unreinforced vessels
The bending stresses shall be determined from the following formulas:
at C,
 b  C
 
 b  D
 
 b  A
 
 b  B
 
e
4I
1

2M

A

2M

A

2

2
 P 2a  L
 2a  L
1
 L
2
2
 
(15.5.1.2-5)
at D,
e
4I
1
 P 2a  L
 2a  L
1
 L
2
2
 L
2
1
 
(15.5.1.2-6)
at A,
M
A
2I
e
(15.5.1.2-7)
1
at B,
e
4I
1
UNI EN 13445-3:2021
2 M
A
 PL
2
2

(15.5.1.2-8)
339
EN 13445-3:2021 (E)
Issue 1 (2021-05)
at the corner,
 b  B  C
 
e
4I
1
2 M
A
2 
 P  2 a L c o s   L ( 1  s in  )  L
2
1
2 





(15.5.1.2-9)
For these formulas the following shall apply:
w) the maximum value of   b 
is given where 
BC
 L1
 arctan
/ L
2
(15.5.1.2-10)

and
x) the bending moment MA per unit length, is given by:
M
A
 P  ( K
3
(15.5.1.2-11)
)
where
L
K

3
2
 

2
1
6
2

2
 3
2
 6
2
 

3
2
3 2
L

L
 3
2
2
2
 6   2  1 .5  
   2

   6  
2

(15.5.1.2-12)
(15.5.1.2-13)
2
1
a
L
2
2
(15.5.1.2-14)
1
At a location, the maximum stress shall be obtained as stated in 15.4 by summarizing the membrane and
bending stresses.
15.5.1.3 Perforated plates
The vessel with perforated side plates shall fulfil the requirements of unperforated plates in 15.5.1.2. Side
plate of vessel (or pipe) may be perforated by row or rows of holes. The pattern of holes placing is triangular
or square. The ligament efficiency of a perforated side plate is given by:

  m in 


p  d
p
;
 p  d 
s



cos   p
s


1
(15.5.1.3-1)
where β is the angle of hole pattern as defined in Figure 15.5-2.
Ligament efficiency μ is used to reduce the allowable stresses in 15.5.5 of membrane and bending stresses in
perpendicular direction to vessel axis. For short vessels acc. 15.5.4 the ligament efficiency shall be minimum
of those defined both in direction of longitudinal axis and perpendicular to longitudinal axis of the vessel and
only the first part of Formula (15.5.1.3-1) shall be used.
If the pitch and diameter varies in plate, the smallest value of μ shall be chosen. The strength at single
opening, even for opening in row of holes, shall be checked acc. to chapter 15.7.
340
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 15.5-2 — Unreinforced vessels with perforated sides
If the ligament efficiency μ is at least 0,2, the membrane stresses shall be determined at point of
consideration (mid of ligament) in direction perpendicular to vessel axis from the following formulas:
On longer side
 m  y

 m  B
 b  y
 
e
4I
1
2 M
(15.5.1.3-2)
A
 PL
2
y

(15.5.1.3-3)
On shorter side
 m  x
 b  x

(15.5.1.3-4)
 m  C
 
e
4I
1


2 M


A

2
 P 2 a  L  2a  L  L

2
1
2

 L1
 L
x

2





(15.5.1.3-5)
Ly and Lx are distances from vessel side plate centrelines to midpoint of ligament measured perpendicularly
to vessel axis.
The allowable values for membrane and bending stresses are given in 15.5.5.
UNI EN 13445-3:2021
341
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The sum of stresses shall fulfil that requirement at all points with no hole circle closer to the other vessel
wall than the distance a or 0,5d, whichever is the largest.
For holes closer to the wall or for   0,2, a stress analyses according to Annex C shall be performed.
15.5.2 Unreinforced vessels with a central partition plate
Figure 15.5-3 — Unreinforced vessel with a central partition plate
For unreinforced vessels with a central partition plate, as shown in Figure 15.5-3 the membrane stresses
shall be determined from the following formulas.
at C,
 m  c


 2  k (5  
P h 
4  

4e 
1  2k
1 

 m  D

 m  c
 m  b

2

)



(15.5.2-1)
at D,
at B,
p H
2e
(15.5.2-2)
2
at A,
342
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
In partition plate
 m  P
k 
 
I
I
2

 2  k (5  

1  2k


P h
2e
3
2
)



(15.5.2-3)
(15.5.2-4)

1
H
(15.5.2-5)
h
The bending stresses shall be determined from the following formulas.
at C,
2

c

 b  D


B

A

b
P h e
24  I
 1  2 2  k 




1  2k


1
1
(15.5.2-6)
at D,
P e

3H


1
48  I
1
2
 2h
2
 1  2 2  k  




1  2k


(15.5.2-7)
at B,
b
P h
2
24 I
e
2
2
 1  2 2  k 




1  2k


(15.5.2-8)
at A,
2

b
Ph e
24 I
2
2
 1  k (3  

1  2k


2
)



(15.5.2-9)
The allowable membrane and bending stresses are given in 15.5.5.
UNI EN 13445-3:2021
343
EN 13445-3:2021 (E)
Issue 1 (2021-05)
15.5.3 Unreinforced vessel, opposite plates of long sides having different thicknesses
Figure 15.5-4 — Unreinforced vessel with different thicknesses in long sides
Membrane stresses in short side plates

m

P h
2 e
(15.5.3-1)
1
Membrane stresses in long side plates
 m  A 1
 m  A


4 N H
P
8NHe
P
8NHe
3
2
4 N H
2
2
 2h
 2h
2
2
 K


 K


2
2
 k
 k
2

k
2

k
1
K 1
 k
1
K 1
 k
2
   2k2 K 2
 K
2
   2k2 K 2
 K
1
1
  
(15.5.3-2)
  
(15.5.3-3)
Bending stresses
Short side plates
 b  C
 b  C 1
Pe h
2
 K  k k
2
1 2


1

8NHI

1
Pe h
 k
2
 
(15.5.3-4)
2
 K k  k
1 1
2


1
8NHI
   2k2 K 2
1
   2k2 K 1
 k
2
 
(15.5.3-5)
Long side plates
344
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)






A
b
3
16 NHI
 A1
b
C
b
3
Pe h
2
16 NHI
2    K
 k k
1
1
k
 K  k k
2
1 2


3
8NHI
3
Pe h
1
2
 k
   2k2 K 2
2
 k
   2k2 K 1
2
 k
  
2
N

   N 
(15.5.3-6)
(15.5.3-7)
8NHI
   2k2 K 2
 k
2
 
(15.5.3-8)
2
 K k  k
1 1
2


2

2
2
2
Pe h

2    K
2

C 1
b
2
Pe h

2
   2k2 K 1
 k
2
 
(15.5.3-9)
where
N  K K
1
K
K
k
k
 2k
1
 3k
2
1

 


2

  


 
I
I
I
1
2
3



 k
2
 2k
2


I 
2 
I
3


I 
1 
I
3
H
(15.5.3-14)
(15.5.3-16)
3
2
12
e
(15.5.3-13)
3
1
12
e
(15.5.3-12)
(15.5.3-15)
h
e
(15.5.3-10)
(15.5.3-11)
 3
2
1
2
2
(15.5.3-17)
3
3
12
(15.5.3-18)
Allowable stresses are given in 15.5.5.
15.5.4 Design of short, unreinforced vessel with length Lv < 2 h
For short, unreinforced rectangular vessels equipped with end plates the design methods of cl. 15.5.1 and
15.5.3 are used with following additional rules. This rule is applicable, when the corner radius a = 0
UNI EN 13445-3:2021
345
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The bending stresses of Formulae (15.5.1.2-5)… (15.5.1.2-9) shall be corrected in the midspans of plates
(points A and D) multiplying them by factor J1 and in corners (B,C) by factor J2 of Table 15.5.4-1.
Bending stresses acc to Formulae (15.5.3-6) and (15.5.3-7) shall be multiplied by J1 and bending stresses of
Formulae (15.5.3-4) and (15.5.3-5) and (15.5.3-8) and (15.5.3-9) shall be multiplied by J2.
Stresses of both side plates shall be calculated separately using the appropriate values of J1 and J2 defined to
each side plate.
For Lv < h the axis of the vessel shall be rotated so that the largest dimension becomes the vessel length and
the new length Lv ≥ 2 h. All stresses shall be calculated using the new orientation.
Table 15.5.4-1
Lv/bv 1
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1,9
2,0
J1
0,56 0,64
0,73
0,79
0,85
0,89
0,92
0,95
0,97
0,99
1,0
J2
0,62 0,70
0,77
0,82
0,87
0,91
0,94
0,96
0,97
0,99
1,0
where
Lv
is the length of vessel
bv
is h or H
15.5.5 Allowable stresses for unreinforced vessel
The membrane stresses shall be limited as follows:

m
 f z
(15.5.5-1)
The sum of membrane stresses and bending stresses shall conform to:

m

b
 1, 5  f  z
(15.5.5-2)
where
z = weld joint efficiency (= 1 for location without longitudinal weld) or ligament efficiency μ of
perforated plate (see 15.5.1.3) whichever is smaller. The bending stresses at the weld location can
be calculated by similar way as the stresses at mid of ligament in Clause 15.5.1.3.
15.6 Reinforced vessels
15.6.1 General
Reinforced vessels, as shown in Figure 15.6-1, have a continuous frame which may either follow the
contour of the vessel or form a closed rectangle. The reinforcing members shall be fitted to the outside of
the vessel in a plane perpendicular to the long axis of the vessel.
This calculation method is applicable if the two opposite sides of the vessel have the same second moment
of area. Where they do not, a special analysis shall be performed. The calculation rule does not cover the
case where reinforcement is a separate pressure chamber.
346
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The effective length be is limited by 10e (EN 1993-1-5 may be used as alternative)
Figure 15.6-1 — Reinforcing member and associated effective plate width
15.6.2 Shear strength of reinforced section
15.6.2.1 General
The reinforcing members and the attached plate elements of the vessel shall be considered to act as a
composite unit when calculating the effective second moment of area of the reinforcing members. In order
to ensure this structural behaviour, the shear stress in the reinforcement web and in the weld between
reinforcing elements and vessel shall be limited as shown below.
15.6.2.2 Continuously welded reinforcements
For continuously welded reinforcements, the shear stress in the weld joining web to vessel shall be
calculated by the following formula.
 
,
Q  A  j
I 

b
 0, 5  f
(15.6.2.2-1)
cw
where
Q
is the shear load at the section near the corner
A’
is the area of that part of the composite section above or below the calculation point
j
is the distance from the neutral axis of the centroid of A’
I
is the second moment of area of the composite cross section
Σbcw
is the net width of the section measured (total thickness of the webs or, in partial penetration welds,
sum of weld throat thicknesses);
15.6.2.3 Reinforcement attached by intermittent welds
Intermittent welding shall be placed on both sides of the reinforcing member with the weld throat bw at least
0,75 × minimum wall thicknesses. The length of each individual fillet weld shall not be less than 50 mm and
and start at the corner (at the radius tangent point) of the reinforcement. The total length of intermittent
UNI EN 13445-3:2021
347
EN 13445-3:2021 (E)
Issue 1 (2021-05)
welds on each side of the reinforcing member shall not be less than one-half of the length being reinforced
on the shell, see Figure 15.6-3.
Welds in reinforcements members shall be full penetration welds.
In the case of vacuum vessels, the maximum length between two adjacent weld segments shall be ≤ 0,5bR .
The maximum spacing between consecutive weld segments of reinforcing member to vessel shall not be
greater than the shorter of the two adjacent welding segments.
The shear stress in intermittent weld segments shall be calculated by the following formula:
τ
w

Q  A
,  j  (l  g )
w
w
I l

w

(15.6.2.2-2)
 0 ,5  f
bw
where
Q
is the shear force
A’
is the area of that part of the composite section above or below the calculation
point
gw is the gap between intermittent welds
j
is the distance from the neutral axis of the centroid of A’
I
is the applicable second moment of area (I11 or I21);
bw is the weld throat of the intermittent weld;
lw
is the length of the intermittent weld.
15.6.2.4 Shear stress in reinforcement webs
In reinforcing elements, the shear stress in the webs shall be calculated by the following formula:

w

Q  A`
I 
w eb

j
t
w eb
 0, 5  f
(15.6.2.3-1)
w
where
Q
is the shear force near the corner
A’web is the area of the reinforcement web
jweb
is the distance from the neutral axis of the centroid of A`web
I
is the applicable second moment of area (I11 or I21);
tw
is the thickness of web;
and when there is only pressure load

h
H 
Q  m ax  P  ; P 
  bR
2
2 

348
(15.6.2.3-2)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 15.6-2 — Reinforcement sections
15.6.3 Stability requirements for compressed parts
The maximum width to thickness ratios for the reinforcement sections shown in Figure 15.6-2 shall be in
accordance with Table 15.6-1.
UNI EN 13445-3:2021
349
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 15.6-1 — Maximum widths of reinforcing elements (For more detailed evaluation
standard EN 1993–1-5 may be used)
WEBS
(Flat elements perpendicular to the bending axis)
Sketch (see
Figure 15.6–
2)
Type of
section
a1, a2, a3
♦ Rolled or cold formed
dw = hr – tf
b1, b2, b3
♦ Welded
dw = hr – tf
c1, c2
♦ Rolled or cold formed
dw = hr
♦ Welded
dw = hr
reinforced
Width evaluation
Maximum ratio
dw/tw < = 50 ε
dw/tw < = 10 ε
FLANGES
(Flat elements parallel to the bending axis)
Sketch
Type of section
Width evaluation
Maximum ratio
a1
♦ Rolled or cold formed
bf
bf/tf < = 30 ε
a2, a3
♦ Welded
bf
b1, b2
b3, a3
♦ Rolled or cold formed
bf = bof+ tw
♦ Welded
bf = bof
VESSEL WALL
(plate space between two reinforcing elements)
Sketch
Type of section
Width evaluation
bf/tw < = 10 ε
Maximum ratio
b1 = 0,5 bf
d
transversal section
reinforced vessel
of
b2 = 0,5 br
bv/e < = 30 ε
bv = max(b1,b2)
 
235
Y

E
210000
where
Y = Rp0,2/T for ferritic steels and Rp1,0/T for austenitic steels
350
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 15.6-3 — Intermittent welds of reinforcing
15.6.4 Wall stresses in unsupported zones
On the unsupported rectangular flat plate elements of the vessel wall between or inside the reinforcing
elements, the longitudinal membrane stress and the longitudinal bending stress adjacent to the
reinforcement webs shall be calculated from the following formulas:


m

P
hH

e 2 h  H
b 
 CP  
b
 e 
(15.6.4-1)

2
(15.6.4-2)
where C is obtained from Table 15.6-2.
Table 15.6-2 — Factor C
g/b
1
1,2
1,4
1,6
1,8
2
> 2,15
C
0,3078
0,3834
0,4356
0,468
0,4872
0,4974
0,5
and
b is the length of the smaller side of the rectangular plate (free width between stiffeners or free
width inside box stiffener)
g is the length of longer side of unsupported plate
UNI EN 13445-3:2021
351
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Separate flat plates’ calculations by other parts of this standard are not required except for end closures.
The stresses shall be limited as given in 15.5.5. Ligament efficiency shall be minimum value of all ligaments
calculated by the first part of Formula (15.5.1.3-1).
15.6.5 Membrane and bending stresses in the transverse section
With reference to Figure 15.6-4, the transverse membrane stresses shall be calculated from the following
formulas:
for the short sides
 m  D

P hb

2 A
1
(15.6.5-1)
R
 b e
R

for the long sides
 m  A

P H b

2 A
2
(15.6.5-2)
R
 b e
R

Figure 15.6-4 — Reinforced vessel
Because of shear plasticity effects in stiffeners at corners, the bending moment in corner is reduced on basis
of cross sectional values of stiffeners to following value:
352
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
M
P b

BC
h
R
2
12


2

k
1  
1

 S

I
S
E
1
21
2



 k  1 

h G  A
I
A
w2
1
11
 w1













(15.6.5-3)
where
H
1 
(15.6.5-4)
1
h
1
Aw1 is cross sectional area of short side stiffener webs at corner
Aw2 is cross sectional area of long side stiffener webs at corner
G
is the shear modulus (by steel appr. E/2.6)
S1
is the first moment of area of short side reinforcement cross section at corner in respect to outside
surface of shell plate
S2
is the first moment of area of long side reinforcement cross section at corner in respect to outside
surface of shell plate
k 
H
h

I
I
(15.6.5-5)
21
11
The bending stresses and moments at midspans shall be determined as follows:
at A,
M
(
A
b
 M
)
A

Pb h
BC
M
A
I
2
(15.6.5-6)
R

8
c
(15.6.5-7)
21
at B
(
b
)
B

M
c
BC
I
(15.6.5-8)
21
at C
(
b
)
c

M
BC
I
c
(15.6.5-9)
11
at D,
M
D
 M
BC

UNI EN 13445-3:2021
Pb h
R
8
2

2
(15.6.5-10)
353
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(
b
)
D
M

D
I
c
(15.6.5-11)
11
If the longitudinal weld is not located at midline of span, the bending stresses at the weld can be calculated
by previous formulas using the following moments Mx and My instead of MA and MD respectively:
M
x
 M
A

P b
y
 M
D
L
2
(15.6.5-12)
x
2
P b
M
R

R
L
2
y
(15.6.5-13)
2
where
Lx and Ly are distances from side span centrelines to longitudinal weld of plate or cross sectional
weld (in longitudinal direction of vessel) of reinforcement depending the point under consideration
15.6.6 Allowable stresses in the stiffeners and associated walls
The membrane stresses shall be limited as follows:

m
(15.6.6-1)
 f z
The sum of membrane stresses and bending stresses shall at all points conform to:
W

m
 
b

W
p
(15.6.6-2)
 f z
where
Wp
is the plastic section modulus of combined (shell wall +stiffener) cross section
NOTE
Wp allows (based on the theoretical plastic bearing behaviour of the cross section) higher deflections of
the reinforced section and does not consider the usability.
Plastic section modulus Wp is calculated as follows:
1) Calculate the location of plastic neutral axis of whole combined cross section (the areas on both
sides of neutral axis are equal),
2) Calculate the distances of both surfaces’ midpoints from the neutral axis defined in 1,
3) Multiply the cross section area above neutral axis by its midpoint’s distance to neutral axis and
add the cross section area below the neutral axis multiplied by its distance to neutral axis,
4) The sum of the two products in 3. is the plastic section modulus.
W is the elastic section modulus of combined cross section
z
= 1 for location without longitudinal (vessel axis direction) weld and no perpendicular welding in the
stiffeners.
If a section is built of more than one material, f is the value for the material at the point under consideration.
354
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The shear stress in the web and in the weld between stiffener and vessel plate shall not exceed 0,5 f.
15.7 Openings
15.7.1 Limitations
The following formulas for reinforcement can be applied only to openings with diameter of the opening not
exceeding 0,8 b. The distance between the edge of any opening and the side of the vessel or between the
edge of opening and reinforcing member shall not be less than the largest of ‘a’ or 0,1 b.
Stress analysis shall be performed for openings in the rounded corner or closer to the vessel wall or
reinforcing member’s wall.
If reinforcement pads are used, their thickness shall be limited to nominal vessel wall thickness and in the
calculations they shall not be extended to more than the distance ‘d’ (diameter of opening) from the centre
of the opening.
No portion of reinforcement shall be considered as applying to more than one opening, nor shall it be
considered more than once in a combined area.
15.7.2 Unreinforced vessels
Perforated plates shall be designed acc. to rules in 15.5.1.3.
Single opening can be reinforced acc. to rules in 15.7.3 with following additions:
The membrane and bending stresses shall be calculated by formulae in 15.5 depending on the location of
the hole on the long side or the short side of the vessel.
In unstayed vessels bending stresses at centre of opening can be calculated more exactly as in rules of
15.5.1.3.
Membrane stress σm and bending stress σb is used in Formulae (15.7.3-1) and (15.7.3-2).
15.7.3 Reinforced vessels
Ligament efficiency of perforated plate between stiffeners or inside stiffeners or in pressurized stiffener
flanges and webs shall be taken into account acc. cl. 15.6.4.
Reinforcement of an opening is not required when:
(σm + σb) ⋅
A
A
 1, 5  f
(15.7.3-1)
h
where
A is the area in vessel’s longitudinal direction without hole between stiffeners or between stiffener walls;
Ah is the same area reduced by the hole.
When reinforcement of an opening is required, the required reinforcement shall be calculated according to
the following formula:
UNI EN 13445-3:2021
355
EN 13445-3:2021 (E)
Issue 1 (2021-05)
A
rf

 0, 5 
m
 
1, 5  f
b
(15.7.3-2)
d e
The reinforcing area A’ shall be at least Arf and shall be calculated as in 10.6.2.2.
f and e in Formulas (15.7.3-1) and (15.7.3-2) are the nominal design stress and thickness of the part and
point of consideration.
The membrane stress σm shall be calculated by Formulae (15.6.5-1) or (15.6.5-2) depending on the
location of the hole on the long side or the short side of the vessel.
The bending moments shall be obtained from the Formulae (15.6.5-12) and (15.6.5-13).
The bending stress σb at the opening on the short side:
(
b
)
x

M
x
I
c
(15.7.3-3)
11
and at the opening on the long side:
M
(
b
)
y

y
I
c
(15.7.3-4)
21
where
Mx is bending moment at opening at distance Lx from short side centreline, see Formula (15.6.5–
12)
My is bending moment at opening at distance Ly from long side centreline, see Formula (15.6.5–13)
16 Additional non-pressure loads
16.1 Purpose
This clause provides rules for the design of vessel shells under non-pressure loads in combination with
pressure:
— Local loads on nozzles in spherical shells;
— Local loads on nozzles in cylindrical shells;
— Line loads;
— Lifting lugs;
— Horizontal vessels on saddle supports;
356
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— Horizontal vessels on ring supports;
— Vertical vessels on bracket supports;
— Vertical vessels with supporting legs;
— Vertical vessels with skirts;
— Vertical vessels with ring supports;
— Global loads.
16.2 Specific definitions
The following definitions are in addition to those in Clause 3.
16.2.1
local load
a direct force, shear force or bending moment applying at a nozzle or attachment and due to a loading
other than the pressure in the vessel
16.2.2
global bending moment
a moment acting in a plane containing the axis of a shell
Note 1 to entry: Examples are moment due to wind loading on a vertical vessel or weight on a horizontal vessel - see
Figure 16.2-1.
16.2.3
global axial force
a force acting along the axis of a vessel
Note 1 to entry: An example is the action of weight on a vertical vessel, see Figure 16.2-1.
16.2.4
global shear force
a transverse force acting perpendicular to the axis of the vessel
Note 1 to entry: An example is the shear force at the saddles on a horizontal vessel due to weight.
16.3 Specific symbols and abbreviations
The following symbols and abbreviation are in addition to those in Clause 4:
e2
is thickness of a reinforcing plate;
f2
is allowable design stress of a reinforcing plate;
Di
is inside diameter of a cylindrical shell or dished head;
Dk
is inside diameter of a conical shell at the centre of the supporting element;
UNI EN 13445-3:2021
357
EN 13445-3:2021 (E)
Issue 1 (2021-05)
F
is global additional axial force (ignoring pressure loads) on a cylindrical, spherical or conical
shell, see Figure 16.2-1;
Fmax
is maximum allowable global additional axial force on a shell;
Hi
is inside height of a dished head measured from the tangent line;
M
is global bending moment of all the external forces relative to the centre of a specific shell
cross-section;
Mmax
is maximum allowable global bending moment on a shell;
P
is calculation pressure as defined in 3.4, noting that internal pressure P is positive and external
pressure is negative;
Q
is global shear force on a shell, see Figure 16.2-1;
Qmax
is maximum allowable transverse force on a shell;
Ri
is inside radius of a spherical or cylindrical shell or the spherical part of a dished head;
K1 to K19
are coefficients;
358
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.2-1 ― Global loads as applied to a cylindrical shell
16.4 Local loads on nozzles in spherical shells
16.4.1 Purpose
This clause provides a method for the design of a spherical shell with a nozzle subjected to local loads and
internal pressure.
In cases where the loads are unknown see Annex V.
16.4.2 Additional specific symbols and abbreviations
The following symbols and abbreviations are in addition to those in Clause 4 and 16.3:
d
is mean nozzle diameter;
di
is inside nozzle diameter;
de
is outside nozzle diameter;
d2
is outside diameter of a reinforcing plate;
ec
is analysis thickness of the combined shell and reinforcing plate;
eeq
is equivalent shell thickness;
eb
is nozzle thickness;
fb
is allowable design stress of nozzle material;
FS
is nozzle shear force;
FZ
is axial nozzle force (positive when force is tensile or radially outwards);
FZ,max
is maximum allowable axial force on the nozzle;
L
is width of the reinforcing plate;
UNI EN 13445-3:2021
359
EN 13445-3:2021 (E)
Issue 1 (2021-05)
MB
is bending moment in the nozzle at the junction with the shell;
MB,max
is maximum allowable bending moment in the nozzle at the shell junction;
MZ
is torsional nozzle moment
R
is mean shell radius at the nozzle;
scfP, scfZ and scfM
are stress factors due to pressure, nozzle axial load and moment respectively;
ΔσP
is stress range due to pressure;
ΔσFZ
is stress range due to axial nozzle load range;
ΔσMB
is stress range due to moment range;
κ
is reinforcement rate factor;
λS
is a geometric parameter applicable to nozzles in spheres;
τ
is the shear stress in shell;
τF
is the shear stress in shell caused by shear force;
τZ
is the shear stress caused by torsional moment;
Φ
is load ratio.
16.4.3 Conditions of applicability
The following conditions apply:
y) 0,001 ≤ ea / R ≤ 0,1 ;
NOTE
Values of ea / R < 0,001 are acceptable provided that the shell wall deflection does not exceed half the
wall thickness.
z) distances to any other local load in any direction shall be not less than
aa) nozzle thickness shall be maintained over a distance of
l 
d  e
b
R  e
c
;
.
16.4.4 Summary of design procedure
The design procedure is as follows:
a) calculate the basic dimensions ec and L from the following:
1) at the nozzle outside diameter, when a reinforcing plate is fitted:
e
c
 e
a
 e
2
 f

2
;1 
 m in 
 f



(16.4-1)
2) at the outside edge (d = d2) of a reinforcing plate, or when no reinforcing plate is fitted:
ec = ea
360
(16.4-2)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Width L of the reinforcing pad given by:
L  0, 5
d2
 d
e

(16.4-3)
b) calculate the maximum allowable individual loads (see 16.4.5);
c) check the load ratios and the interaction of the loads (see 16.4.6);
d) if no reinforcing plate or a reinforcing plate with
L 
R (e
a
 e
2
)
is fitted, go to step f);
e)
calculate the maximum allowable individual loads at the edge of the reinforcing plate (d = d2
and ec = ea), and check the load ratios and the interaction of the loads using 16.4.5 and 16.4.6;
f)
calculate the equivalent shell thickness eeq (see 16.4.7.2) and check the combined stress range
(see 16.4.7) in cases only where one of the ranges for pressure ∆P, force ∆FZ or moment ∆MB
(calculated according to Formulae (16.4-16) to (16.4-18) in 16.4.7.1) is larger than the extreme
absolute values of the pressure P, the force FZ or the moment MB;
alternatively the combined stress range (see 16.4.7) may be applied when the external loads
contain portions from thermal expansions of attached piping; in this case the checks of 16.4.5 and
16.4.6 may be applied for the pressure and the mechanical portions of the external loads only but
the check of 16.4.7 shall be done for the ranges of the pressure and the combined mechanical and
thermal loads;
g) check the nozzle longitudinal stresses (see 16.4.8);
h) if stresses or load ratios are excessive, increase the shell or nozzle thickness, or reduce the loads,
and return to step a).
Step f) shall be made only at the nozzle edge.
16.4.5 Maximum allowable individual loads
16.4.5.1 To determine the maximum allowable values of pressure, axial load and bending moment,
which may be independently applied to a nozzle the following procedure shall be applied.
16.4.5.2
Determine the reinforcement rate factor:
 2 f .e
b
b
  m in 

f .e
c

e
b
d

; 1, 0 


(16.4-4)
For the calculation of the allowable loads at the edge of the reinforcing plate or for a nozzle on a shell
without an opening, the reinforcement factor κ is equal to 1.
NOTE
A shell without opening is used for trunnion loading.
UNI EN 13445-3:2021
361
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.4.5.3
Determine λS:
d
S 
R e
(16.4-5)
c
16.4.5.4 Calculate permissible pressure Pmax from the general formula for reinforcement of isolated
openings in Clause 9. It is reproduced here from 9.5.2 for convenience and the notation is in 9.3.
( Af
P

m ax
NOTE

Ap
b
 Af
w
) .f
 0, 5 A p


 Af
s

b
 f
0, 5 ( A f
ob
s
 Af

Af
p
 f

w
op
Af
b

Af
P
)
(16.4-6)
For application of this formula to different load cases, see 3.16, NOTE 1.
16.4.5.5
F
 Aps
s
Determine the allowable axial nozzle load FZ,max either from Figure 16.4-1 or by calculation:
Z ,m a x
 f e
2
c
 1, 8 2  2, 4 .
1   
S
 0, 9 1   . 
2
S

(16.4-7)
Non-dimensional upper and lower bounds are given in Figure 16.4-1.
16.4.5.6
M
Either read the allowable bending moment MB,max from Figure 16.4-2 or calculate it using:
B ,m a x
 f  e
2
c

d
4
 4 , 9  2, 0 .
1   
S
 0 , 9 1 . . 
2
S

(16.4-8)
Non-dimensional upper and lower bounds are given in Figure 16.4-2.
16.4.5.7
F 

Z

Shear stresses
2F
S
  d  ec
2M
 d
  F  
2
(16.4-8a)
Z
e
c
Z
(16.4-8b)
(16.4-8c)
16.4.6 Combination of external loads and internal pressure
16.4.6.1 To determine the effects of the combination of pressure, axial load and bending moment
acting simultaneously, the following procedure shall be applied.
If the axial force and the bending moment include portions from the thermal expansions of attached piping,
the applied loads need not include the thermal expansion effects. In this case the stress ranges check
Subclause 16.4.7 shall be applied taking into account the total loads including the thermal portions
(see 16.4.4 step f), second paragraph).
362
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.4.6.2



P

Z


B
T


Calculate the individual load ratios as follows:
P
P
F
F



P
Z
B
T
Z
(16.4-10)
Z ,m a x
M
M
B
(16.4-11)
B ,m a x
2
(16.4-11a)
f
16.4.6.3

(16.4-9)
m ax
Check that each individual load ratio is limited as follows:
 1, 0
(16.4-12)
 1, 0
(16.4-13)
 1, 0
(16.4-14)
 1,0
16.4.6.4

m ax

(16.4-14a)
Check that the interaction of all the loads meets the following:


P

Z
; 
Z
; 
P
 0,2 
Z

B


2
 
2
T
 1,0
(16.4-15)
The above formula is based on a linear interaction of pressure and axial load with the bending moment and
yields a conservative result. In specific cases design by analysis, as given in Clause 5, may show that a circular
interaction is less conservative.
16.4.7 Stress ranges and their combination
16.4.7.1 From the minimum and maximum values of the pressure and local loads, determine the
following load ranges:
ΔP = max (P ; 0) – min (P ; 0)
(16.4-16)
ΔFZ = max (FZ ; 0) – min (FZ ; 0)
(16.4-17)
ΔMB = max (MB ; 0) – min (MB ; 0)
(16.4-18)
ΔFS = max (FS ; 0) – min (FS; 0)
(16.6-18a)
ΔMZ = max (MZ ; 0) – min (MZ ; 0)
(16.4-18b)
UNI EN 13445-3:2021
363
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.4.7.2 At the nozzle edge only, calculate the equivalent shell thickness eeq . This is equal to ec unless
a reinforcing plate of width L  R ( e a  e 2 ) is used, in which case eeq is given by:


 e  m in 
e
eq
a


16.4.7.3
e

R e


; e   m in
2


L
2
e
a
2

 f

2

;1
 f



(16.4-19)
Determine the following stresses:
Due to the pressure range:

 scf
P
 P R

 2e

eq

P





(16.4-20)
Due to the range of the axial load:

 scf
FZ
Z

FZ

 d e
eq





R
e
eq
(16.4-21)
Due to the moment range:

4M

B
  M B  s c fM

2
 d
e
eq






R
e
eq
(16.4-22)
where
scfP, scfZ and scfM
NOTE
are taken from Figures 16.4–3 to 16.4–8.
The scf factors in Figures 16.4–3 to 16.4–8 are from BS 5500:1997, G2.5 (see L.2 - ref [6]).
Range of shear stresses
 F 

2 F
S
  d  ec
2 M
Z

 d
2
(16.4-22a)
Z
e
(16.4-22b)
c
   F   Z
16.4.7.4

364
(16.4-22c)
The equivalent stress range shall be restricted as follows:
2
P

   FZ
 
MB

2
 4  
2
 3 f
(16.4-23)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.4.8 Nozzle longitudinal stresses
This subclause may be ignored for a nozzle intended to be attached to a piping of the same resistance
(thickness multiplied by allowable stress).
16.4.8.1
Maximum longitudinal tensile stress in the nozzle shall be limited as follows:
P d
4e
4 M

b
 d
B
2

e
b
F
Z
 d eb

f
b
(16.4-24)
FZ shall be set to zero when resulting in an axial compressive stress.
16.4.8.2
M
M
B
m ax
The longitudinal stability of the nozzle shall be checked (with P = 0) as follows:
| F

F
Z
|

1, 0
(16.4-25)
m ax
FZ shall be set to zero when resulting in axial tensile stress. Mmax and Fmax are respectively the allowable
global moment and force in the nozzle. They are calculated in 16.14.
UNI EN 13445-3:2021
365
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.4-1 — Non-dimensional graphical form of FZ,max
(upper curve = maximum reinforced, lower curve = unreinforced)
Figure 16.4-2 ― Non-dimensional graphical form of MB,max
(upper curve = maximum reinforced, lower curve = unreinforced)
366
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.4-3 ― Stress factor in sphere for internal pressure (flush nozzle)
Figure 16.4-4 — Stress factor in sphere for internal pressure (protruding nozzle)
UNI EN 13445-3:2021
367
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.4-5 — Stress factor in sphere for moment loading (flush nozzle)
Figure 16.4-6 — Stress factor in sphere for moment loading (protruding nozzle)
368
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.4-7 — Stress factor in sphere for thrust loading (flush nozzle)
Figure 16.4-8 ― Stress factor in sphere for thrust loading (protruding nozzle)
UNI EN 13445-3:2021
369
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.5 Local loads on nozzles in cylindrical shells
16.5.1 Purpose
This clause provides a method for the design of a cylindrical shell with a nozzle subjected to local loads and
under internal pressure.
In cases where the loads are unknown see Annex V.
16.5.2 Additional specific symbols and abbreviations
The following symbols and abbreviation are in addition to those in Clause 4 and 16.3:
a0 to a4
are the coefficients of the polynomials;
C1 to C4
are factors;
D
is the mean shell diameter at the opening;
di
is the inside nozzle diameter;
de
is the outside nozzle diameter;
d
is the mean nozzle diameter;
d2
is the external diameter of a reinforcing plate;
ec
is the combined analysis thickness of the shell and reinforcing plate;
eeq
is the equivalent shell thickness;
eb
is the nozzle analysis thickness;
fb
is allowable design stress of nozzle material;
FX
is the shear nozzle force in longitudinal direction of the shell (Figure 16.5–1);
FY
is the shear nozzle force in circumferential direction of the shell (Figure 16.5–1);
FZ
is the axial nozzle force (Figure 16.5–1);
FZ,max
is the maximum allowable axial nozzle force;
L
is the width of the reinforcing plate;
MX
is the circumferential moment applied to the nozzle (Figure 16.5–1);
MY
is the longitudinal moment applied to the nozzle (Figure 16.5–1);
MX,max
is the maximum allowable circumferential moment applied to the nozzle;
MY,max
is the maximum allowable longitudinal moment applied to the nozzle;
MZ
is the torsional nozzle moment;
R
is mean shell radius at the nozzle;
ΔσP
is the stress range due to pressure;
ΔσFZ
is the stress range due to axial nozzle load;
ΔσMx
is the stress range due to circumferential moment;
ΔσMy
is the stress range due to longitudinal moment;
λC
is a parameter applicable to nozzles in cylinders;
τ
is maximum total shear stress in shell at nozzle outside diameter ;
370
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
τX
is the maximum shear stress in shell at nozzle outside diameter due to shear force FX (Figure 16.5–1);
τY
is the maximum shear stress in shell at nozzle outside diameter due to shear force FY (Figure 16.5–1);
τZ
is the shear stress in shell at nozzle outside diameter due to torsional moment MZ (Figure 16.5–1);
Φ
is a load ratio.
16.5.3 Conditions of applicability
The following conditions apply:
a) 0,001 ≤ ea / D ≤ 0,1;
b) 𝜆C =
𝑑
√𝐷 𝑒c
≤ 10;
c) distances to any other local load in any direction shall be not less than
d) nozzle thickness shall be maintained over a distance of:
l 
d e
b
D e
c
;
.
16.5.4 Summary of design procedure
The design procedure is as follows:
a) calculate the basic dimensions ec and L from the following:
1) at the nozzle outside diameter, when a reinforcing plate is fitted:
e
c
 e
a
 e
2
 f

2
;1 
 m in 
 f



2) at the outside edge (d = d2) of a reinforcing plate, or when no reinforcing plate is fitted:
ec = ea
The width L of the reinforcing pad is given by:
L = 0,5 (d2 – de)
b) calculate the maximum allowable individual loads (see 16.5.5);
c) check the load ratios and the interaction of the loads (see 16.5.6);
d) if no reinforcing plate or if a reinforcing plate is applied with
L 
D (e
a
 e
2
)
go to step f);
e) calculate the maximum allowable individual loads at the edge of the reinforcing plate (d = d2 ;
ec = ea and eb / ec ≥ 0,5) and check the load ratios and the interaction of the loads using 16.5.5 and
16.5.6;
f)
calculate the equivalent shell thickness eeq(see 16.5.7.2) and check the combined stress range
(see 16.5.7) in cases only where one of the ranges for pressure ΔP, force ΔFZ or moments ΔMX and
UNI EN 13445-3:2021
371
EN 13445-3:2021 (E)
Issue 1 (2021-05)
ΔMY (calculated according to Formulae (16.5-16) to (16.5-19) in 16.5.7.1) is larger than the
extreme absolute values of the pressure P, the force FZ or the moments MX and MY;
alternatively the combined stress range (see 16.5.7) may be applied when the external loads
contain portions from thermal expansions of attached piping; in this case the checks of 16.5.5 and
16.5.6 may be applied for the pressure and the mechanical portions of the external loads only but
the check of 16.5.7 shall be done for the ranges of the pressure and the combined mechanical and
thermal loads;
g) check the nozzle strength (see 16.5.8);
h) if stresses or load ratios are excessive, increase the shell or nozzle thickness, or reduce the loads
and return to step a).
Step f) shall be made only at the nozzle edge.
16.5.5 Maximum allowable individual loads
16.5.5.1 To determine the maximum allowable values of pressure, axial load and bending moment,
which may be independently applied to a nozzle the following procedure shall be applied.
16.5.5.2 Determine λC thus:
d
C 
D e
(16.5-1)
c
16.5.5.3 Calculate permissible pressure Pmax from the general formula for reinforcement of isolated
openings given in Clause 9. It is reproduced from 9.5.2 for convenience and the notation is
in 9.3.
( Af
P
m ax

NOTE
 Aps

Ap
b
 Af
s
w
) .f
 0, 5 A p


 Af
s

 f
b
0, 5 ( A f
 Af
ob
s

Af
p
w
 f

op
Af
b

Af
P
)
(16.5-2)
For application of this formula to different load cases, see 3.16, NOTE 1.
16.5.5.4 Determine the allowable axial nozzle load FZ,max from the following:
F
Z ,m a x
 f e
2
c
C
(16.5-3)
1
in which C1 is either read from Figure 16.5-2 or calculated from:
C
1
 m ax 


a  a 
1
C
 0
 a
2

2
C
 a
3

3
C
 a
4

4
C
 ; 1 , 8 1 
(16.5-4)
and coefficients a0 to a4 are given in Table 16.5-1.
16.5.5.5 Determine the allowable circumferential moment MX,max from:
M
X ,m a x
 f e
2
c

d
4
 C
2
(16.5-5)
in which C2 is either read from Figure 16.5-3 or calculated from:
372
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C
2


a  a 
1
C
 0
 m ax
 a
2

2
C
 a

3
3
C
 a
4

4
C
 ;4 , 9 0 
(16.5-6)
and coefficients a0 to a4 are taken from Table 16.5-2.
16.5.5.6 Determine the allowable longitudinal moment MY,max from
M
Y ,m a x
 f  e
2
c

d
4
C
3
(16.5-7)
in which C3 is either read from Figure 16.5-4 or calculated from:
C
3
 m ax


a  a 
1
C
 0
 a
2

2
C
 a
3

3
C
 a
4

4
C
 ;4 , 9 0 
(16.5-8)
and coefficients a0 to a4 are given in Table 16.5-3.
If the thickness ratio eb/ec is situated between 0,2 and 0,5, the factor C3 is obtained by linear interpolation
(Figure 16.5-4).
NOTE
The curves of Figures 16.5–2 to 16.5–4 are derived from WRCB No. 297 – see [5] in Annex L, while the
allowable loads are based on a maximum stress concentration factor of 2,25.
16.5.5.7 Shear stresses (directions, see Figure 16.5-1)



X
Y
Z


2F
X
  d  ec
2F
(16.5-8a)
Y
  d  ec
2M

 d
(16.5-8b)
Z
2
e
(16.5-8c)
c
Total shear stress in shell at nozzle
 

2
X
 
2
Y
UNI EN 13445-3:2021
 
Z
(16.5-8d)
373
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.5.6 Combination of external loads and internal pressure
16.5.6.1 To determine the effects of the combination of pressure, axial load and bending moments,
acting simultaneously the following procedure shall be applied:
If the axial force and the bending moment include portions from the thermal expansions of attached piping,
the applied loads need not include the thermal expansion effects. In this case the stress ranges check 16.5.7
shall be applied taking into account the total loads including the thermal portions (see 16.5.4 step f), second
paragraph).
16.5.6.2





P

Z
Calculate the individual load ratios as follows:
P
P
F
F
T



M
Y
 
 M
Y ,m a x





2
(16.5-11)
2
(16.5-11a)
Check that each individual load ratio is limited as follows:
(16.5-12)
 1, 0
(16.5-13)
 1,0
B
T
2
 1, 0
Z





f
P

(16.5-10)

M
X

 M
X ,m a x

16.5.6.3

Z
Z ,m a x

B
(16.5-9)
m ax
(16.5-14)
 1,0
16.5.6.4

m a x


(16.5-14a)
Check that the interaction of all the loads meets the following:





C
P
4

Z
; 
Z
;

C
P
4
 0,2 
Z




2

2
B

2
T
 1,0
(16.5-15)
Factor C4 shall equal 1,1 where nozzle connections are attached to a piping system designed with due
allowance for expansion, thrusts, etc. It shall equal 1,0 for ring reinforcements or rigid attachments. It shall
not exceed 1,10.
374
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
In Formula (16.5–15) a circular interaction with the bending moment load is accepted on the grounds
of a conservative estimate of the stress concentration factor in WRCB No. 297 (see ref [5] in Annex L).
16.5.7 Stress ranges and their combination
16.5.7.1 From the minimum and maximum values of the pressure and local loads in operating
conditions, determine the following load ranges:
ΔP = max (P ; 0) – min (P ; 0)
(16.5-16)
ΔFX = max (FX ; 0) – min (FX ; 0)
(16.5-16a)
ΔFY = max (FY ; 0) – min (FY ; 0)
(16.5-16b)
ΔFZ = max (FZ ; 0) – min (FZ ; 0)
(16.5-17)
ΔMX = max (MX ; 0) – min (MX ; 0)
(16.5-18)
ΔMY = max (MY ; 0) – min (MY ; 0)
(16.5-19)
ΔMZ = max (MZ ; 0) – min (MZ ; 0)
(16.5-19a)
16.5.7.2 At the nozzle edge only, calculate the equivalent shell thickness eeq .This is equal to ec unless
a reinforcing ring of width L  D ( e a  e 2 ) is used, in which case eeq is given by:


 e  m in 
e
eq
a


16.5.7.3
e
. L
2

D e
a
e

2


; e  . m in
2


 f

2

;1 
 f



(16.5-20)
Determine the following stresses:
Due to pressure range:

p

P  D
 
 2e
eq





2  2
d
d e
D
D e
1
e
e
b
 1,25
eq
b
eq
d
D
d e
D e
D
e
eq
b
eq
(16.5-21)
Due to the range of the axial load:

FZ


2,25  FZ

2
C
1  e eq






(16.5-22)
Due to the range of the circumferential moment:

MX



2,25  4 M X 
 2

C
 e
d 
2
 eq

UNI EN 13445-3:2021
(16.5-23)
375
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Due to the range of the longitudinal moment:

MY


2,25  4 M Y 


2
C
 e
d 
3
 eq


(16.5-24)
Range of shear stresses
2 F

X

X
  d  ec
2 F

Y

Y
  d  ec
2 M

Z
(16.5-24a)

 d
2
(16.5-24b)
Z
e
(16.5-24c)
c
Total shear stress range at nozzle
 

16.5.7.4
2
X
2
Y
 
 
(16.5-24d)
Z
The equivalent stress range shall be restricted as follows:
 P
 
FZ

2


2
MX
 
2
MY
  4  
2
 3 f
(16.5-25)
with value of f as defined in C.7.3.
16.5.8 Nozzle longitudinal stresses
This subclause may be ignored for a nozzle intended to be attached to a piping of the same resistance
(thickness multiplied by allowable stress).
16.5.8.1
P
Maximum longitudinal tensile stress in the nozzle shall be limited as follows:
4 
d
4e
b

M
d
2
X
2
 M
e
b
2
Y


F
Z
 de b
 f
b
(16.5-26)
FZ shall be set to zero when resulting in an axial compressive stress.
376
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.5.8.2
M
The longitudinal stability of the nozzle shall be checked (with P = 0) as follows:
2
X
M
 M
2
Y

m ax
| F

F
Z
|

1, 0
(16.5-27)
m ax
FZ shall be set to zero when resulting in axial tensile stress. Mmax and Fmax are respectively the allowable
global moment and force in the nozzle. They are calculated in 16.14.
Table 16.5–1 — Coefficients for C1
eb/ ec
a0
a1
a2
a3
a4
All
0,600 721 81
0,951 962 57
0,005 195 788 1
−0,001 406 381
0
Table 16.5–2 — Coefficients for C2
eb/ ec
a0
a1
a2
a3
a4
All
4,526 315
0,064 021 889
0,158 876 38
−0,021 419 298
0,001 035 040 7
Table 16.5–3 — Coefficients for C3
eb/ ec
a0
a1
a2
a3
a4
≤ 0,2
4,851 751 1
0,025 101 2
0,742 862 4
- 0,015 315 3
0
≥ 0,5
4,858 863 9
2,187 088 7
1,456 705 3
- 0,331 643 0
0,025 385 0
UNI EN 13445-3:2021
377
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.5-1 — Moment and force vectors
Figure 16.5-2 — Graphical form of C1
378
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.5-3 — Graphical form of C2
Figure 16.5-4 — Graphical form of C3
16.6 Line loads
16.6.1 Purpose
This clause gives the general rules for an axisymmetric shell submitted to a local line load in longitudinal or
circumferential direction
UNI EN 13445-3:2021
379
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.6.2 Additional specific symbols and abbreviation
The following symbols and abbreviation are in addition to those in Clause 4 and 16.3:
Deq
is the equivalent calculation diameter;
x
is the distance between the axis of semi-ellipsoidal head and the centre of the supporting element;
FL,max is the maximum allowable local radial force on a shell;
ML,max is the maximum allowable local moment on a shell;
K1
is a factor;
K2
is a factor;

is the semi-angle at apex of conical shell;
1
is the ratio between local membrane stress and local bending stress;
2
is the ratio between global membrane stress and allowable stress (load ratio without local loading);
mx
is the global membrane stress in longitudinal direction;
my
is the global membrane stress in circumferential direction;
b,all
is the bending limit stress of shell.
16.6.3 Definition of equivalent diameter
a) for a cylindrical shell:
(16.6-1)
Deq = Di
b) or a conical shell:
Deq = Dk / cos ()
(16.6-2)
c) spherical shell and central part of torispherical head:
(16.6-3)
Deq = Ri
d) semi-ellipsoidal head (any ratio of Hi/Di)
2
D eq 
Di
4Hi
2x
1 

 Di 
2
2

 H 
1   2 i  

 Di  


(16.6-4)
e) semi-ellipsoidal head (with ratio Hi/Di = 0,25)
D eq  D i
 x 
1 3 

 Di
2
(16.6-5)
16.6.4 Conditions of applicability
The following conditions shall be fulfilled:
380
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) 0,001  en / Deq  0,050;
0  b / Deq < 1,0;
b)
NOTE 1
The lower limit 0 is explicitly allowed because the point load is taken into account.
NOTE 2
For circumferential line loads with b / Deq > 0,5
other cases.
the given results are more conservative than in
c) The line loads act perpendicular to the shell surface. Loading not perpendicular to the shell surface are
ignored but if their values are essentially greater than the perpendicular loads special considerations
are required.
16.6.5 Principle of calculation
At first the acting force FL and the acting moment ML for each existing load case shall be determined. Then
the corresponding maximum allowable force FL,max and moment ML,max shall be calculated according to
16.6.8. Because maximum allowable values are based on the so called “Bending Limit Stress” which depends
on the global membrane stresses the corresponding 16.6.6 and 16.6.7 are to be applied before.
Finally if both loading, the force FL and the moment ML, exist the interaction condition according to 16.6.9
shall be checked.
NOTE 1
The loads at the supporting element are divided into a combination of radial line loads, applied both in
longitudinal and circumferential directions. These line loads result in local membrane forces and bending
moments obtained by theory of elasticity.
NOTE 2
The allowable forces and moments are limited by the global and local strength of the shell and are
based on a mix between theory of elasticity and plastic limit load. The maximum bending stress is limited by the
so called “Bending Limit Stress”, which is determined for a strip of the shell (see clause L.1)
16.6.6 Bending Limit Stress
The bending limit stress is obtained from Formula (16.6-6), which is a function of the membrane stresses due
to local loading and global loadings.
σb,all = K1K2f
(16.6-6)
—
for design conditions:
K2 = 1,25;
—
for test, transport and lifting conditions:
K2 = 1,05 and f = ftest.
The value of K1 is a function of υ1 and υ2and shall be obtained from Figure 16.6-1 or Formula (16.6-7):
1  
K
1

1

    

1
2
3


2
2
1

   

1
2
3


2

1    
2
2
2
1
(16.6-7)
with:
2 

K
2
m
f
UNI EN 13445-3:2021
(16.6-8)
381
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where
υ1 and σm:
see Formula (16.6–14) with the corresponding explanation for υ2, or Formula (16.6–18) respectively.
In this figure when υ2 < 0, the signs of υ1 and υ2 shall be changed simultaneously to determine K1.
Figure 16.6-1 — Factor K1
16.6.7 Global membrane stresses
The global membrane stresses in this clause are required in the following clauses, where the bending limit
stress and the load limits of a shell under internal or external pressure, combined with external loads, are
covered
— Global longitudinal membrane stress in cylindrical shell:
 mx 
382
P D eq
4 ea


M
F  4
 D e q e a 
D eq
1




(16.6-9)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where F as defined in 16.3.
— Global longitudinal membrane stress in conical shell:
 mx 
P D eq
4 ea

1
 D k c o s 


M
F  4

D eq
ea 




(16.6-10)
where F as defined in 16.3.
— Global circumferential membrane stress in cylindrical and conical shell:

my

P D eq
(16.6-11)
2 ea
— Global membrane stress in spherical shell or central part of torispherical head and semi-ellipsoidal
head:

mx

my

P D eq
(16.6-12)
2ea
16.6.8 Single line loads (see Figures 16.6-2 and 16.6-3)
Figure 16.6-2 ― Longitudinal Line Load
UNI EN 13445-3:2021
383
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.6-3 ― Circumferential Line Load
Following procedure shall be followed to define the maximum allowable line loads
1) Determine whether the line load is in the longitudinal or in the circumferential direction;
NOTE Any straight line load on a spherical part of a shell is considered to be in the longitudinal
direction.
2) If the line load is in the longitudinal direction then following parameters shall be applied:


1
b

D eq e a
1
= min (0,08 1 ; 0,20)
2
is to be calculated with m = my from Formula (16.6-11)
(16.6-13)
(16.6-14)
b = longitudinal length of line load
1
K 13 
1,2
2
1
K 14 
0 ,6
384
1  0 ,0 6 
1  0 ,0 3 
2
(16.6-15)
(16.6-16)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Go to step 4.
3) If the line load is in the circumferential direction then following parameters shall be applied:

2

b

D eq e a
1
= min (0,08 2 ; 0,30)
2
is to be calculated with m = mx from Formula (16.6-9 or 16.6-10)
(16.6-17)
(16.6-18)
b = circumferential length of line load
1
K 13 
1  0 ,6 0 
1,2
2
1
K 14 
1  0 ,0 6 
0 ,6
2
(16.6-19)
(16.6-20)
4) Calculate the allowable force and allowable moment:
2
 b ,a ll e a
FL ,m a x 
(16.6-21)
K 13
2
 b , a ll e a b
M L ,m a x 
K 14
(16.6-22)
with bending limit stress b,all from Formula (16.6.6)
16.6.9 Combined line loads
The combination of the pressure and/or global forces and moments with line loads is already included in the
maximum allowable local force and moment by the global membrane stresses.
The additional interaction of combined local force and local moment is given by the condition:
FL
F L, max

M
M
L
 1,0
(16.6-23)
L, max
16.7 Lifting lugs
16.7.1 Purpose
This clause gives rules for the design of shells with local loads due to lifting lugs.
16.7.2 Specific symbols and abbreviations (see Figure 16.7-1 and Figure 16.7-2)
The following symbols and abbreviation are in addition to those in 4.1 and 16.3:
UNI EN 13445-3:2021
385
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a1
is the eccentricity of load;
a2
is the distance from load to shell or reinforcing plate;
b1
is the length of lifting lug at shell junction;
b2
is the width of reinforcing plate;
b3
is the length of reinforcing plate;
x
is the distance between the axis of semi-ellipsoidal head and the centre of the lifting lug ;
FR
is the local force on a shell;
FR,max is the maximum allowable local force on a shell;
Gmax
is the total vessel weight;

is the angle between direction of force and normal to the shell;
386
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.7-1 ― Longitudinal lifting lug
Figure 16.7-2 ― Tangential lifting lug
UNI EN 13445-3:2021
387
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.7.3 Conditions of applicability
The following conditions shall apply:
a) 0,001  en /Deq  0,05;
b) If a reinforcing plate is applied:
e2  en ;
b3  1,5 b1 ;
c) The local force FR acts in the plane of the lifting lug;
d) For torispherical heads the lifting lug is located in the spherical part;
e) For semi-ellipsoidal heads the lifting lug is located between 0  x  0,4 Di ;
16.7.4 Applied force
The applied force FR acting on the lifting lug shall be calculated. In case of a symmetric vessel with two lifting
lugs according to Figure 16.7-3(a):
F
R

1,5G
m ax
2cos
(16.7-1)
16.7.5 Load limits for shell
Following procedure shall be followed to define the maximum allowable lifting lug loads:
1) Determine whether the lifting lug is in the longitudinal or in the circumferential direction;
NOTE A straight lifting lug on a spherical shell is considered a longitudinal lifting lug.
2) For a longitudinal lifting lug define the values of , 1, 2, K13 and K14 shall be taken from 16.6.7,
Formulae (16.6-13) to (16.6-16), with b = b1. If a reinforcing plate is applied b = b3
3) For a circumferential lifting lug define the values of , 1, 2, K13 and K14 shall be taken
from 16.6.7, Formulae (16.6-17) to (16.6-20), with b = b1. If a reinforcing plate is applied b = b3;
4) With the appropriate values of λ, υ1 and υ2, calculate the bending limit stress from 16.6.6,
Formula (16.6-6);
5) If a reinforcing plate is applied, calculate the factor K15 as follows:
K15 for lifting lugs in longitudinal direction:
388
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
K 15

 D eq 

 m in  1  2 , 6 0 

 ea 

0 ,3 0
 b
 2
D
 eq


 ; 2 ,0 




(16.7-2)
K15 for lifting lugs in circumferential direction:
K 15

 D eq 

 m in  1  2 , 6 5 

 ea 

0 ,3 3
 b
 2
D
 eq


 ; 1, 8 




(16.7-3)
6) Calculate the maximum allowable load and compare with the actual load
The following inequality shall be satisfied:
— without reinforcing plate:
2
F R  F R, max 
σ b, all e a
K 13 |cos β | K 14
a 2 sin β  a 1 cos β  / b 1
(16.7-4)
— with a reinforcing plate:
2
F R  F R, max 
K 15 σ b, all e a
K 13 |cos β | K 14
 a 2  e 2  sin β  a 1 cos β  / b 3
(16.7-5)
NOTE
The design procedure normally assumes the use of similar material in shell and reinforcing plate.
Where this is not the case and provided that f2 < f , the thickness e2 in Formula (16.7-5) shall be reduced by the
ratio f2 / f .
UNI EN 13445-3:2021
389
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.7-3 ― Arrangement of lifting lugs
390
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.8 Horizontal vessels on saddle supports
16.8.1 Purpose
This clause gives rules for the design of horizontal cylindrical shells, supported by two or more saddles.
16.8.2 Additional specific symbols and abbreviations (see Figures 16.8-1 to 16.8-5)
The following symbols and abbreviation are in addition to those in Clauses 4, 16.3 and 16.6.2:
a1
is the distance from saddle support to adjacent end of cylindrical part;
a2
is the distance from horn of saddle to end of reinforcing plate;
a3
is the length of equivalent cylindrical shell = a1 + 2 Hi / 3;
b1
is the axial width of saddle of saddle support;
b2
is the width of reinforcing plate;
ec
is the effective combined wall thickness;
li
is the distance between two successive saddles;
n
is the number of saddles;
q
is the load per unit vessel length;
E
is the modulus of elasticity of shell material at design temperature;
F2,max
is the maximum allowable saddle load at location 2 (see Figure 16.8-4);
F3,max
is the maximum allowable saddle load at location 3 (see Figure 16.8-4);
Fi
is the force on the i-th support;
L
is the length of cylindrical part of vessel (including cylindrical part of heads);
Mi
is the global bending moment at saddle i;
Mij
is the maximum global bending moment between saddle i and j;
Qi
is the maximum shear force at saddle i ;
R
is the mean shell radius;
W
is the total vessel weight (including content);
WF
is the fluid weight;

is the included angle of saddle support (in degrees);
2
is the included angle of reinforcing plate (in degrees);

is an influence factor for saddle width;

is an influence factor for saddle distance;
UNI EN 13445-3:2021
391
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.8.3 Conditions of applicability
The following conditions shall apply:
a) 0,001  en / Di  0,05 ;
600    180°;
b) If a reinforcing plate is applied :
e2  en ;
a2  0,1 Di ;
c) The saddles are loaded vertically downwards.
d) It is preferable to weld the saddle to the vessel. However if welding is not possible, care should be
taken to ensure that the vessel is uniformly supported by the saddle.
e) If axial displacements due to thermal dilatation are to be expected, only one saddle shall be fixed
to the foundation, while the other saddles shall be free to move in axial direction. Alternatively all
saddles may be clamped if they are sufficiently designed to withstand the axial deformations.
f)
Distances from saddle to any other local loads in all directions should be not less than
D i en
;
g) Type of saddle supports: type A, B or C (see Figures 16.8-1 to 16.8.3) ;
NOTE
For a fatigue analysis the elastic stress calculation can be carried out with the aid of ref. [4] - see
Clause L.2.
392
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.8-1 ― Type A - Vessel symmetrically on two saddles
Figure 16.8-2 — Type B – Vessel symmetrically on three or more equidistant saddles
Figure 16.8-3 — Type C – Vessel on two or more arbitrary located saddles
UNI EN 13445-3:2021
393
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.8-4 ― Cylindrical shell without reinforcing ring
16.8.4 Exemption from calculation
For vessels with two saddles of type A (Figure 16.8-1), the calculation is not required when the following
conditions are met:
a) no external pressure (P  0);
b) density of fluid  1000 kg /m3;
c) shell material with f  130 MPa;
d) welding factor  0,8;
e) a1  0,5 Di ;
f)
L  Lmax (Lmax derived from Figure 16.8-5);
g)
b 1  1,1
Di en
.
In addition for saddles with a reinforcing plate:
h) e2  en;
i)
b2  K11 . Di + 1,5 b1;
j)
K11 : see Figure 16.8-11 or Formula (16.8-33).
394
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
continuous lines: vessels without reinforcing plate
dotted lines:
vessels with reinforcing plate
Figure 16.8-5 ― Lmax for horizontal vessel symmetrically on two saddles
UNI EN 13445-3:2021
395
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.8.5 Determination of forces, moments and shear forces
16.8.5.1 Calculation model
To calculate the forces Fi on the saddles, the global moments Mi and Mij and the shear force Qi must be
defined. Therefore the shell is considered as a beam of constant cross section supported by the saddles
without any moments acting on the saddle (see Figure 16.8-6).
Figure 16.8-6 ― Calculation model
The loads of the beam are obtained from the following formulae:
q
W
(16.8-1)
L  4 H i /3
M0  q
WF
W
2
(16.8-2)
D i / 16
16.8.5.2 Forces on the saddle
In general the applied forces Fi are obtained from the commonly known rules of mechanical equilibrium.
Application of three or more saddles requires special care when mounting the vessel to guarantee a nearly
equal loading of all saddles.
For symmetric vessels with supporting saddles type A or B (Figure 16.8-1 or Figure 16.8-2) the following
formula may be used:
Fi 
W
(16.8-3)
n
16.8.5.3 Moments and shear forces
This sub-section gives rules for determining the bending moments above the saddles (Mi) and between the
saddles (Mij), where the moment Mij is a maximum. Shear forces must be calculated above the saddles (Qi).
a) Support type A
Moment at saddle:
2
M 1  M 2 q a3 /2 M
396
0
(16.8-4)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Shear force at saddle:
Q i  Fi
L  2 a1
(16.8-5)
L  4 H i /3
Moment between saddles:
M
12
 M

 F1 . L / 2  a 1
0
  q
/2
 . L / 2
 2Hi /3

2
(16.8-6)
b) Support type B
Moment at saddles:
for i = 1 and i = n :
M
2
i
 max ( q a 3 / 2  M
2
0
;q l 1 / 8 )
(16.8-7)
for i = 2 to i = n - 1:
2
M i  q l1 / 8
(16.8-8)
Shear force at saddle:
Q i = 0,5 F i
(16.8-9)
Moment between saddles: not required.
c) Support type C
Mi, Qi and Mij and are to be calculated with the theory of beams. The value Qi is to be considered both at left
and right side of the saddle, with Qi the maximum of both.
16.8.6 Load limit for the shell between the saddles
Calculation of the limit load between the saddles is required only when:
| moment between saddles | > | moment at saddle |
16.8.6.1 Vessel under internal pressure or without pressure
a) strength calculation:
P Di
4 ea
with

4 M ij

2
Di
K 12
ea
 fm a x
(16.8-10)
fmax = f in areas without circumferential welds;
fmax = f z in areas with circumferential welds;
and
K12 = max (m ; 1,0)
UNI EN 13445-3:2021
(16.8-11)
397
EN 13445-3:2021 (E)
Issue 1 (2021-05)
m=
1,6 - 0,20924 (x -1) + 0,028702 x (x - 1) + 0,4795.10-3 y (x -1) - 0,2391.10-6 xy (x -1)
- 0,29936.10-2 (x -1) x2 - 0,85692.10-6 (x -1) y2 + 0,88174.10-6 x2 (x -1) y
- 0,75955.10-8 y2 (x -1) x + 0,82748.10-4 (x -1) x3 + 0,48168.10-9 (x -1) y3
(16.8-12)
where x = L / Di and y = Di / ea
or K12 from Figure 16.8-12
b) Instability check (with P = 0)
M
(16.8-13)
/ M m a x  1,0
ij
16.8.6.2 Vessel under external pressure
Instability check
P / Pmax +  M ij  / Mmax  1,0
(16.8-14)
where
Pmax
is the allowable external pressure (according to Clause 8);
Mmax
is the allowable global moment (see 16.14);
NOTE
For determination of Pmax and Mmax for different load cases, see 3.16, NOTE 1, Table 5.3.2.4–1 and 8.4.4.
16.8.7 Load limit at the saddle (without a reinforcing plate)
The load limits shall be checked at location 2 (longitudinal direction) and at location 3 (circumferential
direction) – Figure 16.8-4. Two different pressure conditions shall be considered: zero pressure condition
and design pressure condition. If the saddles are located symmetrically (type A and B), only the location at
saddle n = 1 needs to be considered. For type C saddles the loads need be checked at both saddles.
Following calculation procedure shall be followed:
1) Determine the parameters  and 
  2 ,8 3  a 1 / D i 
  0 ,9 1 b 1 /
(16.8-15)
ea / Di
(16.8-16)
Di ea
2) Calculate the factors K3 to K10
398

K
3
 m a x 2 ,7 1 8 2 8 2
K
4


 1  2 ,7 1 8 2 8 2  
s in  /  ; 0 , 2 5
cos 
/

(16.8-17)
(16.8-18)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
K
5

K6 
K7 
K
K
8
9
1,1 5  0 , 0 0 2 5 
s in  0 , 5 

(16.8-19)
m a x  1,7  0 , 0 1 1 6 6 7  ; 0 
s in  0 ,5 
(16.8-20)
1, 4 5  0 , 0 0 7 5 0 5 
s in  0 , 5 

(16.8-21)

0 ,8   6 
 m in  1, 0 ;

0 ,0 1 7 4 5 3 

 1
0 ,6 5
1  6 




(16.8-22)
60


2
(16.8-23)
1
K 10 
1  0 ,0 1 0 4 7 2
NOTE

3
Di
b1
ea
Di

(16.8-24)
The factors K3 to K9, K11 and K12 may also be read from the graphs: Figure 16.8-7 to Figure 16.8-12.
3) Calculate the ratios 1 at location 2 and 3 (see Table 16.8-1)
4) Calculate the ratios 2 at location 2 and 3 (see Table 16.8-1) for each pressure condition
For zero pressure the ratio 2 is equal to 2,1, while for design pressure condition 2 is equal to 2,2.
5) With the appropriate values 1 and 2, and for each pressure condition and each location,
calculate the factor K1 from Formula 16.6-7 and determine K2 (see 16.6-6)
Table 16.8-1 ― Parameters 1 and 2 for saddles
1
Location
 0 ,2 3
2
3
UNI EN 13445-3:2021
 0 ,5 3
K
6
K8

P=0
P = Design pressure
2,1
2,2
4M
D
K5 K3
2
i
i
1
ea K
2
0
K4

K 7 K 9 K 1 0 s in 0 ,5 

f
P D
4Mi
i


 4 e
2
 D i ea

a

1

 K f

2
P Di
1
2 ea
K2 f
399
EN 13445-3:2021 (E)
Issue 1 (2021-05)
6) From Formula (16.6-6) determine the bending limit stress b,all,2 at location 2, both in the zero
pressure and the design pressure condition. The resulting bending limit stress b,all,2 shall be
the smallest of both values
7)
From Formula (16.6-6) determine the bending limit stress b,all,3 at location 3, both in the zero
pressure and the design pressure condition. The resulting bending limit stress b,all,3 shall be
the smallest of both values
8) Calculate the maximum allowable saddle load F2,max at location 2
F 2, max 
0 ,7
b, all,2
K3K
D i e a .e a
(16.8-25)
5
9) Calculate the maximum allowable saddle load F3,max at location 3
F 3, max 
0 ,9
b, all,3
D i e a .e a
K 7 K 9 K 10
(16.8-26)
10) Check that
F i  min  F 2, max ; F 3, max

(16.8-27)
11) Instability check
The condition in Formula (16.8-28) shall be fulfilled.
P/Pmax +Mi/Mmax + Feq / Fmax + (Qi / Qmax)2  1,0
(16.8-28)
where
Pmax is the allowable external pressure (according to Clause 8);
Mmax is the allowable global moment (see 16.14);
Fmax is the allowable global compression force (from 16.14);
Feq
is the equivalent global axial force, taking into account local membrane stresses near the
saddle, obtained by Formula (16.8-29):
Fe q  F i

Di
4
ea
K6 K8
(16.8-29)
Qmax is the allowable global shear force from the following formulae (see Clause L.2, ref. [2]);
NOTE
For determination of Pmax and Mmax for different load cases, see 3.16, NOTE 1, Table 5.3.2.4–1 and 8.4.4.
For internal pressure set |P|=0 in Formula (16.8-28) and Pmax is not needed.
400
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For cylindrical shells where
Q m ax 
R
 8 ,7
 ea 
0 ,7 5  R e a E 

 R 
L
R
 8 ,7
 ea 
0 ,2 5  R e a E 

 R 
R
ea
then:
1, 2 5
1, 5
For cylindrical shells where
Q m ax 
L

R
1  4 2  
 L 
L 

R
R
ea
3
ea 


 R 
1. 5




(16.8-30)
then:
1,5
1,5
(16.8-31)
16.8.8 Load limit at a saddle with additional reinforcing plate
If an additional reinforcing plate is applied, the following procedure shall be followed :
1) Evaluate the result of Formula (16.8-32)
b 2  K 11 D i 1, 5 b1
(16.8-32)
where
5
K 11 
 0 ,10472   3
(16.8-33)
Di
ea
2) If the condition in Formula (16.8-32) is not met then go to step 5
3) Calculate the maximum allowable forces F2,max and F3,max respectively from Formulae (16.8-25)
and (16.8-26)
4) Check that next inequality is satisfied
Fi  1,5 min (F2;max; F3;max)
(16.8-34)
Go to step 6.
5) Perform both following calculations according to the procedure in 16.8.7 and dimensions
defined as follows:
a) Calculation 1:
The reinforcing plate is considered as a saddle with a width b2 and an angle 2 instead of b1 and .
The wall thickness of the shell is ea, while the thickness of the reinforcing plate is not considered;
UNI EN 13445-3:2021
401
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) Calculation 2:
The reinforcing plate is considered as a reinforcing to the vessel wall. The considered saddle width
is equal to b1 and the saddle angle equal to , while the actual calculation shell thickness is replaced
by a combined thickness ec
2
ec 
  f  
2
 
e a  e 2 .min  1; 
  f  


2
2
(16.8-35)
6) Check the instability condition by Formula (16.8-28). Hereby the thickness of the reinforcing
plate shall not be taken into account.
Figure 16.8-7 ― Factors K3 and K4
402
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.8-8 ― Factors K5, K6 and K 7
Figure 16.8-9 ― Factor K 8
UNI EN 13445-3:2021
403
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.8-10 ― Factor K 9
404
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.8-11 ― Factor K 11
Figure 16.8-12 ― Factor K 12
UNI EN 13445-3:2021
405
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.9 Horizontal vessels on ring supports
16.9.1 Purpose
This clause provides the rules for the design of horizontal cylindrical shells with stiffening rings, welded to
the inside or outside of the shell (see Figures 16.9-1 to 16.9-3). The rings are supported by saddles or legs or
otherwise.
Figure 16.9-1 ― Ring supported by a clamped zone
Figure 16.9-2 ― Ring supported by two points (legs or otherwise)
406
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.9.2 Additional specific symbols and abbreviations
The following symbols and abbreviation are in addition to those in Clause 4 and 16.3.
b2
is the total width of ring cross section (see Table 16.9-1);
e1
is the web thickness of ring section (see Table 16.9-1);
e2
is the flange thickness of ring section (see Table 16.9-1);
fR
is the allowable design stress of ring;
h1
is the total height of ring cross section;
hG
is the distance from neutral axis of ring cross section to shell (see Table 16.9-1);
hH
is the distance from neutral axis for pure plastic bending of ring cross section to shell (for  = 1, hH is
the distance from the middle of the area);
le
is the effective length of vessel wall;
t
is the contact width of ring and shell;
AR
is the ring cross section area (without the shell);
FH
is the horizontal force on the ring;
FH,max is the maximum allowable horizontal force on the ring;
FV
is the vertical force on the ring;
FV,max is the maximum allowable vertical force on the ring;
H
is the distance from foundation to ring support hinges;
RR
is the radius of neutral axis of ring cross section;
Wp
is the plastic bending section modulus of ring cross section;

is the angle of support (in degrees);

is the relative effective design stress of shell (related to the ring);
16.9.3 Conditions of applicability
The following conditions shall apply:
a) h1 / Di  0,20 ;
30 °    330° ;
b) The loads taken into account are vertical and horizontal forces in the vessel cross section;
c) Axial forces to the vessel are not considered. Therefore special care is required if such forces
occur, e.g. due to axial displacements from thermal expansion.
UNI EN 13445-3:2021
407
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.9.4 Applied Loads
The calculation of the vertical force FV and the bending moments in the shell shall be according to 16.8.5,
while the horizontal load FH shall be obtained from a static analysis.
Figure 16.9-3 ― Cylindrical shell with reinforcing rings on saddles
16.9.5 Load limit of the shell
With the applied maximum absolute bending moment |Mi|, following expression shall be satisfied:
P / P max  M
i
/M
max
 F eq / F max   Q i / Q max

2
(16.9-1)
 1, 0
The values in Formula (16.9-1) shall be derived from 16.8.7, Formula (16.8-28)
16.9.6 Load limit of the ring
The load limit of the ring shall be obtained by the following procedure:
1) Define whether the ring is supported by a clamped zone (Figure 16.9-1) or by two hinges
(Figure 16.9-2);
2) Define the type of ring cross section and calculate Wp (see Table 16.9-1), with:
 
f

P

l e  m in t  4
3)
408

Di / 4 ea
  / fR
(16.9-2)

D i e a ; AR /  . e a

(16.9-3)
Calculate the factors K18 and K19 ;
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) For a ring supported by a clamped zone (Figure 16.9-1) :
K18 = 0.1616 x4 - 0,0268 x 6 + 0,0101 x 8
(16.9-4)
K19 = 0,4224 x 3 - 0,0524 x 5 + 0,1297 x 7
(16.9-5)
x = 1 -  / 360
(16.9-6)
where
b) For a ring supported by two hinges (Figure 16.9-2):
K18 and K19 as before (Ring with clamped zone), except when 150° <  < 210°, then K18 is equal to:
K18 = 0,0137 + 0,148 (2 x - 1)2
(16.9-7)
x = max ( / 360 ; 1 -  / 360 )
(16.9-8)
where
4) Calculate the allowable single loads :
F V ,m a x  f R W p /
R R
K 18

(16.9-9)
FH ,m a x  f R W p /
R R
K 19

(16.9-10)
5) Check the allowable combined loads, which shall meet the condition imposed by next formula:
F V / F V, max  2  F H / F H, max 
 1,0
(16.9-11)
Attention is drawn to the fact, that if supporting legs are used, they shall resist the bending moment = FH·H,
because the connection to the ring should be nearly momentless.
UNI EN 13445-3:2021
409
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 16.9-1 ― Parameters of ring cross section
Type of profile
Formulae

e1 h1   e le
; 0
hH  m ax 
2 e1


e1
W
p

 h
1
 hH

2
 h
2

2
H

e

  e le  hH  

2


e h  e b  e   e l

 1 1
2
2
1
e
; 0
hH  m ax 
2 e1


e1
Wp 
 h
1
 hH 
2
2
 hH

2
 e2
b2
e2 
e


 e 1   h1  hH 
   e le  hH 



2 
2
 2 e 1 h 1  e 2  b 2  2 e 1    e l e

; 0
hH  m ax 
4 e1


W p  e1
 h
1
 hH 
2
2
 hH

 e2
b2
e2 
e


 2 e 1   h1  hH 
   e l e  hH 



2 
2
Arbitrarily ring cross section with section area AR
Provided
AR   e l e
hH = 0
W p  AR hG   ele e / 2
410
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.10 Vertical vessels on bracket supports
16.10.1 General
This clause gives rules for the design of vertical cylindrical or conical shells supported by brackets
16.10.2 Additional specific symbols and abbreviations (see Figure 16.10-1)
The following symbols and abbreviation are in addition to those in Clause 4 and 16.3.
a1
is the distance from centre of load to shell or reinforcing plate;
a1eq
is the equivalent lever arm;
b1
is the flange width of bracket;
b2
is the width of reinforcing plate;
b3
is the height of reinforcing plate;
Deq
is the equivalent calculation diameter (see 16.6.3);
FVi
is the vertical force acting in the leg at bracket i;
FH
is the horizontal force acting at the base of the legs;
FHi
is the horizontal force acting at the base of leg i;
g
is the distance between webs of bracket;
h
is the vertical distance from the centre of the bracket to the base of the leg (see Figure 16.10-1a);
h1
is the height of bracket;
h2
is the depth of bracket;
MA
is the global moment at the centre-point of the cross section at the base of the legs;
n
is the number of brackets;
16.10.3 Conditions of applicability
The following conditions shall apply:
a) 0,001  en / Deq  0,05 (with Deq from 16.6.3);
b) For bracket supports type A, B and C (Figure 16.10-1)
0,2  g / h1  1,0 ;
c) For bracket supports type D (Figure 16.10-1)
0,5  b1 / h1  1,5 ;
d) If a reinforcing plate is applied:
e2  en ;
UNI EN 13445-3:2021
411
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b3  1,5 h1 ;
b2  0,6 b3 ;
e) The bracket is connected to a cylindrical or a conical shell;
f)
The local bracket force Fi acts parallel to the shell axis.
NOTE 1
Application of more than 3 brackets requires special care during assembly to guarantee a nearly equal
loading of all brackets
NOTE 2
Special considerations should be given to the stability of the vessel in the case where n = 2
16.10.4 Applied forces
The applied vertical force Fvi on the brackets is obtained from:
FV i 
F
n
4 M


(16.10-1)
A

n D i  2 a1  e a  e 2

The horizontal force at each leg:
FH i 
NOTE
FH
(16.10-2)
n
A better estimation for FHi may be obtained using:
FH i  FH
Ixxi

, where Ixxi is the 2nd area
Ixxi
i
moment of the cross section of the considered leg for
an axis normal to FH and

Ixxi
is the sum over all
i
legs.
16.10.5 Load limits of the shell
To obtain the load limit of the shell the following procedure shall be followed:
1) Determine the type of bracket: type A, B, C or D (see Figure 16.10-1);
2) If a reinforcing plate is applied then go to step 6;
3) Determine the parameters , K16,
1
and
2
:
a) for brackets type A, B and C:
  h1 /
K 16 
(16.10-3)
D eq e a
1
0 ,3 6  0 ,4 0   0 ,0 2 
412
(16.10-4)
2
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
1
= min {0,08  ; 0,30}
2
= see Formula (16.6-8) with m = my from Formula (16.6-11)
(16.10-5)
a) for bracket type D:
  b1 /
(16.10-6)
D eq ea
1
K 16 
(16.10-7)
0 ,3 6  0 ,8 6 
2
1
= min {0,08  ; 0,30}
2
= see Formula (16.6-8) with m = mx from Formula (16.6-9) or Formula (16.6-10)
(16.10-8)
4) With the appropriate values of
from Formula (16.6-6);
1
and
2 ,
calculate the allowable bending limit stress b,all
5) Calculate the equivalent lever arm and the resulting maximum allowable bracket load:
a 1, e q  a 1 
F i, m a x 
F i, max

FH i . h
(16.10-9)
FV i
2

. e a . h1 
 b , a ll

. m in
 K

16 . a1,eq


2

 e a  h1
 b, all
 K
16  a 1, eq

 1 ; 0 ,5
 g / h1





for types A, B and C
(16.10-10a)
for type D
(16.10-10b)
Go to step 9
6) Bracket with a reinforcing plate : determine the parameters , K17,
  b3 /
1
and
2
(16.10-11)
D eq e a
1
K 17 
0 ,3 6  0 ,5 0   0 ,5 0 
(16.10-12)
2
1
= min {0,08  ; 0,40}
2
= see Formula (16.6-8) with m = my from Formula (16.6-11)
7) With the appropriate values of
from Formula (16.6-6);
(16.10-13)
1
and
2 ,
calculate the allowable bending limit stress b,all
8) Calculate the equivalent lever arm and the maximum allowable bracket load:
a 1, e q  a 1  e 2 
UNI EN 13445-3:2021
FH i . h
Fvi
(16.10-14)
413
EN 13445-3:2021 (E)
Issue 1 (2021-05)
2

. e a . b3
 b , a ll
F i, m a x 

K 17 . a1eq





(16.10-15)
The design procedure normally assumes the use of similar material in shell and reinforcing plate. Where this is
not the case and provided that f2 < f , the thickness e2 shall be reduced by the ratio f2 / f in Formula (16.10-12).
9) Check that:
(16.10-16)
F V i  F i, m a x
Key
1
centre of the bracket
NOTE
centre of the bracket means the location of the horizontal neutral axis of bracket joint to shell or
reinforcing plate.
Figure 16.10-1a — Explanation of h
414
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.10-1 ― Brackets for support of vertical vessel
UNI EN 13445-3:2021
415
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.11 Vertical vessels with supporting legs
16.11.1 Purpose
This subclause gives rules for the design of vertical vessels, with legs located on the dished end.
Figure 16.11-1 ― Supporting legs for vertical vessels
16.11.2 Specific symbols and abbreviations (see Figure 16.11-1)
The following symbols and abbreviation are in addition to those in Clause 4, 16.3 and 16.6:
d1
is the leg circle diameter;
d2
is the outside diameter of supporting leg;
d3
is the diameter of reinforcing plate;
d4
is the diameter at junction of legs with head;
deff
is the effective diameter of supporting leg;
Fi
is the force on the leg;
n
is the number of legs;

is the angle of tangent to the dished end at the leg junction;
x
is the distance between the axis of the semi-ellipsoidal head and the centre of the supporting leg;

is the angle between leg axis and vertical axis;

is a geometric parameter;
416
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.11.3 Conditions of applicability
The following conditions shall apply:
a) 0,001  en / Deq  0,05 (with Deq from 16.6.3);
b) if a reinforcing plate is applied:
e2  en ;
d3  1,6 d2 ;
c) External pressure is excluded;
d) Appropriate steps must be taken to ensure that movement of the legs does not produce additional
bending stresses in the shell;
e) On torispherical ends the supporting legs shall be located in the central spherical part;
On elliptical ends the supporting legs shall be located within 0  x  0.4 Di ;
f)
g) Application of more than four legs is not recommended;
h) A global moment can be allowed only if the number of legs is > 2 and if the supporting legs are
fixed at the foundation. Furthermore the following requirement shall be met:
NOTE
legs.
F 
4 M
d4
;
Application of four legs requires special care during assembly to guarantee a nearly equal loading of all
16.11.4 Applied force
The applied local force Fi on the legs is obtained from:
Fi 
F
n

4 M
n d4
(16.11-1)
16.11.5 Load limits for the shell
To define the load limit of the shell and the maximum allowable force Fi,max and Pmax the following
procedure shall be applied:
1) Determine the parameter:

d eff
(16.11-2)
D eq e a
where
deff
= d2 for supporting legs without reinforcing plate;
= d3 for supporting legs with reinforcing plate;
Deq
see 16.6.3
UNI EN 13445-3:2021
417
EN 13445-3:2021 (E)
Issue 1 (2021-05)
2) Calculate the maximum allowable force Fi,max
cos β
2
F i, max  f e a 
NOTE
1,82  3 ,6 λ  0 ,91 λ 
(16.11-3)
2
cos α  β 
For application of this formula to different load cases, see 3.16, NOTE 1.
3) Obtain the maximum allowable pressure Pmax
Pmax is to be defined for a spherical shell (see Clause 7). When the end is elliptical, then the
diameter of this spherical shell shall be taken as equal to twice Deq obtained from Formula (16.6-4),
where x = d4.
4) Check that:
Fi
F i,m a x
(16.11-4)
 1, 0
5) Check that:
2
F i  P π d eff / 4
F i, max

P
P max
(16.11-5)
 1,0
Any support legs shall be checked for buckling. In this check the legs should be considered as:
i)
hinged at the base plate, and
j)
free to move laterally, but not free to rotate at the vessel.
The same results will be obtained for legs both sides hinged with a calculation length twice the actual length
of the legs.
16.12 Vertical vessels with skirts
16.12.1 Purpose
This clause gives rules for the design of support skirts for vertical vessels. It deals with the skirt itself and
local stresses in the region where skirt and pressure vessel join and with the design of the base ring.
16.12.2 Specific symbols and abbreviations (see Figure 16.12-1, Figure 16.12-2, Figure 16.12-3
and Figure 16.12-4)
The following symbols and abbreviations are in addition to those in Clause 4 and 16.3:
a
is the lever-arm due to offset of centre-line of shell wall;
eB
is the analysis thickness of vessel wall;
eZ
is the analysis thickness of skirt;
fZ
is the allowable design stress of skirt;
fT
is the allowable design stress of the ring (Shape A);
418
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
r
is the inside knuckle radius of torispherical end;
R
is the inside crown radius of torispherical end;
DB
is the mean shell diameter;
DZ
is the mean skirt diameter;
FZn
is the equivalent force in the considered point (n = p or n = q) in the skirt;
FG
is the weight of vessel without content;
 FG
is the vessel weight below section 2-2;
FF
is the weight of content;
M
is the global bending moment, at the height under consideration;
 M
is the moment increase due to change of centre of gravity in cut-out section;
PH
is the hydrostatic pressure;
W
is the section modulus of ring according to Figure 16.12-1;
α
is a stress intensification factor (see Formulae (16.12-33) to (16.12-36));
γa
is the knuckle angle of a domed end (see Figure 16.12-2);
γ
is part of the knuckle angle (see Figure 16.12-2);
σ
is the stress;
Subscripts:
a
refers to the external shell surface, i.e. side facing away from central axis of shell;
b
refers to bending;
m
refers to membrane stress;
i
refers to the inside shell surface;
o
refers to the outside shell surface;
p
is the point in the section under consideration where the global moment causes the
greatest tensile force in the skirt (e.g. side facing the wind = windward side);
q
is the point in the section under consideration where the global moment causes the
greatest compressive force in the skirt (e.g. side facing away from the wind = leeward
side);
1
is the section 1-1 (see Figures 16.12-1 to 16.12-4);
2
is the section 2-2;
3
is the section 3-3;
4
is the section 4-4;
5
is the section 5-5.
UNI EN 13445-3:2021
419
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.12.3 Connection skirt / shell
16.12.3.1 Conditions of applicability
a)
For tall vertical vessels, the loads on the skirt shall be determined according to Clause 22.
b) Attention shall be paid to the need to provide inspection openings.
16.12.3.2 Forms of construction
The forms of construction covered in this section are:
a)
Structure
shape A:
Skirt connection via support in cylinder area – Figure 16.12-1;
Cylindrical or conical skirt with angle of inclination ≤ 7° to the axis;
b)
Structure
shape B:
Frame connection in knuckle area - Figure 16.12-2;
Cylindrical or conical stand frame with angle of inclination ≤ 7° to the
axis and welded directly onto the domed end in the area 0° ≤ γ ≤ 20° ;
Wall thickness ratio: 0,5 ≤ eB/eZ ≤ 2,25;
Torispherical end of Kloepper or Korbbogen type (as defined in 7.2) or
elliptical end having an aspect ratio K ≤ 2 (where K as defined in
Formula (7.5-18)) and a thickness not less than that of a Korbbogentype end of same diameter;
c)
Structure
shape C:
Skirt slipped over vessel shell - Figure 16.12-3;
Cylindrical skirt slipped over vessel shell and welded on directly
It is assumed that, on either side of the joining seam for a distance of
3 eB, there is no disturbance due to openings, end connections, vessel
circumferential welds, etc.;
Note has to be taken of the risk of crevice corrosion.
Outside the above limitations, subclauses 16.12.3.4.1 and 16.12.3.4.2 do not apply. Nevertheless, subclause
16.12.3.4.3 may be used subject to calculate existing stresses by elastic shell theories.
420
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.12-1 ― Shape A: Skirt connection with supporting ring
(Membrane forces due to self weight and fluid weight)
UNI EN 13445-3:2021
421
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.12-2 ― Shape B: Skirt connection in knuckle area
(Membrane forces due to self weight and fluid weight)
422
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.12-3 ― Shape C: Skipped-over skirt area
(Membrane forces due to self weight and fluid weight)
UNI EN 13445-3:2021
423
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(a) = Section 1-1 to 5-5
(b) = Section 4-4
Figure 16.12-4 ― Schematic diagram of stand frame - sections
16.12.3.3 Forces and moments
The values Fn and Mn at the respective sections n = 1 to n = 4 are determined as a function of the
combination of all the loads to be taken into consideration in this load case (see Figure 16.12-4). Further
checking may be necessary if the wall thickness in the skirt is stepped.
16.12.3.4 Checking at connection areas (sections 1-1, 2-2 and 3-3)
In the connection area, sections 1, 2 and 3 defined in Figure 16.12-1, Figure 16.12-2 and Figure 16.12-3
have to be checked. Checking is required for the membrane and the total stresses, while only the respective
longitudinal components are being taken into account.
The section force FZ in the skirt in the region of the joint depends on the position (n), i.e. whether the
moment strengthen (q) or weakens (p) the load component:
424
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
F Z p   F1  F G  F F  4
F Z q   F1  F G  F F  4
M
1
DZ
M1
DZ
(16.12-1)
(16.12-2)
where
F1
is the global additional axial force in section 1-1;
M1
is the resulting moment due to external loads in section 1-1 above the joint; between the
pressure-loaded shell and skirt.
16.12.3.4.1 Membrane stresses
The checking procedure for membrane stresses is the same for structural shapes A, B and C. The membrane
stresses at point 1-1 are:
m
 1p 
m
 1q 
FZp   FG  FF
 D B eB
FZq   FG  FF
 D B eB


P DB
4 eB
P DB
4 eB
(16.12-3)
(16.12-4)
Check that:
 1p
m
 f
(16.12-5)
m
 f
(16.12-6)
 1q
The minimum required wall thickness in section 1-1 are obtained from next formulae:
m
e1 p 
m
e1 q 
P DB 
1  FZp   FG  FF



4
f 
 DB

(16.12-7)
P DB 
1  FZq   FG  FF



4
f 
 DB

(16.12-8)
The calculation of this wall thickness is necessary for structural shape A.
m
m
If  1 p or  1 q is a compressive stress, a stability check shall be carried out according to 16.14. This check is
not required if the longitudinal stress component is less than 1,6 times the value of the resulting meridian
membrane compressive stress for a vacuum or partial vacuum load case, provided the latter was checked
according to Clause 8. This applies also to other sections in the cylindrical area of the shell.
Regardless of the check point, the membrane stress in section 2-2 is:
UNI EN 13445-3:2021
425
EN 13445-3:2021 (E)
Issue 1 (2021-05)

m

2
m

2q
m
2p

FF   FG
 D B eB

P DB
(16.12-9)
4 eB
Check that:

m
(16.12-10)
 f
2
The minimum required wall thickness in section 2-2 is obtained from next equation:
m
e2 
P DB 
1   FG  FF



f   DB
4

(16.12-11)
The calculation of this wall thickness is necessary for structural shape A.
In section 3-3 of the skirt, the membrane stresses are equal to:
m

3p

3q
m


FZp
(16.12-12)
 D Z eZ
FZq
(16.12-13)
 D Z eZ
Check that:
m

3p

3q
m
 fZ
(16.12-14)
 fZ
(16.12-15)
The minimum required wall thicknesses in section 3-3 are obtained from next formulae:
m
e3 p 
m
e3 q 
1
fZ
1
fZ
 FZp 


  DZ 
(16.12-16)
 FZq 


  DZ 
(16.12-17)
The calculation of this wall thickness is necessary for structural shape A.
m
m
If  3 p or  3 q is a compressive stress, the stability check may also be carried out according to 16.14.
16.12.3.4.2 Bending stresses
a) Structural shape A - Figure 16.12-1
426
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The local bending moment at points p and q is:
M
p
 0, 5  D Z  D B

M
q
 0, 5  D Z  D B
(16.12-18)
FZp

(16.12-19)
FZq
The total section modulus of the support ring at the point n is calculated as follows:
Wp 
Wq 

 D  e  D  e
Z
Z
B
B
4 

 D  e  D  e
Z
Z
B
B
4 
h
2
h
2

2 e
B

2 e
B
2
2
m 2
 e1 p
m 2
 e1 q
m2
 e2
m2
 e2
D
B
 0 , 5  e Z  e3p
D
Z
D
B
 0 , 5  e Z  e3q
D
Z
2
2
m 2
m 2


(16.12-20)


(16.12-21)
The factor 0,5 in the third summand allows for the type of transition from the skirt to the connecting ring as
shown in Figure 16.12-1. If the allowable stresses f of the vessel and/or fZ of the skirt are less than that of
the support ring fT, the 2nd and/or the 3rd summand in formulae (16.12-20) and (16.12-21) have to be
reduced with the respective ratio f / fT and/or fZ / fT
b) Structural shape B - Figure 16.12-2
The eccentricity a of the shell wall centreline causes a bending moment:
M
p
 a . FZp
(16.12-22)
M
q
 a . FZq
(16.12-23)
with:
a  0, 5
cos 
eB  eZ  2 eB eZ co s  
2
2

D B  eB  D Z  eZ
1
2  r  eB

(16.12-24)
(16.12-25)
The corresponding bending stresses in sections 1-1 to 3-3 at the outer surface (a):
 1p  a   
2p
 1q  a   
2q
b
b
b
b

3p

3q
b
b
a
 C
a
 C
a
 C
a
 C
6 M
p
2
(16.12-26)
2
(16.12-27)
 D B eB
6 M
q
 D B eB
(16.12-28)
2
(16.12-29)
q
 D Z eZ
UNI EN 13445-3:2021
p
2
 D Z eZ
6 M
6 M
427
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Within the range 0,5 ≤ eB /eZ ≤ 2,25, the correction factor C can be taken approximately equal to:
C = 0,63 - 0,057 (eB /eZ)2
(16.12-30)
This relationship was determined from numerical calculations using the finite element method. Because of
the large number of parameters, a simplification is made which, under certain circumstances, can lead to
significant over-dimensioning, e.g. in the case of “Korbbogen” ends.
In the region of sections 1-1 to 2-2 the above bending stress components are superimposed by the bending
effect caused by the internal pressure in the knuckle.
b
1
 p

b
2
 p

P
 PH
 DB
4 eB
 

  1

a

(16.12-31)
The stress intensification factor α is obtained as follows:
1) calculate the intermediate value y
y = 125 eB/DB
(16.12-32)
2) For Kloepper-type ends (with γa = 45°)
— for eB/DB > 0,008:
  9, 3 3 4 1  2, 2 8 7 7 y  0, 3 3 7 1 4 y
2
(16.12-33)
— for eB/DB ≤ 0,008:
  6, 3 7 1 8 1  2, 7 1 8 2 8
 1 6 ,1 y
 3, 6 3 6 6  2, 7 1 8 2 8
 1,6 1 5 3 6 y
 6, 6 7 3 6
(16.12-34)
3) for Korbbogen-type ends or elliptical ends which fulfil the requirements of 16.12.3.2 b
(with γa = 40°)
for eB/DB > 0,008:
—
(16.12-35)
  4, 2  0, 2 y
— for eB/DB ≤ 0,008:
  1, 5 1 8 6 1  2, 7 1 8 2 8
c)
4 ,233 5 y
 3, 9 9 4
(16.12-36)
Structural shape C - Figure 16.12-3
The eccentricity a off the shell axis causes a bending moment at point n:
M
p
 0 , 5  D Z  D B   FZn
(16.12-37)
M
q
 0 , 5  D Z  D B   FZq
(16.12-38)
Resulting bending stresses in section 1-1 and section 2-2:
428
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b
 1p  
b
 1q  
b
2p
b
2q

3 M
p
2
(16.12-39)
2
(16.12-40)
 D B eB
3 M

q
 D B eB
In section 3-3:
b

3p

3q

b

6 M
p
2
(16.12-41)
2
(16.12-42)
 D Z eZ
6 M
q
 D Z eZ
Bending stresses caused by pressure are ignored, e.g.:
b
1
 p  2  p 
b
(16.12-43)
0
16.12.3.4.3 Total stresses and strength conditions
The total stresses shall be obtained as follows:
a) Structure shape A
At each point, the strength condition shall be checked as follows:
1) location p : with Mp from Formula (16.12-18) and Wp from Formula (16.12-20)
M
p
(16.12-44)
/ W p  fT
2) location q: with Mq from Formula (16.12-19) and Wq from Formula (16.12-21)
M
q
(16.12-45)
/ W q  fT
b) Structure shape B and C
1) the total stresses at point p, section 1-1, are obtained from next formulae
— on the inner surface (i)
 1pi   1p   1p  a    1
b
 p
(16.12-46)
 1po   1p   1p  a    1
 p
(16.12-47)
to t
m
b
— on the outer surface (o)
to t
m
b
b
2) the total stresses at point q, section 1-1, are obtained from next formulae
UNI EN 13445-3:2021
429
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— on the inner surface (i)
 1qi   1q   1q  a    1
to t
m
b
b
 p
(16.12-48)
 p
(16.12-49)
— on the outer surface (o)
 1qo   1q   1q  a    1
to t
m
b
b
3) The total stresses in section 2-2 at point p are:
— on the inner surface (i)
 2pi   2p   2p  a    2
b
 p
(16.12-50)
 2po   2p   2p  a    2
 p
(16.12-51)
to t
m
b
— on the outer surface (o)
to t
m
b
b
4) The total stresses in section 2-2 at point q are:
— on the inner surface (i)
 2qi   2q   2q  a    2
to t
m
b
b
 p
(16.12-52)
— on the outer surface (o)
 2qo   2q   2q  a    2
to t
m
b
b
 p
(16.12-53)
5) In section 3-3 the total stresses at point p are:
— on the inner surface (i)
to t
m
b
 3pi   3p   3p
(16.12-54)
— on the outer surface (o)
to t
m
b
 3po   3p   3p
(16.12-55)
6) In section 3-3 the total stresses at point q are:
— on the inner surface (i)
to t
m
b
 3qi   3q   3q
(16.12-56)
— on the outer surface (o)
to t
m
b
 3qo   3q   3q
430
(16.12-57)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
7) In case of ductile materials the total stresses obtained by Formulae (16.12-46) to (16.12-57)
shall satisfy next formula where fs is the design stress in each part:
i)
Section 1-1
to t
 1pi
to t
 1po
to t
 1qi
to t
 1qo

1
 fS  3 
1, 5


  1p

 f






1
 fS  3 
1, 5


  1p

 f

m





1
 fS  3 
1, 5


  1q

 f

m





1
 fS  3 
1, 5


  1q

 f

m




m
m
2
2
2
2




(16.12-58)




(16.12-59)




(16.12-60)




(16.12-61)




(16.12-62)




(16.12-63)




(16.12-64)




(16.12-65)




(16.12-66)
ii) Section 2-2




to t
2pi
to t
2po
to t
2qi
to t
2qo

1
 fS  3 
1, 5


  2p

 f






1
 fS  3 
1, 5


  2p

 f

m





1
 fS  3 
1, 5


  2q

 f

m





1
 fS  3 
1, 5


  2q

 f

m




m




2
2
2
2
iii) Section 3-3

to t
3pi

1
 fS  3 
1, 5


UNI EN 13445-3:2021
  3p

 f
 Z
2
431
EN 13445-3:2021 (E)
Issue 1 (2021-05)



to t
3po
to t
3qi
to t
3qo

1
 fS  3 
1, 5


  3p

 f
 Z

1
 fS  3 
1, 5


  3q

 f
 Z





1
 fS  3 
1, 5


  3q

 f
 Z
m




m
m




2
2
2




(16.12-67)




(16.12-68)




(16.12-69)
16.12.4 Design of skirts without and with openings
16.12.4.1 Specific symbols and abbreviations
d
mean diameter of the opening reinforcement (see Figure 16.12-5)
ea3
analysis wall thickness of the skirt wall thickness e3
eat
analysis wall thickness of the reinforcement thickness et (see Figure 16.12-5)
ht
length of outer part of the opening reinforcement (see Figure 16.12-5)
lt
total length of the opening reinforcement (see Figure 16.12-5)
(i
index of the opening when more than one opening exist)
yG
distance between neutral axis and centre of gravity at section 4-4
ymax
maximum distance between centre of gravity and outer edge of section 4-4
A4
area of the cross section with openings at section 4-4
including analysis wall thicknesses of skirt and nozzles
D3
mean diameter of the skirt
F4
vertical compressive force acting in cross section 4-4, see Figure 16.12-4
Fc,max
maximum compressive force according to Formula (16.14–2)
with σc,all according to Formula (16.14–29) as defined in Table 5.3.2.4–1
M4
bending moment acting in cross section 4-4, see Figure 16.12-4
Mmax
maximum bending moment according to Formula (16.14–3)
with σc,all according to Formula (16.14–29) as defined in Table 5.3.2.4–1”.
W4
elastic section modulus of the cross section with openings at section 4-4 including
analysis wall thicknesses of skirt and nozzles
δ
half angle of the opening, see Figure 16.12-4 (b)
Ψ1, Ψ2
weakening factors of area and elastic section modulus of cross section 4-4
16.12.4.2 Check of the skirt in regions without openings
For skirts without openings and in regions of skirts where no openings exist the design check shall be
performed as described in 22.6.3.
432
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
Cross sections below regions with openings may be governed because the acting forces and moments
are higher.
16.12.4.3 Check of the skirt in regions with openings
Determine values of F4 and M4 acting in cross section 4-4 and Fc,max and Mmax with σc,all for all load cases
defined in Table 5.3.2.4-1.
The check according to Formula (16.12-70) shall be performed for the cross section where the largest
weakening effect exists, e.g. where the left term in Formula (16.12-70) is maximal.
F4
 1  Fc ,m ax

M
 F4  y G
4

2
M
 1, 0
(16.12-70)
m ax
with:

A
1
 m in {1 ;
4
 D e
3
}
a3
and
4 W

2
 m in {1 ;
4
}
2
  D3  e
(16.12-71)
a3
16.12.4.4Cross section parameter for cross section with one opening
Figure 16.12-5 ― Skirt cross section with one opening
The half angle of the opening δ in radians is determined in Formula (16.12-72) and the parameters A4, W4
and yG of the cross section are given in Formulae (16.12-73) to (16.12-75).
  arcsin ( d / D 3 )
(16.12-72)
A 4  A S  At
(16.12-73)
UNI EN 13445-3:2021
433
EN 13445-3:2021 (E)
Issue 1 (2021-05)
with:
A S  (   )  D 3  e a 3
and
yG 
0 , 5  D 3  e a 3  d  2  lt  e a t  y t
(16.12-74)
A4
with:
y t  0, 5  D 3  co s   h t  0, 5  l t
W4 

2
S
2
2
 At  ( y t  lt / 1 2 )  A 4  y G
(16.12-75)
y m ax
with:

S
 [     s in   c o s  ]  e a 3  (
D3
2
)
3
and
y m ax  m a x  0 , 5  D 3  c o s   ht  y G
; 0, 5  D3  yG

16.12.4.5 Cross section parameter for cross section with more than one opening
In the general (but seldom) case that more similar-sized openings exist in the section 4-4 (see Figure 16.126 with the example of two openings) the parameters A4, W4 and yG of the whole cross section shall be
calculated accordingly.
Figure 16.12-6 ― Skirt cross section with two openings
434
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)

i
NOTE
Whereas the calculation of the section area A4 is easy done by replacing ΣAti instead of At and
instead of δ in formula for AS, the calculation of elastic section modulus W4 requires to find the weakest axis with
the corresponding distances yG and ymax and second moments of area in this direction using the rules for
transforming second moments of area due to translation and rotation.
In the special (but common) case that one large opening and one or more small openings exist in the
section 4-4 the following procedure may be used:
1.
Check that the condition (16.12-76) is fulfilled for each of the small openings i:
A t , i  2  l t , i  e a t , i  A , i   i  D 3  e a 3
(16.12-76)
in which the limitation: l t , i  8  e a t , i is met.
2.
When condition (16.12-76) is not fulfilled then increase the reinforcement area At,i of the opening in question.
3.
Apply conditions and Formulae (16.12-70) to (16.12-75) taking into account the one large opening in
section 4-4 only.
16.12.5 Design of anchor bolts and base ring for skirts
16.12.5.1 Specific symbols and abbreviations
b1
radial width of bearing plate
b2
outer radial width of bearing plate (outer radius of bearing plate minus outer radius of skirt)
b3
lever arm of bolts (bolt circle radius minus outer radius of skirt)
b4
width of top plate in circumferential direction for type 3 (at least distance b6 plus two times en7 and two
times fillet weld leg (see Figure 16.12-9)
b5
radial width of top plate or top ring plate (outer radius of top plate minus outer radius of skirt)
b6
spacing (measured as arc length on bolt circle diameter) between gussets or support plates with bolts in
between for type 2 and 4 version B (see Figures 16.12-8, 16.12-10) and distance between the parallel
support plates for type 3 (see Figure 16.12-9)
b7
spacing (measured as arc length on bolt circle diameter) between gussets or support plates without
bolts in between for type 2 and 4 version B and type 3 but with bolts in between for type 2 and 4
version A (see Figures 16.12-8,16.12-9 and 16.12-10)
b8
spacing (measured as arc length on bolt circle diameter) between anchor bolts
dB0
nominal bolt diameter
f3
nominal design stress for skirt wall as defined in Table 5.3.2.4–1 depending on load condition
UNI EN 13445-3:2021
435
EN 13445-3:2021 (E)
Issue 1 (2021-05)
f4
nominal design stress for bearing plate as defined in Table 5.3.2.4–1 depending on load condition
f5
nominal design stress for top plate or top ring plate as defined in Table 5.3.2.4–1 depending on load
condition
f7
nominal design stress for gussets or support plate as defined in Table 5.3.2.4–1 depending on load
condition
fB
nominal design stress for anchor bolts as defined in Table 5.3.2.4–1 depending on load condition”.
fC
allowable concrete compression stress for permanent actions
en3
nominal wall thickness of the skirt thickness e3
ea3
analysis wall thickness of the skirt
en4
nominal wall thickness of the bearing plate thickness e4
ea4
analysis wall thickness of the bearing plate
en5
nominal wall thickness of the top plates or top ring plate thickness e5
ea5
analysis wall thickness of the top plates or top ring plate
en7
nominal wall thickness of the gussets or support plates thickness e7
ea7
analysis wall thickness of the gussets or support plates
h1
height of the gussets or base ring assembly
h1S
height of the support plates (h1S = h1 - ea4 - ea5)
nB
number of anchor bolts
AB
tensile stress area of one bolt
D3
internal diameter of the skirt
D4
internal diameter of the bearing plate
DBC
bolt circle diameter
DCR
mean diameter of bearing ring plate (DCR = D4 + b1)
E7
modulus of elasticity of gussets or support plates
FB
bolt load on one bolt as defined in 16.12.5.2
436
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
FB,d
design bolt load on one bolt as defined in 16.12.5.2
FC
load on concrete below whole bearing plate as defined in 16.12.5.2
FC,d
design load on concrete below whole bearing plate as defined in 16.12.5.2
16.12.5.2 Anchor bolt and concrete forces
The maximum anchor bolt forces FB and the maximum concrete force FC caused by the global axial force F5
and the global bending moment M5 acting in section 5-5 (see Figure 16.12-4) shall be calculated by
Formulae (16.12-77) and (16.12-78) respectively:
 4M 5
 1
FB  
 F5  
 D BC
 nB
(16.12-77)
 4M 5

FC  
 F5 
 DCR

(16.12-78)
NOTE
For tall vertical vessels F5 and M5 are defined in Table 22–1 as vertical force FV and as bending moment
MB respectively for the different load condition status.
The required nominal bolt dB0 diameter may be calculated according to Formula (16.12-79) or chosen and
then checked by Formula (16.12-85). The calculations are valid only for corrosion protected anchor bolts.
d B0 
4  FB
  fB
 
(16.12-79)
B
with:
0, 9382  P ,
B  
 0 ,9 7 4 3  P ,
w h e r e P is b o lt th r e a d p itc h f o r m e tr ic b o lts , s e e IS O 2 6 1
w h e r e P is b o lt th r e a d p itc h f o r U N , U N R b o lts , s e e A S M E B 1 .1
The preloading force FA of the anchor bolts applied during assembly and the associated torque moment Mt
shall be calculated by Formulae (16.12-80) and (16.12-81) respectively:
F A    A B  f B ,o p
Φ
assembly factor (recommended value Φ = 0,5):
M t    FA  d B 0
μ
(16.12-80)
(16.12-81)
effective friction factor (recommended value μ = 0,2 as combination of friction in the thread
and at the nut for unlubricated torqueing):
AB 

4
2
 d Be
UNI EN 13445-3:2021
(16.12-82)
437
EN 13445-3:2021 (E)
Issue 1 (2021-05)
dBe
effective bolt diameter = tensile stress diameter of bolt ( d B e  d B 0   B );
ΔB
see above.
The design anchor bolt force FB,d and the design concrete force FC,d are defined by Formulae (16.12-83) and
(16.12-84) respectively:
FB ,d  m a x  F A ; FB 
(16.12-83)
FC , d  m a x  n B  F A ; FC 
(16.12-84)
16.12.5.3 Stress checks for anchor bolts and concrete
The tensile stress check of anchor bolts is given in Formula (16.12-85).

B

NOTE
FB ,d
AB
(16.12-85)
 fB
Check of pull-out load in concrete for FB,d is required by civil engineering.
The compression stress check of the concrete below the base ring bearing plate is given in
Formula (16.12-86).
C 
FC , d
  D C R  b1
(16.12-86)
 f C  f c d / 1, 3 5
fC
allowable concrete compression stress for permanent actions
fCd
allowable concrete compression strength according to EN 1992-1-1:2005, 3.16 with the
specific values specified in the National Annex of countries.
Recommended conservative values fC for preliminary design only (has to be checked by civil engineering).
Strength class of concrete
C20
C25
C30
C35
Allowable concrete compression stress fC
5,9 MPa
7,4 MPa
8,9 MPa
10,4 MPa
The width b1 of the base ring bearing plate shall be chosen fulfilling Formula (16.12-87).
b1 
438
FC , d
  DCR  fC
(16.12-87)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.12.5.4Design of base ring assemblies
16.12.5.4.1 Types of base ring assemblies
Four types of base rings are taken into consideration:
Type 1: to be checked according to 16.12.5.4.3
Simple bearing plate (see Figure 16.12-7)
Type 2: to be checked according to 16.12.5.4.4
Bearing plate with gussets (see Figure 16.12-8)
Type 3: to be checked according to 16.12.5.4.5
Bearing plate with chairs (see Figure 16.12-9)
Type 4: to be checked according to 16.12.5.4.6
Bearing plate with top ring plate (see Figure 16.1210)
16.12.5.4.2 General condition of applicability for the types
For type 1 and 2:
2 d B 0  3 0 m m  b2 
2
3
b1
(16.12-88a)
For type 3 and 4:
2 d B 0  3 0 m m  b5 
2
3
b1
and
b 2  b5
m in  d B 0  4 5 m m ;1, 5  d B 0  1 0 m m   b 3  m a x  b 2 ; b 5   ( d B 0  1 0 m m )
NOTE
(16.12-88b)
(16.12-89)
Formula (16.12-89) ensures enough space for mounting the nuts.
The welds between the different plates, and between the plates and the skirt, shall be double fillet welds.
Each fillet shall have a minimum weld throat thickness equal to half the thickness of the thinner of the parts
being joined.
UNI EN 13445-3:2021
439
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1
bearing plate
2
skirt
Figure 16.12-7 ― Type 1: Simple bearing plate
440
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1
bearing plate
2
gussets
3
skirt
Figure 16.12-8 ―Type 2: Bearing plate with gussets
UNI EN 13445-3:2021
441
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1
bearing plate
2
support plates
3
top plates
4
skirt
Figure 16.12-9 ―Type 3: Bearing plate with chairs
442
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1
bearing plate
2
support plates
3
top ring plate
4
skirt
Figure 16.12-10 ―Type 4: Bearing plate with top ring plate
16.12.5.4.3 Checks for type 1 – Simple bearing plate
The nominal thickness en4 of the bearing plate shall be equal to or thicker than the nominal skirt wall
thickness en3.
Analysis thickness ea4 of the bearing plate:
for FB > 0

ea 4  m a x  b2 

UNI EN 13445-3:2021
3  C
f4
;
4  n B  F B  b 3 

  D 3  f 4 
(16.12-90a)
443
EN 13445-3:2021 (E)
Issue 1 (2021-05)
for FB ≤ 0
ea 4  b2 
3 
(16.12-90b)
C
f4
When the thickness e4 of the bearing plate is chosen the stress check of the bearing plate shall fulfil the
condition (16.12-91):
for FB > 0
 3  b 2 4  n  F  b 
c 2
B
B
3
m ax 
;
 f4
2
2 

e
D
e


3
a4

 a 4
(16.12-91a)
for FB ≤ 0
3 c b 2
ea 4
2
2
(16.12-91b)
 f4
FB
bolt force according to (16.12-77);
σC
concrete stress according to (16.12-86).
When type 1 gives no suitable results the three other types (2 or 3 or 4) with higher bearing capability are
available.
16.12.5.4.4 Checks for type 2 – Bearing plate with gussets
The number of gussets is equal the number of bolts (version A of Figure 16.12-8) or twice the number of
bolts (version B of Figure 16.12-8) and the gussets are symmetrically spaced around the bolts and their
height h1 shall be at least two times the width b2 (h1 > 2b2).
16.12.5.4.4.1 Checks for the bearing plate
The nominal thickness en4 of the bearing plate shall be equal to or thicker than the nominal skirt wall
thickness en3.
Analysis thickness ea4 of the bearing plate:
for FB > 0

ea 4  m a x  1  b2 

3 
f4
C
;  2
F B 

f 4 
(16.12-92a)
for FB ≤ 0
ea 4   1  b2 
3 
f4
C
(16.12-92b)
When the thickness e4 of the bearing plate is chosen the stress check of the bearing plate shall fulfil the
condition (16.12-93):
444
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
for FB > 0
2

FB
 3  c b 2
2
2
m ax 
1 ;
 2   f4
2
2
ea 4
 e a 4

(16.12-93a)
for FB ≤ 0
3 c b 2
ea 4
2
2
(16.12-93b)
2
1  f4
FB
bolt force according to (16.12-77);
σC
concrete stress according to (16.12-86).
with:

 b
 1  1, 8 1   2

 bX
1 

 1  2 , 9 7   b2


 bX

3



3 
 
 
 



2
(16.12-94)
fo r v e rs io n A
 b7
bX  
 m a x (b6 ; b7 ) fo r v e rs io n B
2 
(16.12-95)
b  
e 
3  Z  1  s 
bY 
 bY  

es   bZ 
1 


bY   bY 

 b7
bY  
 b6
(16.12-96)
2
f o r v e r s io n A
(16.12-97a)
f o r v e r s io n B
bZ  b2
(16.12-97b)
eS width across corners of anchor
nuts.
For metric nuts the following values for eS may be used:
Size
M16 M20 M24 M30 M36 M42 M48 M56 M64 M72 M80 M90 M100 M110 M120
eS in mm 26
UNI EN 13445-3:2021
34
40
51
61
72
84
94
105 117 128 145 162
173
190
445
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.12.5.4.4.2 Checks for the gussets
Analysis thickness ea7 of the gusset plate:
 
C
ea 7  b2  m a x 
 3  4 ;
f
 7
3

 3  5 

C
f7
(16.12-98)
When the thickness e7 of the gusset plates is chosen the check of the gusset plate shall fulfil the condition
(16.12-99):

C

σC
b2
ea 7
2

 b2 

  3  m ax  4 ; 
  5
e
a
7






  f7


(16.12-99)
concrete stress according to (16.12-86)
with:
3
2


1  2  b 2 / b8

 
1
1


 1  2  b2 / b6
1  2  b2 / b7

2
4 
2

b  
b 
1  3   2    3   2 

 h1  
 h1 
2
2
f o r v e r s io n A
(16.12-100)
f o r v e r s io n B
2
b  
f  h  
 5  1, 8  7   1   1   2  
E 7  b2  
 h1  

(16.12-101)
2
(16.12-102)
NOTE
The first terms of the maximum in Formulae (16.12-98) and (16.12-99) result from protection against
plastic collapse and the second terms results from protection against stability collapse with a safety factor of 3.
16.12.5.4.4.3 Check of the skirt at gussets
The check of the skirt loaded by the line loads (acting in longitudinal direction) imposed by the gussets is
adapted from 16.6.6 to 16.6.8.
2
C
 b2  b2
6  K 13  K 14

 3 
 f3
 
4


e
h
K
K
1
1
2
 a3 
(16.12-103)
with:
σC
concrete stress according to (16.12-86);
κ3
geometrical parameter according to formula (16.12-100).
446
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
h1
 
(16.12-104)
D 3 . ea3
1
K 13 
1, 2 1  0 , 0 6 
2
1
K 14 
0, 6 1  0, 03
2
 1  m in  0 , 0 8  ; 0 , 2 0 
3
K1 
1
2
(16.12-105)
(16.12-106)
(16.12-107)
(16.12-108)
1  9  1
 1 ,2 5
K2  
 1 ,0 5
f o r o p e r a tio n a n d s h u t d o w n c o n d itio n s
f o r te s t a n d in s ta lla tio n c o n d itio n s
(16.12-109)
Formula (16.12-108) follows from (16.6-7) with  2  0 since no circumferential membrane stress due
NOTE 1
to pressure occurs in the skirt.
NOTE 2
When type 2 gives no suitable results the both other types (3 or 4) with higher bearing capability are
available.
16.12.5.4.5 Checks for type 3 – Bearing plate with chairs
The number of chairs shall be equal to the number of bolts. The chairs shall be symmetrically spaced around
the bolts and their height h1 shall be at least two times the width b2 (h1 > 2b2).
16.12.5.4.5.1 Check for the bearing plate
The nominal thickness en4 of the bearing plate shall be equal to or thicker than the nominal skirt wall
thickness en3.
Analysis thickness ea4 of the bearing plate:
ea 4   1  b2 
3 
C
f4
(16.12-110)
When the thickness en4 of the bearing plate is chosen the stress check of the bearing plate shall fulfil the
condition (16.12-111):
3 c b 2
ea 4
2
2
2
1  f4
(16.12-111)
with:
σC
concrete stress according to (16.12-86);
UNI EN 13445-3:2021
447
EN 13445-3:2021 (E)
Issue 1 (2021-05)
κ1
geometrical parameter according to Formula (16.12-94);
with b X  m ax ( b 6 ; b 7 ) .
16.12.5.4.5.2 Check for the top plates
The nominal thickness en5 of the top plates shall be equal to or thicker than the nominal skirt wall thickness
en3.
Analysis thickness ea5 of the top plates:
FB ,d
ea 5   2 
(16.12-112)
f5
When the thickness e5 of the top plates is chosen the stress check of the top plates shall fulfil the condition
(16.12-113):
FB ,d
ea 5
2
2
(16.12-113)
  2  f5
with:
FB,d
design bolt force according to Formula (16.12-83);
σC
concrete stress according to Formula (16.12-86);
κ2
geometrical parameter according to Formula (16.12-96);
with bY  b 6 and b Z  b 5 .
16.12.5.4.5.3 Check for the support plates
The analysis thickness ea5 of the support plates may be calculated by iteration using Formulae (16.12-114)
and (16.12-116). The iteration may be started with κ6 = 0:
ea 7 
FB ,d
2  b2  f 7
2
 1 6
(16.12-114)
When the thickness e7 of the support plates is chosen the stress check of the support plates shall fulfil the
condition (16.12-115):
FB ,d
2
2  b2  ea 7
6
FB,d
448
 1   6  f7
2
 b2 
 2, 5 

 
E 7  ea 7 
f7
(16.12-115)
(16.12-116)
design bolt force according to Formula (16.12-83).
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
The first terms below the square root in Formulae (16.12-114) and (16.12-115) result from protection
against plastic collapse and the second terms results from protection against stability collapse with a safety factor
of 3.
16.12.5.4.5.4 Check of the skirt at top plates
The check of the skirt loaded by the line load (acting in circumferential direction) imposed by the top plate is
adapted from 16.6.6 to 16.6.8.
FB
2
ea 3
 b3 
K 13


 h1  K 1  K
 f3
(16.12-117)
2
with:
FB
bolt force according to Formula (16.12-77).
b4
 
(16.12-118)
D 3 . ea3
K 13 
1
1, 2 1  0 , 6 0 
(16.12-119)
2
 1  m in  0 , 0 8  ; 0 , 3 0 
2 
K2
(16.12-120)
n B  FB
(16.12-121)
  D 3  ea 3  f3  K 2
as given by Formula (16.12-109).
1 
K1 
2
2
2
1

   1 2  
3

(16.12-122)
1

2
2
   1 2   (1   2 )  1
3

16.12.5.4.5.5 Checks for type 4 – Bearing plate with top ring plate
The number of lateral plates shall be equal to the number of bolts (version A of Figure 16.12-8) or to twice
the number of bolts (version B of Figure 16.12-8). The support plates shall be symmetrically spaced around
the bolts and their height h1S shall be at least two times the width b2 (h1S > 2b2).
Check for the bearing plate:
The nominal thickness en4 of the bearing plate shall be equal to or thicker than the nominal skirt wall
thickness en3.
Analysis thickness ea4 of the bearing plate:
ea 4   1  b2 
UNI EN 13445-3:2021
3 
f4
C
(16.12-123)
449
EN 13445-3:2021 (E)
Issue 1 (2021-05)
When the thickness e4 of the bearing plate is chosen the stress check of the bearing plate shall fulfil the
condition (16.12-124):
3 c b 2
ea 4
2
2
(16.12-124)
2
1  f4
with:
σC
concrete stress according to Formula (16.12-86);
κ1
geometrical parameter according to Formula (16.12-94);
with bX according to Formula (16.12-95).
Check for the top plates:
The nominal thickness en5 of the top plates shall be equal to or thicker than the nominal skirt wall thickness
en3.
Analysis thickness ea5 of the top plates:
ea 5   2 
FB ,d
(16.12-125)
f5
When the thickness e5 of the top plates is chosen the stress check of the top plates shall fulfil the condition
(16.12-126):
FB ,d
ea 5
2
2
(16.12-126)
  2  f5
with:
FB,d
design bolt force according to (16.12-83);
σC
concrete stress according to (16.12-86);
κ2
geometrical parameter according to Formula (16.12-96);
with bY according to formula (16.12-97a) and b Z  b 5 .
Check for the support plates:
The analysis thickness ea7 of the support plates may be calculated by iteration using Formulae (16.12-127)
and (16.12-129). The iteration may be started with κ6 = 0:
ea 7 
FB ,d
n S  b2  f 7
2
 1 6
(16.12-127)
When the thickness e7 of the support plates is chosen the stress check of the support plates shall fulfil the
condition (16.12-128):
450
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
FB ,d
2
n S  b2  ea 7
(16.12-128)
 1   6  f7
with:
6
 b2 
 2, 5 


E 7  ea 7 
f7
1
nS  
2
FB,d
2
(16.12-129)
f o r v e r s io n A
(16.12-130)
f o r v e r s io n B
design bolt force according to Formula (16.12-83).
NOTE
The first terms below the square root in Formulae (16.12-127) and (16.12-128) result from protection
against plastic collapse and the second terms results from protection against stability collapse with a safety factor
of 3.
16.12.5.4.5.6 Check of the skirt at top ring plate
The check of the skirt loaded by the line load (acting in circumferential direction) imposed by the top ring
plate is adapted from 16.6.6 to 16.6.8.
FB
2
ea 3
 b3 
K 13


 h1  K 1  K
(16.12-131)
 f3
2
with:
FB
bolt force according to Formula (16.12-77);
K1, K2, K13
according to Formulae (16.12-119) to (16.12122);
but with:  
b8
D 3 . ea3
.
(16.12-132)
16.13 Vertical vessels with ring supports
16.13.1 Purpose
This clause shall be used for the design of integral ring supports and loose ring supports. The ring is
supported on a number of uniformly distributed local supports or on a continuous support over the entire
periphery of the ring.
16.13.2 Definitions
16.13.2.1
integral ring support
rings permanently welded to the vessel and the wall of the vessel takes part of the load (see
Figure 16.13-1(a))
UNI EN 13445-3:2021
451
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.13.2.2
loose ring support
rings that are not joined to the vessel (see Figure 16.13-1(b))
16.13.3 Specific symbols and abbreviations (see Figure 16.13-1and Figure 16.13-2)
The following symbols and abbreviation are in addition to those in Clause 4 and 16.3:
b
is the width of ring (see Figure 16.13-2);
d1
is the inside diameter of the vessel;
d2
is the outside diameter of the vessel;
d3
is the inside diameter of ring;
d4
is the outside diameter of ring;
d5
is the diameter to transverse force mid-point;
d6
is the diameter to line-load;
d7
is the diameter to supporting force;
e1
is the wall thickness of vessel;
e3
is the thickness of ring (see Table 16.13-2);
e4
is the thickness of ring (see Table 16.13-2);
e5
is the thickness of ring (see Table 16.13-2);
fT
is the allowable design stress of ring material;
f *T
is the reduced allowable design stress of ring material;
h
is the height of ring (see Figure 16.13-2);
mb
is the allowable unit bending moment (see Table 16.13-1);
mt
is the allowable unit torsional moment (see Table 16.13-1);
ns
is the number of local supports of the ring;
q
is the line load;
qt
is the allowable unit transverse force (see Table 16.13-2);
t0
is the clearance;
AT
is the cross section area of ring (see Figure 16.13-1);
F
is the equivalent total vertical force depending on the load case (see 16.13.6);
FS,max
is the allowable force depending on load case;
G
is the weight of the vessel including vessel content;
452
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
M
is the global bending moment in vessel resulting from external loads at height of ring, depending
on the load case;
Mt
is the torsional moment in ring cross section depending on the load case;
Mt,max
is the allowable torsional moment (for ring cross section only when subject to torsion load);
Mb
is the bending moment in ring cross section;
Mb,max
is the allowable bending moment (for ring cross section only when subject to bending load);
Q
is the transverse force in ring cross section;
Qmax
is the allowable transverse force (for ring cross section only when subject to transverse load);
Wb
is the section modulus;
WT
is the torsional section modulus;
Z0
is a coefficient;
Z1
is a coefficient;

is dimensionless lever arm of supporting force;

is dimensionless lever arm of line-load;
16.13.4 Conditions of applicability
Calculations according to this clause are based on the following assumptions:
a) The profile of the ring is constant over its circumference;
b) In case of open profiles, gussets may be needed in order to preserve the cross-sectional shape ;
c) In case of thin-walled profiles : b / e3 > 5 and h / e4 > 5 ;
d) For loose ring supports (see Figure 16.13-1b) no flexible layer is allowed between the loose ring
and the ring attached at the vessel.
NOTE
This condition is necessary because the calculation is only valid for a favourable non-uniform load
distribution over the circumference of the ring.
e) The supports of the ring are evenly distributed and each support bears a local uniform load;
f)
The profile is one of those covered by Figure 16.13-2;
g) The lever arm ratios  and  shall be  | 0,2 |; see Formulae (16.13-9) and (16.13-10);
UNI EN 13445-3:2021
453
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.13.5 Design procedure
16.13.5.1 Strength for the ring
For all relevant loading cases, the total equivalent force F according to 16.13.6 shall be not greater than the
allowable force FS,max according to Formulae (16.13-7) or (16.13-8).
16.13.5.2 Local design
The welds, gussets and any bolted connections are to be designed by any generally accepted method.
16.13.6 Total equivalent force F
The equivalent force F is equal to:
F 

1  M
 G
4
ns  d7

(16.13-1)
In case of uniform support of the ring F is equal to:
F 
4 M
d7
(16.13-2)
 G
16.13.7 Allowable section values for rings
For type I integral and loose ring supports the allowable stress of the ring is fT, while for type II integral ring
supports the allowable reduced stress of the ring becomes equal to:

P h d1 
*
fT  fT  1 

2 A T fT 

(16.13-3)
NOTE
Box section or U-section rings are considered type II, when the width b is larger then the height h (see
Table 16.13-2)
The allowable section values in the ring are obtained by multiplying the allowable unit quantities from
Table 16.13-2 with the allowable stress or the allowable reduced stress
*
(16.13-4)
*
(16.13-5)
fT q t
(16.13-6)
M t,m a x  f T m t
or
fT m t
M b ,m a x  f T m b
or
fT m b
Q max  f T q t
or
*
16.13.8 Load-bearing capacity of ring
The allowable force as a single load on the support is obtained as the minimum value of the allowable
bending moment load and the allowable transverse force load:
454
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)




F S ,m a x  m in


 d4

4  M b ,m a x
 M b ,m a x
2
2
 Z 
Z
0
1 
 M T ,m a x




2




; 2 Q m ax




(16.13-7)
If the support is uniform
F S ,m a x 
4  M b ,m a x
  
(16.13-8)
d4
The values for Z0 and Z1 may be taken from the Table 16.13-1. However those values lead to conservative
results. A more accurately estimation of the allowable forces is obtained by using the values Z0 and Z1 from
Figures 16.13-3 to 16.13-6.
Table 16.13-1 ― Values of Z0 and Z1
nS
Z0
Z1
2
1,8
1,1
3
1,9
0,7
4
2,1
0,7
6
2,7
0,7
8
3,5
0,7
The lever arm ratios  and  are calculated by next formulae, with diameters as shown in Figure 16.13-1.
 0 ,2   
d 7
 d5
/d4
 0 ,2
(16.13-9)
 0 ,2   
d 6
 d5
/d4
 0 ,2
(16.13-10)
For externally fitted rings:
d5  d3  e4  2 t0
(16.13-11)
For internally fitted rings:
d 5  d 3  e4  2 t0
(16.13-12)
For closed cross sections:
t0 shall be taken from Table 16.13-2;
For open ring cross section:
t0 = 0.
UNI EN 13445-3:2021
455
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 16.13-2 ― Allowable unit section values
mt
mb
qt
t0
if h  b
hb
2

4
b
3
bh
12
2
4
bh
b
2
2
if h  b
bh
2
4

h
3
12
b.h. min {e3;e4;e5}

 e 3 b h  e 4  e 5




4 

h
2
e 4
 e5

h
2
b e5
e4  e5
e3. e4. e5  0
2
e3 b
2
2

2
e3 b
4
e4 h
4
2

e4 h
4
e4 h
2

e4 h 

e 3 b h 
4


e4 h
4
2
0
2
2
2

4 e 3 b e 3 b  e 4 h   e h
4

2

e 3 b  e 4 h 





e4 h
0
2
 d4
 d1
 d3
 d5
(a) integral ring support
(b) Loose ring support
Figure 16.13-1 ― General principle
456
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.13-2 ― Design types for ring supports
(shaded area = cross sectional area AT of ring)
UNI EN 13445-3:2021
457
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.13-3 ― Parameter Z0, with ns = 2, 3 or 4
458
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.13-4 ― Parameter Z0, with ns = 6 or 8
UNI EN 13445-3:2021
459
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.13-5 ― Parameter Z1, with ns = 2, 3 or 4
460
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 16.13-6 ― Parameter Z1, with ns = 6 or 8
UNI EN 13445-3:2021
461
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.14 Global loads on cylindrical shells
16.14.1 Purpose
Rules are given for determining the minimum thickness of a cylindrical shell subject to a combination of
loads in addition to pressure, at sections remote from the area of application of local loads and from
structural discontinuities.
16.14.2 Specific symbols and abbreviations
The following symbols and abbreviation are in addition to those in Clause 4 and 16.3:
Cx
is a factor given by Formula (16.14–17), (16.14–18) or (16.14–19);
Cxb
is a factor from Table 16.14–1;
D
is the mean shell diameter;
Dmax
is the maximum measured external diameter;
Dmin
is the minimum measured external diameter;
Dnom
is the nominal internal diameter;
d1
is the maximum measured offset between the middle lines of adjacent parts at circumferential welds
(see EN 13445-4:2019, Figure 6.2–1);
dn
is the non-intended offset between the middle lines of adjacent parts at circumferential welds, given by
Formula (16.14–31);
dn,max
is the maximum non-intended misalignment at circumferential welds from Table 16.14–4;
E
is the modulus of elasticity of shell at design temperature (see O.4);
e1
is the analysis thickness of the thinner of the adjacent parts at circumferential welds (see EN 13445-4:2019,
Figure 6.2–1);
e2
is the analysis thickness of the thicker of the adjacent parts at circumferential welds (see EN 13445-4:2019,
Figure 6.2–1);
F
is the total axial force carried by shell at transverse section under consideration including pressure effects,
positive if leading to tensile stresses;
K
is a factor given by Formula (16.14–20);
KD
is a factor used in Table 16.14–7;
L
is the length of the shell segment under consideration;
l
is the length of template for checking shape deviations;
M
is the global bending moment carried by shell at tranverse section considered. It is always positive;
Pe
is the (external) calculation pressure;
Q
is the fabrication quality parameter from Table 16.14–2;
U0
is the profile irregularity parameter given by Formula (16.14–33);
U0,max
is the maximum profile irregularity parameter from Table 16.14–6;
Un
is the non-intended misalignment parameter given by Formula (16.14–32);
Un,max
is the maximum non-intended misalignment parameter from Table 16.14–5;
Ur
is the out of roundness given by Formula (16.14–30);
Ur,max
is the maximum out of roundness from Table 16.14–3;
462
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
w
is the deviation from perfect shape;
α
is the elastic imperfection reduction factor given by Formula (16.14–22);
Δ
is the buckling reduction factor given by Formula (16.14–26), (16.14–27) or (16.14–28);
Δwk
is the characteristic imperfection amplitude given by Formula (16.14–21);
λp
is the plastic limit relative slenderness given by Formula (16.14–24);
λx
is the shell relative slenderness for longitudinal buckling given by Formula (16.14–25);
λx0
is the longitudinal squash limit slenderness given by Formula (16.14–23);
σc
is the maximum longitudinal compressive stress;
σc,all
is the maximum permitted compressive longitudinal stress (see 16.14.8.1);
σe
is the elastic limit as defined in 8.4;
σmax
is the maximum longitudinal stress (positive if tensile), taking account of all loads;
σmin
is the minimum longitudinal stress (positive if tensile), taking account of all loads;
σP
is the stress calculated from the pressure;
ψ
is a correction factor from Table 16.14–7, 16.14–8, 16.14–9 or 16.14–10;
ω
is the length parameter given by Formula (16.14–16).
16.14.3 General
The loads to be considered are an axial force (F) and a bending moment (M). Consideration shall be given to
load cases with zero pressure, when considering compressive stresses, to account for possible loss of
pressure during operation.
For the determination of the total axial force (F) two cases shall be distinguished:
1) The end of the cylindrical shell is free, movements not restricted. In this case the total axial
force F is defined as:
F  F add 
π
4
D
2
P
where
Fadd
is the additional axial force without effect of pressure (Fadd> 0 for tensile, Fadd < 0 for
compression);
P
is the calculation pressure (P > 0 internal pressure, P < 0 external pressure)
The pressure component of the axial force is calculated with the mean diameter D to allow for the
influence of radial stresses in the cylinder.
2) The movement of the end of cylindrical shell is restricted (e.g. heat exchanger tubes, jacketed
walls). In this case the total axial force may be calculated by means of any statically allowable
assumptions (calculations by means of elastic theory are statically allowable but not the most
favourable solution).
UNI EN 13445-3:2021
463
EN 13445-3:2021 (E)
Issue 1 (2021-05)
In a vertical vessel (F) also includes the weight of the vessel and its contents (including liquid) above (or
below) the point under consideration, depending on whether the vessel support is below (or above) that
point.
The moment (M) includes the effect of wind on a vertical vessel or weight for a horizontal vessel.
Special consideration is required if there is a significant torque (twisting moment) carried by the cylinder.
16.14.4 Permissible individual loads
The maximum tensile force is:
(16.14-1)
F t, max  π D  e a f
The maximum compressive force is:
F c, max   D  e a   c, all
(16.14-2)
The maximum bending moment is:
M

max

4
2
D  ea 
c, all
(16.14-3)
16.14.5 Longitudinal stresses
The maximum longitudinal stress is:
σ

max
F  D  4M
πD
2
 ea
(16.14-4)
The minimum longitudinal stress is:
σ
If

min


min
c
F  D  4M
πD
2
ea
(16.14-5)
< 0 the compressive longitudinal stress is:
 
m in
(16.14-6)
16.14.6 Cylinder under internal pressure (P > 0)
The circumferential pressure stress is:
σP 
P D
2e a
(16.14-7)
The design procedure is as follows:
3) Choose a value of ea that meets the requirement of 7.4.2;
4) Check that:
464
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)

max
f
(16.14-8)
5) if min > 0 then go to step 7);
6) Find c,all the maximum allowable longitudinal compressive stress in the cylinder,
from 16.14.8.1;
7) check that:
 c 
(16.14-9)
c, all
8) Check that:

P

c
(16.14-10)
 f
9) If the criteria are met the design is satisfactory, if not ea should be increased and the calculation
repeated;
16.14.7 Cylinder under external pressure ( P < 0)
The external pressure is:
Pe = - P
(16.14-11)
The circumferential pressure stress is:
σP 
Pe  D
(16.14-12)
2e a
The design procedure is as follows:
10) Choose a value of ea that meets the requirements of Clause 8;
11) Check that:
(16.14-13)
 m ax   P  f
12) if min > 0 then go to step 6);
13) Find Pe,max the maximum permissible external pressure in the absence of other loadings, from
Clause 8 and c,all from 16.14.8.1;
14) Check that:
Pe
P e, max
σ

c

σ
Pe  D
4ea
 1
(16.14-14)
c, all
15) If both inequalities are satisfied then the design is satisfactory; if not ea should be increased
and the calculation repeated;
UNI EN 13445-3:2021
465
EN 13445-3:2021 (E)
Issue 1 (2021-05)
16.14.8 Global longitudinal compressive stress limits
16.14.8.1 Calculation
Cylinders need not be checked against longitudinal buckling, and the permissible longitudinal compressive
stress may be taken as being equal to the design stress f if the following condition is satisfied:
D
e
 0,06
a
E

(16.14-15)
e
where the nominal elastic limit σe is obtained from 8.4.
The following procedure shall be used to find the permissible longitudinal compressive stress in a cylindrical
shell when the condition in Formula (16.14-15) is not satisfied.
The methods for measuring tolerances are given in 16.14.8.2.
16) Calculate the length parameter:
L
 
0,5D  e
(16.14-
a
16)
17) For short cylinders (ω ≤ 1,7):
C
x
 1,36 
1,83


2,07

2
(16.14-
17)
for medium length cylinders (1,7 < ω ≤ 0,25D/ea):
C
x
 1,0
(16.14-
18)
for long cylinders (ω > 0,25D/ea) Cx is the greater of:
(16.14-19)
where factor Cxb is obtained from Table 16.14-1.
466
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 16.14–1 — Factor Cxb
Case
Boundary condition
Factor Cxb
1
cylinders that are restrained in the axial direction at both ends
6,0
3,0
2
cylinders that are restrained in the axial direction at one end (e.g. the
bottom of the skirt on a vertical vessel that is fixed with anchor bolts
or a shell welded to a girth flange)
3
cylinders that are not restrained in the axial direction at either end
1,0
NOTE 1
The end of a cylinder that is restrained in the axial direction is one where the axial displacement at the
end is constant around the circumference.
NOTE 2
Taking Cxb = 1,0 is a conservative assumption.
18) Calculate:
1,21E  C
K 

e
x
e
a
D
(16.14-20)
19) Determine the fabrication tolerance quality class using the procedures given in 16.14.8.2 and
obtain the value of the fabrication quality parameter Q from Table 16.14-2:
Table 16.14–2 — Fabrication quality parameter Q
Fabrication tolerance
quality class
Fabrication quality
parameter Q
Class A (Excellent)
40
Class B (High)
25
Class C (Normal)
16
20) Calculate the characteristic imperfection amplitude:
0,5 D  e
w

k
a
(16.14-21)
Q
21) Calculate the elastic imperfection reduction factor:
0,62
 

1  1,91 w
k
e
a

1, 44
(16.14-22)
22) The longitudinal squash limit slenderness λx0 shall be taken as:
λx0 = 0,2
(16.14-23)
23) Calculate the plastic limit relative slenderness:
UNI EN 13445-3:2021
467
EN 13445-3:2021 (E)
Issue 1 (2021-05)
p 
2,5 
(16.14-24)
24) Calculate the shell relative slenderness for longitudinal buckling:
1
x 
(16.14-25)
K
25) Calculate the buckling reduction factor:
 1
  
x
x0
  1  0,6 
  
x0
 p
  K




when λx ≤ λx0
(16.14–26)
when λx0 < λx < λp
(16.14–27)
when λp ≤ λx
(16.14–28)
26) Calculate the maximum allowable longitudinal compressive stress:

c ,a ll

 
S
e
(16.14-29)
where the factor ψ is obtained from 16.14.8.2 and the safety factor S is taken as 1,5 for loading
cases where the allowable compressive stress for shells is given as σc,all in Table 5.3.2.4-1, or 1,05
for loading cases where the allowable compressive stress for shells is given as σc,all,test..
16.14.8.2 Tolerances
The fabrication tolerance quality class shall be chosen as Class A, Class B or Class C according to the tolerance
definitions given in the following procedure. The tolerance class shall be determined separately for the out
of roundness, misalignment and profile irregularity tolerances: the lowest fabrication tolerance quality class
obtained shall then be used to determine the value of the fabrication quality parameter Q from Table 16.142.
NOTE 1
The lowest fabrication tolerance quality class is that which gives the lowest value of the fabrication
quality parameter Q.
If none of the tolerances exceeds the relevant maximum recommended value given in Tables 16.14-3,
16.14-4, 16.14-5 or 16.14-6 for fabrication tolerance class C then factor ψ = 1,0. If any of the tolerances
exceeds the relevant maximum recommended value for fabrication tolerance class C then the fabrication
quality parameter Q shall be obtained from Table 16.14-2 for tolerance class C and factor ψ shall be
obtained from step 10 below.
At the design stage the fabrication tolerance quality class may be chosen based on the fabrication tolerances
that are expected for the completed vessel. After fabrication is complete the tolerances shall be measured
and the actual fabrication tolerance quality class shall be determined. If this is lower than that assumed at
the design stage then the maximum allowable longitudinal compressive stress shall be recalculated using the
actual fabrication tolerance quality class, and the design re-assessed to ensure that the compressive stresses
are acceptable.
468
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 2
Using fabrication tolerance quality class C and taking factor ψ = 0,75 is a conservative assumption for
vessels that satisfy the manufacturing tolerance requirements of EN 13445-4:2019, Clause 6.
NOTE 3
For vessels subject to external pressure where the circularity tolerance requirements of
Subclause 8.5.1 are satisfied the fabrication tolerance quality class from Table 16.14–3 is Class A. However, the
overall fabrication tolerance quality class can be lower depending on misalignment and profile irregularity.
If a particular fabrication tolerance quality class is assumed in the calculations in order to obtain a specific
value of maximum permitted compressive longitudinal stress then the corresponding maximum permitted
tolerances for out of roundness, non-intended misalignment and profile irregularity from Table 16.14-3,
Table 16.14-4, Table 16.14-5 and Table 16.14-6 shall be specified on the drawing.
1) Evaluate the out of roundness – see EN 13445-4:2019, Formula (6.4-1):
U
r
 O %  
 

2 D
m ax
D m ax
 D
 D
m in

m in 
100
(16.14-30)
2) Determine the fabrication tolerance quality class so that the relevant maximum out of
roundness Ur,max from Table 16.14-3 satisfies the following condition:
U
r
 U
r ,m a x
Table 16.14–3 — Maximum out of roundness Ur,max
Diameter range
Fabrication
quality class
NOTE 4
Dnom ≤ 500
tolerance
500 < Dnom < 1 250
1 250 ≤ Dnom
Recommended value of Ur,max [%]
Class A (Excellent)
1,4
0,7 + 0,000 933(1 250 – Dnom)
0,7
Class B (High)
2,0
1,0 + 0,001 333(1 250 – Dnom)
1,0
Class C (Normal)
3,0
1,5 + 0,002 000(1 250 – Dnom)
1,5
The nominal shell internal diameter Dnom is in millimetres in the above table.
NOTE 5
For fabrication purposes the maximum permissible out of roundness for vessels subject to external
pressure is specified in 8.5.1, and for vessels subject to internal pressure in EN 13445-4:2019, 6.4.2.
3) Determine the non-intended misalignment at circumferential welds:
d
n


e  e
2
1
; 0
 m ax  d 
 1

2


(16.14-31)
where
d1, e1 and e2
are as shown in EN 13445-4:2019, Figure 6.2–1.
4) Determine the fabrication tolerance quality class so that the relevant maximum non-intended
misalignment dn,max from Table 16.14-4 satisfies the following condition:
d
n
 d
UNI EN 13445-3:2021
n ,m a x
469
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 16.14–4 — Maximum non-intended misalignment dn,max
Fabrication tolerance
quality class
Recommended value of
dn,max
Class A (Excellent)
2 mm
Class B (High)
3 mm
Class C (Normal)
4 mm
NOTE 6
For fabrication purposes the maximum permissible misalignment at circumferential welds is specified
in EN 13445-4:2019, Table 6.2–3.
5) Determine the non-intended misalignment parameter:
U
n

2d
e1
n
 e
2

(16.14-32)
6) Determine the fabrication tolerance quality class so that the relevant maximum non-intended
misalignment parameter Un,max from Table 16.14-5 satisfies the following condition:
U
n
 U
n ,m a x
Table 16.14–5 — Maximum non-intended misalignment Un,max
Fabrication
quality class
tolerance
Recommended value of
Un,max
Class A (Excellent)
0,14
Class B (High)
0,20
Class C (Normal)
0,30
7) The depth w of local irregularities in the shell shall be measured in both the longitudinal and
circumferential directions using templates as shown in Figure 16.14-1:
a)
a straight bar of length
l
x
 4
D e
2
n
but no longer than 95 % of the distance between
circumferential welds;
b) a circular template bent to the radius of the outside surface of the shell, with a length lθ
which is the same as length lx in a) but no longer than 95 % of the distance between
longitudinal welds;
c) for circumferential and longitudinal welds a straight bar or circular template of length
l
w
 25e
n
(where en is the thinner of the adjacent parts at the weld), but no longer than
500 mm.
8) Determine the value of the profile irregularity parameter U0:
470
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
U
0
w
w
w

x
w
= m ax 
;
;
 l
l
l
w

 x




(16.14-33)
where
wx
is the depth measured in a) above, wθ is the depth measured in b) above, and ww is the depth
measured in c) above.
9) Determine the fabrication tolerance quality class so that the relevant maximum profile
irregularity parameter U0,max from Table 16.14-6 satisfies the following condition:
U
0
 U
0 ,m a x
Table 16.14–6 — Maximum profile irregularity parameter U0,max
Fabrication tolerance
quality class
Recommended value of
U0,max
Class A (Excellent)
0,006
Class B (High)
0,010
Class C (Normal)
0,016
NOTE 7
For fabrication purposes the maximum permissible irregularities in profile are specified in
EN 13445-4:2019, 5.4.4.
10) If any of the tolerances exceeds the relevant maximum recommended value given in
Tables 16.14-3, 16.14-4, 16.14-5 or 16.14-6 for fabrication tolerance class C then determine the
value of factor ψ from Tables 16.14-7, 16.14-8, 16.14-9 and 16.14-10 for each case where the
tolerance exceeds the relevant maximum recommended value, and take the smallest value of ψ
for use in Formula (16.14-29).
Table 16.14–7 — Correction factor ψ for out of roundness
Nominal
internal
diameter (mm)
Dnom ≤ 500
500 < Dnom < 1250
Dnom ≥ 1250
Correction factor ψ
λx < 1,5
  1
  1
x Ur


 1

3  3


x  Ur


 1


K
3
 D

Not permitted
λx ≥ 1,5
  1,5  0,5
U
r
3
  1,5  0,5
U
K
r
D
Not permitted
where the factor KD = 1,5 + 0,002(1 250 – Dnom)
NOTE 8
The nominal shell internal diameter Dnom is in millimetres in the above table.
UNI EN 13445-3:2021
471
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 16.14–8 — Correction factor ψ for non-intended misalignment
Shell relative slenderness
λx < 1,5
λx ≥ 1,5
NOTE 9
Correction factor ψ
  1
x  dn


 1

3  4


  1,5  0,5
d
n
4
The offset dn is in millimetres in the above table.
Table 16.14–9 — Correction factor ψ for non-intended misalignment
Shell relative slenderness
Correction factor ψ
λx < 1,5
  1
λx ≥ 1,5
x  Un


 1

3  0,3


  1,5  0,5
U
n
0,3
Table 16.14–10 — Correction factor ψ for profile irregularity
Shell relative slenderness
Correction factor ψ
λx < 1,5
  1
λx ≥ 1,5
x 

U
0

 1

3  0,016


  1,5  0,5
U
0
0,016
16.14.9 Wind and earthquake loads
Calculation of wind and earthquake loadings shall be carried out in the manner recommended for structures
in the territory in which the vessel is to operate.
The method how to combine wind and earthquake loads with pressure loads is described in Clause 22.
472
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a)
b)
c)
Figure 16.14-1 ― Templates for checking tolerances
17 Simplified assessment of fatigue life
17.1 Purpose
17.1.1 This clause specifies
— an alternative to the 500 cycles rule stated in 5.4.2 for vessels predominantly subjected to pressure
fluctuations,
— a substitute to the 500 cycles rule stated in 5.4.2 for vessels subjected additionally to thermal
gradient fluctuations, and
— rules for the simplified assessment of fatigue damage due to both pressure and thermal gradients
fluctuations.
NOTE
The rules in this clause are based on simplified and conservative assumptions. More precise, less
conservative results will usually be obtained by application of Clause 18.
17.1.2 Other cyclic loads, e.g. due to variation of external loads, are normally to be assessed according
to Clause 18. However, it is permitted to take non-pressure cyclic loads into account in this clause by:
UNI EN 13445-3:2021
473
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— adding the stress ranges resulting from such cycles to the stress range resulting from pressure
cycles, as given by Formula (17.6-1), if the non-pressure load cycles occur simultaneously to the
pressure cycles,
— or adding the fatigue damage resulting from such cycles to the damage resulting from pressure
cycles, as given by Formula (17.7-1), if the non-pressure load cycles and the pressure cycles act
independently.
For non-pressure loads acting in combination with pressure in a more complex manner, they shall be
assimilated to one of the two preceding cases, in a way such that conservatism is assured.
NOTE
This clause gives information for estimating the stress ranges due to pressure and thermal loads only.
When other loads are taken into account, the determination of the corresponding stress ranges is under the
responsibility of the Manufacturer.
17.2 Specific definitions
The following terms and definitions apply in addition to those in Clause 3.
17.2.1
cut-off limit
cyclic stress range below which fatigue damage is disregarded
17.2.2
design stress range spectrum
histogram of the number of occurences of all stress cycles of various ranges anticipated during the
design lifetime
17.2.3
effective notch stress
the stress which governs fatigue behaviour at a notch
474
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.2.4
effective stress concentration factor
ratio of effective notch stress (total stress), to structural stress at same point
17.2.5
endurance limit
cyclic stress range below which no fatigue damage occurs under constant amplitude loading
17.2.6
full pressure cycles
pressure cycles of range
P
 P max
Note 1 to entry: See also 5.4.2.
17.2.7
equivalent number of full pressure cycles
number n e q of full pressure cycles that cause the same damage as all the applied cycles of various
sources and ranges
Note 1 to entry: For pressure loading only,
n
eq
is given by Formula (17.5–1).
Note 2 to entry: For pressure + thermal loading,
17.2.8
fatigue design curves
curves given in this clause of

R
n
eq
is given by Formula (17.5–4).
against N for welded and unwelded material
17.2.9
range
value from maximum to minimum (stress or load) in the cycle (twice the stress amplitude)
17.2.10
pseudo-elastic stress
stress calculated assuming purely linear elastic material behaviour
17.2.11
structural stress
stress distribution in a stress-concentration-free model of the structure, a model which reflects the
global geometrical configuration of the structure, but excludes the local structural discontinuities
(e.g. weld toe, small radii)
In the vessel regions of plate or shell type, the structural stress due to pressure is linearly distributed across
the thickness.
Note 1 to entry: For more details on structural stress see Clause 18.
17.2.12
notch stress (total stress)
local stress located at the root of a notch of the structure, calculated on an elastic basis
Note 1 to entry: For more details on notch stress see Clause 18.
UNI EN 13445-3:2021
475
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.2.13
pressure stress factor
factor for determination of the maximum structural stress that may occur under pressure loading in a
vessel detail, due to the geometrical configuration of component(s)
17.2.14
thermal stress factor
factor for determination of the maximum structural stress that may occur under some thermal gradient
type in a vessel detail, due to the geometrical configuration of component(s)
17.2.15
adjacent point
point to be considered for determination of the metal temperature difference on which thermal stresses
are estimated.
Note 1 to entry: They are defined as any two points:
—
on the inside and outside surfaces, for a gradient through the thickness;
—
along the surface within a distance
1, 7 5
D e
for a gradient along the longitudinal and/or circumferential
directions of a shell;
—
along the surface within a distance 3,5R, for a gradient along the longitudinal and/or circumferential
directions of a flat end, where R is the radius of the point at the highest temperature in the flat end.
17.2.16
metal temperature difference between adjacent points
temperature difference between adjacent points, determined by reference to the metal temperature at
these points (not the fluid temperature at these points)
17.2.17
theoretical stress concentration factor
ratio of notch stress, calculated on purely elastic basis, to structural stress at same point
17.2.18
total fatigue damage index
value representing the amount of design fatigue damage caused by application of the design stress
range spectrum
Note 1 to entry: Failure is deemed to occur when this value reaches 1.
476
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.2.19
critical area
area where the total cumulative fatigue damage (usage factor) exceeds the value Dmax = 0,5
17.2.20
fatigue class of a welded joint
the fatigue class C is the value in MPa taken from Table 17-3, column “Class", depending from weld detail
and testing group.
17.3 Specific symbols and abbreviations
The following symbols and abbreviations are in addition to those in Clause 4:
Symbol
Description
Unit
C
fatigue class C (see Table 17–3)
MPa
lowest fatigue class C (see 17.5.4.1)
MPa
C
m in
N
eq
D
D
allowable number of full pressure cycles
total fatigue damage index, see Formula (17.7–1)
m ax
C
e
maximum allowable value of total fatigue damage index in non-critical areas
correction factor to account for influence of wall thickness on fatigue resistance
CT
correction factor to account for influence of temperature on fatigue resistance
E
Young's modulus of the material
K
K
f
t
MPa
effective stress concentration factor
theoretical stress concentration factor
k
number of pressure ranges which together form the loading specification
N
allowable number of cycles obtained from the relevant fatigue design curve
th
(suffix i refers to number for i stress range, i  1, ... k )
n
number of applied stress cycles
(suffix i refers to number for i th stress range, i  1, ... q )
n
n
n
eq
P
T
equivalent number of full pressure cycles
number of applied pressure cycles
(suffix i refers to number for i th pressure range,
i  1, ... q )
i
number of applied cycles of temperature difference
(suffix j refers to number for j th range of temperature difference,
UNI EN 13445-3:2021
j  1, ... q )
j
477
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Symbol Description
n
Unit
number of applied cycles of combined pressure + temperature difference
(suffix k refers to number for k th range of pressure + temperature difference,
PT
k  1, ... q )
k
R
radius of the point at the highest temperature in the flat end
mm
r
transition radius at junction of walls
mm
metal temperature difference between adjacent points (see 17.2.15)
°C
minimum operating temperature during a cycle
°C
maximum operating temperature during a cycle
°C
T*
assumed mean cycle temperature
°C
u
ovality (of circular cross section of a vessel)
α
thermal expansion coefficient of the material
(°C)-1
δ
parameter for measure of misalignment, peaking or flat
mm
P
pressure range calculated from the algebraic difference of the maximum and MPa
minimum pressures which apply in the cycle under consideration. Vacuum and
other external pressures stress shall be considered negative
NOTE In that case, some cycles may have a range ΔP greater than the
maximum calculation pressure Pmax of the vessel or part thereof.
∆T
range of metal temperature difference between adjacent points (adjacent points °C
are defined at 17.2.15)

pseudo-elastic stress range
N/mm2
 *
fictitious stress range for insertion into the fatigue design curves
N/mm2

reference stress range of fatigue design curves
N/mm2
endurance limit at constant stress range
N/mm2
cut-off limit
N/mm2
T
T
T
d iff
m in
m ax


R
D
Cut
κ
thermal stress factor for a vessel detail, given in Table 17–1

pressure stress factor for a vessel detail, given in Table 17–2
 m ax
maximum pressure stress factor found throughout the vessel
NOTE
The pressure Pmax used in Clause 17 is defined in 3.16, NOTE 3.
478
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.4 Conditions of applicability
17.4.1 This clause applies to pressure-bearing components and junctions of pressure vessels designed
in accordance with Clauses 7 to 16 without Clause 15, Clauses 20 and 21 and Annex G (i.e. those clauses
and annexes where design by formula applies), with the exception of:
— bellows;
— heat exchanger tubesheets.
NOTE 1
Fatigue assessment of heat exchanger tubesheets can be performed using Annex J of this Standard.
Application of this clause to jacketed vessels is permitted if subjected to pressure cycles only. For jacketed
vessels subjected to both pressure and thermal cycles, application is limited to the non-jacketed parts.
NOTE 2
Clause.
It is not necessary to check flanges and their bolts if the adjacent shells are designed according to this
It is assumed that the vessels have been designed, manufactured and tested in accordance with all other
requirements of this standard.
17.4.2 This clause does not apply to vessels of testing group 4.
17.4.3 Application of this clause is limited to ferritic and austenitic steels (rolled, forged and cast).
17.4.4 This clause applies only to components operating below the creep range. Thus, the fatigue
design curves are applicable up to 375 °C for ferritic steels and 425 °C for austenitic steels.
17.4.5 As regards weld defects:
For application of this clause, the following conditions (as required by EN 13445-5:2021, Annex G) shall be
met in addition to the general acceptance criteria for weld imperfections given in EN 13445-5:2021:
— no undercut,
— no root concavity,
— no lack of penetration for full penetration welds, except as permitted by Table 17-3,
— 100 % inspection, visually and by NDT, with acceptance criteria as specified in EN 13445-5:2021,
AnnexG, of all critical areas.
17.4.6 As regards tolerances:
— manufacturing tolerances shall not exceed those given in EN 13445-4:2021;
— for seam welds, the Manufacturer shall assume certain tolerances and derive the corresponding
stress factors to be used for fatigue assessment (see Table 17-2, cases S1.2 to S1.5, S2.2 to S2.4 and
S5.2 to S5.4). Then the assumed tolerances shall be checked and guaranteed after manufacturing.
UNI EN 13445-3:2021
479
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.4.7 The data on which these requirements are based are valid for fatigue in dry air. It is
presupposed that there are no environmental effects which can reduce the fatigue life further. For
designs involving such effects, see 18.4.5.
NOTE
For vessel parts made from non-austenitic steels and operating in contact with water at temperatures
exceeding 200 °C, the stress change due to pressure variations above and below the operating pressure where the
magnetite protective layer forms, may result in cracking of this layer. For assessment of this risk, reference may be
made to EN 12952-3:2001, 13.4.3.
17.4.8 Vessels which fulfil the requirements of 17.5.3 or 17.5.4 or 17.5.5 are of non-cyclic nature and
the standard requirements of non-destructive testing given in EN 13445-5 shall be applied.
17.4.9 For application of 17.6, instructions for appropriate maintenance shall be included in the
operating instructions.
NOTE
Recommendations on appropriate maintenance are given in Annex M.
17.4.10
Guidance for metal temperature estimates:
For cases where significant thermal loading occurs, attention is drawn to the importance of approximating as
closely as possible the temperature distributions that appear in the vessel walls during service, in order to
reduce as much as possible the conservatism of the thermal stress estimate and resulting fatigue
assessment.
In this respect, the quite common approach which consists in taking the fluid temperature variations as
representative of the temperature variations of the vessel wall surface is not recommended because it
generally leads to strong over-estimates of the real thermal gradients. As far as possible these gradients
should be determined from thermal calculations (even simple ones based on analytic models) in which the
thermal exchange which takes place at the fluid-metal interface is taken into account.
To enable such calculations, enough information on the thermodynamic conditions attached to the process
should be obtained from the Purchaser (e.g.: fluid heating or cooling rate, thermal exchange coefficient at
fluid-metal interface, etc.).
17.5 General
17.5.1 Pressure and temperature ranges to be considered for the fatigue assessment:
P shall be obtained by applying either the simplified cycle counting method described in 18.9.2 or the
reservoir cycle counting method in 18.9.3 and considering fluctuations of pressure instead of stress.
The various
( T
d iff
)
i
to be considered for the fatigue assessment shall be obtained by applying the same
cycle counting methods but considering fluctuations of the metal temperature difference
T
d iff
instead of
fluctuations of stress.
To distinguish whether the pressure and the thermal cycles act simultaneously or not simultaneously, the
load history (variation with time) of the both loads shall be considered. When the duration time of the cycle
(time from minimum value via maximum value to minimum value) from one load type (e.g. pressure) is
overlapped with the duration time of the other load type (e.g. temperature differences) then these cycles
act simultaneously. On the contrary, if during the complete cycle time of one load type the other load type
does not change then the cycles act not simultaneously.
480
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The  P ranges are normally valid for assessment of all vessel parts subjected to the same pressure
fluctuations. In case where pressure fluctuations result (at least partly) from hydrostatic pressure or from
pressure differences between adjacent vessel chambers, the pressure ranges may be different from part to
part.
The
 T d iff
ranges are valid only for assessment of the vessel detail where the particular metal temperature
difference fluctuations considered take place. If the most critical detail for fatigue under combined pressure
+ thermal loading is not known at first, all candidate details should be investigated and the corresponding
sets of  T d iff established.
17.5.2 The calculations according to 17.6 shall be performed for the various components of the vessels.
The lowest life obtained is the fatigue life of the vessel.
17.5.3 Pressure and temperature ranges which may be neglected for the fatigue assessment:
When designs meet the requirements:
η ≤ 3,
f ≤ 160
C
e
C
T
MPa with f taken at the calculation temperature T,
pressure fluctuations of range
P
lower than the following percentages of
P
m ax
can be neglected,
regardless of their number:
3,5 % of
P
4,5 % of
P
5,5 % of
P
6 % of
P
7 % of
P
7,5 % of
m ax
m ax
m ax
m ax
m ax
P
m ax
for C = 40
for C = 56
for C = 63
for C = 71
for C = 80
for C = 90 and Class UW
Otherwise, if the number of start-up and shut-down cycles at operating pressure is smaller than 500 and if
no cycle of intermediate range between operating pressure and the neglected fluctuations occur:
6 % of
P
m ax
8,5 % of
P
9,5 % of
P
11 % of
P
12,5 % of
14 % of
P
m ax
m ax
m ax
P
m ax
m ax
UNI EN 13445-3:2021
for
C = 40
for
C = 56
for
C = 63
for
C = 71
for
C = 80
for
C = 90 and Class UW
481
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For other values of η and f, the above percentages shall be multiplied by the ratio
480
  f
.
This rule for neglecting pressure ranges is applicable:
— for the vessel as a whole if the same ΔP acts on all vessel parts,
— component by component if different ΔP act on different parts (see 17.5.1, fourth paragraph).
For simplification,
P
m ax
may be replaced by the calculation pressure P.
For guidance on negligible thermal cycles
( T
d iff
)
i
, see Annex U.
17.5.4 Alternative to the 500 cycles rule stated in 5.4.2:
Provided the conditions required in 17.5.4.2 are fulfilled, the condition stated in 5.4.2, Formula (5.4-1), for
checking the number of full pressure cycles (or equivalent number of full pressure cycles) against the
uniform 500 cycles limit valid for any vessel designed according to EN 13445-3 may be disregarded and
replaced by condition (17.5-1):
n
eq


i
n
P ,i
 P
i

 P
 m ax




3
 N
(17.5-1)
eq
where:
n
n
P
eq
is the equivalent number of full pressure cycles,
P ,i
is the number of pressure cycles at pressure ranges ΔPi lower than or equal to the full
pressure P
m ax
is the maximum permissible pressure calculated in the normal operating load case
(see 5.3.2.1)
NOTE 1
In Formula (17.5–1),
N
is the allowable number of full pressure cycles defined in 17.5.4.1.
eq
n
is defined as in Formula (5.4–2).
eq
Condition (17.5-1) may be checked:
— for the vessel as a whole, with
n
eq
calculated using for
 Pi
the pressure fluctuations acting at the
location where their range is maximum and for Pmax the maximum permissible pressure of the
vessel (see 3.16),
— component by component, with
n
eq
calculated using for
 Pi
the pressure fluctuations acting on the
component and for Pmax the maximum permissible pressure of the same component.
NOTE 2
The check component by component is of interest only if the range of the pressure fluctuations varies
along the vessel due to additional hydrostatic pressure, or if the vessel has parts which separate different pressure
chambers.
For simplification, Pmax may be replaced by the calculation pressure P.
482
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Use of Formula (17.5-1) to calculate
n
eq
is valid under the condition that the contribution of non-pressure
loads to cyclic loading can be neglected.
When this condition is not met, a fatigue life assessment of the vessel is necessary and shall be performed
using the rule given in 17.5.5 (if applicable), a simplified fatigue analysis according to the rest of Clause 17
(Subclauses 17.6 to 17.7) or a detailed fatigue analysis according to Clause 18.
NOTE 3
The rule given in 17.5.5 allows taking into account additional cycles of thermal origin only. The rest of
Clause 17 is mainly devoted to pressure and thermal cycles, but can take into account loading cycles of other
origins (see 17.1.2). Clause 18 enables consideration of all types of loading cycles.
17.5.4.1 Allowable number of full pressure cycles based on nominal design stress, weld types
and maximum stress factor:
The allowable number of full pressure cycles is given by:
N
eq
 2  10
6
C
C C
m in
e


 f
m ax

T



3
(17.5-2)
where
C
m in
is the lowest fatigue class C among all welded joints of the vessel or the class of the
component if a check component by component is made, or C m in = 40 MPa alternatively as
a conservative assumption.
The value C m in = 40 MPa shall be used if the vessel includes welded details which cannot be
found (directly or by assimilation) in Table 17–3 and are likely to present a low fatigue
resistance.
For vessels which do not contain any welded zone, the
C
C
e
T
 m ax
is the thickness correction for
e  25 m m
is the temperature correction for
C
m in
= 90 shall be used.
, as defined in 17.6.2.1
T *  100 C
, as defined in 17.6.2.2.
is the maximum pressure stress factor found throughout the vessel:
In looking for the maximum pressure stress factor  m a x , shape deviations (mainly peaking)
at longitudinal seam welds should always be considered, because they often may be source
of high values of η.
f
is the nominal design stress at calculation temperature of the load case for which
calculated.
If, for simplification, n e q is calculated using the calculation pressure P instead of
P
m ax
P
m ax
is
, as permitted by
5.4.2, f is the nominal design stress, at the corresponding calculation temperature.
UNI EN 13445-3:2021
483
EN 13445-3:2021 (E)
Issue 1 (2021-05)
When applying this formula:
—
 m ax
shall be selected according to Table 17-2.
In case where the vessel comprises details for which no  value is given in Table 17-2 and no conservative
value of  can be safely estimated, Formula (17.5-2) is not applicable and condition (17.5-1) shall not be
used.
— the thickness to be considered for calculation of
in the welded joints of the fatigue class
C
m in
C
e
shall be the largest of all components involved
.
— the temperature T * to be considered for calculation of C T shall be calculated taking for Tmax and
Tmin respectively the maximum and minimum temperatures occurring during the whole cycling
period.
— the nominal design stress f to be considered shall be the largest of all materials involved in the
welded joints of the fatigue class C m in . In case of uncertainty, the largest among all vessel
components shall be used.
In case where the allowable number of full pressure cycles
N
eq
given by Formula (17.5-2) is lower than 500,
the design should be modified to reach that number.
The curves showing the number of cycles
N
eq
given by Formula (17.5-2) greater than or equal to 500 are
plotted in Figure 17.5-1 for the case where  m a x = 3 and where no correction is needed (i.e. when
and
484
C
t
 1
C
e
 1
).
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1 = class 90
2 = class 80
3 = class 71
4 = class 63
5 = class 56
6 = class 40
7 = 500 cycles
Figure 17.5–1 — Allowable number of equivalent full pressure cycles (assuming  m a x = 3 and
C
17.5.4.2
e
 C
T
 1
)
Conditions of application of Formula (17.5-2):
— No pressure cycle range
 Pi
shall be greater than
3 .P
m ax
 m ax
;
— No welded flat end shall be designed using the alternative rule of 10.4.4.4;
— No flat end shall have pairs of adjacent openings designed as a fictitious single opening using the
alternative calculation given at end of 10.6.2.1.
UNI EN 13445-3:2021
485
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.5.5 Substitute to the 500 cycles rule stated in 5.4.2 or to the alternative rule stated in 17.5.4,
for cases where thermal cycles cannot be neglected
17.5.5.1
Global assessment
When the 500 cycles rule stated in 5.4.2 or the alternative rule stated in 17.5.4 is not applicable because
additional thermal cycles cannot be neglected, the following condition may be used:
n
eq

 P 
i


n
P ,i 

P
m
a
x


i

3

 E      T
j
d iff, j

n
T,j 
 m ax  f

j







3


E      T
k
d iff, k
 Pk


n
P T ,k 
 m ax  f
 Pm ax
k







3
 N
eq
(17.5-3)
where
n
N
P
is the equivalent number of full pressure cycles,
eq
eq
is the allowable number of full pressure cycles defined in 17.5.4.2 and calculated with
Formula (17).5–2),
m ax
is the maximum permissible pressure of the whole vessel (for simplification,
be replaced by the calculation pressure P of the vessel),
P
m ax
may
is the greatest pressure stress factor found throughout the vessel,
 m ax
is the largest product of coincident thermal stress factor and range of temperature
difference found throughout the vessel.
In this condition:
   T d iff
a)
the number of cycles and the ranges with index “i” relate to the pressure cycles which act independently
of thermal cycles,
b)
the number of cycles, the ranges and the thermal stress factors with index “j” relate to the cycles of
temperature difference which act independently of pressure cycles,
c)
the number of cycles, the ranges and the thermal stress factors with index “k” relate to the cycles of
pressure and temperature difference which act in combination with each other,
d)
any pressure cycle ΔP (respectively thermal cycle  T d iff ) shall be counted either as
n
T
) or as
n
PT
P
(respectively as
as appropriate, to avoid double counting of cycles,
e)
the nominal design stress f shall be expressed in MPa,
f)
the value of the thermal stress factor κ shall be as given in Table 17-1,
486
n
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
g)
the values of E and α may be taken at ambient temperature.
For simplification the following values may be used:
E*α = 2,4 MPa/°C for carbon steels (steel groups 1 to 4, 5.1 and 5.2)
E*α = 2,2 MPa/°C for low allow steels (steel groups 5.3, 5.4,6 and 7)
E*α = 3,1 MPa/°C for austenitic steels (steel groups 8.1 and 8.2)
h)
the conditions stated in 17.5.4.2 for application of Formula 17.5-2 shall be fulfilled.
Table 17–1 — Value of the thermal stress factor κ for different thermal gradient types
Thermal gradient type
Linear gradient through thickness or
Linear gradient along surface direction in shell
Linear gradient along surface direction in flat
end
Thermal shock
κ
0,75
1
1,5
17.5.5.2 Local assessment
The fatigue assessment of the vessel as a whole using condition (17.5-3) may be replaced by a fatigue
assessment component by component, using condition 17.5-4:
n
eq

 P 
i


n
P ,i 

P
 m ax 
i

3

 E      T
j
d iff, j

n
T,j 
  f

j







3


E      T
k
d iff, k
 Pk


n
P T ,k 
  f
 Pm ax
k







3
 N
eq
(17.5-4)
where
n
N
P
eq
eq
m ax

is the equivalent number of full pressure cycles;
is the allowable number of full pressure cycles calculated according to 17.5.4.2 and
calculated with Formula (17.5–2), but replacing  m a x by the pressure stress factor  of
the component;
is the maximum permissible pressure of the component (for simplification,
replaced by the calculation pressure P of the component);
P
m ax
may be
is the pressure stress factor of the component;
is the product of the coincident thermal stress factor and range of temperature
difference which are relevant for the vessel detail.
When performing a local assessment:
   T d iff
— all components which are likely to be critical for the fatigue life of the vessel shall be considered, in
order to find the most critical one, on which the assessment shall be based;
— the provisions a) to h) stated in 17.5.5.1 apply.
UNI EN 13445-3:2021
487
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.6 Determination of allowable number of pressure and thermal cycles
17.6.1 Pseudo-elastic stress range
17.6.1.1 Pseudo-elastic stress range for pressure cycles acting independently of thermal cycles
17.6.1.1.1
 

P
P
shall be calculated from
P
as follows:
(17.6-1a)
  f
m ax
where
Pmax is the maximum permissible pressure of the component or vessel part under consideration as
defined in Clause 4, except for dished ends where a specific definition of Pmax applies
(see Footnote 7) of Table 17–2);
f
is the nominal design stress of the component or vessel part under consideration, at
calculation temperature.
At vessel parts having a maximum permissible pressure which depends on more than one value of f (e.g. at
openings with different materials in nozzle and shell), it is permitted to derive a fictitious value of Pmax
calculated assuming a unique and arbitrary value of f for the whole part, and then to use it to determine Δσ
according to Formula (17.6-1), provided the same value of f is also used in that equation. If the true Pmax
value is used, then the value of f to be used in Formula (17.6-1) shall be the highest of the nominal design
stresses of the different materials which have, in the part under consideration, an influence on Pmax.
For simplification, either the maximum permissible pressure of the whole vessel may be used instead of that
of the component or part (Pmax), or the calculation pressure P may be used, together with the highest
nominal design stresses among all vessel components.
NOTE 1
These simplifications lead to more conservative results.
NOTE 2
Since f in Formula (17.6–1) is taken at the calculation temperature, the ratio Pmax/f is independent of
temperature.
17.6.1.1.2 The value of the pressure stress factor η is obtained from Table 17-2 for each vessel detail. It
is an upper bound of the following ratio:
m a x im u m s t r u c t u r a l s t r e s s in d e t a il u n d e r c o n s id e r a t io n u n d e r p r e s s u r e P
m ax
n o m in a l d e s ig n s t r e s s a t c a lc u la t io n t e m p e r a t u r e
To assess the fatigue life of a detail not covered by Table 17-2, the η value shall be obtained through an
estimate of the maximum structural stress in the detail under pressure Pmax.
For simplification, the maximum value η for the whole vessel can be taken for any detail.
NOTE
In some cases, detailed calculation according to Clause 18 may be more accurate than estimating a η
value. This applies particularly to cam closures, self-sealing closures, threaded closures and clamping joints.
488
UNI EN 13445-3:2021
S2.4
General case (combined offset
and unequal thicknesses)
S4
S2.3
with offset δ 2) and with equal
wall thicknesses
Stiffening ring (with inter-stiffener distance b)
S2.2
with unequal wall thicknesses,
without offset
S3
S2.1
S1.5
General case (combined either
offset and ovality or
offset and peaking or flat)
with equal wall thicknesses,
without offset
S1.4
S1.3
with ovality u 3),
if there is no ovality η2 = 0
with peaking or flat δ 2),
if there is no peaking η4 = 0
S1.2
with offset δ 2),
if there is no offset η1 = 0
Circumferential joggle joint
Circumferential
butt weld
UNI EN 13445-3:2021
Cylindrical
or conical
shells
Longitudinal butt
weld
S1.1
Detail
No.
without shape imperfection
Detail description
4)
conical shell:
Formula (7.6–4)
4)
cylindrical shell:
Formula (7.4–3)
Maximum
permissible
pressure Pmax
e1 ≤ e2,
b 
D .e
1,8z
1,0z
D .e
b 
(1+η0+η1)z 1)
(1+η1)z 1)
(1+η0)z 1)
1,8z
η1 = δ
/2e2
η1 = δ /2e
η0 = 0,1
1,0z 1)
(1+max{η1+η2; η1+η4})z 1)
1,0z 1)
η
e1 = e2
e1 = e2 (=
e),
D1 = D2,
D1 = D2 and e1 = e2
η4 = 6δ /e
η2 = 0,5
η1 = 3δ /e
Conditions / Single
stress factors
Table 17-2 — Stress factors  and associated maximum permissible pressures
5.3
1.7
1.1 to 1.3,
1.5 and 1.6
1.3, 1.5
and 1.6
1.2
1.1 and 1.2,
1.5 and 1.6
1.1 to 1.3,
1.5
Relevant
details in
Table 17–3
489
EN 13445-3:2021 (E)
Issue 1 (2021-05)
CE1.1
Large end without knuckle
490
Conical
ends
DE1
Knuckle region
Dished
ends
S5.3
CE1.2
CE2
Large end with knuckle
Small end
General case (combined offset and
S5.4
angular misalignment)
with angular misalignment  6),
without offset
All butt
welds
S5.2
with offset  2), without angular
misalignment
Spherical
shells
S5.1
Detail
No.
Formula (7.6-27)
given in 7.6.7.3
see procedure
see procedure given
in 7.6.6.3
Formula (7.5-7) 7)
Formula (7.4-6) 4)
Maximum
permissible
pressure Pmax
0 ,01  r / D c  0 ,3
All parameters
Other values of parameters
R D i  0 ,8 and r D e  0 ,15
Conditions
2e
50
2,5
MAX 1 ; 3 ,0  9 r / D c 
3,0
2,5
2,0
(1+1+3)z 1)
(1+3)z 1) ,  3 
Dm

(1+1)z 1) , 1  3 /e
1,0z 1)

Table 17-2 — Stress factors  and associated maximum permissible pressures (continued)
without shape imperfection
Detail
description
EN 13445-3:2021 (E)
Issue 1 (2021-05)
UNI EN 13445-3:2021
1.1 to 1.3,
1.4 and 1.5
1.1 to 1.3,
1.5
1.4
1.1 to 1.3,
1.5,
or unwelded
1.1 to 1.3,
1.5
Table 17–3
Relevant
details in
OS3.2
with fillet or partial
penetration welds with
throat  0,8emin
OS3.3
OS3.1
with full penetration welds
OS2.4
OS2.3
with fillet or partial
penetration welds with
throat  0,8emin
with fillet or partial
penetration welds with
throat < 0,8emin 8)
OS2.1
OS1
Detail
No.
with full penetration welds
Nozzle
(with thickness en)
with reinforcing
plate (with thickness
with fillet or partial
ep)
penetration welds with
throat < 0,8emin 8)
UNI EN 13445-3:2021
Openings in
shells (with
thickness es)
Nozzle
(with thickness en),
without reinforcing
plate
without a nozzle
Detail
description
Pmax of component
of thickness emin
(unpierced shell or
nozzle)
Formula (9.5-10) or
(9.5-12)
Formula (9.5-10) or
(9.5-12)
Pmax of component
of thickness emin
(unpierced shell or
nozzle)
Formula (9.5-10) or
(9.5-12)
Formula (9.5-10) or
(9.5-12)
Formula (9.5-10) or
(9.5-12)
Maximum
permissible
pressure Pmax
and
e p / e s  1,0
d i / D i  0 ,6
0 ,7  e n / e s  1,5
and d i / D i  0 ,6
0 ,7  e n / e s  1,5
d i / D i  0 ,6
Conditions
2,4 with Class 32
4,0 with Class acc. Table 17-3
4,0
4,0
1,8 with Class 32
3,0 with Class acc. Table 17-3
3,0
3,0
3,0

Table 17-2 — Stress factors  and associated maximum permissible pressures (continued)
3 b)
3 a)
3 b)
3 a)
unwelded
Relevant
details in
Table 17–3
491
EN 13445-3:2021 (E)
Issue 1 (2021-05)
492
Bolted flat ends
(centre of end)
Welded flat ends
(junction to shell)
Set-in or set-on
pad
(in shell of
thickness es)
with fillet or partial penetration
welds with throat < 0,8es 8)
with fillet or partial penetration
welds with throat  0,8es
FE1.3
FE1.2
Flat end butt welded to shell with transition
radius or knuckle
FE4
FE3
Flat end butt welded to shell with relief groove FE2
Welded-on
or set-in
flat end
FE1.1
P3
with fillet or partial penetration welds with
throat < 0,8es 8)
with full penetration welds
P2
with fillet or partial penetration welds with
throat  0,8es
Detail
No.
P1
Detail
description
see Clause 10 9)
see Clause 10 9)
1,8 with Class 32
Pmax of shell
1,0
1,5
3,0
3,0 with Class acc. Table 17-3
3,0
3,0
1,8 with Class 32
see Clause 10 9)
see Clause 10 9)
Pmax of unpierced
shell
3,0 with Class acc. Table 17-3
Formula (9.5-14)
or (9.5-17)
3,0 5)

3,0 5)
No central
opening
Conditions
Formula (9.5-14)
or (9.5-17)
Formula (9.5-14)
or (9.5-17)
Maximum
permissible
pressure Pmax
unwelded
UNI EN 13445-3:2021
1.1 to 1.3
1.5 and 1.6
2.2
2.1 b) and 2.3 b)
2.1 a) and 2.1 c)
2.3 a) and 2.3 c)
7.3 b) and 7.4
7.1 b) and 7.3 a)
Relevant details in
Table 17-3
Table 17-2 — Stress factors  and associated maximum permissible pressures (continued)
with full penetration welds
EN 13445-3:2021 (E)
Issue 1 (2021-05)
W2
W3
Bracket or support
W1
Reinforcing plate (with thickness ep)
Rib, clip or lifting lug
J2
Conical junction 11) of jacket at one end to cylindrical shell,
and at the other end to dished end
J1
Ring or conical junction of jacket at both ends to cylindrical
shell
welded to shell with fillet or
partial penetration weld with F2.3
throat < 0,8es 8)
F3
Slip-on
flange
welded to shell with fillet or
partial penetration weld with F2.2
throat  0,8es
F2.1
F1
Detail
No.
hub to plate junction
UNI EN 13445-3:2021
Weld-on
parts
Jackets
Flanges
junction to shell
(of thickness es)
welded to shell with full
penetration weld
Welding neck flange (butt welded to the
shell)
Detail
description
as for shell details
(No. S.1 to No. S.3)
see procedure given in
7.6.6.3 or 7.6.7.3
-conical junction:
see procedure
given
in 7.6.6.3 or
7.6.7.3
-ring junction:
Formula 7.4-3
see Clause 11
or Annex G 10)
2,5
2,0z 12)
2,0z 12)
2,0z 12)
e p  1,5 e s
Without external
force
With constant
support load
3,0
With knuckle
Without knuckle
2,0z 1)
1,5
0,9 with Class 32
10)
Pmax of shell
1,5
1,5
1,5

1,5 with Class acc.
Table 17-3
D 2 / D 1  1,2
Conditions
see Clause 11 10)
or Annex G 10)
see Clause 11
or Annex G 10)
10)
see Clause 11 10)
or Annex G 10)
Maximum permissible
pressure Pmax
Table 17-2 — Stress factors  and associated maximum permissible pressures (continued)
6.1 to 6.5
5.1
5.2
4
unwelded
7.2 b)
7.2 a)
7.1 a)
Relevant
details in
Table 17-3
493
EN 13445-3:2021 (E)
Issue 1 (2021-05)
494
Table 17-2 — Stress factors  and associated maximum permissible pressures (concluded)

m ax
 D
m in
  D m ax
 D
m in

When e1≠e2, Pmax shall be calculated using the smaller thickness.
u  2 D
UNI EN 13445-3:2021
11)
At present state of knowledge, there is no η value available for junctions by ring in that case. Detailed fatigue assessment according to Clause 18
should be used.
12)
The value of the joint coefficient to be used for determination of η is that which applies for calculation of the thickness of the shell on which the part
under consideration is welded.
10)
The maximum calculation pressure is not given explicitly in Clause 11. It shall be calculated as the pressure which gives stresses equal to their
allowable limits, or in Annex G a load ratio equal to 1,0. As a conservative simplification Pmax may be taken as Pdesign.
5)
Deleted.
6)
θ is the angle between tangents to the abutting plates, in degrees.
7)
For use within the present clause, Pmax is taken as equal to Py given by Formula (7.5–7). The other possible determinations PS and Pb (given by
Formulae (7.5–6) and (7.5–8) respectively) are not relevant here.
8)
For such a detail, a double calculation shall be made:
one with the class given by Table 17–3 for the detail under consideration,
one with class 32,
taking for each of them the appropriate Pmax value as given at relevant line of Table 17–2, together with the corresponding f value.
NOTE The first calculation is intended to cover the risk of cracking from weld toe, the second the risk of cracking from weld root.
9)
The maximum calculation pressure is that of the flat end (not that of the adjacent cylindrical shell). In Formula (17.6–1a), the value f to be
introduced is the lowest of that for the end and that for the shell.
Since no explicit formula is given for Pmax in Clause 10, Pmax shall be calculated as the pressure which gives the required end thickness equal to the analysis
thickness. As a conservative simplification Pmax may be taken as Pdesign.
4)
3)
1)
The value of the joint coefficient z to be used for determination of η is that which applies for calculation of the thickness of the shell under
consideration.
2)
The way to measure δ is shown in Figure 17–1.
EN 13445-3:2021 (E)
Issue 1 (2021-05)
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) longitudinal weld in a cylindrical shell


b) weld in a spherical shell
Figure 17-1 — Definition of parameters for shape imperfections in butt welds
17.6.1.2 Pseudo-elastic stress range for thermal cycles acting independently of pressure cycles
17.6.1.2.1

shall be calculated from
 T d iff
as follows:
(17.6-1b)
     E     T d iff
In this equation, E and α shall be taken at the assumed mean cycle temperature T*.
At vessel details where materials having different values of E and α are connected, the calculation of   shall be
made using average values of these characteristics. For simplification, the highest of these characteristics may
also be used, as a conservative solution.
17.6.1.2.2 The value of the thermal stress factor κ is given by Table 17-1 (see 17.5.5) as a function of the
type of thermal gradient present in the vessel detail under consideration.
17.6.1.3 Pseudo-elastic stress range for thermal cycles acting simultaneously to pressure cycles

shall be calculated from
 P
P
and
 T d iff

   f     E    T
d iff
 P

 m ax

  
UNI EN 13445-3:2021


as follows:
(17.6-1c)
495
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For calculation of the terms accounting for pressure and for temperature in the right-side member of this
equation, the same rules as given in 17.6.1.1 and 17.6.1.2 respectively apply.
17.6.1.4 Elastic-plastic cycles
Where   > 3 f ,
conditions.

shall be increased according to the rule given in 18.8 to account for elastic-plastic cyclic
17.6.2 Corrections to stress range
17.6.2.1 Thickness
The correction factor to take account of wall thickness is:
for 25 mm <
C
e
en
 25 
 

 en 
< 150 mm:
0 , 25
(17.6-2)
The correction factor
Ce
is plotted in Figure 17-2.
This correction shall apply to all welded joints, except those of class 32 and flush ground butt welds.
At junctions of components of different thicknesses,
NOTE
en
shall be taken on the thinner component.
The thinner part is the one where fatigue cracking is most likely to occur.
 1.
For
en
< 25 mm,
For
en
> 150 mm, the correction factor for
Ce
en
 150 mm applies.
1
0 ,9
0 ,8
C
e
0 ,7
0 ,6
0 ,5
0
25
50
75
e
100
125
150
(m m )
Figure 17-2 — Thickness correction factor
496
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.6.2.2 Temperature
The correction factor to take account of the temperature is:
For
T *  100  C
:
— for ferritic materials:
C T  1, 03  1, 5  10
4
T*  1, 5  10
6
T*  2
(17.6-3)
— for austenitic materials:
C T  1, 043  4 , 3  10
4
(17.6-4)
T*
where
T*
, in °C, is the assumed mean cycle temperature, defined as:
(17.6-5)
T*  0 , 75 T max  0 , 25 T min
For
T *  100 C
,
CT
 1.
This correction is illustrated in Figure 18-10.
17.6.2.3 Notch effect
At an unwelded region, the effective stress concentration factor
K
f
 1
1,5  K
t
Kf
shall be calculated as follows:
 1

1  0,5  MAX  1 ; K

t
(17.6-6)
 

 D 
where K t is the theoretical stress concentration factor at point under consideration, and
limit of Class UW (see 17.6.4.3).

D
the endurance
This factor shall be applied to the structural stress to get the notch stress, which is the stress type used for
assessment of unwelded regions (see Formula (17.6-9)).
NOTE
K t is only of significance at locations where a noticeable notch effect exists.
At corners with small transition radii r (e.g. at base of forged/machined nozzles, see Figure 17-3), the following
estimates of K t may be assumed:
for r  e/4:
K
t
 1,4
(17.6-7)
for r  e/8:
K
t
 1,8
UNI EN 13445-3:2021
(17.6-8)
497
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where
e
is the thickness of the thinner wall at the junction.
Figure 17-3 — Typical corners with small transition radii (unwelded regions)
17.6.3 Fictitious stress range
17.6.3.1 At a welded joint


 *  
 C C
 e
T




(17.6-9)
NOTE
This is the range of the structural stress (as defined in 17.2.11), to be used in conjunction with the design
fatigue curves of welded joints, in which the notch effect is included.
17.6.3.2 At an unwelded region


 *  
 C C
 e
T

K


(17.6-10)
f
NOTE
This is the range of the effective notch stress (as defined in 17.2.3), to be used in conjunction with the design
fatigue curve of unwelded regions, in which no notch effect is accounted for.
17.6.4 Fatigue design curves
17.6.4.1 The fatigue design curves are given by formulae given below and are plotted in Figure 17-4.
The curves are identified by the class numbers. The single curve marked Class UW applies to unwelded regions.
The other curves refer to welded joints.
NOTE
6
The "class" value corresponds to the allowable stress range at N  2  10 cycles.
There are two parts to each curve, corresponding to endurances below and above the number of cycles
corresponding to constant amplitude endurance limit
for unwelded regions.

D
, i.e
5  10
6
cycles for welded joints and
2  10
6
cycles
The dotted lines in Figure 17-4 apply only to variable amplitude loading which includes stress ranges larger than
 D .
498
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The curves end at N  1  10 8 cycles. The corresponding stress range is the cut-off limit   Cut  Stress ranges
below this limit are assumed to be non-damaging in fatigue, and need not be considered.
Figure 17-4 — Fatigue design curves
17.6.4.2 For welded joints, the fatigue design curves in Figure 17-4 are described by the following
formulae
— for
N  5  10
6
cycles:
1

R
 2  10 6
 C 

N

3



(17.6-11)
6
— for N  5  1 0 cycles:
— for assessment of variable amplitude loading:
1
 5  10 6  5

  R  0 ,737  C  


N


(17.6-12)
— for assessment of constant amplitude loading:
 R   D
(17.6-13)
where
  R  0 ,737  C

cut
 0 , 405  C
UNI EN 13445-3:2021
499
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
The notch effects of welds and the maximum possible influence of residual stresses have been taken into
account in preparing the fatigue design curves.
17.6.4.3 For unwelded regions, the Class UW fatigue design curve in Figure 17-4 is described by the
following formulae:
— for
N  2  10

R
46000

cycles:
6
(17.6-14)
 140
N
6
— for N  2  1 0 cycles:
— for assessment of variable amplitude loading (i.e. cycles of various ranges with at least one of
them which exceeds   D ):
1
 2  10 6  10

  R  172 ,5  


N


—
(17.6-15)
for assessment of constant amplitude loading (i.e. cycles of only one range):
(17.6-16)
 R   D
where
  D  175 ,2 MPa
  cut  116 ,7 MPa
NOTE 1
Class UW has been derived for unnotched regions. Notch effects (if relevant) are accounted for by K t in the
calculation of
 *
.
NOTE 2
Curve UW takes into account surface roughness up to that of rolled or extruded surfaces. It also covers the
maximum possible effect of mean or residual stresses.
17.6.5 Classification of welded joints
The welded joints shall be allocated to the classes given in Table 17-3, which are testing group dependant.
For simplification, the class for the worst weld detail existing in the whole vessel can be taken for all welded
joints.
NOTE 1
The requirements associated with each testing group are given in Annex A and in EN 13445-5:2021.
NOTE 2
In most cases, welded joints of testing group 3 are allocated to lower classes than those of testing group 1 or
2. Thus, for any particular detail, selection of a higher testing group than initially required is an approach which may be
chosen to justify use of a higher class in the fatigue assessment.
NOTE 3
Class 32, which represents the fatigue resistance of fillet welds for cracking through weld throat, is not
mentioned in Table 17-3. The reason is that this class is never used alone for a welded joint, but only in connection with
the relevant class given by Table 17-3 for assessing cracking from weld toe (see note 12 of Table 17-2).
500
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.6.6 Allowable number of cycles
17.6.6.1 When
 *   D
:
— for welded joints:
N  2  10
6
 C 


  * 
3
(17.6-17)
— for unwelded regions:

 46000
N  

   *  140 
17.6.6.2 When

Cut
2
(17.6-18)
  *   D
In cases where all stress ranges are
:
 
D
:
N  unlimited (infinite)
In all other cases (i.e. when at least one stress range exceeds

D
):
— for welded joints
N  5  10
6
 0 ,737  C 


 * 

5
(17.6-19)
— for unwelded regions
N  2  10
6
 172 ,5 


  * 
17.6.6.3 When
10
  *    C ut
(17.6-20)
:
the fatigue action of the cycles shall be ignored.
UNI EN 13445-3:2021
501
502
Full penetration butt
weld made from both
sides or from one side
on to consumable
insert or temporary
non-fusible backing
1.2
1.4
1.3
Full penetration butt
weld flush ground,
including weld repairs
Joint type
1.1
No.
Detail
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Sketch of detail
80
71
80
80
90
testing
group
1 or 2
Class
63
56
63
63
71
testing
group
3
If   30°
If  > 30°
Weld proved free from significant flaws by non destructive
testing (see 17.4.5)
Weld proved free from significant flaws by non destructive
testing (see 17.4.5)
Weld proved free from significant flaws by non destructive
testing (see 17.4.5)
Ce  1
Weld proved free from surface-breaking and significant subsurface flaws by non destructive testing (see 17.4.5)
Comments
Table 17-3 — Classification of welded joints
a) Seam welds
UNI EN 13445-3:2021
CE1.1, CE2
S1.2 and S1.5,
S2.3 and S2.4,
S5.2 and S5.4,
DE1, CE1.2,
FE3
S1.1 to S2.4,
S5.1 to S5.4,
DE1, CE1.2,
FE3
S1.1 to S2.4,
S5.1 to S5.4,
DE1, CE1.2,
FE3
Relevant
details in
Table 17-2
Full penetration
butt weld made
from one side onto
permanent backing
plate 3
Joggle joint2,3
1.6
1.7
Sketch of detail
Circumferential seams only (see 5.7)
Minimum throat = shell thickness
Weld root pass inspected to ensure full fusion
Single pass weld
56
40
Weld root pass inspected to ensure full fusion
Single pass weld
40
If full penetration and the absence of root defects
cannot be ensured.
Circumferential seams only (see 5.7)
Minimum throat = shell thickness
40
40
If full penetration and the absence of root defects can
be ensured1.
Comments
56
40
71
testing testing
group 1 group 3
or 2
S3
S2.1 to S2.4
S1.1 to S2.4,
S5.1 to S5.4,
DE1, CE1.2,
FE3
Relevant
details in
Table 17–2
UNI EN 13445-3:2021
1
The NDT methods used shall be capable of assuring full weld penetration and the absence of root defects. If these cannot be ensured, then Class 63
shall be used providing the inside surface is accessible for visual examination. In case of misalignment, see 18.10.4.
2
Under the criteria of 5.7.4.1
3
In general for welds for which no NDT is possible only a damage factor D of 0,5 is allowed and the method of Annex M is not applicable.
Full penetration
butt weld made
from one side
without backing
Joint type
1.5
Detail
No.
Class
a) Seam welds
Table 17-3 — Classification of welded joints (continued)
503
EN 13445-3:2021 (E)
Issue 1 (2021-05)
504
2.2
2.1
No.
Detail
Sketch of detail
Welded-on head
with relief
groove
(c)
(b)
Welded-on head (a)
Joint type
EN 13445-3:2021 (E)
Issue 1 (2021-05)
63
40
80
40
63
63
71
80
testing
group
1 or 2
Class
40
63
40
63
63
63
testing
group
3
FE2
FE1.1 to
FE1.3
Relevant
details in
Table 17-2
UNI EN 13445-3:2021
Full penetration weld, proved free from significant flaws by non
destructive testing (see 17.4.5).
Head plate shall have adequate through-thickness properties to resist
lamellar tearing
Made from both sides, or from one side with the root pass ground flush
Made from one side, as welded:
— inside visually inspected and proved to be free from overlap or root
concavity
— if the inside cannot be visually inspected
— in all cases
(c) Full penetration welds made from one side without back-up weld:
— inside weld visually inspected and proved to be free from overlap or
root concavity.
— if the inside cannot be visually inspected, and full penetration cannot
be assured
— in all cases
(b) Partial penetration welds made from both sides
Head plate must have adequate through-thickness properties to resist
lamellar tearing
(a) Full penetration welds made from both sides:
— as welded
— if weld toes dressed
Comments
Table 17-3 — Classification of welded joints (continued)
b) Shell to head or tubesheet
Set-in head
Joint type
UNI EN 13445-3:2021
2.3
No.
Detail
(c)
(b)
(a)
Sketch of detail
40
63
63
71
80
testing
group
1 or 2
Class
40
63
63
63
testing
group
3
Full penetration weld made from one side without back-up
weld:
— inside visually inspected and proved to be free from overlap
or root concavity.
— if the inside cannot be visually inspected
— in all cases
Partial penetration welds made from both sides
Full penetration welds made from both sides (refers to fatigue
cracking from weld toe in shell):
— as welded
— if weld toes dressed
17.6.7 Comments
b) Shell to head or tubesheet
Table 17-3 — Classification of welded joints (continued)
FE1.1 to FE1.3
Relevant
details in
Table 17-2
505
EN 13445-3:2021 (E)
Issue 1 (2021-05)
506
3
No.
Detail
All types
Joint type
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(b)
(a)
Sketch of detail
63
71
71
80
testing
group
1 or 2
Class
63
63
testing
group
3
Partial penetration welds, with weld throat  0,8 x thinner
thickness of connected walls:
— as welded
— if weld toes dressed
— in all cases
Full penetration welds:
— as welded
— if weld toes dressed
— in all cases
Comments
c) Branch connections
Table 17-3 — Classification of welded joints (continued)
UNI EN 13445-3:2021
OS2.1 to OS3.3
Relevant
details in
Table 17-2
Jacket connection
weld with shaped
sealer ring
Joint type
UNI EN 13445-3:2021
4
No.
Detail
Sketch of detail
71
40
63
testing
group
1 or 2
Class
56
40
testing
group
3
d) Jackets
Welded from both sides, or from one side with backup weld
Welded from one side:
— multi-pass weld, with root pass inspected to ensure
full fusion
— single pass weld
— in all cases
Full penetration required, weld proved free from
significant flaws by non destructive testing (see 17.4.5)
Comments
Table 17-3 — Classification of welded joints (continued)
J1 and J2
Relevant
details in
Table 17-2
507
EN 13445-3:2021 (E)
Issue 1 (2021-05)
508
Attachment of any
shape with an edge
fillet or bevel - butt
welded to the
surface of a
stressed member,
with welds
continuous around
the ends or not
Attachment of any
shape with surface
in contact with
stressed member,
with welds
continuous around
ends or not
Continuous
stiffener
5.2
5.3
Joint type
5.1
No.
Detail
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Sketch of detail
71
80
71
80
71
80
testing
group
1 or 2
Class
71
71
71
80
71
80
testing
group
3
As welded
For full penetration welds, if weld toes dressed
As welded
For details with welds continuous around ends, if
weld toes dressed
As welded
For details with welds continuous around ends, if
weld toes dressed
Comments
e) Attachments attached by non pressure load carrying welds
Table 17-3 — Classification of welded joints (continued)
UNI EN 13445-3:2021
S4
W1
W2
Relevant
details in
Table 17-2
Trunnion support, with
fillet weld to vessel
continuous all around
Saddle support, with
fillet weld to vessel
continuous all around
6.2
6.3
UNI EN 13445-3:2021
Support on either
horizontal or vertical
vessel, with fillet weld
to vessel continuous all
around
Joint type
6.1
No.
Detail
f)
Sketch of detail
71
80
71
80
71
80
testing
group
1 or 2
Class
71
80
71
80
71
80
testing
group
3
As welded
If weld toe in shell dressed
As welded
If weld toe in shell dressed
As welded
If weld toe in shell dressed
Comments
Supports not subject to additional external fluctuating loads, assessment of the vessel wall
Table 17-3 — Classification of welded joints (continued)
W3
W3
W3
Relevant
details in
Table 17-2
509
EN 13445-3:2021 (E)
Issue 1 (2021-05)
510
Skirt support, with fillet
weld to vessel
continuous all around
Leg support (with or
without reinforcing
pad), with fillet weld to
vessel continuous all
around
6.5
Joint type
f)
6.4
No.
Detail
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Sketch of detail
71
71
80
testing
group
1 or 2
Class
71
71
80
testing
group
3
Full or partial penetration welds:
— as welded
— if welded from both sides and weld toes in shell dressed
Comments
Supports not subject to additional external fluctuating loads, assessment of the vessel wall
Table 17-3 — Classification of welded joints (continued)
UNI EN 13445-3:2021
W3
W3
Relevant
details in
Table 17-2
welded flange
7.2
UNI EN 13445-3:2021
Full penetration butt
welded neck flange or
compensation flange
with welding lug
Joint type
7.1
No.
Detail
b)
a)
b)
a)
Sketch of detail
63
71
80
63
40
80
testing
group
1 or 2
Class
63
63
63
40
63
testing
group
3
Partial penetration welds
Full penetration weld:
— as welded
— if weld toe dressed
Weld made from one side:
— if full penetration can be assured
— if the inside cannot be visually inspected, and full
penetration cannot be assured
— in all cases
Weld made from both sides or from one side with back-up
weld or on to consumable insert or temporary non-fusible
backing
Weld proved free from significant flaws by non destructive
testing (see 17.4.5)
Comments
g) Flanges and pads
Table 17-3 — Classification of welded joints (continued)
F2.1 to F2.3
F1 or P1
Relevant
details in
Table 17-2
511
EN 13445-3:2021 (E)
Issue 1 (2021-05)
512
Set-in flange or pad
Set-on flange or pad,
welded from both sides
7.4
Joint type
7.3
No.
Detail
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b)
a)
Sketch of detail
63
63
71
80
testing
group
1 or 2
Class
63
63
63
63
testing
group
3
Fillet weld on both sides:
Full penetration weld:
— as welded
— if weld toe dressed
Comments
g) Flanges and pads (continued)
Table 17-3 — Classification of welded joints (continued)
UNI EN 13445-3:2021
P2 and P3
P1 to P3
Relevant
details in
Table 17-2
EN 13445-3:2021 (E)
Issue 1 (2021-05)
17.7 Assessment rule
17.7.1 Variable amplitude loading (general case)
17.7.1.1 The total fatigue damage index due to the cumulative effect of the cycles that form the design
stress range spectrum is calculated as follows:
D 
where
n1
N1
ni

n2
N2

n3
N3
k
 etc   
1
ni
(17.7-1)
Ni
are the numbers of cycles of each stress range    *  i applied during the design life of the vessel,
and N i are the allowable numbers of cycles corresponding to the ranges    *  i , obtained in accordance
with 17.6.6 from the appropriate fatigue design curve.
NOTE
Summation of damage due to all individual cycle types is made according to MINER's rule (linear
summation).
17.7.1.2 The design is acceptable if the following condition is met:
(17.7-2)
D 1
If the condition is not met, the design shall be modified or a detailed fatigue analysis according to clause 18
shall be performed.
17.7.2 Constant amplitude loading (particular case)
The design is acceptable if the following condition is met:
 *   R
with
N.
 R
(17.7-3)
calculated according to 17.6.4.2 or 17.6.4.3 for the applied number of pressure cycles n instead of
17.8 Design and manufacture
NOTE 1
The number and size of the pressure fluctuations which a vessel can withstand during its lifetime
depend on its design, material and method of manufacture.
NOTE 2
High stress peaks should be avoided where possible. Guidance for selection of appropriate design,
particularly at junctions of components, may be found from comparison between factors  of various vessel
details (see Table 17.2) as well as between fatigue classes of various welded joints (see Table 17.3).
NOTE 3
Low general levels of stress are beneficial. Overthickness against non-cyclic design therefore
contributes to reduction of cyclic stress. Yet, a part of the benefit gained from using walls having extra-thickness
may be lost due to the adverse effect of increased thickness on fatigue resistance (accounted for through the
thickness correction factor C e ).
NOTE 4
For unwelded regions, softer steels are generally less notch sensitive than other materials.
UNI EN 13445-3:2021
513
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 5
In welded joints, the strength of the weld metal should be equal to or just slightly higher than that of
the base metal.
NOTE 6
Residual stresses and weld imperfections should be kept to the minimum. Structural integrity is more
sensitive to manufacturing defects under fatigue loading than under non-cyclic loading. The design requirements
for pressure bearing welds, given in Annex A, should be applied.
NOTE 7
Smooth surfaces (machining, grinding of welds) are beneficial for fatigue life.
17.9 Testing
For testing before, during, and after manufacture, the following subclauses shall be observed in addition to
the requirements of EN 13445-5:2021:
17.9.1 Initial review of testing requirements
An initial review shall be made at the design stage to clearly identify and designate the critical areas of the
vessels (see definition in 17.2.20).
17.9.2 Testing during production and final inspection
For the non-destructive test, the provisions of EN 13445-5:2021, Annex G shall be observed in all critical
areas, in addition to the general requirements of EN 13445-5:2021.
NOTE
If the method of non-destructive testing is not specified, ultrasonic testing (UT) or magnetic particle
testing (MT) for surfaces, should be given preference.
17.9.3 In-service inspection
NOTE
Recommendations about in-service inspection and measures to be adopted in service are given in
Annex M.
The designer/manufacturer shall report to the users in the operating instruction the numbers of cycles for
which the components of the vessel are specified during its lifetime.
If the component has to be inspected after 50 % of the calculated lifetime or in cases where it is expected
that the component will operate beyond the specified lifetime (see M.3) it may be agreed between
purchaser/user and manufacturer that all locations with a total fatigue damage index D equal or larger 0,25
for the numbers of cycles at the end of the specified lifetime shall be reported in the operating instruction.
This requires that Subclause 17.6 shall be used and that the component is not specified for endurance.
514
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18 Detailed assessment of fatigue life
18.1 Purpose
18.1.1 This clause specifies requirements for the detailed fatigue assessment of pressure vessels and
their components that are subjected to repeated fluctuations of stress.
18.1.2 The assessment procedure assumes that the vessel has been designed in accordance with all
other requirements of this standard.
18.1.3 These requirements are only applicable to the ferritic and austenitic steels specified in
EN 13445-2:2021.
NOTE
The requirements can also be applied to steel castings, but in case of finishing welding on steel
castings, the requirements for welded regions apply.
18.1.4 These requirements are not applicable to testing group 4 pressure vessels. For testing group 3
welded joints, see the special provisions in 18.10.2.1.
18.1.5 This method is not intended for design involving elastic follow-up (see reference [1] in
Annex N).
18.2 Specific definitions
The following terms and definitions apply in addition to those in Clause 3:
18.2.1
fatigue design curves
curves given in this clause of
against N for bolts
 R
against N for welded and unwelded material, and of
  R /Rm
18.2.2
discontinuity
shape or material change which affects the stress distribution
18.2.3
gross structural discontinuity
structural discontinuity which affects the stress or strain distribution across the entire wall thickness
18.2.4
local structural discontinuity
discontinuity which affects the stress or strain distribution locally, across a fraction of the wall
thickness
18.2.5
nominal stress
stress which would exist in the absence of a discontinuity
Note 1 to entry: Nominal stress is a reference stress (membrane + bending) which is calculated using elementary
theory of structures. It excludes the effect of structural discontinuities (e.g. welds, openings and thickness
changes). See Figure 18-1.
UNI EN 13445-3:2021
515
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Note 2 to entry: The use of nominal stress is permitted for some specific weld details for which determination of
the structural stress would be unnecessarily complex. It is also applied to bolts.
Note 3 to entry: The nominal stress is the stress commonly used to express the results of fatigue tests performed
on laboratory specimens under simple unidirectional axial or bending loading. Hence, fatigue curves derived from
such data include the effect of any notches or other structural discontinuities (e.g. welds) in the test specimen.
18.2.6
notch stress
total stress located at the root of a notch, including the non-linear part of the stress distribution.
Note 1 to entry: See Figure 18-1 for the case where the component is welded, but notch stresses may similarly be
found at local discontinuities in unwelded components.
Note 2 to entry: Notch stresses are usually calculated using numerical analysis. Alternatively, the nominal or
structural stress is used in conjunction with the effective stress concentration factor, K f .
Key
1
Nominal stress
2
Structural stress
3
Notch stress
4
Extrapolation to give structural stress at potential crack initiation site.
Figure 18-1 — Distribution of nominal, structural and notch stress at a structural discontinuity
18.2.7
equivalent stress
uniaxial stress which produces the same fatigue damage as the applied multi-axial stresses
Note 1 to entry: The Tresca criterion is applied in this clause but use of the ‘von Mises' criterion is also permitted.
516
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Note 2 to entry: The rule for calculation of the equivalent stress is given in C.4.1. The rule for calculation of the
equivalent stress range between two individual load conditions is given in C.4.2. In this clause, equivalent stress
ranges is determined for full loading cycles, i.e. for variations that cover various load conditions. The
corresponding rules are given in 18.6.2.2 for welded components and in 18.7.1.2 for unwelded ones. These rules
are different depending on whether the principal stress directions remain constant or not during the cycle.
18.2.8
stress on the weld throat
average stress on the throat thickness in a fillet or partial penetration weld
Note 1 to entry: In the general case of a non-uniformly loaded weld, it is calculated as the maximum load per unit
length of weld divided by the weld throat thickness and it is assumed that none of the load is carried by bearing
between the components joined.
Note 2 to entry: If there is significant bending across the weld throat, the maximum value of the linearised stress
should be used.
Note 3 to entry: The stress on the weld throat is used exclusively for assessment of fatigue failure by cracking
through weld metal in fillet or partial penetration welds.
18.2.9
stress range (   )
value from maximum to minimum in the cycle (see Figure 18-2) of a nominal stress, a principal stress
or a stress component, depending on the rule that is applied
Key
1
One cycle;  Stress range
Figure 18-2 — Stress range
18.2.10
structural stress
linearly distributed stress across the section thickness which arises from applied loads (forces,
moments, pressure, etc.) and the corresponding reaction of the particular structural part
UNI EN 13445-3:2021
517
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Note 1 to entry: Structural stress includes the effects of gross structural discontinuities (e.g. branch connections,
cone/cylinder intersections, vessel/end junctions, thickness change, deviations from design shape, presence of an
attachment). However, it excludes the notch effects of local structural discontinuities (e.g. weld toe) which give
rise to non-linear stress distributions across the section thickness. See Figure 18-1.
Note 2 to entry: For the purpose of a fatigue assessment, the structural stress shall be evaluated at the potential
crack initiation site.
Note 3 to entry: Structural stresses may be determined by one of the following methods: numerical analysis
(e.g. finite element analysis (FEA)), strain measurement or the application of stress concentration factors to
nominal stresses obtained analytically. Guidance on the use of numerical analysis is given in Annex N reference
[2].
Note 4 to entry: Under high thermal stresses, the total stress rather than the linearly distributed stress should be
considered.
18.2.11
weld throat thickness
minimum thickness in the weld cross-section
18.2.12
endurance limit
cyclic stress range below which, in the absence of any previous loading, no fatigue damage is assumed
to occur under constant amplitude loading
18.2.13
cut-off limit
cyclic stress range below which fatigue damage is disregarded
18.2.14
theoretical elastic stress concentration factor
ratio of notch stress, calculated on purely elastic basis, to structural stress at same point
18.2.15
effective notch stress
the stress which governs fatigue behaviour at a notch
18.2.16
effective stress concentration factor
ratio of effective notch stress (total stress) to structural stress at same point
18.2.17
critical area
an area where the total fatigue damage index exceeds the maximum value
518
D max
 0,8 for 500 <
D max
 0,5 for 1000 <
D max
 0,3 for
n eq
n eq
D max
defined as follows:
 1000
n eq
 10 000
> 10 000
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in Clause 4.
C, C1 and C2
are the constants in formula of fatigue design curves for welded components;
D
is the cumulative fatigue damage index;
E
is the modulus of elasticity at maximum operating temperature;
Fe, Fs
are coefficients;
fb
is the overall correction factor applied to bolts;
fc
is the compressive stress correction factor;
fe
is the thickness correction factor in unwelded components;
few
is the thickness correction factor in welded components and bolts;
fm
is the mean stress correction factor;
fs
is the surface finish correction factor;
fT*
is the temperature correction factor;
fu
is the overall correction factor applied to unwelded components;
fw
is the overall correction factor applied to welded components;
g
is the depth of groove produced by weld toe grinding;
Kf
is the effective stress concentration factor given in Formula (18.7-3);
Km
is the stress magnification factor due to deviations from design shape;
Kt
is the theoretical elastic stress concentration factor;
ke
is the plasticity correction factor for stress due to mechanical loading;
k
is the plasticity correction factor for stress due to thermal loading;
M
is the mean stress sensitivity factor;
m, m1 and m2
are exponents in formulae of fatigue design curves for welded components;
UNI EN 13445-3:2021
519
EN 13445-3:2021 (E)
Issue 1 (2021-05)
N
is the allowable number of cycles obtained from the fatigue design curves (suffix i refers to
life under ith stress range);
n
is the number of applied stress cycles (suffix i refers to number due to ith stress range);
R
is the mean radius of vessel at point considered;
Rmin
is the minimum inside radius of cylindrical vessel, including corrosion allowance;
Rmax
is the maximum inside radius of cylindrical vessel, including corrosion allowance;
Rz
is the peak to valley height;
r
is the radius of groove produced by weld toe grinding;
Sij
is the difference between either principal stresses (i and j) or structural principal stresses
(struc,i and struc,j) as appropriate;
Tmax
is the maximum operating temperature;
Tmin
is the minimum operating temperature;
T*
is the assumed mean cycle temperature;
T
is the total strain range;

is the stress range (suffix i refers to ith stress range; suffix w refers to weld);
eq
is the equivalent stress range (suffix i refers to ith stress range);
R
is the stress range obtained from fatigue design curve;
D
is the endurance limit;
Cut
is the cut-off limit;
struc
is the structural stress range;
 f
is the effective total equivalent stress range;
eq,l
is the equivalent stress range corresponding to variation of equivalent linear distribution;
eq,t
is the total (or notch) equivalent stress range;
eq,nl
is the stress range corresponding to variation of non-linear part of the stress distribution;

is the total deviation from mean circle of shell at seam weld;
520
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
1
is the offset of centre-lines of abutting plates;

is the angle between tangents to abutting plates at a seam;

is the direct stress or stress range as indicated (suffix w applies to weld);
(
eq, t
) op
is the equivalent total stress due to operating pressure (for specific use in 18.4.6)
(eq,t)max
is the maximum equivalent total stress;
(eq,t)min
is the minimum equivalent total stress;
 eq
is the mean equivalent stress;
 eq, r
is the reduced mean equivalent stress for elastic-plastic conditions;
struc1
is a structural principal stress (1, 2 , 3 apply to the axes) at a given instant;

is the total principal stress
total
1
is a principal stress (1, 2, 3 apply to the axes) at a given instant;
V1, V2
are stress ranges obtained in the example of reservoir cycle counting in 18.9.3;

is the shear stress or stress range as indicated (suffix w applies to weld);
18.4 Limitations
18.4.1 Where a vessel is designed for fatigue, the method of manufacture of all components, including
temporary fixtures and repairs, shall be specified by the manufacturer.
18.4.2 There are no restrictions on the use of the fatigue design curves for vessels which operate at
sub-zero temperatures, provided that the material through which a fatigue crack might propagate is
shown to be sufficiently tough to ensure that fracture will not initiate from a fatigue crack.
18.4.3 These requirements are only applicable to vessels which operate at temperatures below the
creep range of the material. Thus, the fatigue design curves are applicable up to 380 °C for ferritic steels
and 500 °C for austenitic stainless steels.
18.4.4 It is a condition of the use of these requirements that all regions which are fatigue-critical
(see 18.10.5) are accessible for inspection and non-destructive testing, and that instructions for
appropriate maintenance are established and included in the operating instructions.
NOTE
Recommendations on appropriate maintenance are given in Annex M.
As regards weld defects:
UNI EN 13445-3:2021
521
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For application of this clause, the following conditions (as required by EN 13445-5:2021, Annex G) shall be
met in addition to the general acceptance criteria for weld imperfections given in EN 13445-5:2021:
— no undercut,
— no root concavity,
— no lack of penetration for full penetration welds,
— 100 % inspection, visually and by NDT, with acceptance criteria as specified in EN 13445-5:2021,
Annex G, of all critical areas.
18.4.5 Corrosive conditions are detrimental to the fatigue lives of steels. Environmentally-assisted
fatigue cracks can occur at lower levels of fluctuating stress than in air and the rate at which they
propagate can be higher. The fatigue strengths specified do not include any allowances for corrosive
conditions. Therefore, where corrosion fatigue is anticipated and effective protection from the corrosive
medium cannot be guaranteed, a factor should be chosen, on the basis of experience or testing, by which
the fatigue strengths given in these requirements should be reduced to compensate for the corrosion. If,
because of lack of experience, it is not certain that the chosen fatigue strengths are low enough, the
frequency of inspection should be increased until there is sufficient experience to justify the factor used.
As regards tolerances:
— manufacturing tolerances shall not exceed those given in EN 13445-4:2021;
— for seam welds, the Manufacturer shall assume certain tolerances and derive the corresponding
stress factors to be used for fatigue assessment. Then the assumed tolerances shall be checked and
guaranteed after manufacturing.
18.4.6 For water conducting parts made from non-austenitic steels, operating at temperatures
exceeding 200 °C, conservation of the magnetite protective layer shall be ensured. This will be obtained
if the stress at any point on the surface in contact with water always remains within the following
limits:
 eq,t  max
 

eq,t
 op
 200 MPa

(18.4-1)
 eq,t  min
 

eq,t
 op
 600 MPa

(18.4-2)
(18.4-2)
NOTE
It is assumed that under the operating conditions at which the magnetite layer forms, there is no stress
in that layer.
18.4.7 Where vibration (e.g. due to machinery, pressure pulsing or wind) cannot be removed by
suitable strengthening, support or dampening, it shall be assessed using the method in this clause.
18.5 General
18.5.1 A fatigue assessment shall be made at all locations where there is a risk of fatigue crack
initiation.
522
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
It is recommended that the fatigue assessment is performed using operating rather than design loads.
18.5.2 In fatigue, welds behave differently from plain (unwelded) material. Therefore the assessment
procedures for welded and unwelded material are different.
18.5.3 Plain material might contain flush ground weld repairs. The presence of such repairs can lead to
a reduction in the fatigue life of the material. Hence, only material which is certain to be free from
welding shall be assessed as unwelded.
18.5.4 A typical sequence in the design of a vessel for fatigue is shown in Table 18-1.
18.5.5 The fatigue life obtained from the appropriate fatigue design curves (for welded components,
unwelded components and bolts) for constant amplitude loading is the allowable number of cycles.
18.5.6 For calculation of cumulative damage under variable amplitude loading, D is given by:
D 
n1
N1

n2
N
2
 ...... 

ni
N
(18.5-1)
i
The following condition shall be met:
D  1
UNI EN 13445-3:2021
(18.5-2)
523
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-1 — Summary of fatigue assessment process
Task
Comment
Relevant clause(s)
1.
Design vessel for static
loads
Gives layout, details, sizes
Part 3
2.
Define fatigue loading
Based on operating specification,
secondary effects identified by
manufacturer, etc.
18.5, 18.9.1
3.
Identify locations of vessel
to be assessed
Structural discontinuities, openings,
joints (welded, bolted), corners,
repairs, etc.
18.5
4.
At each location, establish
stress range during time
period of operation
considered
a) Calculate structural principal
stresses
Welded: 18.6, 18.8 and 18.10.4;
At each location, establish
design stress range
spectrum
a) Perform
operation
5.
b) Deduce equivalent or principal
stress ranges
cycle
Unwelded: 18.7 and 18.8
Bolts: 18.7.2.
counting 18.9
18.8
b) Apply
plasticity
correction
18.7
factors where relevant
c) Unwelded material: derive
effective notch stress ranges
6.
7.
8.
524
Identify fatigue strength
data, including allowance
for overall correction
factor
a) Welded material
18.10, Tables 18-4 & Annex P
b) Unwelded material
18.11
c) Bolted material
18.12
Note relevant implications
and inform relevant
manufacturing and
inspection personnel
a) Inspection requirements for
welds
Tables 18-4 or Annex P
b) Control of or assumptions about
misalignment
18.10.4
c) Acceptance levels for weld flaws
18.10.5
a) Welded material
18.10, Table 18-7
b) Unwelded material
18.11, Table 18-10
c) Bolts
18.12
d) Assessment method
18.5.5, 18.5.6
Extract allowable fatigue
lives from fatigue design
and perform assessment
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-1 (continued)
9.
Further action if location
fails assessment
a) Re-assess using more refined
stress analysis
18.6 (welded), 18.7 (unwelded)
b) Reduce stresses by increasing
thickness*
c) Change detail
Table 18-4 or Annex P
d) Apply weld toe dressing (if
appropriate)
18.10.2.2
* - for mechanical loading, this is obtained by increasing the wall thickness in the most cases but in some cases (connections of
parts with different wall thicknesses) a better distribution of the wall thicknesses can reduce the stresses too.
- for thermal loading, more adjusted modifications are required, e.g. stiffness reduction at appropriate locations of the
structure and/or increase of the fatigue strength of the weak parts.
18.6 Welded material
18.6.1 Stresses
For the assessment of simple attachments and aligned seam welds, provided they are not located in regions
affected by gross structural discontinuities, use can be made of nominal stresses calculated on an elastic
basis.
In the fatigue check of the root region of directly loaded fillet or partial penetration welds, as illustrated
in 18.6.3, the stress range used shall be based on the stress on weld throat, see 18.2.8.
In all other cases, structural stresses shall be determined. They shall be:
— either calculated using elastic theory from the structural stresses at the potential crack initiation
site, taking account of all membrane, bending and shearing stresses;
— or deduced from strains measured on the vessel and converted to linear-elastic conditions.
Where the structural stress is obtained by detailed stress analysis (e.g. FEA) or by measurement, it shall be
determined from the principal stress that acts in the direction which is closest to the normal to the weld by
extrapolation using the procedures detailed in Figure 18-3.
NOTE 1
In arriving at the structural principal stress, it is necessary to take full account of the structural
discontinuities (e.g. nozzles) and all sources of stress. The latter may result from global shape discontinuities such
as cylinder to end junctions, changes in thickness and welded-on rings; deviations from intended shape such as
ovality, temperature gradients, peaking and misaligned welds (note some misalignment is already included in
some of the fatigue design curves). Methods in this clause and in the published literature (see references [3] to [7]
in Annex N) provide estimates of such stresses for many geometries, or at least enable a conservative assessment
to be made.
UNI EN 13445-3:2021
525
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 2
Since the maximum range of stress on the weld throat can be expressed as a sum,  is the scalar value
of the greatest vector difference between different stress conditions during the cycle.
Figure 18-3 — Extrapolation to obtain structural stress from FEA or strain gauge results ([2] in
Annex N)
Locations of stresses for determination of structural stress by extrapolation to point of stress concentration
(weld toe in this case):
d) low bending stress component, gauge length ≤0,2e, linear extrapolation;
e) high bending stress component, stiff elastic foundation, gauge length ≤0,2e, quadratic
extrapolation;
f)
gauge length > 0,2e, linear extrapolation
where "gauge length" refers to size of strain gauge or FE mesh.
18.6.2 Stress range in parent material and butt welds
18.6.2.1 Options
For the assessment of simple attachments and aligned seam welds, provided they are not located in regions
affected by gross structural discontinuities, the nominal equivalent stress range (see Tables 18-4a) and 184e)) or the nominal principal stress range (see Annex P) can be used. This shall be calculated in the same way
as structural stress ranges (see Formulae (18.6-4), (18.6-5), (18.6-6) and (18.6-7)) using nominal principal
stresses instead of structural principal stresses.
For all other welded components, depending on the calculation method:
— either the principal stress range shall be determined from the range of the structural principal
stresses and used with Annex P;
— or the equivalent stress range shall be calculated from the range of the equivalent stresses
determined from the structural principal stresses and used with Table 18-4.
526
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Tension stresses are considered positive and compression stresses negative. In both cases, an important
aspect is whether, under multiple load actions, the directions of the structural principal stresses remain
constant or not.
Where applicable, the elastically calculated principal or equivalent stress range shall be modified by the
plasticity correction factors given in 18.8.
NOTE
For welded components, the full stress range is used regardless of applied or effective mean stress. The
fatigue design curves incorporate the effect of tensile residual stresses; post-weld heat treatment is ignored in the
fatigue analysis.
18.6.2.2 Equivalent stress range eq
18.6.2.2.1 Structural principal stress directions constant
When the structural principal stress directions are constant, eq shall be calculated as follows.
The variation with time of the three structural principal stresses shall be established. The variation with time
of the three principal stress differences shall be calculated as follows:

(18.6-1)
S12  
s tru c 1
S 23  
s tru c 2

s tru c 3
(18.6-2)
S 31  
s tru c 3

s tru c 1
(18.6-3)
s tru c 2
Applying Tresca's criterion, eq is:
  eq  m ax

S 1 2 m a x  S 1 2 m in ; S 2 3 m a x  S 2 3 m in ; S 3 1 m a x  S 3 1 m in

(18.6-4)
NOTE
A typical example is shown in Figures 18-4(a) and (b). eq is twice the greatest shear stress range
and occurs on one of the three planes of maximum shear.
UNI EN 13445-3:2021
527
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) — Typical variation with time of the structural principal stresses
b) — Variation with time of the principal stress differences and the resulting eq
Figure 18-4 — Typical example of stress variation when the
principal stress directions remain constant
528
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18.6.2.2.2 Structural principal stress directions change
When the structural principal stress directions change during cycling between two load conditions, eq shall
be calculated as follows.
Determine the six stress components (three direct and three shear) at each load condition with reference to
some convenient fixed axes. For each stress component, calculate the difference between the two
conditions. Calculate the principal stresses from the resulting stress differences and call them ()1, ()2,
()3. Then
  eq  max      1      2 ;     2      3 ;     3      1 
(18.6-5)
Where cycling is of such a complex nature that it is not clear which two load conditions will result in the
greatest value of eq they shall be established by carrying out the above procedure for all pairs of load
conditions.
The two load conditions which result in the greatest value for eq shall be used as "min" and "max" loading
conditions for the calculation of the mean equivalent stress according to 18.7.1.2.2, using Formula (18.7-7).
NOTE
This procedure is the same as described in C.4.2 for the case when the Tresca criterion is used.
18.6.2.3 Principal stress range
18.6.2.3.1 Application
If the potential fatigue crack initiation site is at the weld toe or on the surface of the weld, the structural
stress range in the material adjacent to the weld is required for the fatigue assessment. In the maximum
principal stress approach, use is made only of the two structural principal stresses struc1 and struc2 acting
essentially (i.e. within 45°) parallel and normal to the direction of the weld respectively, on each material
surface.
18.6.2.3.2 Structural principal stress directions constant
Where the directions of the structural principal stresses remain fixed,  is determined as follows.

struc1
=
struc1max

struc2
=
struc2ma
x
-
struc1min
(18.6-6)
-
struc2min
(18.6-7)
NOTE
Both principal stress ranges may need to be considered, depending on their directions and fatigue
classes applicable to each of these directions.
18.6.2.3.3 Structural principal stress directions change
When the structural principal stress directions change during cycling between two load conditions,  shall
be calculated as follows.
Determine the three stress components (two direct and one shear) at each load condition with reference to
some convenient fixed axes. For each stress component, calculate its difference between the two conditions.
Calculate the principal stresses from the resulting stress differences.
NOTE
Both principal stress ranges may need to be considered, depending on their directions and the fatigue
classes applicable to each of these directions.
UNI EN 13445-3:2021
529
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Where cycling is of such a complex nature that it is not clear which two load conditions will result in the
greatest value of , they shall be established by carrying out the above procedure for all pairs of load
conditions. Alternatively, it is conservative to assume that  is the difference between the algebraically
greatest and smallest principal stresses occurring during the whole loading cycle regardless of their
directions, and assume the lower of the classifications for the two principal stress directions (see Tables P.1 –
P.7).
18.6.3 Stress range on the throat of directly loaded fillet or partial penetration welds
 is the maximum range of stress on the weld throat, as defined in 18.2.8.
Where stress cycling is due to the application and removal of a single load,
 =

2
w
 w
2

1/ 2
(18.6-8)
where
w is the normal stress range on the weld throat and w is the shear stress range on the weld throat.
Where stress cycling is due to more than one load source, but the direction of the stress stress vector on the
weld throat remain fixed,  is determined from the maximum range of the load per unit length of the weld.
Where the direction of the stress vector on the weld throat changes during the cycle between two extreme
load conditions,  is the magnitude of the vector difference between the two stress vectors.
Where cycling is of such a complex nature that it is not clear which two load conditions will result in the
greatest value of , then the vector difference should be found for all pairs of extreme load conditions.
Alternatively, it is conservative to assume:
  = [(  m a x -  m in )
2
+ (  1 m a x -  1 m in )
2
(18.6-9)
2 1/ 2
+ (  2 m a x -  2 m in ) ]
where
1 and 2 are the two components of shear stress on the weld throat.
18.7 Unwelded components and bolts
18.7.1 Unwelded components
18.7.1.1 Stresses
The assessment of unwelded components shall be based on effective equivalent total stresses. These
effective equivalent total stresses can be calculated either from structural stresses or from total stresses.
When calculated from structural stresses, the effective total stress range is given by:
530
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(18.7-1)
  f  K f .   eq, struc
The structural stresses used for this calculation shall be determined from a model which incorporates the full
effect of gross structural discontinuities, but not that of local ones (i.e. notches).
When calculated from total stresses, the effective total stress range is given by:


f
K
f
K
t

eq, total
(18.7-2)
The total stresses used for this calculation shall be determined from a model which incorporates the full
effect of all structural discontinuities, including that of local ones (i.e. notches).
In that case, it is permitted to avoid the calculation of the theoretical stress concentration factor
provided a ratio
Kf Kt  1
t
is assumed in Formula (18.7-2), as a conservative simplification.
The effective stress concentration factor
K
f
is given
by:
1,5  K t  1 
Kf  1
1  0 ,5 max{ 1; K t 
where :
K

(18.7-3)
struc, eq

}
D
  D    R for N  2106 cycles for unwelded material,

struc, eq
is the structural equivalent stress range corrected to account for plasticity correction (if
relevant, see 18.8)
NOTE
This coefficient reflects the effective influence of a notch on fatigue life, as derived from fatigue tests.
The theoretical stress concentration factor
K
t


total

struc
K
t
shall be defined and calculated as follows:
(18.7-4)
If the theoretical stress concentration factor is given by an analytical formula found in the literature it has to
be based on this definition.
If the total stresses are calculated directly by analysis (e.g. FEA) or determined experimentally (e.g. strain
gauges), the structural and peak stresses may be separated (as described in Annex C) to give the total stress
as follows:

total
  struc
  peak
(18.7-5)
Then
K
t
 1

peak

struc
UNI EN 13445-3:2021
(18.7-6)
531
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
Formulae (18.7-4) to (18.7-6) are written for the simple case of uniaxial stress state to understand the
principle. In the general case of multiaxial stress states Formula (18.7-5) shall be applied for the stress
components (see C.4.4) and Formula (18.7-4) shall be applied for the calculation of the theoretical stress
concentration using the equivalent stress ranges (see 18.7.1.2.1). If the equivalent total stresses are determined
directly by analysis (e.g. FEA) the model shall include any notches in sufficiently fine detail. If they are determined
experimentally (e.g. strain gauges), measurements shall be made within the notch, or sufficiently close to enable
the total stress to be established by extrapolation (see reference [2] in Annex N). Strains shall be converted to
stresses assuming linear elastic conditions.
The equivalent stress range eq,l and equivalent mean stress  eq shall be determined. Two methods are
given for this depending on whether, under multiple load actions, the directions of the structural principal
stresses remain constant or not. Tension stresses are considered positive and compression stresses negative.
18.7.1.2 Equivalent stress range and equivalent mean stress
18.7.1.2.1 Principal stress directions constant
When the principal stress directions remain constant, eq shall be determined per 18.6.2.2.1 and
Formula (18.6-4).
NOTE 1
For multiaxial stress states the equivalent stress range is calculated as equivalent stress of the range
(differences between the two states) of the stress components and not as the range (difference) between the
equivalent stresses at the two states (compare C.4.2)
The corresponding mean equivalent stress  eq is the average of maximum and minimum values taken
during the cycle by the sum of the two total principal stresses, total,i and total,j, which produced eq. Thus:

eq
=
1
2

to ta l, i
+

to ta l, j
m a x
+
 to ta l, i
+

to ta l, j
m in 
(18.7-7)
NOTE 2
A typical example is shown in Figure 18-5.  eq is twice the mean value of the direct stress, averaged
over time, normal to the plane of maximum shear stress range.
532
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 18-5 — Example of the variation with time of the difference between the total principal
stresses which determine eq (i.e. total,1 and total,3 in this case) and the resulting mean  eq
18.7.1.2.2 Principal stress directions change
When the principal stress directions change:
— the equivalent stress range
  eq
— the equivalent mean stress

eq
shall be calculated as described in 18.6.2.2.2
shall be calculated according to Formula (18.7-7), in which :
— the loading conditions "min" and "max" to be considered shall be as defined in 18.6.2.2.2
—
 total,
i

  total, j
max
shall be the sum of the two principal stresses (marked by i and j) whose
difference is the greatest in the load condition "max"
—
 total,
i

  total, j
min
shall be the sum of the two principal stresses (marked by i and j) whose
difference is the greatest in the load condition "min".
NOTE
Since different stress states act in the load conditions "max" and "min", the pair of indices i and j to be
retained for each of them may be different.
18.7.2 Bolts
For bolts,  is the maximum nominal stress range arising from direct tensile and bending loads on the core
cross-sectional area, determined on the basis of the minor diameter. For pre-loaded bolts, account may be
taken of the level of pre-load, with  based on the actual fluctuations of bolt load
NOTE
The fatigue design curve for bolts takes account, for any form of thread, of the stress concentrations at
the thread root.
UNI EN 13445-3:2021
533
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18.8 Elastic-plastic conditions
18.8.1 General
For any component, if the calculated pseudo-elastic structural stress range for both welded joints and
unwelded parts exceeds twice the yield strength of the material under consideration, i.e. if

eq, l
 2 R p0,2/T
*
,
see note, it shall be multiplied by a plasticity correction factor. The correction factor to be applied to the
stress range of mechanical origin is ke and to the stress range of thermal origin is k .
NOTE
This applies to ferritic steels; for austenitic steels, use
R p1,0/T
*
.
18.8.1.1 Mechanical loading
For mechanical loading, the corrected structural stress range struc,eq = ke eq,l , where:
k e  1 A0
 
eq, l

 2 R
p0,2/T

1
*




(18.8-1)
where
A0 = 0,5 for ferritic steels with
= 0,4 for ferritic steels with
=
0 ,4 
R m
 500
3000
800  R m  1000 (MPa )
R m  500 (MPa )
for ferritic steels with
;
and for all austenitic steels (see note in 18.8.1);
500  R m  800 (MPa ) .
The procedure for determining the mean equivalent stress to allow for elastic-plastic conditions is shown in
Figure 18-6 and applied in 18.11.
534
UNI EN 13445-3:2021
*
.
UNI EN 13445-3:2021
Figure 18-6 — Modifications to mean equivalent stress to allow for elastic-plastic conditions due to mechanical loadings
(**)This applies to ferritic steels; for austenitic steels, use R p1,0/T
(*) For unwelded parts,  or  values are notch stresses or stress ranges
535
EN 13445-3:2021 (E)
Issue 1 (2021-05)
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18.8.1.2 Thermal loading
In the case of a thermal stress distribution which is non-linear through the material thickness, both the nonlinear and the equivalent linear stress distributions shall be determined for each stress component. Using
eq,l, k shall be calculated by:
k


0 ,7

= max

0 ,4
 0 ,5 +

  eq, l / R p0,2/T

*



; 1, 0




(18.8-2)
The corrected stress range shall be either eq = k . eq,l for welded joints or f = k . eq,t for unwelded
zones.
18.8.1.3 Elastic-plastic analysis
If the total strain range T (elastic plus plastic) due to any source of loading is known from theoretical or
experimental stress analysis, correction for plasticity is not required and
 = E ·  
(18.8-3)
T
18.9 Fatigue action
18.9.1 Loading
18.9.1.1 All sources of fluctuating load acting on the vessel or part shall be identified.
NOTE
Such loads are fluctuations of pressure; variations in contents; temperature transients; restrictions of
expansion or contraction during temperature variations; forced vibrations; and variations in external loads.
Account shall be taken of all operational and environmental effects defined in the purchase specification.
18.9.2 Simplified cycle counting method
18.9.2.1 Loads shall be grouped into specific loading events. Loading events shall be independent of
each other and shall be considered separately.
18.9.2.2 A loading specification shall be prepared stating for each loading event the stress range
(calculated from 18.5, 18.6, 18.7 and 18.8 as appropriate for the component and load) and number of
cycles for each load.
As shown in Figure 18-7 and Table 18-3, the stress ranges shall be plotted or tabulated against number of
cycles. The loading with the lowest number of cycles shall be plotted or tabulated at the top and the cycles
summed as shown.
536
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
 combined stress range
n number of applied cycles
c4 cycles of 4 + 3 + 2 + 1
c3 cycles of 3 + 2 + 1
c2 cycles of 2 + 1
c1 cycles of 1
Figure 18-7 — Simplified counting method
NOTE
An example is shown in Table 18-3.
UNI EN 13445-3:2021
537
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-3 — Example of determination of stress cycles using simplified cycle counting method
Individual loadings
Loading events
Loading
Stress range No of cycles
Example
Number
Stress range No of cycles
4
4
n4
Full pressure A
range
4 + 3+
2+ 1
c4 = n4
3
3
n3
Temperatur
e difference
B
3+ 2+
1
c3 = n3 - n4
2
2
n2
Pressure
fluctuation
C
2 + 1
c2 = n2 -n3 -n4
1
1
n1
Mechanical
loading
D
1
c1 = n1 -n2 -n3
-n4
18.9.3 Reservoir cycle counting method
18.9.3.1 As an alternative to the simplified counting method given in 18.9.2, the more accurate
reservoir cycle counting procedure may used, provided the principal stress directions remain constant
with time.
NOTE 1
This method is based on an analysis of the applied stress history. Therefore it is necessary that the load
history is defined in the vessel specification or can be conservatively assumed at the design stage. If the exact
sequence of loads is not known, alternatives should be examined to establish the most severe from the fatigue
point of view, that is the one giving the highest value of D in Formula (18.5-1).
NOTE 2
When principal stress directions vary with time (e.g. when multiple loads act out of phase), there is no
particular stress which can be used for cycle counting. For such cases, stress history simplification that result in
fixed principal stress directions should be made, if conservative, or the simplified cycle counting method of 18.9.2
should be used.
18.9.3.2 Determine the stress history, i.e. the stresses resulting from all applied loads at any time of
the load history.
18.9.3.3 Derive the variation with time of either the structural principal stresses  struc,1 and  struc,2
for an assessment based on principal stresses according to Annex P (see Figure 18-4a) or the principal
stress differences S 12 , S 23 and S 31 for an assessment based on equivalent stresses (see Figure 18-4b).
The principal stress or stress difference to be retained for assessment shall be that which leads to the
largest value of D in Formula (18.5-1), for the cycles found in its variation.
NOTE 1
The conservatism of this method is well established for load histories where the stress variations
concern mainly the same principal stress or stress difference. It has not been proven for more general cases. For
load histories where the situation is quite different, it is recommended to use the simplified cycle counting method
of 18.9.2 to avoid possible lack of conservatism.
538
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 2
When only one load varies with time, the cycle counting may also be performed on the basis of the
variation of this load and the stress range of each stress cycle then derived from the load range of the
corresponding load cycle.
18.9.3.4 Plot the peak and trough values for two occurrences of the stress history as shown in
Figure 18-8.
18.9.3.5 Mark the highest peak stress in each cycle and join the two peaks together with a straight
line. If there are two or more equal highest peaks in a cycle, mark only the first such peak in the
occurrence.
18.9.3.6 Join the two marked points and consider only that part of the plot which falls below this
line, like the section of a full reservoir.
18.9.3.7 Drain the reservoir from the lowest point leaving the water that cannot escape. If there are
two or more equal lowest points, drainage may be from any one of them.
18.9.3.8
List one cycle having a stress range, V1, equal to the vertical height of water drained.
18.9.3.9 Repeat both steps 18.9.3.7 and 18.9.3.8 successively with each remaining body of water
until the reservoir is emptied, listing one cycle at each draining operation.
18.9.3.10
List all the individual stress ranges in descending order of magnitude, V1, V2, V3, V4
etc. Where two or more cycles of equal stress range occur, record them separately. This provides the
design stress range spectrum.
Figure 18-8 — Reservoir cycle counting method
UNI EN 13445-3:2021
539
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18.10 Fatigue strength of welded components
18.10.1 Classification of weld details
18.10.1.1 Use of the tables
Welds shall be classified to Tables 18-4 and Annex P according to whether the stress range is calculated from
equivalent or principal stresses. In Annex P, the classification depends on the potential mode of cracking
corresponding to the position and direction of the fluctuating stress shown.
All deviations from the ideal shape (misalignment, peaking, ovality etc.) shall be included in the
determination of the stresses.
NOTE 1 In general, fatigue strength depends on the direction of the fluctuating stress relative to the weld detail;
the locations of possible fatigue crack initiation at the detail; the geometrical arrangement and proportions of the
detail; and the methods of manufacture and inspection. Consequently, a detail may appear several times in the
tables because of the different modes in which it might fail.
NOTE2
A given weld detail may need to be assessed for potential fatigue crack initiation from more than one
location using different classifications and corresponding design curves.
NOTE 3 The fatigue life of a vessel or part of a vessel may be governed by one particular detail. Therefore, the
classes of other details which experience the same fatigue loading need be no higher. For example, the potentially
high class attainable from perfectly-aligned seams may not be required if overall fatigue life is governed by fillet
welds.
18.10.1.2 Classification of weld details to be assessed using equivalent stress range
Weld details and their corresponding classes for use in assessments based on equivalent stress range are
given in Table 18-4. The classification refers either to fatigue cracking in the parent metal from the weld toe
or end, which shall be assessed using eq in the parent metal adjacent to the potential crack initiation site,
or to fatigue cracking in the weld itself from the root or surface, which shall be assessed using  in the
weld, with  as defined in 18.6.3.
Since eq has no direction, the class indicated in Table 18-4 refers to the least favourable stressing direction
for the particular weld detail and mode of fatigue cracking shown.
540
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range
a) — Seam welds
Class
Detail
No.
Testing
group
1 or 2
Testing
group 3
Weld to be proved free from
surface-breaking flaws and
significant sub-surface flaws (see
EN 13445-5:2021) by nondestructive testing.
Use fe instead of few
90
71
Weld to be proved free from
significant
flaws
(see
EN 13445--5:2021) by nondestructive testing and, for
welds made from one side,
full penetration*.
80
63
1.3
Weld to be proved free from
significant flaws by non-destructive
testing (see EN 13445--5:2021)*.
Effect of centre-line offset to be
included in calculated stress*.
80
63
1.4
Weld to be proved free from
significant flaws (see
EN 13445--5:2021) by nondestructive testing
  30°
80
63
 > 30°
71
56
1.1
1.2
Joint type
Full penetration butt weld
flush ground, including
weld repairs
Full penetration butt weld
made from both sides or
from one side on to
consumable insert or
temporary non-fusible
backing
Sketch of detail
Fatigue cracks usually initiate at weld
flaws
Comments
*In case of misalignment, see 18.10.4.
UNI EN 13445-3:2021
541
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (continued)
a) Seam welds
Class
Detail
No.
1.5
1.6
1.7
Joint type
Full penetration butt
welds made from one
side without backing
Full penetration butt
welds made from one
side onto permanent
backing.
Joggle joint
Sketch of detail
Testing
group
1 or 2
Testing
group 3
If full penetration can
be assured*.
63
40
If inside cannot be
visually inspected and
full penetration cannot
be assured*.
40
40
Weld root pass inspected to
ensure full fusion to backing.
56
40
Single pass weld.
40
40
Weld root pass inspected to
ensure full fusion to backing.
56
40
Single pass weld.
40
40
Comments
Circumferential seams only
(see 5.7) Minimum throat =
shell thickness
Circumferential seams only
(see 5.7) Minimum throat =
shell thickness.
*In case of misalignment, see 18.10.4.
542
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (continued)
b) — Shell to head or tubesheet
Class
Detail
No.
2.1
Joint type
Sketch of detail
Comments
Testing
group
1 or 2
Testing
group 3
71
80
63
63
32
32
63
63
63
40
40
40
80
63
63
40
40
40
Head plate shall have adequate
through-thickness properties to
resist lamellar tearing.
Welded-on head
Full penetration welds made from
both sides (detail a):
(a)
- as-welded
- weld toes dressed (see 18.10.2.2).
Partial penetration welds made from
both sides (detail b):
(b)
(c)
- fatigue cracking in weld*
- fatigue cracking in shell from weld
toe.
Full penetration welds made from
one side without back-up weld
(detail c):
- if the inside weld can be visually
inspected and is proved to be free
from overlap or root concavity.
- if the inside cannot be visually
inspected and full penetration cannot
be assured.
2.2
Welded-on head
with relief groove
Weld to be proved free from
significant flaws (see
EN 13445--5:2021) by NDT.
Full penetration welds made from
both sides, or from one side with the
root pass ground flush.
Full penetration welds made from
one side:
- if the inside weld can be visually
inspected and is proved to be free
from weld overlap and root
concavity.
- if the inside cannot be visually
inspected.
*To be considered only if weld throat < 0,8 x shell thickness
UNI EN 13445-3:2021
543
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (continued)
b) — Shell to head or tubesheet
Class
Detail
No.
2.3
Joint type
Sketch of detail
Set-in head
(a)
Testing
group 1 or
2
Testing
group 3
71
80
63
63
- refers to fatigue cracking in weld,
based on weld throat stress range.
32
32
- weld throat 0,8 x head thickness.
63
63
63
40
40
40
Comments
Full or partial penetration welds made
from both sides (detail a).
(Refers to fatigue cracking from weld
toe in shell) :
- as-welded;
- weld toes dressed (see 18.10.2.2).
Partial penetration welds made from
both sides (detail b):
(b)
Full penetration weld made from one
side without back-up weld (detail c):
- if the inside weld can be visually
inspected and is proved to be free from
overlap or root concavity.
- if the inside cannot be visually
inspected.
(c)
544
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (continued)
c) — Branch connections
Class
Detail
No.
3.1
Joint type
Sketch of detail
Testing
group 1 or
2
Testing
group 3
100
100
71
80
63
63
- weld throat  0,8 x thinner
thickness of connecting walls, as
welded
- weld throat < 0,8 x thinner thickness
of connecting walls
- weld toes dressed (see 18.10.2.2)
63
63
32
71
32
63
Comments
Assessment by the method for
unwelded parts is the normal
approach. However, simplified
assessment using class 100 according
to Annex Q is allowed.
Crotch corner
Use fe instead of few
1 Crack
radiates
from
corner into piece, sketches
show plane of crack
3.2
Weld toe in shell
Full penetration welds:
- as welded
- weld toes dressed (see 18.10.2.2)
Partial penetration welds:
3.3
Stressed weld metal
Fillet and partial penetration welds.
32
32
3.4
Weld toe in branch
- As-welded.
- Weld toes dressed (see 18.10.2.2)
71
80
63
63
en = branch thickness in
Formula (18.10-6).
UNI EN 13445-3:2021
545
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (continued)
d) Jackets
Class
Detail
No.
4.1
Joint type
Jacket connection weld
with shaped sealer ring
Sketch of detail
Comments
Testing
group 3
63
40
40
40
71
56
Full penetration weld to be
proved free from significant
flaws (see EN 13445-5:2021)
by non-destructive testing
Welded from one side:
- multi-pass weld with root
pass inspected to ensure full
fusion;
- single pass weld.
Welded from both sides or
from one side with back-up
weld.
546
Testing
group 1 or
2
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (continued)
e) — Attachments
Class for use with:
Detail
No.
5.1
5.2
5.3
Joint type
Attachment of any shape
with an edge fillet or
bevel butt-welded to the
surface of a stressed
member, with welds
continuous around the
ends or not
Attachments of any
shape with surface in
contact with stressed
member, with welds
continuous around ends
or not
Continuous stiffener
UNI EN 13445-3:2021
Sketch of detail
Structural
equivalent
stress
Nominal
equivalent
stress
Testing
group
1, 2, 3
Testing
group
1, 2, 3
L  160mm, t  55mm
71
56
L > 160mm
71
50
L  160mm, W  55mm
71
56
L > 160mm, W  55mm
71
50
L > 160mm, W  55mm
71
45
t  55mm
71
56
t > 55mm
71
50
Comments
For details with welds
continuous around ends, one
class increase if weld toes
dressed (see 18.10.2.2)
For details with welds
continuous around ends, one
class increase if weld toes
dressed (see 18.10.2.2)
For full penetration welds, one
class increase if weld toes
dressed (see 18.10.2.2)
547
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (continued)
f) Supports
Detail
No.
6.1
Joint type
Sketch of detail
Comments
As-welded.
Support on either
horizontal or vertical
vessel
Class
Testing
Testing
group 1 or group 3
2
71
71
Weld toe in shell dressed
(see 18.10.2.2)
80
80
As-welded.
71
71
Weld toe in shell dressed
(see 18.10.2.2)
80
80
As-welded.
71
71
Weld toe in shell dressed
(see 18.10.2.2)
80
80
as-welded;
71
71
weld toe in shell dressed
(see 18.10.2.2).
80
80
Welded from one side
56
56
71
71
1 Fillet welded to vessel all
round
2 Backing plate
6.2
Trunnion support
1
6.3
Backing plate
Saddle support
1 Fillet welded to vessel all
round
6.4
6.5
548
Skirt support
Leg support (with or
without reinforcing pad)
with fillet weld to vessel
continuous all around.
Welded from both sides:
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (continued)
g) Flanges and pads
Class
Detail
No.
7.1
Joint type
Full penetration butt
welded neck flange or
compensation flange with
welding lug.
Sketch of detail
Testing
group 1 or
2
Testing
group 3
80
63
63
40
40
40
71
80
63
63
63
63
32
32
71
80
63
63
- if full penetration can be
assured ;
- if the inside cannot be visually
inspected ;
Fillet welded on both sides:
63
40
40
40
- weld throat  0,8 x shell
thickness;
- weld throat < 0,8 x shell
thickness.
63
32
32
32
Comments
Weld to be proved free from
surface-breaking and significant
sub-surface flaws (see EN 134455:2021) by non-destructive
testing.
Weld made from both sides or
from one side with back-up weld
or onto consumable insert or
temporary backing.
Weld made from one side:
- if full penetration can be
assured ;
- if the inside cannot be visually
inspected ;
7.2
Welded flange
Full penetration welds:
- as-welded
- weld toe dressed (see 18.10.2.2);
Partial penetration welds:
- weld throat  0,8 x shell
thickness;
- weld throat < 0,8 x shell
thickness.
7.3
Set-in flange or pad
Full penetration weld:
- as-welded;
- weld toe dressed (see 18.10.2.2).
Weld made from one side:
UNI EN 13445-3:2021
549
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-4 — Class of weld details for use with structural equivalent stress range (concluded)
g) Flanges and pads
Class
Detail
No.
7.4
Joint type
Set-in flange or pad,
welded from both sides
Sketch of detail
Testing
group 1 or
2
Testing
group 3
Weld throat  0,8 x shell
thickness
63
63
Weld throat < 0,8 x shell
thickness
32
32
Comments
18.10.1.3 Classification of weld details to be assessed using principal stress range
Weld details and their corresponding classes for use in assessment based on principal stress range are given
in Annex P.
18.10.1.4 Exclusions
The classification tables do not include any bolts which are welded. The assessment method in this clause is
not applicable to such bolts.
18.10.2 Change of classification
18.10.2.1 Welds in testing group 3
Welds in testing group 3 shall be assessed according to the specific column "Testing group 3" in Table 18-4 or
to Tables P.1 to P.7.
18.10.2.2 Weld toe dressing
Fatigue cracks readily initiate at weld toes on stressed members partly because of the stress concentration
resulting from the weld shape but chiefly because of the presence of inherent flaws. The fatigue lives of
welds which might fail from the toe can be increased by locally machining and/or grinding the toe to reduce
the stress concentration and remove the inherent flaws.
The classification of fillet welds (including full penetration welds with reinforcing fillets) may, where
indicated in Tables 18-4 and Annex P, be raised when dressing of the toe is carried out according to the
following procedure. Tables 18-4 and Annex P include the revised class.
550
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 18-9— Weld toe dressing
The weld toe is machined using a rotating conical tungsten-carbide machining burr. In order to ensure that
weld toe flaws are removed, the required depth of machining is 0,5 mm below any undercut (see Figure 189). The area should be inspected using dye penetrant or magnetic particle. Such inspection is facilitated if the
machined toe is ground using emery bands, a measure which also improves fatigue life. The resulting profile
should produce a smooth transition from the plate surface to the weld, as shown in Figure 18-9, with all
machining marks lying transverse to the weld toe.
Toe dressing only affects the fatigue strength of a welded joint as regards failure from the weld toe. The
possibility of fatigue crack initiation from other features of the weld (e.g. weld root in fillet welds) should not
be overlooked.
Weld toe dressing cannot be assumed to be effective in the presence of any corrosive environment which
can cause pitting in the dressed region.
18.10.2.3Dressing of seam welds
Dressing or flush grinding of the seam welds justifies an upgrade from Class 80 to Class 90. A fatigue strength
higher than Class 90 cannot be justified because of the possible presence of weld flaws which are too small
for reliable detection by non-destructive inspection methods but are of sufficient size to reduce the fatigue
strength of the joint.
The detrimental effect of misalignment can, to some extent, be alleviated by weld toe dressing
(see 18.10.2.2).
Previously buried flaws revealed by dressing, which could reduce the fatigue strength of the joint, should be
assessed (see 18.10.5).
UNI EN 13445-3:2021
551
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18.10.3 Unclassified details
Details not fully covered in Table 18-4 and Annex P shall be treated as Class 32 unless superior resistance to
fatigue is proved by special tests or reference to relevant fatigue test results. To justify a particular design
R-N curve, at least two tests shall be performed on specimens that are representative of the design,
manufacture and quality of the relevant detail in the actual vessel. Test stress levels shall be chosen to result
in lives no more than 2 x 106 cycles. The geometric mean fatigue life obtained from the tests at a particular
stress range shall be not less than that from the R-N curve at that stress range multiplied by the factor F
from Table 18-6.
Table 18-6 — Values of the factor
F
Number of tests
F
2
15,1
3
13,1
4
12,1
5
11,4
6
11,0
7
10,6
8
10,3
9
10,1
10
9,9
NOTE
F is based on assumed standard deviation of log N of 0,283, the largest value found from fatigue tests
of pressure vessels failing from a weld detail. If a lower value is known to be applicable, it may be applied in
conjunction with the test factors presented in 20.6.3.
18.10.4 Deviations from design shape
Discontinuities and departures from the intended shape of a vessel (i.e. "misalignments") will cause local
increases in pressure-induced stresses in shells, as a result of secondary bending, and hence reduce fatigue
life. This is true even if the allowable assembly tolerances given in EN 13445-4:2021 are met.
Departures from intended shape include misalignment of abutting plates, an angle between abutting plates,
roof-topping where there is a flat at the end of each plate, weld peaking and ovality (see Figure 18-10). In
most cases these features cause local increases in the hoop stress in the shell but deviations from design
shape associated with circumferential seams cause increases in the longitudinal stress.
552
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 18-10 — Deviations from design shape at seam welds
NOTE
When stresses greater than yield arise as a result of deviation from design shape, the pressure test will
lead to an improvement in the shape of the vessel due to plastic deformation. However, vessels made from
materials with yield strengths considerably higher than the specified minimum are less likely to benefit in this
way. The beneficial effect of the pressure test on the shape of the vessel cannot be predicted and therefore if some
benefit is required in order to satisfy the fatigue analysis, it is necessary to measure the actual shape after
pressure test. Similarly, strain measurements to determine the actual stress concentration factor should be made
after pressure test.
The influence of misalignment shall be considered at the design stage using one of the following approaches.
In each case, the aim is to deduce assembly tolerances which are consistent with the required fatigue life.
a) Assume values for misalignment, calculate the resulting secondary bending stresses, and include
them in the calculation of structural stress for the detail under consideration. Adopt the class
from Table 18-4 or Tables in Annex P and check the fatigue life. If unacceptable, tighten some or
all of the tolerances to meet the required life;
b) For a detail of nominal class Ccla1, determine the class actually needed to meet the required
fatigue life, Ccla2. Then, the allowable increase in stress due to misalignments is Km = Ccla1/Ccla2.
Assembly tolerances which result in Km Ccla1/Ccla2 can then be deduced.
A conservative estimate of Km is:
UNI EN 13445-3:2021
553
EN 13445-3:2021 (E)
Issue 1 (2021-05)
K
 1  A1  A 2  A 4
m
for cylinders
(18.10-1)
or
K m  1  A 1  A 3  A 4 for spheres
(18.10-2)
where
— A1 caters for axial misalignment and is given by:
x
 61
e n1
A1  

 e n 1   e x  e x
n1
n2




(18.10-3)
where
1
is the offset of the centre lines of abutting plates;
en1  en2 where en1 and en2 are the nominal thicknesses of the two abutting plates;
is 1,5 for a sphere or circumferential seam in a cylinder and 0,6 for a longitudinal seam in a
cylinder.
x
— A2 caters for ovality in cylinders and is given by:
A2 
3  R max  R min 

(18.10-4)

3
2

P 1
 2 R  
e 1 

 
2E
 e n  

where
R
is the mean radius
— A3 caters for poor angular alignment of plates in spheres and is given by:
 R 

 en 
0 ,5
 
A3 
(18.10-5)
49
where

is the angle (in degrees) between tangents to the plates, at the seam (see Figure 18-10(c);
— A4 caters for local peaking and is given by:
A4 
6
en
(18.10-6)
where

554
is the deviation from true form, other than above, and other terms are defined in Figure 18-10.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
This estimate of A4 ignores the beneficial reduction of the peaking due to pressure and is therefore
conservative. Corrections due to non-linear effects, which reduce A4 , are permissible (See reference [11] in
Annex N).
In the case of seam welds, the incorporation of a transition taper at a thickness change does not affect the
value of A1.
Formula (18.10-1) will overestimate Km if local bending is restricted, for example: at short shape
imperfections, when there will be a stress redistribution around the imperfection; at imperfections in short
cylindrical vessels, which can get support from the ends; adjacent to attachments which stiffen the shell.
However, special analysis shall be performed to justify lower Km values.
18.10.5 Welding flaws
Fatigue cracks can propagate from welding flaws and, therefore, depending on the required fatigue life, the
flaws tolerated in EN 13445-4:2021 and EN 13445-5:2021 of this standard for non-cyclic operation may or
may not be acceptable. Thus, in fatigue-loaded vessels the following apply:
a) Planar flaws are unacceptable;
b) Acceptance levels for embedded non-planar flaws and geometric imperfections of critical areas
are given in EN 13445-5:2021, Annex G. Fatigue critical areas are those for which the cumulative
fatigue damage index D (see 18.5.6) is greater than Dmax:
(18.10-7)
D  D max
With
D
D
D
= 0,8 for 500 <
max
ne q
= 0,5 for 1 000 <
max
= 0,3 for
max
ne q
 1 000
ne q
(18.10-8)
 10 000
> 10 000
(18.10-9)
(18.10-10)
NOTE
All other flaws can be assessed using an established fitness-for-purpose flaw assessment method, such
as that in reference [8] in Annex N. The fatigue strengths of welds containing flaws can be expressed in terms of
the classification system in 18.10.1. 3. Thus, they can be readily compared with those of other weld details.
18.10.6 Correction factors
18.10.6.1 To take account of material thickness en > 25 mm, few shall be calculated as follows:
f
ew
=
 25 


 en 
0 ,2 5
(18.10-11)
where en refers to the thickness of the stressed member under consideration or the thickest part of the
detail if this is not clear.
For en  25 mm, few = 1.
UNI EN 13445-3:2021
555
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For en > 150 mm, the value few = 0,6389 corresponding to en = 150 mm applies.
NOTE 1
In all cases, fatigue cracking from the toe of the weld in the stressed member is being considered. Thus,
the correction is not required (i.e. few = 1) for some details, see Tables 18-4 and Annex P, or fe should be used
instead.
18.10.6.2 For temperatures T* exceeding 100 °C, fT* is given by:
— for ferritic materials:
f T *  1, 03  1, 5  10
4
T *  1, 5  10
6
T *
(18.10-12)
2
— and for austenitic materials:
f T *  1, 043  4 , 3  10
4
(18.10-13)
T *
where
(18.10-14)
T *  0 , 75  T max  0 , 25  T min
For temperatures T* not exceeding 100 °C, fT* = 1.
NOTE 2 Temperatures in 18.10.6.2 are all in degrees Celsius.
fT* is illustrated in Figure 18-11.
18.10.6.3 The overall correction factor for welded components,
f
w
 f
ew
f
fw
, shall be calculated as follows:
(18.10-15)
T *
Key
1 Ferritic
2 Austenitic
T* Mean cycle temperature, C
Figure 18-11 — Correction factor fT*
556
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18.10.7 Fatigue design curves
Fatigue strength is expressed in terms of a series of R-N curves in Figure 18-12, each applying to particular
construction details. The curves are identified by the fatigue strength value R (MPa) at fatigue life
N = 2 × 106 cycles.
NOTE 1
The curves have been derived from fatigue test data obtained from appropriate laboratory specimens,
tested under load control or, for applied strains exceeding yield (low cycle fatigue), under strain control.
Continuity from the low to high cycle regime is achieved by expressing the low cycle fatigue data in terms of the
pseudo-elastic stress range (i.e. strain range multiplied by elastic modulus, if necessary corrected for plasticity
(see 18.8)). The failure criterion on which these curves are based is break-through of the weld or parent metal (to
an extent that in a pressure retaining component a measurable leak exists). Such data are compatible with results
obtained from pressure cycling tests on actual vessels.
NOTE 2
The fatigue strength design curves are approximately three standard deviations of log N below the
mean curve, fitted to the original test data by regression analysis. Thus, they represent a probability of failure of
approximately 0,14 %.
The design curves have the form as shown in Figure 18-13 and conform to the Formula ((18.10-16):
N =
C
R
(18.10-16)
m
where
m and C are constants whose values are given in Table 18-7.
Different values apply for fatigue lives up to 5 x 106 cycles and for lives above 5 x 106 cycles. For constant
amplitude loading, the endurance limit D (see definition in 18.2.12) corresponds to the stress range at
5 x 106 cycles. For variable amplitude loading, the cut-off limit Cut (see definition in 18.2.13) is that at
108 cycles. The values taken by D and Cut for each fatigue curve are given also in Table 18.7.
NOTE 3
Alternative curves and constant amplitude endurance limits are permissible if they can be justified. For
lives above 2 × 106 cycles the curves, which are consistent with reference [9] of Annex N, are conservative.
To obtain the permissible number of load cycles, N, at a specified stress range, eq or , the following
shall be calculated.
If
  eq
  D
fw
N
or

fw
  D
then
C1

   eq 


 fw 
m1
(18.10-17)
or
N 
C1
 

 f
 w




m1
UNI EN 13445-3:2021
(18.10-18)
557
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where C1 and m1 are the values applicable to the range N  5 x 106 cycles.
If


Cut

eq
fw
 
D
or

Cut


fw
 
D
:
— in case where all applied stress ranges are smaller than D then N = infinity (i.e. fatigue damage
contribution n/N in Formula (18.5-1) is zero).
— in all other cases, N is given by:
C2
N 
   eq 



 fw
(18.10-19)
m2
or
C2
N 
  


 fw 
(18.10-20)
m2
where
C2 and m2 are the values applicable to the range N > 5 x 106 cycles.
If

eq
fw
 
Cut
or

fw
   Cut
then N = infinity (i.e. fatigue damage contribution n/N in Formula (18.5-1)
is zero).
Alternatively, for use as a design curve to obtain the allowable stress range eq or  for a specified
number of applied load cycles, n,
1

eq
or
  
R
 fw
 C1 
 

 n 
m1
 fw
(18.10-21)
for n  5 x 106 cycles.
For n > 5 x 106 cycles, the allowable stress range is D.
NOTE 4
The interest in determining the allowable stress range for a specified number of applied load cycles n
exists only in the case of constant cyclic amplitude. In the case of variable amplitude loading, fatigue assessment
requires calculation of the cumulative damage due to all cycle types. This can be performed only using the
allowable number N of each type of cycles, not their allowable stress ranges.
558
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
(1) Curves for assessing variable amplitude loading.
(2) For constant amplitude loading, endurance limit D at 5 x 106 cycles.
NOTE
For N>2 x 106 cycles, alternative curves and R values are permissible, see NOTE 3 in 18.10.7.
Figure 18-12 — Fatigue design curves for welded components
Figure 18-13 — Form of the fatigue design curves for welded components
UNI EN 13445-3:2021
559
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-7 — Coefficients of the fatigue design curves for welded components
Constants of R - N curve*
Class
Stress range at N cycles,
MPa
For 102 < N < 5x106
For 5x106 < N < 108
N = 5 x 106
N = 108
m1
C1
m2
C2
D
Cut
100
3,0
2,00 x 1012
5,0
1,09 x 1016
74
40
90
3,0
1,46 x 1012
5,0
6,41 x 1015
66
36
80
3,0
1,02 x 1012
5,0
3,56 x 1015
59
32
71
3,0
7,16 x 1011
5,0
1,96 x 1015
52
29
63
3,0
5,00 x 10
11
5,0
1,08 x 10
15
46
26
56
3,0
3,51 x 1011
5,0
5,98 x 1014
41
23
50
3,0
2,50 x 1011
5,0
3,39 x 1014
37
20
45
3,0
1,82 x 1011
5,0
2,00 x 1014
33
18
40
3,0
1,28 x 1011
5,0
1,11 x 1014
29,5
16
32
3,0
6,55 x 1010
5,0
3,64 x 1013
24
13
* For E = 2,09 × 105 MPa
18.11 Fatigue strength of unwelded components
18.11.1 Correction factors
18.11.1.1 Surface finish correction factor
To take account of surface finish, fs shall be calculated as follows:
f
( 0 ,1 ln N  0 , 465 )
s
 Fs
 Fs
6
if N  2 x 10
(18.11-1)
cycles
where
F s  1  0 ,0 5 6  ln R z
and
Rz

0 ,6 4
 ln R m  0 ,2 8 9  ln R z

0 ,5 3
(18.11-2)
is the peak-to-valley height (m).
NOTE The value Fs given by Formula (18.11-2) does not apply to deep drawn components and forgings.
If not specified, the manufacturing-related peak-to-valley heights in Table 18-8 shall be used in
Formula (18.11-2).
For polished surfaces with a peak-to-valley height Rz < 6 m, assume fs = 1. Values of fs for as-rolled plate are
given in Figure 18-14.
560
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table 18-8 — Base values for peak-to-valley heights
Surface condition
RZ
Rolled or extruded
200
Machined
50
Ground, free of notches
10
Key
N
Fatigue life cycles.
Figure 18-14 — Correction factor fs for as-rolled plates
18.11.1.2Thickness correction factor
For wall thicknesses 25 mm < en
fe is:
( 0 ,1 ln N  0 , 465 )
f e F e
 Fe
if N  2 x 10
6
(18.11-3)
cycles
where
F
e
 25 

= 
 e 
 n 
0,182
(18.11-4)
For en > 150 mm, the value of fe for e = 150 mm applies.
18.11.1.3Correction factor to take account of the influence of mean stress
18.11.1.3.1 Full mean stress correction (purely elastic behaviour)
For

eq
 2 R p0,2/T
*
and 
eq max <
Rp0,2/T* , the mean stress correction factor fm for N  2 × 106 cycles is to
be determined for rolled and forged steel as a function of the mean stress sensitivity M from:
UNI EN 13445-3:2021
561
EN 13445-3:2021 (E)
Issue 1 (2021-05)
M  2  M   2  eq  

f m  1 


1 M
  R 

for
 R p0,2/T
 
*

eq

0 ,5
(18.11-5)
R
2 (1  M )
or
fm 
for

1 M /3
1 M
R
2 (1  M )

M  2  eq 


3   R 

 R p0,2/T
eq
(18.11-6)
*
where for rolled and forged steel:
M = 0 ,0 0 0 3 5 R m - 0 ,1
(18.11-7)
For N  2 × 106 cycles, fm shall be taken from Figure 18-15.
NOTE
In this case, fm is independent of stress range.
18.11.1.3.2 Reduced mean stress correction (partly plastic behaviour)
For

eq
 2 R p0,2/T
*
andeq max > Rp 0,2/T* , Formula (18.11-5) or (18.11-6) shall also be used to determine
fm, although the reduced mean equivalent stress, as calculated from Formula (18.11-8) or (18.11-9) shall be
used instead of
If

 0
eq

eq, r

. See Figure 18-6.
eq
,
= R
p 0.2/ T *
-

eq
(18.11-8)
2
If  eq  0 ,

eq, r
=

eq
2
(18.11-9)
 R
p 0.2/ T *
18.11.1.3.3 No mean stress correction (plastic cycling)
For

eq
 2 R p0,2/T
*
, then 
eq
 0
and fm=1. In that case, a plasticity correction of the stress range is
required (see 18.8).
562
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
 eq
mean equivalent stress, MPa
Figure 18-15 — Correction factor fm to take account of mean equivalent stress in
unwelded material for N > 2x106 cycles
18.11.2 Overall correction factor for unwelded components
The overall correction factor for unwelded components, f u, shall be calculated as follows:
(18.11-10)
fu  fs  fe  fm  fT *
in which fs, fe, and fm are given in 18.11.1.1 to 18.11.1.3 respectively; and fT* is given in 18.10.6.2.
18.11.3 Design data
R-N curves,
each
applying to a particular tensile strength of steel, as given in Figure 18-16.
NOTE 1
The curves have been derived from fatigue test data obtained from unnotched polished ferritic and
austenitic rolled and forged steel specimens at room temperature, under alternating (mean load = 0) load control
or, for applied strains exceeding yield (low-cycle fatigue), strain control. The failure criterion on which these
curves are based is (macro) crack initiation (with crack depth of approximately 0,5 mm to 1,0 mm).
NOTE 2
Compared with the mean curve fitted to the original data, the curves incorporate safety factors of 10 on
fatigue life and 1,5 on stress range.
The fatigue design curves in Figure 18-16 are given by:
N =


   R
4 ,6 . 1 0 4
- 0 ,6 3 R m


+ 1 1,5 
2
(18.11-11)
for lives up to 2 x 106 cycles.
UNI EN 13445-3:2021
563
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For cumulative damage calculations using Formula (18.5-1), the curves are linear for N = 2 x 106 to 108 cycles,
and are given by:
N 
 2 , 69 R m  89 ,72 


 R


10
(18.11-12)
Values of the endurance limit D and cut-off limit Cut for selected tensile strengths are given in Table 1810.
To obtain the allowable number of load cycles, N, at a specified stress range f, the following applies.
If

f
 
fu
:
D


46000
N  
  f
 0 , 63 R m  11 ,5

 fu
If

Cut


f
fu
 
D






2
(18.11-13)
:
— in case with constant amplitude loading where the only applied stress range /fu is D and in
case of
variable amplitude loading (cumulative damage) where all applied stress ranges f/fu
are < D then
N = infinity (i.e. fatigue damage contribution n/N in Formula (18.5-1) is zero);
— in all other cases with variable amplitude loading (cumulative damage):

 2 , 69 R
m  89 ,72
N  
 f


fu
If
 f
fu
   Cut





10
(18.11-14)
: N = infinity (i.e. fatigue damage contribution n/N in Formula (18.5-1) is zero).
Alternatively, for use as a design curve to obtain the allowable stress range for a specified number of load
cycles, n, which is the upper limit for the acting stress range f.
for n  2×106 :
 46000
  f, all    R  f u  
n


(18.11-15)
 0,63R m  11,5   f u

For n > 2×106, the allowable stress range is that given by Formula (18.11-15) for n = 2×106.
564
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 3
The interest of determining the allowable stress range for a specified number of applied load cycles n
exists only in case of constant cyclic amplitude. In case of variable amplitude loading, fatigue assessment requires
calculation of the cumulative damage due to all cycle types, which can be performed only using the allowable
number N of each type of cycles, not their allowable stress ranges.
Table 18-10 — Stress range R for N  2 x 106 cycles for unnotched test bars of ferritic and
austenitic rolled and forged steels at room temperature and zero mean stress
Tensile strength
Stress range at N cycles, MPa
Rm ,
MPa
N  2x106
N  108
D
Cut
400
273
185
600
399
270
800
525
355
1000
651
440
Key
N
Fatigue life cycles.
Figure 18-16 — Fatigue design curves for unwelded ferritic and austenitic forged
and rolled steels (mean stress = 0)
18.12 Fatigue strength of steel bolts
18.12.1 General
These requirements apply only to axially-loaded steel bolts. They do not apply to other threaded
components such as flanges, ends or valves.
UNI EN 13445-3:2021
565
EN 13445-3:2021 (E)
Issue 1 (2021-05)
18.12.2 Correction factors
18.12.2.1 For bolt diameters > 25 mm, the correction factor fe shall be calculated using Formula (18.113), with en put equal to the bolt diameter. For bolt diameters  25 mm, fe = 1.
18.12.2.2 Overall correction factor for bolts
fb shall be calculated as follows:
(18.12-1)
fb  fe  fT *
in which fe is given in 18.12.2.1 and fT* is given in 18.10.6.2.
18.12.3 Design data
The fatigue strength of axially loaded bolts is expressed in terms of the ratio:
m a x im u m n o m in a l s tre s s ra n g e
n o m in a l u ltim a te te n s ile s tre n g th o f b o lt m a te ria l
=

Rm
The single design curve
  R 


 Rm 
3
(18.12-2)
 N  285
with an endurance limit
 D
Rm
= 0,0522 at 2 × 106 cycles, shown in Figure 18-17, is used for any thread form
(machined, ground or rolled) and core diameters up to 25 mm. However, regardless of the actual tensile
strength of the bolt material, a value of Rm greater than 785 MPa shall not be used in the calculations.
566
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
N
Fatigue life cycles.
Figure 18-17 — Fatigue design curve for bolts
NOTE
The design curve has been derived from fatigue test data obtained from axially-loaded threaded
connections. The design curve is three standard deviations of log N below the mean curve, fitted to the original
test data by regression analysis. Thus, the curve represents a failure probability of approximately 0,1 %.
To obtain the allowable number of load cycles, N, at a specified stress range, :
If

Rm
 0 ,0522
:
 R m  fb 
N  285 

 

If

Rm
 0 ,0522
3
(18.12-3)
: N = infinity (i.e. fatigue damage contribution n/N in Formula (18.5-1) is zero).
Alternatively, for use of the design curve to obtain the allowable stress range, , for a specified number of
load cycles, n,
1
  
R
 fb  R m
 285 


 n 
3
(18.12-4)
for n  2106.
For n > 2106, the allowable stress range is that which corresponds to the endurance limit:
 = D = 0,0522Rm.
UNI EN 13445-3:2021
567
EN 13445-3:2021 (E)
Issue 1 (2021-05)
19 Creep design
19.1 Purpose
This clause is for the design of vessels or vessel parts if the calculation temperature is in the creep range. It
may be applied for pressure and mechanical loading.
NOTE 1
A definition of the creep range is given in 3.8. See also 5.1b.
NOTE 2
A pre-supposition of the requirements in this clause is usage of sufficiently creep ductile materials. In
that regard, the steels and steel castings listed in Table E.2-1 of EN 13445-2:2021 for which, for the relevant
temperature range, creep strengths are given in the referred to material standards, are considered to be
sufficiently creep ductile.
19.2 Specific definitions
period
duration of a load case with constant loading and constant temperature inside the creep range.
Note 1 to entry: All individual intervals of time with identical creep conditions (same temperature and same
applied loading) occurring separately during the vessel life should be grouped to form a unique period.
single creep load case
case where only one period occurs in the whole lifetime of the vessel.
multiple creep load case
case where more than one period occur in the whole lifetime of the vessel.
lifetime monitoring
requirements for control and examination as stated in the operating instructions with the minimum
requirement for continuous recording of pressure and temperature and retention of records.
Note 1 to entry: See Annex M for guidance.
19.3 Specific symbols and abbreviations
is the total number of periods of
n
SF
f
Fi
, Ti .
is the safety factor for mean creep rupture strength (see 19.5.1 and 19.5.2)
c
R p1,0/ T / t
is the mean 1% creep strain limit at calculation temperature T and lifetime
R m/ T
is the mean creep rupture strength at calculation temperature T and lifetime
NOTE
/t
t
The creep rupture strengths given in harmonised material standards are always mean values.
T
is the calculation temperature in °C
t
is the specified lifetime in hours (h) of the pressure vessel (see 19.4)
568
t
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
t
is the duration (h) of the i-th period, during which the fictitious design stress
i
f
Fi
acts at the
calculation temperature T i .
t
D, f
Fi
,T
is the allowable time (h) to damage (caused by creep rupture or creep strain) for the
i
material at fictitious design stress
f
Fi
and temperature T i , taken from the creep design
curve or Formula (19-11) respectively.
t
P ,f
Fi
,T
is the allowable time (h) to reach the 1% creep strain limit for the material at fictitious
i
design stress
t
R ,f
Fi
,T
f
Fi
and temperature T i calculated according to Formula (19-20).
is the allowable time (h) to creep rupture for the material at fictitious design stress
i
f Fi
and
temperature T i calculated according to Formula (19-12) or (19-17) respectively.
f
is the fictitious design stress for creep design of the i-th period, as defined
Fi
in 19.8.2.
f
is the nominal design stress based solely on time independent behaviour, as defined
nc
in 19.5.1
z
is the weld creep strength reduction factor, as defined in 19.6.
c
19.4 Design in the creep range
This sub-clause applies for the design by formula in Clauses 7, 9, 10, 11, 12, 15 and 16 with the exception of
bolts according to Clauses 11 and 12 and the exception of compressive stresses in 16.14.
For Clauses 8, 13, 16.14 and Annexes G and J the design in the creep range is only applicable as far as the
modulus of elasticity is known in the creep range. In this case in Clause 8 the minimum yield strength
R
R
p0 ,2 / T
has to be replaced by
p 1,0 / T / t
1,3
.
— When the vessel has to be designed for a single creep load case only: the design procedure
described in 19.8.1 shall be used. This procedure is based on use of the nominal design stress
defined in 19.5. For determination of that nominal design stress, the lifetime t = 100 000 h shall be
used if no lifetime t is specified.
— When the vessel has to be designed for multiple creep load cases: the design procedure based on
cumulative damage described in 19.8.2 shall be used. Alternatively, a simplified and conservative
design may also be made, using the procedure described in 19.8.1, replacing the various applied
creep load cases by a unique one whose temperature shall be the highest among all individual creep
load cases and whose duration shall be the total of that of all individual creep load cases.
In both procedures, the weld joint factor shall be modified by the weld creep strength reduction factor
according to 19.6.
UNI EN 13445-3:2021
569
EN 13445-3:2021 (E)
Issue 1 (2021-05)
19.5 Nominal Design stress in the creep range
19.5.1 Case where no lifetime monitoring is provided
19.5.1.1 General
R

m /T/ t

f  min  f
;
;R
nc
p 1, 0 / T / t
SF

c






(19-1)
where:
SF
c
 1,5
Determination of
f nc
shall be made in accordance with Clause 6, with the following provisions:
— For calculation temperatures T not exceeding by more than 200 °C the highest temperature T H at
which material characteristics are available in the material standard, extrapolated values of f nc can
be taken as given in Annex S.
— For calculation temperatures T  T H  200  C the nominal design stress f nc shall be ignored in
Formula (19-1) and the further terms in this formula shall be determined for a lifetime not shorter
than the lowest lifetime for which material creep characteristics are available in the material
standard.
NOTE
The extrapolated values given in Annex S for T  T H  200 C are useful only for determination of the
hydrotest pressure (See 10.5.3.3 in EN 13445-5:2021)
19.5.1.2 Case where material creep characteristics are available for the specified lifetime but
not for the calculation temperature
19.5.1.2.1 General
In the case where for the calculation temperature T no mean creep rupture strength or no mean 1% creep
strain limit is available in the harmonised materials standard, the interpolation Formulae (19-2), (19-3) or
(19-5), (19-6) respectively may be used (or the value in the harmonised material standard for the higher
temperature may be used as a conservative value) to determine the appropriate creep characteristics.
If the calculation temperature is higher than the highest temperature for which a mean creep rupture strength or a
mean 1 % creep strain limit is available, application of Clause 19 is not permitted.
19.5.1.2.2 Mean creep rupture strength
R
R
m /T/ t

m/ T / t
1
 (T
2
T) R
(T
2
m/ T
T )
1
R
 m/ T 2 / t
R
 R

m / T/ t
m/ T / t 
1
 R m/ T / t
1

Z
 R




2
/t
 (T  T )
1
for T2-T1 ≤ 20 °C
(19-2)
for T2-T1 > 20 °C
(19-3)
where:
570
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Z
R

lg T  lg T
lg T
2
1
 lg T
with:
lg  log
(19-4)
10
1
T1
is the nearest temperature below T for which a mean creep rupture strength is available in
the harmonised material standard
T2
is the nearest temperature above T for which a mean creep rupture strength is available in
the harmonised material standard
19.5.1.2.3 Mean 1% creep strain limit
R
R

p1,0/T/t
p1,0/ T / t
1
 (T
2
T ) R
(T
2
p1,0/ T
T )
1
R
 p1,0/ T 2 / t
R
 R

p1,0 / T / t
p1,0/ T / t
1
 R p1,0/ T / t
1






Z
2
/t
 (T  T )
1
for T2-T1 ≤ 20 °C
(19-5)
for T2-T1 > 20 °C
(19-6)
P
where:
Z
P

lg T  lg T
lg T
2
1
 lg T
with:
lg  log
10
1
T1
is the nearest temperature below T for which a mean 1 % creep strain limit is available in
the harmonised material standard
T2
is the nearest temperature above T for which a mean 1 % creep strain limit is available in
the harmonised material standard.
19.5.1.3 Case where material creep characteristics are available for the calculation
temperature (including cases where these values are calculated by 19.5.1.2) but not for
the specified lifetime t
19.5.1.3.1 General
In the case where for the specified lifetime t no mean creep rupture strength value or no mean 1 % creep
strain limit is available in the harmonised material standard the interpolation Formula (19-7) or (19-9)
respectively may be used (or the value in the harmonised material standard for a lifetime longer than the
specified lifetime can be used as a conservative value) to determine the appropriate creep characteristics.
In the case where the specified lifetime t is longer than the highest lifetime for which a mean creep rupture
strength is available in the harmonised materials standard, the extrapolation method given in the
informative Annex R may be applied.
In the case where the specified lifetime t is longer than the highest lifetime for which a mean 1 % creep
strain limit is available in the harmonised material standard, the value for the highest lifetime for which a
mean 1 % creep strain limit is available shall be used in Formula (19-1).
NOTE
In the case of the last paragraph, the accumulated creep strain may exceed the 1 % limit before the end
of the lifetime.
UNI EN 13445-3:2021
571
EN 13445-3:2021 (E)
Issue 1 (2021-05)
19.5.1.3.2 Mean creep rupture strength
 R
 m/ T / t B
R
 R

m/ T / t
m/ T / t A  R
 m/ T / t
A






X
R
(19-7)
where:
X
R
R

lg t  lg t
lg t
m /T / t
B
A
A
 lg t
with:
lg  log
(19-8)
10
A
is the mean creep rupture strength for the nearest lifetime
t
A
below
t
for which a
B
above
t
for which a
mean creep rupture strength is available
R
m/ T / t
is the mean creep rupture strength for the nearest lifetime
B
t
mean creep rupture strength is available
In the case where the specified lifetime t is shorter than the lowest lifetime for which a mean creep rupture
strength is available in the material standard, then the following terms may be used in Formulae (19-7) and
(19-8) respectively:
R
m/ T / t
A
and
t
R
B
m/ T / t
B
are the mean creep rupture strengths for the two shortest lifetimes
t
A
and
for which a mean creep rupture strength is available
An alternative method for extrapolation to shorter time is given in Annex R.
19.5.1.3.3 Mean 1 % creep strain limit
R
p 1,0 / T / t
 R
 p 1,0 / T / t B
 R

p 1,0 / T / t A 
 R p 1,0 / T / t
A






X
P
(19-9)
where:
X
R
P

lg t  lg t
lg t
p1,0 / T / t A
B
A
 lg t
with:
lg  log
10
A
is the mean 1 % creep strain limit for the nearest lifetime
t
A
below
t
for which a mean 1 %
creep strain limit is available
R
p1,0 / T / t B
is the mean 1 % creep strain limit for the nearest lifetime
t
B
above
t
for which a mean 1 %
creep strain limit is available
In case where the specified lifetime t is shorter than the lowest lifetime for which a mean 1 % creep strain
limit is available in the material standard then the third term (creep strain) within the minimum in
Formula (19-1) does not apply.
NOTE
572
In that case the accumulated creep strain may exceed the 1 % limit before the end of the lifetime.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
19.5.1.4 Case where material creep characteristics are available neither for the calculation
temperature nor for the specified lifetime:
In the case where values for creep characteristics are not available in the material standard for both the
calculation temperature T and the specified lifetime t , the nominal design stress shall be determined using
19.5.1.2 first and 19.5.1.3 afterwards.
A typical form for the creep design curve showing the nominal design stress
calculation temperature T is shown in Figure 19-1.
f
as a function of lifetime
t
and
Key:
1) maximum time
2) longest time
t
B
t
R, T , max
i
 2 t
B
for which linear log-log extrapolation versus time is allowed
for which time depending creep strength data are available in the materials
standard
a) curve of time dependent material characteristics
b) curve of short time (time independent) material characteristics
Figure 19-1 — Typical creep design curves for explanation of the method
19.5.2 Case where lifetime monitoring is provided
Nominal design stress in the creep range shall be calculated using Formula (19-10):
R

m /T/ t

;
f  min  f
nc
SF

c




(19-10)
where:
UNI EN 13445-3:2021
573
EN 13445-3:2021 (E)
Issue 1 (2021-05)
SF
NOTE
c
 1,25
See informative Annex M for monitoring.
19.6 Weld joint factor in the creep range
In the creep range, the value of the weld joint factor z to be used in the relevant design formulae shall be
that defined in Table 5.6-1 multiplied by the weld creep strength reduction factor z c .
NOTE
For vessels working in the creep range the testing sub-groups 1c and 3c only are allowed, see EN
13445-5:2021.
The values for the weld creep strength reduction factor shall be:
z c  1,0
determined by tests according to Annex C of EN 13445-2:2021 if the conditions for the value 1
are fulfilled
z c  1,0
determined by tests according to Annex C of EN 13445-2:2021 if the conditions for the
value 1 are not fulfilled
z c  0 ,8
otherwise, except for specific cases where the literature or industrial feedback indicates a
lower value
19.7 Pressure loading of predominantly non-cyclic nature in the creep range
The requirement for pressure loading of non-cyclic nature given in 5.4.2 is considered to be met (i.e. the
number of full pressure cycles or equivalent full pressure cycles is less than 500) when the vessel design
fulfils all relevant formula in clauses defined in 19.4, making use of the nominal design stress determined as
defined in 19.5.
NOTE
In the present edition of the standard no rule concerning creep/fatigue interaction is given in this
clause. If this interaction is to be taken into account, the design methods of Annex B may be used.
19.8 Design procedures for DBF
19.8.1 When the vessel has to be designed for a single creep load case only, f shall be obtained from
19.5 and the required component thickness shall be determined or checked according to the clauses of
this Part defined in 19.4.
19.8.2 When the vessel has to be designed for multiple creep load cases an assessment of the
cumulative creep damage resulting from all creep load cases occurring during the lifetime of the vessel
shall be made, according to the following procedure:
a) An analysis thickness
NOTE 1
e
a
The assumed thickness
for the component shall be assumed.
e
should at least be equal to the largest thickness found necessary through
a
the calculations made in application of 19.8.1 for the load cases of greatest significance. During application of the
given procedure this start value will be increased as far as necessary.
b) For each load case,
e
a
is inserted into the relevant DBF formulae (clauses defined in 19.4) and the
formulae solved for the fictitious design stress for creep design
exactly. This fictitious stress
574
f
Fi
f
Fi
which gives the thickness
is the minimum value for the design stress
f
e
a
which fulfils all the
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
design conditions of the relevant clause of this Part for the analysis thickness
e
a
and for the load
case i under consideration.
NOTE 2
This may require a trial and error calculation.
c) For each load case, the allowable time to damage,
t
D, f
Fi
,T
i
shall be calculated according to the
following procedure:
1) If fFI  fnc then
e
shall be increased (tD, f
Fi, Ti
a
= 0)
2) If fFI  fnc then:
t
D, f
,T
Fi


 min  t
;t
R, f , T
P, f , T 
Fi i
Fi i 

i
(19-11)
3) Allowable time to creep rupture:
t
R ,f
Fi
,T
 t
i


A 

Y
 R
B 

t
A 
t
(19-12)
where:
lg( f
y

R
Fi
lg( f
Rt
)  lg( f
Rt
A
)  lg( f
Rt
B
A
)
with:
)
lg  log
(19-13)
10
with:
R
f
Rt

m/ T / t
i A
SF
A
(19-14)
c
and:
R
f
Rt

m/ T / t
i B
SF
B
(19-15)
c
fRt and fRt being the closest values to fFI with the corresponding lifetimes tA and tB, as defined in 19.5.1.3,
A
B
which fulfil the condition:
fRt  fFI  fRt
A
If
f
Fi
(19-16)
B
is smaller than the smallest available value fRt (this is the value at the longest lifetime for which mean
B
creep rupture strength is available in the material standard) then the following formula shall be used instead
of Formula (19-12):
t
R ,f
Fi
,T
i


 min  t
;t
R , f ,T , ex R , T , max 
Fi i
i


(19-17)
where:
UNI EN 13445-3:2021
575
EN 13445-3:2021 (E)
Issue 1 (2021-05)
tR,f
is the allowable time (h) to damage (caused by creep rupture) for the material at fictitious
Fi,Ti,ex
design stress fFI and temperature
T
i
which may be calculated according to the informative
Annex R.
tR,T ,max is the maximum time for which the extrapolation method used is valid (the informative
i
Annex R may be used)
Alternatively the following formulae may be used:
t
 2 t
R, T , max
i
(19-18)
B

t
 t

R , f ,T , ex
A 
Fi i

Y
 R
B 
t 
A 
t
(19-19)
where:
tB is the longest lifetime for which a mean creep rupture strength is available in the material standard
tA is the next lower lifetime which a mean creep rupture strength is available in the material standard
YR as given in Formulae (19-13) until (19-15) calculated for the here defined lifetimes tA and tB
NOTE 3
The extrapolation is not based on experimental verification. Possible changes in the long term creep
strength due to micro-structural changes are not considered.
NOTE 4
It is advisable to determine as far as possible the complete creep design curve versus lifetime for the
needed calculation temperatures (see Figure 19-1) for a better overview to find the relevant times tA and tB for
which condition (19-16) or (19-24) respectively is fulfilled.
4) Allowable time to reach the 1 % creep strain limit.
This allowable time shall be calculated only if no monitoring is provided. If monitoring is provided tp,f
Fi,Ti
shall be omitted in Formula (19-11).
t
P, f
Fi
,T
i
 t


A 

Y
 P
B 

t
A 
t
(19-20)
where:
y

P
lg( f )  lg( f
Fi
Pt
lg( f
Pt
B
A
)  lg( f
Pt
)
A
)
with:
lg  log
10
(19-21)
with:
f
Pt
 R
A
p1,0/ T / t
i A
(19-22)
and:
576
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
f
Pt
 R
B
fPt and fPt being the closest values to
A
(19-23)
p 1,0 / T / t
i B
B
f
Fi
with the corresponding lifetimes tA and tB, as defined in 19.5.1.3,
which fulfils the condition:
fPt  fFI  fPt
A
If
f
Fi
(19-24)
B
is smaller than the smallest available value fPt (this is the value at the longest lifetime for which mean
B
1 % creep strain limit is available in the material standard) then tp,f
Fi,Ti
may be omitted in Formula (19-11).
NOTE 5
If more than one material in the creep range is used in the part or component under consideration,
then a more general procedure should be used. The aim of this procedure is to search the allowable time to
damage tD,f ,T for which (using the different f values according to 19.5 for the different materials at t = tD,f ,T ) all
Fi
i
the design conditions and formulae are fulfilled for the analysis thickness
Fi
e
a
i
and for the load case i under
consideration.
d) The accumulated creep damage resulting from all applied load cases shall be determined by the
following time-fraction rule:
n
t
i
 1 ,0

t
i  1 D, f , T
Fi i
(19-25)
e) If condition (19-25) is not fulfilled the assumed thickness shall be increased and the procedure
shall be repeated starting from b).
If the quantity on the left hand side of Formula (19-25) does not reach the value of 1,0 the assumed
thickness may be decreased and the procedure shall be repeated starting from b).
20 Design rules for reinforced flat walls
20.1 General
Flat walls may be reinforced either by stays and staybolts, which are intended to take a fraction of the
pressure load acting on the wall (Stayed Flat Walls), or by stiffeners welded to the same in order to increase
their section modulus and their moment of inertia (Stiffened Flat Walls).
20.2 Stayed flat walls
Design requirements for stayed flat walls are provided in 20.1 to 20.8. Requirements for the plate thickness
and requirements for the staybolt or stay geometry including size, pitch, and attachment details are
provided.
20.3 Specific definitions for stayed flat walls
C
is the stress factor for braced and stayed surfaces (see Table 20.8-1).
UNI EN 13445-3:2021
577
EN 13445-3:2021 (E)
Issue 1 (2021-05)
p
is the maximum pitch. The maximum pitch is the greatest distance between any set of parallel straight
lines passing through the centres of staybolts in adjacent rows. Each of the three parallel sets running in
the horizontal, the vertical, and the inclined planes shall be considered.
20.4 Required thickness of stayed flat walls
20.4.1 The minimum thickness for stayed flat walls and those parts that, by these rules, require staying
as flat plates with braces or staybolts of uniform diameter symmetrically spaced, shall be calculated by
the following formula.
e  p
P
fC
(20.4.1)
20.4.2 When stays are used to connect two plates, and only one of these plates requires staying, the
value of C shall be governed by the thickness of the plate requiring staying.
20.5 Required dimensions and layout of staybolts and stays
20.5.1 The required area of a staybolt or stay at its minimum cross section, usually located at the root
of the thread, exclusive of any corrosion allowance, shall be obtained by dividing the load on the
staybolt computed in accordance with paragraph 20.5.2 by the nominal design stress value for the
staybolt material, multiplying the result by 1.10.
20.5.2 The area supported by a staybolt or stay shall be computed on the basis of the full pitch
dimensions, with a deduction for the area occupied by the stay. The load carried by a stay is the
product of the area supported by the stay and the design pressure. When a staybolt or stay is
unsymmetrical because of interference with other construction details, the area supported by the
staybolt or stay shall be computed by taking the distance from the centre of the spacing on one side of
the staybolt or stay to the centre of the spacing on the other side.
578
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
20.5.3 When the edge of a flat stayed plate is flanged, the distance from the centre of the outermost
stays to the inside of the supporting flange shall not be greater than the pitch of the stays plus the inside
radius of the flange.
20.6 Requirements for threaded staybolts
20.6.1 The minimum thickness of plates to which stays may be applied shall be 8 mm.
20.6.2 The maximum pitch shall be 220 mm.
20.6.3 Acceptable proportions for the ends of through stays with washers are shown in Figure 20.9-1.
Holes for screw stays shall be drilled full size or punched not to exceed 6 mm less than the full diameter
of the hole. The hole shall then be drilled or reamed to the minor diameter of the thread, and tapped fair
and true with a full thread.
20.6.4 The ends of staybolts or stays screwed through the plate shall extend beyond the plate not less
than two threads when installed, after which they shall be riveted over or upset by an equivalent
process without excessive scoring of the plates. Alternatively, the ends of staybolts or stays screwed
through the plate shall be fitted with threaded nuts through which the bolt or stay shall extend.
20.6.5 The ends of threaded steel stays or staybolts, which are to be riveted shall be fully annealed.
20.7 Requirements for welded-in staybolts and welded stays
20.7.1 Welded-in staybolts may be used provided the following requirements are satisfied.
f)
The configuration is in accordance with the typical arrangements shown in Figure 20.9-2.
g) The required thickness of the plate shall not exceed 35 mm.
h) The maximum pitch shall not exceed 15 times the diameter of the staybolt; however, if the
required plate thickness is greater than 20 mm, the staybolt pitch shall not exceed 500 mm.
i)
The size of the attachment welds is not less than that shown in Figure 20.9-2.
j)
The allowable load on the welds shall be equal to the product of the weld area (based on the weld
dimension parallel to the staybolt), the nominal design stress of the material being welded, and a
weld joint factor of 60 %.
20.7.2 Welded stays may be used provided the following requirements are satisfied.
k) The pressure does not exceed 2 MPa.
l)
The configuration is in accordance with the typical arrangements shown in 20.9-2 (sketches a, b,
e, f, g and h).
m) The required thickness of the plate does not exceed 13 mm.
n) The maximum pitch p is determined by Formula (20.4.1) with C = 2,1 if either plate thickness is
less than or equal to 11 mm thick, and C = 2,2 for all other plate thicknesses.
UNI EN 13445-3:2021
579
EN 13445-3:2021 (E)
Issue 1 (2021-05)
o) The size of the fillet welds is not less than the plate thickness. The allowable load on the fillet welds
shall be equal to the product of the weld area (based on the minimum leg dimension), the nominal
design stress of the material being welded, and a weld joint factor of 55 %.
p) The maximum diameter or width of the hole in the plate shall not exceed 30 mm.
q) The inside welds are properly inspected before the closing plates are attached.
20.8 Tables for stayed flat walls
Table 20.8-1 — Stress factors for braced and stayed surfaces
Braced and stayed surface construction
Stress
Factor
Welded stays or threaded stays through plates not over 11 mm thickness with ends riveted over
(e.g. Figure 20.9-2 sketches a and b)
Welded stays or threaded stays through plates over 11 mm in thickness with ends riveted over
(e.g. Figure 20.9-2 sketches a and b)
Threaded stays through plates with single nuts outside of plate, threaded stays through plates
with inside and outside nuts without washers, and stays screwed into plates as shown in
Figure 20.9-1 sketch b
2,1
Stays with heads not less than 1.3 times the stay diameter screwed through plates or made a
taper fit and having the heads formed on the stays before installing them, and not riveted over,
said heads being made to have a true bearing on the plate (e.g. Figure 20.9-1 sketch a)
2,8
Stays fitted with inside and outside nuts and outside washers where the diameter of washers is
not less than 0,4 p and thickness not less than e (e.g. Figure 20.9-1 sketch a)
3,2
2,2
2,5
20.9 Figures for Stayed Flat Walls
DW = not less than 2,5 times the nominal bolt diameter, but it must be at least 0,4 times the pitch of stays if
C = 3,2.
eW = not less than e/2 if C = 2,8 or less, and not less than e if C = 3,2.
580
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
k = not less than 1,5 times the major diameter of bolts as measured on the outside of the threaded portion
Figure 20.9-1 — Threaded end stays
UNI EN 13445-3:2021
581
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(1) Complete penetration
(2) Details in (c) and (d) consider a round anchor bloc to be fitted between the staybolt and the wall
(3) In Details (g) and (h) Ds is the stay diameter to be used in the calculations according to 20.5, after consideration of
corrosion and possible negative material tolerances
Figure 20.9-2 — Typical forms of welded staybolts
582
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Min. width of stay bar = d
Figure 20.9-3 — Use of plug and slot welds for staying plates
UNI EN 13445-3:2021
583
EN 13445-3:2021 (E)
Issue 1 (2021-05)
21 Circular flat ends with radial reinforcement ribs
21.1 Purpose
The purpose of the rules in this Clause is to allow the design of circular flat ends reinforced by radial ribs,
with or without uniformly distributed peripheral bending moment, subject to pressure.
The components considered in this Clause consist of a circular flat end, reinforced by radial uniformly spaced
ribs; the height of the ribs is generally constant, however their profile may be slightly inclined at the outer
edge (see Figures 21.2-1, 21.2-2, 21.2-3 and 21.2-4).
The ribs shall be connected with each other at the centre of the end; this may be obtained either by welding
them together, or by welding them to a central ring or to a rigid plug. The number of the ribs should be
neither smaller than 3 nor greater than 24.
These rules do not deal with the calculation for leak tightness of the connection between the end and the
corresponding flange on the vessel; in case the leak tightness has to be assured, the required thickness of
the end might be greater than the thickness required by the static calculation, at least in the area of the
gasket and relevant bolting.
This kind of construction is not recommended in case of cyclic loadings or in case of external corrosion.
21.2 Specific definitions
The following definitions are in addition to those in Clause 3.
21.2.1
reinforcing rib
rectangular plate located along the radius of a circular flat end, located perpendicularly to its plane and
welded to it from both sides
21.2.2
continuous weld
weld between the rib and the end, located on both sides of the rib, for its entire length
21.2.3
intermittent weld
weld between the rib and the end, located on both sides of the rib, composed by different segments
interesting only a portion of its length.
584
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(a)
(b)
Figure 21.2-1 Welded ends with ribs
Figure 21.2-2 Welded end with ribs (Ribs
welded to a protruding shell)
UNI EN 13445-3:2021
Figure 21.2-3 Bolted end with ribs and additional
peripheral bending moment
585
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(section AA)
(view from Top)
Figure 21.2-4 — Bolted end with ribs without additional peripheral bending moment
21.3 Specific symbols and abbreviations
The following symbols and abbreviations are in addition to those in Clause 4.
d1
diameter of central plug or ring
d2
diameter subject to pressure
d3
diameter of bolt circle
d4
outside diameter of end
e
thickness of end
eR
thickness of reinforcing ribs
eC
thickness of central circular ring
f
nominal design stress of end at design temperature
fR
nominal design stress of rib at design temperature
fB
nominal design stress of bolts at design temperature
fC
nominal design stress of central ring at design temperature
NOTE
testing).
go
Design temperature means the temperature of the condition to be assessed (bolting-up, operating or
minimum required throat thickness of the weld between end and reinforcing rib
g1 …… gi throat thicknesses of the intermittent welds between end and reinforcing ribs (Figure 21.7-1)
h
586
height of reinforcing ribs
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
l
length of reinforcing ribs
lo
in case of intermittent welds is the length of the most external weld between end and
reinforcing rib
l1 ……
li lengths of the intermittent welds between end and reinforcing ribs
nV
number of reinforcing ribs
pA
maximum allowable pressure in operating or testing conditions
t
spacing between two consecutive ribs calculated on the diameter d2
W
total bolt load in the different conditions (bolting-up, operating and testing) as defined in Clause 11
zR
joint efficiency of the weld between the end and the reinforcing ribs
zC
joint efficiency of the weld in the central ring
β
angle of the circular sectors free of openings
21.4 Ends without additional peripheral bending moment
21.4.1 Maximum allowable pressure
The maximum allowable pressure shall be the smaller of the values calculated with the following formulae:
2

 f


P max
 e
 

C d2
P max

2
0 ,25   h 

   u 
K  l 

(21.4-1)
 h 2

 
   u 
  l 

2
h 
 4  
 l 
2

 eR

 f R 
 d2






(21.4-2)
where
C and K are taken from Figures 21.4-1 and 21.4-2 respectively, while u is equal to 0,5 for continuous welds
between the end and the ribs; when these welds are intermittent as in Figure 21.7-1, and are composed by
m segments having each one the length li, , u shall be calculated with the following formula:
u  0 ,9 
1

2l
im
i 1
li
(21.4-3)
NOTE 1
The length l of the reinforcing ribs shall be extended, whenever possible, up to the external diameter
d4, in any case at least up to the diameter d3.
NOTE 2
When a central ring as in Figure 21.2-4 is provided, this one shall comply with the provisions of 7.4.2.
UNI EN 13445-3:2021
587
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 21.4-1 — Factor C for end without
peripheral bending moment
Figure 21.4-2 — Factor K for ends without
peripheral bending moment
21.4.2 Minimum Dimensions
The minimum end thickness e and the minimum height h of the ribs shall be calculated with the following
formulae:
e  C d
P
2
h  0 ,5 d 2
(21.4-4)
f
Z
Z  u
Z 1
(21.4-5)
where Z is given by:
Z 
2K d2 P
fR e R
(21.4-6)
in the above formulae C, K and u shall be determined according to 21.4.1.
588
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
21.5 Ends with additional peripheral bending moment
Figure 21.5-1 — Factor Co for ends with peripheral bending moment
UNI EN 13445-3:2021
589
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The minimum end thickness e and the minimum height h of the ribs shall be calculated with the following
formulae:
e  Co d2
h  0 ,5 d 2
P
(21.5-1)
f
Zo
Zo  u
(21.5-2)
Zo  1
where Zo is given by:
Zo 
2Ko d2 P
(21.5-3)
fR e R
In the above formulae u shall be determined with Formula (21.4-3), while Co and Ko shall be taken from
Figures 21.5-1 and 21.5-2 after determining the parameter x as follows:
4W
x 
P
590
2
d2
 d3  d2


d2
 




(21.5-4)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure 21.5-2 — Factor Ko for ends with peripheral bending moment
UNI EN 13445-3:2021
591
EN 13445-3:2021 (E)
Issue 1 (2021-05)
By the graph in Figure 21.5-1 it is possible to check if there is an advantage in increasing the number of ribs:
for high values of x the coefficient Co remains constant (it cannot be lower than the minimum values
determined by the curve labelled with ‘S’); therefore a number of ribs higher than 5 is ineffective if x ≥ 0,25,
a number higher than 4 is ineffective if x ≥ 0,37, a number higher than 3 is ineffective if x ≥ 0,55.
NOTE 1
The first term of Formula (21.5-4) is the ratio between the total bolt load and the total pressure load
over the end, which is normally higher than 1 in operating and testing conditions (because the bolts shall develop
a reaction higher than the pressure load in order to keep the gasket compressed); since the second term is
normally much smaller than 1, the resulting values of x in these conditions are generally lower than 0,6; for higher
values of x the ribs are not effective, and a normal unstayed flat end would be recommended.
NOTE 2
The above method is not adequate for the bolting-up condition, where the pressure is 0 and the value
of x would become infinite; in order to verify the end also in this condition an equivalent plate thickness shall be
calculated with the formula:
2
e
3

eR h
2
4

eR h
t e
e EQ 
t
4 e
2
 4h
2
 6 eh

e  h
(21.5-5)
where t is given by:
t 
 d2
(21.5-6)
nV
in the calculation of eEQ all the negative tolerances for corrosion and fabrication shall be taken into account.
The reinforced end is able to withstand the bolting-up load W if:
e EQ 
3 d 3  d 2   W


 d2
 f MIN




(21.5-7)
In the above formula fMIN is the lower of the nominal design stress of the end and the nominal design stress
of the ribs.
592
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
21.6 Openings
The openings shall be located at a reasonable distance from the ribs, the welds, the central radius of each
sector and the periphery of the end; this condition is satisfied if the angle β in Figure 21.6-1 complies with
21.6-1:
Key
1 Central axis of a sector
Figure 21.6-1 — Reinforced end with openings
 
360
(21.6-1)
8 nV
If the above condition is verified, no additional calculation for opening reinforcement will be required;
otherwise an alternative design method shall be used (e.g. Design by Analysis).
21.7 Welds
Continuous welds between end and reinforcing ribs shall be calculated with Formula (21.7-1); if the welds
are intermittent, the conditions provided by Formulae (21.7-2), (21.7-3) and (21.7-4) shall also be met.
0 ,3
go 
n v
2 l


h
 1  

 2 l  d 1





2
 d1

h
 0 ,6 
 2l  d
1








P
f MIN z R
(21.7-1)
In the above formula fMIN is the lower of the nominal design stress of the end and the nominal design stress
of the ribs.
l o  0 ,2 l
m
 l
i
g i   2 log o
(21.7-2)
(21.7-3)
i 1
NOTE
The throat thickness to be used in the above formula is the minimum thickness calculated by
Formula (21.7-1)
UNI EN 13445-3:2021
593
EN 13445-3:2021 (E)
Issue 1 (2021-05)
m
lo 

(21.7-4)
l i  0 ,8 l
i 1
When the throat thicknesses obtained by Formula (21.7-1) for a continuous weld is very small, the use of
intermittent welds can be considered, unless other considerations (e.g. cyclic loading) would not make it
advisable. For fillet or partially penetrated welds without NDT the value of zR shall not be taken higher than
0,7.
Figure 21.7-1 — Intermittent welds between end and reinforcing rib
21.8 Central Ring
The central ring shall satisfy the following formula:
P  P max 
4
ech
K nV
d
3
2
2
z c fc
 h
1 
n e
 v c




(21.8-1)
2
where K shall be taken from Figure 21.4-2 for ends without peripheral bending moment; for ends with
peripheral bending moment, K shall be replaced by Ko to be taken from Figure 21.5-2.
When
d 1  2ec 
2d 4
nV
, the central portion of the end (with diameter d1-2ec) shall be verified according to the
following formula:
e  0 , 41 d 1  2 e c

P
(21.8-2)
f
For fillet or partially penetrated welds without NDT the value of zC shall not be taken higher than 0,7.
594
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
22 Static analysis of tall vertical vessels on skirts
22.1 Purpose
This clause provides rules for the design of tall vertical vessels under pressure and additional loads such as
weights, live loads, wind and earthquake loads and external forces from attached external piping.
The design of the components of the column for internal and external pressures and for non-pressure local
loads (where relevant), according to design by formula or design by analysis methods, shall be done prior to
this analysis.
This clause provides the additional calculations for global loads in combination with the pressure loads only.
22.2 Specific definitions
22.2.1 General
The following specific definitions apply in addition to those in Clause 3, 5.3.2.4 and Clause 16.
22.2.2 Tall vertical vessels
Tall vertical vessels (referred to as columns in this clause) are vessels with a total height h < 10 m and with a
ratio of total height to outside diameter h/d > 6,5, and vessels with h > 10 m and with a ratio h/d > 4.
22.3 Specific symbols and abbreviations
The following symbols, subscripts and abbreviations apply in addition to those in Clause 4 and 5.3.2.4:
AB
cross section of one anchor bolt
cf
force coefficient
clat
lateral force coefficient, see EN 1991-1-4:2005, Annex E 3
clat,0
basic value of lateral force coefficient, see EN 1991-1-4:2005, Annex E 2
DBC
bolt circle diameter
Dc
outside diameter of insulation on column
Dc1/3
averaged outside diameter of the upper third of the column including insulation
Dp
outside diameter of insulation on pipe
d
outside diameter of column excluding insulation (in metres)
dc
outside diameter of column excluding insulation
dp
outside diameter of pipe excluding insulation
en
smallest nominal wall thickness in the area of the skirt connection (shell, head and skirt thickness)
3
EN 1991-1-4:2005 is impacted by the stand-alone amendment EN 1991-1-4:2005/A1:2010 and the
corrigendum EN 1991-1-4:2005/AC:2010.
UNI EN 13445-3:2021
595
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Fvmax
maximum vertical force
F0
inertia force per unit length
G
gust factor
h
total height of column above ground level (in metres)
Kw
correlation length factor, see EN 1991-1-4:2005, Annex E 2
K
mode shape factor (K = 0,13 for columns)
MB
bending moment at the base of the column caused by vortex shedding
M(z)
bending moment at the height z, measured from the base of the column caused by vortex shedding
me
equivalent mass per unit length over the upper third of the height of the column for the load case under
investigation (see EN 1991-1-4:2005, F.4 2)
nB
number of anchor bolts
n1
natural frequency of the column [Hz] for the load case under investigation (see 22.10.3)
Rp0,2/TB
0,2 % proof strength at temperature TB
Sc
Scruton number
St
Strouhal number (St = 0,18 for columns)
TB
design temperature for anchor bolts
vcrit,1
is the critical wind velocity for mode 1, as defined in EN 1991-1-4
vm
is the characteristic 10 min mean wind velocity specified in EN 1991-1-4 at the cross section where
vortex shedding occurs.
Wsm
section modulus of the cross section
xmax
is the limit of deflection at top of column for column to be considered as rigid cantilever beam
xs
is the deflection at top of column subject to a virtual horizontal load equal to its own weight
yF,max
largest displacement at the top of the column caused by vortex shedding
δs
structural damping expressed by the logarithmic decrement
ρ
air density under vortex shedding conditions. The value of the air density ρ may be given in the National
Annex of EN 1991-1-4. The recommended value is 1,25 kg/m3.
22.4 Loads
22.4.1 Pressures
All combinations of the calculation pressure P and the coincident calculation temperature T as defined in
5.3.10 and 5.3.11 shall be considered. Since the pressure shall be superposed with other global loads it is not
certain that the governing condition of coincident pressure and temperature is also governing for the load
combinations (see remark on LC1 and LC2 in Table 5.3.2.4-1).
596
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
22.4.2 Dead loads
The weight of the un-corroded column shall include the weights of all shells and heads, all nozzles with
attached flanges and blinds, the skirt with attached base ring, the lifting lugs and any other clips, the
stiffening rings, the supporting rings and any other fixed internals. This weight shall be called the “fabricated
weight” and shall be stated on the drawing.
When removable internals and insulation are already mounted on the column in the workshop this
completed weight shall be called the “transport weight Gtrans” and shall be stated on the drawing.
When removable internals, insulation, fire protection, ladders, platforms and other external attachments are
mounted on the column before erection on site this completed weight shall be called the “lifting weight”
and shall be stated on the drawing.
If the lifting procedure has been specified, the minimum dead load Gmin is the lifting weight, otherwise the
transport weight or the fabricated weight shall be used.
The maximum dead load Gmax includes all the above mentioned weights and the weight of additional fixed
mounted equipment and external piping as defined below.
The corroded dead load Gcorr takes into account the loss of the fabricated weight due to the specified
corrosion allowance of all parts.
Loads due to weight of piping (to be included in the dead weight Gmax and Gcorr for piping supported by the
column – see 5.3.2.4.2.1):
Vertical pipes:
Weight of whole pipe between lower and upper elbows (bends)
Horizontal pipes:
Weight of whole pipe between nozzle and supports on column
Weight of pipe between the joint on the column and a point half the distance
to the next external pipe support
Weights of pipes with dp ≤ 0,04·dc may be neglected
22.4.3 Live loads
The weight of the contents of fluids or solids during operation shall be calculated for the maximal possible
levels in the bottom of the vessel, on the trays and in the packing, and using the maximal specified density.
The maximum levels shall be ensured or controlled.
The weight of the contents during hydro-test shall be calculated for the whole internal volume of the
column.
Since packing is removed during hydro-test the packing weight may be excluded from Gmax. For
simplification, it can be subtracted from the weight of the water filling.
The maximum dead load plus the weight of operating contents shall be called the “operation weight” and
the maximum dead load plus the weight of test contents shall be called the “site test weight”. Both shall be
stated on the drawing.
UNI EN 13445-3:2021
597
EN 13445-3:2021 (E)
Issue 1 (2021-05)
When no particular values are specified, a uniformly distributed load on platforms of 2,5 kN/m2 shall be
taken as traffic load. This includes loads from personnel, snow or ice and light machinery (service tools).
Traffic loads on platforms due to heavy machinery shall be considered by its weight and a uniformly
distributed load of 2 kN/m2.
If more than two platforms exist the traffic loads on the three largest platforms only shall be considered.
22.4.4 Wind loads
The wind loads W used in this clause (see 5.3.2.4.2.3) are characteristic values as defined in EN 1991-1-4.
No partial safety factors shall be included in the calculation of the wind load W.
The characteristic values shall be calculated as given in EN 1991-1-4 and the relevant National annex, taking
into account the site conditions (exposure and terrain profile) and the following specific parameters for
columns:
For wind codes which are not based on EN 1991-1-4 the wind loads shall be determined in as similar a
manner as possible to the definitions and requirements given in EN 1991-1-4 and here.
Force coefficient cf for columns and attachments:
cf = 0,7 for column body and skirt (with projected area based on outside diameter of insulation, excluding
the areas where the coefficient cf for platforms is used). This is the minimum value. If local regulations
requires a higher value this value shall be used. For column provided with corrugated insulation cover plates,
cf shall be calculated in accordance with EN 1991-1-4 (min. value still 0.7) or conservative value of cf = 1,1
may be used.
cf = 1,4 for platforms (with a minimum projected area based on half of the total platform height multiplied
by: outer diameter of platform for platform coverage angle > 100° outer diameter of column + 1 × width of
platform for platform coverage angle < 100°)
cf = 1,2 for ladders (with projected area based on ladder height × 0,33 m)
cf = 1,2 for scaffolds (with projected area based on height × outer diameter or diagonal)
Force coefficient cf for attached piping:
Vertical pipes: (with projected area based on pipe height × outer diameter of pipe insulation)
cf = 1,5 for attached parallel pipes if w ≤ 0,7 (Dc+Dp)
cf = 0,7 for attached parallel pipes if w > 0,7 (Dc+Dp)
(where w is the interspace width between outer diameters of insulation on column Dc and pipe Dp)
Horizontal pipes: (with projected area based on half the distance from the joint on the column to the next
external pipe support × outer diameter of pipe insulation)
cf = 0,7 for attached horizontal pipes
598
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
In cases where multiple pipes are arranged around the column the sum of the areas of those pipes shall be
determined taking into account only those pipes which lie in the projected plane which gives the maximum
sum.
Wind loads on pipes with Dp ≤ 0,04·Dc may be neglected.
Gust factor G for columns (referred to as structural factor cs·cd in EN 1991-1-4):
For rigid columns (not vibration sensitive) a simplified constant value given in the wind code may be used
(G = cs·cd = 1,0 according to EN 1991-1-4).
Otherwise (for flexible or vibration sensitive columns) the gust factor shall be calculated according to the
rules given in the wind code. Rigid columns may be considered as those satisfying one of the following three
conditions:
— columns with a height h < 10·d;
— columns with a height h < min {60 m; 6,5·d};
— columns which fulfil the condition:
x
S
 x
m ax
32  h





h 
200
h


h
(h  d ) 

d

2
(22.4-1)
with xmax, h and d in metres.
Where xs is the deflection at top of column subject to a virtual load equal to its own weight acting
horizontally, and xmax is the limit of deflection at top of column for column to be considered as rigid.
NOTE
h > 12·d.
For columns with constant cross sections the above condition (Formula (22.4–1)) is never fulfilled for
22.4.5 Earthquake loads
The earthquake loads E used in this clause (see 5.3.2.4.2.4) are design values as defined in EN 1990 and
EN 1998-1. The importance factor shall be included in the calculation of E, with no partial safety factors. For
steel columns the “lateral force method of analysis” using the base shear force based on the “design
spectrum for elastic analysis” with the behaviour factor q = 2 shall be applied.
NOTE 1
The design spectrum depends on the seismic zone, the importance factor (including hazard to human
life and consequential loss) and the soil ground type. These influences are given in the relevant National Annex to
EN 1998-1 or are specified for the site where the column is installed.
NOTE 2
It is possible to neglect vertical earthquake loads for columns because they are vertical structures and
are skirt supported (see EN 1998-1:2004, 4.3.3.5.2).
For seismic codes which are not based on EN 1998-1 the earthquake loads shall be determined in as similar
a manner as possible to the definitions and requirements given in EN 1998-1 and here.
UNI EN 13445-3:2021
599
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Earthquake loads from attached vertical and horizontal pipes and other attachments on the column are
included by taking into account their weights in the dead weight of the column as specified in 22.4.2, and
using this total weight and the distribution of the weights for the calculation of the earthquake loads.
Earthquake loads of pipes with dp ≤ 0,04·dc may be neglected.
22.4.6 Additional loads from attached external piping at nozzles and supports
Additional forces from attached piping, other than weight, wind and earthquake loads, shall be considered,
see 5.3.2.4.2.5. It is the responsibility of the designer to decide to what extent additional forces from
attached piping shall be taken into account for the static analysis of columns since their influence depends
on the whole behaviour of the column and piping configuration (see NOTE in 5.3.2.4.2.5).
Guidelines for application when additional forces are considered:
Horizontal and vertical reaction forces only shall be taken into account, bending moments should be
neglected.
Horizontal and vertical reaction forces act at the elevation where the external horizontal pipe runs arrive at
or leave the column; therefore they shall be incorporated into the calculation at this level. At other levels the
forces are internal forces without influence on the global equilibrium because they result from restraint
between nozzles and supports on the column (see NOTE in 5.3.2.4.2.5).
In the piping analysis the local elasticity of the column wall should be taken into account. The global elasticity
of the whole column may be taken into account provided that all essential pipes attached to the column are
considered in the piping analysis.
In the case that multiple pipes are connected to the column the resulting horizontal reaction forces and their
directions shall be vector combined at each elevation taking into account the direction of each of the single
pipe forces. Where actual forces and their directions are not available it is not reasonable to assume that all
horizontal forces act in the same direction. The maximum resulting shear force at the base of the column
shall be vector combined from the horizontal resulting forces and their directions of all elevations. The
maximum resulting bending moment at the base of the column shall be vector combined from the moments
and their directions determined from these horizontal resulting forces with their directions and elevations.
22.5 Load combinations
See 5.3.2.4.
22.6 Stress analysis of pressure vessel shells and skirts
22.6.1 Cylindrical pressure vessel shells
The stresses in the cylindrical shell of the pressure vessel shall be checked in accordance with 16.14 at each
critical cross section for the vertical force and the bending moment calculated at the level of the cross
section under consideration. These checks shall be performed for each relevant load case and the relevant
allowable stresses as defined in Table 5.3.2.4-1. The vertical force and the bending moment shall be applied
as given in Formulae (16.14-4) and (16.14-5) to determine the maximum and minimum longitudinal stresses.
The calculation of the total axial forces in 16.14.3 shall be performed using case (1) and using the internal
calculation pressure, excluding the hydrostatic pressure. For the calculation of the circumferential pressure
stress in accordance with Formula (16.14-7) the internal calculation pressure including the hydrostatic
pressure shall be used.
600
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
22.6.2 Conical sections of the pressure vessel
For conical sections with a semi angle of cone at apex less than 7° the stresses shall be checked using the
procedure for cylindrical shells at both the small and the large end of the cone, using the appropriate wall
thickness and diameter.
NOTE
For conical sections with a semi angle of cone at apex larger than 7° no method for analysing global
forces and moments is given at present in EN 13445-3 either for the conical shell itself or for the cone/cylinder
intersection.
22.6.3 Skirt shell
For skirts composed of a cylindrical shell, or a conical shell with a semi angle at apex less than 7°, the stresses
shall be checked as described in 22.6.1 and 22.6.2 with the simplification that P = 0.
For skirts with openings that weaken the skirt, the additional calculations in accordance with 16.12.4 are
required.
22.7 Design of joint between skirt and pressure vessel (at dished end or cylindrical
shell)
The stress check for the joint between the skirt and the vessel is provided in 16.12.3.
22.8 Design of anchor bolts and base ring assembly
The design of the anchor bolts and base ring assembly shall be performed in accordance with 16.12.5. The
calculations shall be performed for each relevant load case with the allowable stresses as defined in
Table 5.3.2.4-1. Nominal design stress for anchor bolts is defined by Formula (6.7-1).
The resulting anchor bolt forces (including the influence of preloading) shall be provided in Table 22-1.
NOTE
The anchor bolt design procedure provided in 16.12.5 is a conservative method including preloading of
the bolts for quasi static loads. Recommendations for preloading of anchor bolts are also provided. Calculations
for the compressive stresses induced by the base ring on the surface of the concrete of the foundation are also
given in 16.12.5.
22.9 Foundation loads
Foundation loads and anchor bolt loads shall be provided for the design of the foundation. The specified
foundation loads are characteristic values as defined in EN 1990, with the exception of the wind loads for
Installation and Testing where reduced values are already given (see remark on LC5 and LC9 in Table 5.3.2.41).
The following foundation loads shall be provided for the different load condition status during the column’s
life:
— minimum and maximum Vertical Forces;
— maximum Lateral Forces (due to Wind, Piping Forces, Earthquake);
— maximum Bending Moment (due to Wind, Piping Forces and eccentric Weights, Earthquake);
UNI EN 13445-3:2021
601
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— maximum Anchor bolt load;
— Torque Moment for preloading the anchor bolts.
Table 22-1 shows the required loads and the corresponding load cases from Table 5.3.2.4-1 to give the
appropriate values. Values or lines in the table may be omitted if the type of load is not relevant or may be
set to zero.
Table 22.1 — Data for foundation design
Type of Load
Symbol
for
Load
Load Condition Status
Installation
Testing
Operation
Shutdown
Maximum Vertical Force
Fvmax
-
LC9
LC1 or LC2 or LC3
-
Minimum Vertical Force
Fvmin
LC5
-
-
LC4
Lateral Force due to Wind
FH,W
LC5
LC9
(LC1 or LC2 or LC3)/1,1
LC4/1.1
Lateral Force due to add.
Piping Forces
FH,F
-
-
LC1 or LC2 or LC3
-
Lateral
Force
Earthquake
FH,E
-
-
LC6 or LC7 or LC8
-
MB,W
LC5
LC9
(LC1 or LC2 or LC3)/1,1
LC4/1,1
Bending Moment due to
additional Piping Forces and
eccentric Weights
MB,F
-
-
LC1 or LC2 or LC3
-
Bending Moment
Earthquake
MB,E
-
-
LC6 or LC7 or LC8
-
Anchor bolt Force including
Wind and Add. Forces
FA,W+F
LC5
LC9
LC1 or LC2 or LC3
LC4
Anchor bolt Force including
Earthquake
FA,E
-
-
LC6 or LC7 or LC8
-
Torque
Moment
preloading anchor bolts
Mt
given by Formula (16.12–81)
Bending
Wind
due
Moment
due
due
to
to
to
for
22.10 Vortex shedding
22.10.1 General
In all formulae consistent units are necessary.
22.10.2 Criteria for vortex shedding
The effect of vortex shedding need not be investigated when at least one of the following conditions is met:
a)
h
D
b)
602
 15
(22.10–1)
c 1/ 3
for operating conditions
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
0,004 m
e
2
(22.10–2)
 0,8
  D c1/ 3
c)
for erection condition or for a conditions with no platforms and piping
0,004 m
(22.10–3)
e
 1 ,1
2
  D c1/ 3
d)
vcrit,1 > 1,25 vm
(22.10–4)
22.10.3 Parameters for vortex shedding
For load conditions where no liquid or only liquid at the bottom can be taken into account (erection load
case) the structural damping expressed by the logarithmic decrement δs can be assumed as 0,012.
For load conditions where liquid may be taken into account (operating load case) the structural damping
expressed by the logarithmic decrement δs can be assumed as 0,04.
The basic value of the lateral force coefficient clat,0 is defined in EN 1991-1-4:2005, Figure E.2 4.
The influence of neighbouring columns according to EN 1991-1-4:2005, E.1.5.2.7 3 shall be taken into account.
The correlation length factor Kw can be taken from EN 1991-1-4:2005, Table E.5 3, first row with n = 1 and
m = 1.
NOTE 1
The formulas are based on approach 1 of EN 1991-1-4:2005 2.
NOTE 2
Instead of EN 1991-1-4:2005, Annex E alternative required national annexes are possible.
3
The Scruton number Sc is:
2
Sc 
m
s
 D
e
(22.10-5)
2
c1/ 3
The largest displacement yF,max can be calculated:
y
F ,m a x
1

St
2

1
Sc
K K
w
c
la t
D
c 1/ 3
(22.10-6)
The natural frequency of the column can be calculated (approximate formula):
n
1
=
62
10 x
(22.10-7)
s
where the value of the calculated deflection xs as defined in 22.3 is in millimetres.
Natural frequency calculated by EN 1991-1-4:2005, Annex F, Formula (F.3) 3, or by finite element method,
may be used instead of Formula (22.10-7).
4
EN 1991-1-4:2005 is impacted by the stand-alone amendment EN 1991-1-4:2005/A1:2010 and the
corrigendum EN 1991-1-4:2005/AC:2010.
UNI EN 13445-3:2021
603
EN 13445-3:2021 (E)
Issue 1 (2021-05)
3
NOTE 3
EN 1991-1-4:2005, Formula (F.3) is suitable for columns with nearly constant weight distribution.
22.10.4 Reactions
The reactions caused by vortex shedding can be calculated:
F
0
 m
e

 2  n
1

2
y
(22.10-8)
F ,m a x
1
2
Bending moment at the base
M
Bending moment at the height z:
4

4 z
1  z 

M (z )  1 


 

3 h
3  h 

B

4
F
0
h
(22.10–9)

 M


B
(22.10–10)
The formulae are valid only for columns with constant diameter; for other cases appropriate analysis is
required.
22.10.5 Fatigue design
A fatigue analysis shall be carried out with the reaction of the vortex shedding calculation according to
Clause 18:
— at each cross section of the shell where the wall thickness changes,
— at the bottom head / skirt connection,
— at the base of the skirt,
— for the anchor bolts.
The stress ranges at the different locations shall be calculated to determine the allowable number of cycles.
The stress range at the cross section is:
 
2 M (z )
W
(22.10-11)
sm
A conservative stress range at the anchor bolts is:

 4M
   m a x 0 ; 


B
 D
BC

 F
vm ax

1

 n  A
B
B





(22.10-12)
A more detailed analysis can take into account the prestress of the anchor bolts and the stiffness of all parts
of the foundation (Petersen “Stahlbau”, Munich 1997).
604
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The number of load cycles caused by vortex excited oscillation can be calculated according to
EN 1991-1-4:2005, Annex E, Formula (E.10) 5.
For different load cases the cumulative fatigue damage index D defined in Clause 18 shall be calculated.
5
EN 1991-1-4:2005 is impacted by the stand-alone amendment EN 1991-1-4:2005/A1:2010 and the
corrigendum EN 1991-1-4:2005/AC:2010.
UNI EN 13445-3:2021
605
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex A
(normative)
Design requirements for pressure bearing welds
This annex specifies design requirements of welds for permanent use to be applied in the construction of
pressure vessels.
NOTE
See also EN 13445-4:2021 and EN 13445-5:2021 for possible additional requirements on welds.
The following data are included:
— a figure of the joint in finished condition;
— design requirements mainly on geometry;
— a list of applicable testing groups as referred to in EN 13445-5:2021;
— the applicable fatigue class as referred to in this Part, Clauses 17 and 18 (This does not apply to
testing group 4 vessels);
— recommendations for prevention of lamellar tearing;
— recommendations for prevention of corrosion;
— reference to the recommended weld details given in EN 1708-1:2010;
The following groups of welded joints are included:
— group M: longitudinal welds in cylinders and cones, welds in spheres and dished ends (Table A-1);
— group C: circumferential welds in cylinders and cones, connecting weld between dished end and
shell (Table A-2);
— group E: welds for flat end to shell (Table A-3);
— group TS: welded joints for tubesheet to shell (Table A-4);
— group T: welded joints for tube to tubesheet (Table A-5);
— group S: welded joints for socket connections (Table A-6);
— group F: welded joints for flanges and collars (Table A-7);
— group N: welded joints for nozzles (Table A-8);
— group B: circumferential welds in bellows (Table A-9).
In each group the preferred joints are given first.
606
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-1 — Pressure bearing welds - Longitudinal welds in cylinders and cones,
welds in spheres and dished ends
Ref.
Type of joints
Design requirements
M1
M2
e 2  e 1  Min
0 , 3 e 1
; 6
Applicable
weld testing
group
1, 2, 3, 4
l 3  2 e1
l 3  2 e1
e 2  e 1  Min
0 ,15 e 1
; 3
1.1.4
A
N
1.1.4
1, 2, 3, 4
see Table
18-4
details n°
1.1 and
1.2
A
N
1.1.6
1, 2, 3, 4
see Table
18-4
details n°
1.1 and
1.2
A
N
1.1.6
1, 2, 3, 4
see Table
18-4
details n°
1.3
A
N
1.1.4
l1 / l 2  1 / 4
M5
EN 17081:2010
see Table
18-4
details n°
1.1 and
1.2
l1 / l 2  1 / 4
M4
see Table
18-4
details n°
1.1 and
1.2
Lamellar
Corrosion 3)
tearing
susceptibility 2)
A
N
1, 2, 3, 4
a2  3 m m
M3
Fatigue
class 1)
l1 / l 2  1 / 4
M6
slope : see M3
with smooth transition
1, 2, 3, 4
see Table
18-4
details n°
1.3
A
N
1.1.5
M7
slope : see M3
with smooth transition
1, 2, 3, 4
see Table
18-4
details n°
1.3
A
N
1.1.4
l1 / l 2 1 / 4
1, 2, 3, 4
see Table
18-4
details n°
1.3
A
N
1.1.5
A
N
1.1.5
M8
with smooth transition and
angles > 150 °
M9
l1 / l 2  1 / 4
4
with smooth transition
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
UNI EN 13445-3:2021
607
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-1 — Pressure bearing welds - Longitudinal welds in cylinders and cones,
welds in spheres and dished ends (continued)
Ref.
Type of joints
Design requirements
M 10
allowed for fatigue only if
full penetration can be
verified at least by visual
inspection
M 11
e
a
2
3
e
1
0 , 3 e 1 ; 6 
0 ,1 e1 ; 2 
 Min
 Min
Applicable
weld testing
group
1, 2, 3, 4
Fatigue class
1, 2, 3, 4
1, 2, 3, 4
see M 10 for fatigue
M 12
see M 4
see M 11
M 13
NOT ALLOWED
M 14
NOT ALLOWED
M 15
NOT ALLOWED
M 16
NOT ALLOWED
1)
2)
3)
Lamellar
tearing
susceptibility 2)
A
Corrosion
N
1.1.1
see Table
18-4 details
n° 1.1 and
1.5
A
N
1.1.1
see Table
18-4 details
n° 1.1 and
1.5
A
N
1.1.3
1)
see Table
18-4 details
n° 1.1 and
1.5
3)
EN 17081:2010
Fatigue class: see Clauses 17 and 18.
Lamellar tearing susceptibility: A = no risk B = possible risk.
Corrosion N = normal conditions S = not permitted.
608
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-2 — Pressure bearing welds - Circumferential welds in cylinders and cones, connecting
weld between dished end and shell
Ref.
Type of joint
Design requirements
C1
C2
e
C3
e
2
2
 e
 e
1
1
Applicable
weld testing
group
1, 2, 3, 4
see Table
18-4 details
n° 1.1 and
1.2
Lamellar
tearing
susceptibility 2)
A
Corrosion 3)
EN 17081: 2010
N
1.1.4
 Min
0 ,15 e1 ; 3 
1, 2, 3, 4
see Table
A
18-4 details
n° 1.1 and
1.2
N
1.1.4
 Min
0 , 3 e1 ; 6 
1, 2, 3, 4
see Table
A
18-4 details
n° 1.1 and
1.2
N
1.1.4
1, 2, 3, 4
see Table
A
18-4 details
n° 1.1 and
1.2
N
1.1.6
a2  3 m m
C4
Fatigue
class 1)
l 3  2 e1
l1 / l 2  1 / 3
C5
l1 / l 2  1 / 3
1, 2, 3, 4
see Table
18-4 detail
n° 1.3
A
N
1.1.4
C6
see C 4
1, 2, 3, 4
see Table
A
18-4 details
n° 1.1 and
1.2
N
1.1.6
l1 / l 2  1 / 3
1, 2, 3, 4
see Table
A
18-4 details
n° 1.3
N
1.1.5
C7
with smooth transition
C8
See C 5
1, 2, 3, 4
see Table
A
18-4 details
n° 1.3
N
1.1.4
C9
l1 / l 2 1 / 3
1, 2, 3, 4
see Table
A
18-4 details
n° 1.3
N
1.1.5
3, 4
see Table
A
18-4 details
n° 1.3 for
testing
group 3
N
1.1.5
with smooth transition and
angles > 150 °
C 10
l1 / l 2  1 / 3
with smooth transition
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
609
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-2 — Pressure bearing welds - Circumferential welds in cylinders and cones, connecting
weld between dished end and shell (continued)
Ref
Type of joint
Design requirements
Applicable
weld testing
group
1, 2, 3, 4
Fatigue class
1)
1.1.1
EN 17081: 2010
C 11
allowed for fatigue only if full
penetration can be verified
C 12
see C 3
1, 2, 3, 4
see Table 184 details n°
1.1 and 1.5
A
N
1.1.1
C 13
see C 4
1, 2, 3, 4
see Table 184 details n°
1.1 and 1.5
A
N
1.1.3
C 14
see C 10
with smooth transition
1, 2, 3, 4
see Table 184 details n°
1.3 and 1.5
A
N
1.1.2
C 15
NOT ALLOWED
1, 2, 3, 4
see Table 18- A
4 detail n° 1.4
N
-
1, 2, 3, 4
see Table 18- A
4 detail n° 1.4
N
-
C 16
  3 0
in case of unequal
thicknesses, limited to:
e
C 17
  3 0
2
 e
1
 Min
0 , 3 e1 ; 4 
in case of unequal
thicknesses, limited to:
e
2
 e
1
 Min
0 , 3 e1 ; 4 
see Table 184 details n°
1.1 and 1.5
Lamellar
Corrosion 3)
tearing
susceptibility 2)
A
N
— calculation of stresses
— round the weld inside by
grinding
1), 2), 3) see Table A-1.
610
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-2 — Pressure bearing welds - Circumferential welds in cylinders,
cones and dished ends (continued)
Ref.
C 18
Type of joint
 30°
Design requirements
in case of unequal
thicknesses, limited to:
e
C 19
> 30°
2
 e
1
 Min
0 , 3 e1 ; 4 
in case of unequal
thicknesses, limited to:
e
2
 e
1
 Min
Applicable
weld testing
group
1, 2, 3, 4
Fatigue class
1)
63 with 100
% surface
NDT
80 if root
flush
grounded
Lamellar
Corrosion
3)
tearing
susceptibility 2)
A
N
EN 1708-1:
2010
-
1, 2, 3, 4
50 with 100
% surface
NDT
71 if root
flush
grounded
A
N
-
0 , 3 e1 ; 4 
d o  600 m m
C 20
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
see
§ 5.7.4.2
see Table
18-4 detail
n° 1.6
A
S
-
C 21
see
§ 5.7.4.1
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
see
§ 5.7.4.1
see Table
18-4 detail
n° 1.7
A
S
-
C 22
see
§ 5.7.4.1
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
see
§ 5.7.4.1
see Table
18-4 detail
n° 1.7
A
S
-
C 23
l is the minimum required
thickness
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
see
§ 5.7.4.2
see Table
18-4 detail
n° 1.6
A
S
-
C 24
see C 2
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
see
§ 5.7.4.2
see Table
18-4 detail
n° 1.6
A
S
-
C 25
see C 4
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
see
§ 5.7.4.2
see Table
18-4 detail
n° 1.6
A
S
-
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
611
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-2 — Pressure bearing welds - Circumferential welds in cylinders,
cones and dished ends (continued)
Ref
Type of joint
Design requirements
Applicable
weld testing
group
see
§ 5.7.4.2
testing group
4
Fatigue class
1)
Corrosion 3)
S
-
EN 1708-1:
2010
C 26
see C 10
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
C 27
NOT ALLOWED
C 28
see C 4
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
see
§ 5.7.4.2
see Table
18-4 detail
n° 1.6
A
S
-
C 29
see C 4
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
see
§ 5.7.4.2
testing group
4
not allowed
A
S
-
C 30
NOT ALLOWED
C 31
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
4
-
B
N
-
C 32
A = circumferential weld
l  2 m in ( e 1 , e 2 ) see C 35
4
-
B
S on L side
N on R side
9.1.2
4
-
B
S on L side
N on R side
9.1.2
C 33
L left side
R right side
Pressure applied on either
side
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
A = plug weld
l  2 m in ( e 1 , e 2 ) see C 35
-
Lamellar
tearing
susceptibility 2)
A
L left side
R right side
Pressure applied on either
side
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
1), 2), 3) see Table A-1.
612
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-2 — Pressure bearing welds - Circumferential welds in cylinders,
cones and dished ends (concluded)
Ref
Type of joint
C 34
Design requirements
l  2 m in ( e 1 , e 2 )
Applicable
weld testing
group
Fatigue
class 1)
4
-
Lamellar
tearing
susceptibility
2)
B
4
-
B
Corrosion
3)
S on L side
N on R side
EN 1708-1:
2010
N
-
see C 35
L left side
R right side
Pressure applied on either
side
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
C 35
l  2 m in ( e 1 , e 2 )
C 36
if the weld is at the end of a
shell, minimum distance
between the weld and the
end shall be 5 mm.
L left side
R right side
Pressure applied on either
side
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
NOT ALLOWED
C 37
NOT ALLOWED
C 38
NOT ALLOWED
9.1.1
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
613
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-3 — Pressure bearing welds - Flats ends
Ref.
Type of joint
Design requirements
Applicable
weld testing
group
Fatigue
class 1)
Lamellar
tearing
susceptibility
Corrosion 3)
EN 1708-1:
2010
2)
E1
all allowed circumferential
joints can be used
r  1,3 e
1, 2, 3, 4
adopt class
of relevant
reference C
A
N
see for
relevant
reference C
E2
all allowed circumferential
joints can be used
r  1,3 e
1, 2, 3, 4
adopt class
of relevant
reference C
A
N
see for
relevant
reference C
1, 2, 3, 4
see Table
18-4 detail
n° 2.2
B
N
8.1.9
1, 2, 3, 4
see Table
18-4 detail
n° 2.2
A if forged
B if machined
from plate
N
and r  8 m m
E3
all allowed circumferential
joints can be used
r  0 ,2 e r
E4
all allowed circumferential
joints can be used
r  e / 3
-
1), 2), 3) see Table A-1.
614
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-3 — Pressure bearing welds - Flats ends (continued)
Ref.
Type of joint
Design requirements
Applicable
weld testing
group
3, 4
Lamellar
tearing
susceptibility 2)
see Table A if   15°
18-4 detail B if   15°
n° 2.1 a
for testing
group 3
Corrosion 3)
see Table A if   15°
18-4 detail B if   15°
n° 2.1 c for
testing
group 3
N
A if   15°
B if   15°
S
see Table A if   15°
18-4 detail B if   15°
n° 2.1 a or
b for
testing
groups 1,
2, and 3
N
8.1.8
A if   15°
B if   15°
S
8.1.7
E5
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
E6
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
3, 4
E7
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
4
E8
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
3, 4
1, 2 if ground
and back
welded
E9
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
4
Fatigue
class 1)
-
-
N
EN 17081: 2010
8.1.2
8.1.3
-
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
615
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-3 — Pressure bearing welds - Flats ends (continued)
Ref.
Type of joint
Design requirements
Applicable weld
testing group
Fatigue class
1)
Lamellar
Corrosion EN 1708-1:
3)
tearing
2010
susceptibility
2)
E 10
3, 4
a  es
NOT ALLOWED FOR DBA-DR if a  1 6 m m
AND CREEP DESIGN
4
if a  1 6 m m
see Table
18-4 detail
n° 2.1 b for
testing
group 3
B
N
-
E 11
3, 4
a  es
NOT ALLOWED FOR DBA-DR if a  1 6 m m
AND CREEP DESIGN
4
if a  1 6 m m
see Table
18-4 detail
n° 2.1 b for
testing
group 3
B
N
8.1.1
E 12
NOT ALLOWED
E 13
NOT ALLOWED
E 14
1, 2, 3, 4
see Table
18-4 detail
n° 2.3 a
B
N
8.1.5
E 15
1, 2, 3, 4
see Table
18-4 detail
n° 2.3 c
B
N
8.1.5
1), 2), 3) see Table A-1.
616
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-3 — Pressure bearing welds - Flats ends (continued)
Ref.
Type of joint
Design requirements
Applicable weld
testing group
E 16
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
4
E 17
b  es
3, 4
if b  1 6 m m
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
E 18
a  1, 4 e s
1, 2, 3, 4
if
b  16 m m
4
Fatigue class
1)
-
see Table
18-4 detail
n° 2.3 b
-
Lamellar
Corrosion 3)
tearing
susceptibility 2)
B
S
EN 17081: 2010
-
B
N
8.1.5
B
N
8.1.6
B
N
8.1.5
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
E 19
a  0 ,7 e s
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
3, 4
if
a  16 m m
4
if
a  16 m m
see Table
18-4 detail
n° 2.3 b for
testing
group 3
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
617
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-3 — Pressure bearing welds - Flats ends (continued)
Ref.
Type of joint
E 20
Design requirements
a  1, 4 e s
Applicable
weld testing
group
Fatigue
class 1)
Corrosion 3)
S
-
4
-
Lamellar
tearing
susceptibility 2)
B
EN 17081: 2010
4
-
B
S
-
4
-
B
S
-
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
E 21
a  1, 4 e s
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
E 22
a  0 ,7 e s
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
E 23
NOT ALLOWED
1), 2), 3) see Table A-1.
618
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-3 — Pressure bearing welds - Flats ends (concluded)
Ref.
Type of joint
E 24
Design requirements
a  0 ,7 e s
Applicable
weld testing
group
Fatigue
class 1)
4
-
Lamellar
tearing
susceptibility 2)
B
4
-
B
Corrosion 3)
N
-
N
-
EN 17081: 2010
b  es
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
E 25
a  es
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
E 26
NOT ALLOWED
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
619
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-4 — Tubesheets - Tubesheets to shell
Ref.
Type of joint
Design requirements
Applicable
weld testing
group
Fatigue
class 1)
Lamellar
tearing
susceptibility
2)
Corrosion
3)
EN 17081: 2010
see flat ends to shell with following additional cases
TS 1
NOT ALLOWED FOR DBA- 1, 2, 3, 4
DR AND CREEP DESIGN
unless the tubesheet is a
plate or a forging with Z
quality testing. At least
one tension test shall be
made according to the
figure below. The
specimen (sub-size if
necessary) shall be taken
from the actual
tubesheet with its
centreline normal to the
tubesheet. It is not
acceptable for the test
pieces to come from a
separated forging as per
EN 10222-1:1998 12.2.2.
TS 2
b  2 es
4
see Table A if forged
18-4 detail B if machined
n° 2.2
from plate
-
A
N
8.1.9
S
8.1.7
NOT ALLOWED FOR DBADR AND CREEP DESIGN
1), 2), 3) see Table A-1.
620
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-5 — Tubesheets - Tubes to tubesheets
Ref.
Type of joint
Design requirements
T1
Applicable
weld testing
group
1, 2, 3, 4
Fatigue
class 1)
see Table
18-4 detail
1.5
Corrosion 3)
Lamellar
tearing
susceptibility 2)
A
EN 1708-1:
2010
N
-
T2
NOT ALLOWED FOR DBA- 1, 2, 3, 4
DR AND CREEP DESIGN
not
allowed
A
N
-
T3
NOT ALLOWED FOR DBA- 1, 2, 3, 4
DR AND CREEP DESIGN
not
allowed
A
N
-
T4
NOT ALLOWED FOR DBA- 1, 2, 3, 4
DR AND CREEP DESIGN
not
allowed
A
N
T5
w  et
1, 2, 3, 4
not
allowed
A
N
1, 2, 3, 4
not
allowed
A
N
7.1.7
1, 2, 3, 4
not
allowed
B
S
7.1.6
NOT ALLOWED FOR DBADR AND CREEP DESIGN
T6
w  et
NOT ALLOWED FOR DBADR AND CREEP DESIGN
T7
e t  l  1, 4 e t
NOT ALLOWED FOR DBADR AND CREEP DESIGN
7.1.8
-
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
621
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A.5 — Tubesheets - Tubes to tubesheets (continued)
Ref.
Type of joint
Design requirements
T8
e t  l  1, 4 e t
Applicable
weld testing
group
1, 2, 3, 4
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
T9
l1  1 , 4 e t
Fatigue
class 1)
not
allowed
Lamellar
tearing
susceptibility 2)
B
Corrosion 3)
EN 17081: 2010
S
7.1.5
1, 2, 3, 4
40
A
S
-
1, 2, 3, 4
40
A
S
-
1, 2, 3, 4
40
B
S
-
1, 2, 3, 4
40
B
S
-
1, 2, 3, 4
40
B
S
-
1, 2, 3, 4
40
B
S
-
l2  4 e t
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
T 10
l2  4 e t
l1  e t  3 m m
for stay tubes
l1  e t  2 m m
for other tubes
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
T 11
l  et
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
T 12
l  1, 4 e t
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
T 13
l  et
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
T 14
l  0 ,7 e t
m ax 2et
l
et
n o c le a r a n c e
1), 2), 3) see table A-1.
622
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A.5 — Tubesheets - Tubes to tubesheets (concluded)
Ref.
Type of joint
Design requirements
Applicable
weld testing
group
1, 2, 3, 4
Fatigue
class 1)
Corrosion 3)
40
Lamellar
tearing
susceptibility 2)
B
S
T 15
l  et
T 16
e t  l  1, 4 e t
1, 2, 3, 4
40
A
S
T 17
l  1, 4 e t
1, 2, 3, 4
32
B
S
1, 2, 3, 4
40
B
S
EN 17081: 2010
-
7.1.1
-
a  et
T 18
l  1, 4 e t
T 19
NOT ALLOWED
7.1.2
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
623
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-6 — Socket connections
Ref.
Type of joint
Design requirements
S1
S2
allowed for fatigue only if
full penetration can be
verified
S3
S4
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
Applicable
weld testing
group
1, 2, 3, 4
Fatigue
class 1)
see Table
18-4 detail
n° 7.1
Lamellar
tearing
susceptibility 2)
-
Corrosion 3)
EN 17081: 2010
N
1, 2, 3, 4
see Table
18-4 detail
n° 7.1
-
N
-
1, 2, 3, 4
see Table
18-4 detail
n° 7.1
-
N
-
3, 4
if
d  150 m m
see Table
18-4 detail
n° 7.1
-
N
-
see Table
18-4 detail
n° 7.2
-
N
-
see Table
18-4 detail
n° 7.2
-
N
-
see Table
18-4 detail
n° 7.4
-
N
-
see Table
18-4 detail
n° 7.4
-
N
1, 2, 3, 4
if
d  150 m m
S5
a  0 , 7 e m in for each
weld
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
S6
a  0 , 7 e m in for each
weld
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
S7
a  0 , 7 e m in for each
weld
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
S8
a  0 , 7 e m in for each
weld
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
3, 4
if
d  150 m m
1, 2, 3, 4
if
d  150 m m
3, 4
if
d  150 m m
1, 2, 3, 4
if
d  150 m m
3, 4
if
d  150 m m
1, 2, 3, 4
if
d  150 m m
3, 4
if
d  150 m m
2.1.8
1, 2, 3, 4
if
d  150 m m
1), 2), 3) see Table A-1.
624
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-7 — Flanges and collars
Ref.
Type of joint
Design requirements
F1
all allowed circumferential
joints can be used
F2
full penetration
F3
g 1  g 2  1, 4 e
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
Applicable
weld testing
group
1, 2, 3, 4
Fatigue
class 1)
Lamellar tearing
Corrosion 3)
susceptibility 2)
EN 1708-1:
2010
see Table A
18-4 detail
n° 7.1
N
5.1.2
1, 2, 3, 4
see Table A
18-4 detail
n° 7.2
N
5.1.1
3, 4
if
d  150 m m
see Table A
18-4 detail B if St1 or St2
n° 7.4
N
see Table A
18-4 detail B if St1 or St2
n° 7.4
N
5.1.8
see Table A
18-4 detail
n° 7.2
N
5.1.1
63
A
50 if inside
not
visually
inspected
N
-
1, 2, 3, 4
if
d  150 m m
F4
g 1  g 2  1, 4 e
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
3, 4
if
d  150 m m
1, 2, 3, 4
if
d  150 m m
F5
g1  g 2  2 e
g 1  g 2  0 ,2 5 e
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
F6
full penetration
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
3, 4
if
d  150 m m
1, 2, 3, 4
if
d  150 m m
3, 4
if
d  150 m m
1, 2, 3, 4
if
d  150 m m
-
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
625
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-7 — Flanges and collars (concluded)
Ref.
Type of joint
F7
Design requirements
g1  g 2  2 e
g 1  g 2  0 ,2 5 e
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
F8
F9
Fatigue
class 1)
Lamellar tearing
susceptibility 2)
Corrosion 3)
EN 1708-1:
2010
see Table A
18-4 detail B if St1 or St2
n° 7.2
N
5.1.5
1, 2, 3, 4
if
d  150 m m
all allowed circumferential
joints can be used
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
1, 2, 3, 4
see F 1
A
N
a  0 , 7 e m in
3, 4
if
d  150 m m
32
A
B if St1 or St2
N
for each weld
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
F 10
Applicable
weld testing
group
3, 4
if
d  150 m m
-
5.1.4
1, 2, 3, 4
if
d  150 m m
NOT ALLOWED
1), 2), 3) see Table A-1.
626
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-8 — Nozzles
N1
Full penetration
Applicable
weld testing
group
1, 2, 3, 4
N2
Full penetration
1, 2, 3, 4
see Table
18-4 detail
n° 3.2
B
N
2.2.6
N3
Full penetration
1, 2, 3, 4
see Table
18-4 detail
n° 3.2
B
N
2.2.6
N4
Full penetration
1, 2, 3, 4
see Table
18-4 detail
n° 3.2
B
N
2.1.5
N5
Full penetration
1, 2, 3, 4
see Table
18-4 detail
n° 3.2
B
N
2.1.1
N6
Full penetration
1, 2, 3, 4
see relevant A
reference in
C
N
2.4.1
N7
a  0 , 7 e m in
3, 4
if
d  150 m m
see Table
B
18-4 detail
n° 3.2 or 3.3
N
2.2.2
Ref.
Type of joint
Design requirements
Fatigue
class 1)
Lamellar tearing
susceptibility 2)
Corrosion 3)
EN 17081: 2010
see Table
18-4 detail
n° 3.2
B
N
2.2.6
2.3.3
Key
A shell or head
B nozzle neck
for each weld
d  600 m m
d / D 1/3
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
1, 2, 3, 4
if
d  150 m m
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
627
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-8 — Nozzles (concluded)
Ref.
Type of joint
N8
Design requirements
a  0 , 7 e m in
for each weld
d  800 m m
d / D 1/3
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
N9
a  0 , 7 e m in
Applicable
weld testing
group
3, 4
if
d  150 m m
Fatigue
class 1)
see Table
18-4 detail
n° 3.2 or 3.3
Lamellar
Corrosion 3)
tearing
susceptibility 2)
B
N
EN 17081: 2010
2.2.5
1, 2, 3, 4
if
d  150 m m
3, 4
not allowed
B
S
1, 2, 3, 4
see relevant A
reference in
C
N
-
for each weld
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
N 10
NOT ALLOWED
N 11
all allowed circumferential
joints can be used
), 2), 3) see Table A-1.
628
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table A-9 — Circumferential welds in bellows
Ref.
Type of joint
Design requirements
B1
Full penetration
B2
a  0 ,7 e b
Lamellar
tearing
susceptibility 2)
A
Corrosion 3)
N
-
1, 2, 3
B
S
-
1, 2, 3
A
S
-
1, 2, 3
A
N
-
1, 2, 3
B
S
-
Applicable
weld testing
group
1, 2, 3
Fatigue
class 1)
EN 17081: 2010
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
B3
a  0 ,7 e b
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
B4
a  0 ,7 e b
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
B5
a  0 ,7 e b
NOT ALLOWED FOR DBA-DR
AND CREEP DESIGN
1), 2), 3) see Table A-1.
UNI EN 13445-3:2021
629
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex B
(normative)
Design by Analysis – Direct Route
B.1 Introduction
B.1.1 General
This annex is currently limited to sufficiently ductile materials, like the whole standard, but it is, for
components operating in the creep range, also limited to sufficiently creep ductile materials.
NOTE
The steels and steel castings listed in EN 13445-2:2021, Table E.2-1 for which, for the relevant
temperature range, creep strengths are given in the referred to material standards, are considered to be
sufficiently creep ductile.
B.1.2 Purpose
Design-by-analysis (DBA) provides rules for the design of any component under any action. It may be used:
— as an alternative to design-by-formulas (see 5.4.1)
— as a complement to design-by-formulas for:
— cases not covered by that route;
— cases involving superposition of environmental actions;
— cases where the manufacturing tolerances given in EN 13445-4:2021, Clause 6, are not fulfilled,
in agreement with the parties concerned.
In the last item, any deviations beyond tolerance limits shall be clearly documented.
B.1.3 Special requirements
Due to the advanced methods applied, until sufficient in-house experience can be demonstrated, the
involvement of an independent body, appropriately qualified in the field of DBA, is required in the
assessment of the design (calculations) and the potential definition of particular NDT requirements.
B.1.4 Creep design
For components which, under reasonably foreseeable conditions, may operate in the creep range, the
lifetime of this creep load case (or the lifetimes for more than one of such load cases) shall be specified (by
the user or his representative). For each load case which includes operation in the creep range, the specified
time for operation in the creep range shall not be less than 10 000 h. If none is specified, the manufacturer
shall assume a reasonable time, but at least 100 000 h.
630
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
Whereas for structures with solely non-creep load cases the load cases can be specified quite
independently, the specification of load cases for structures with creep load cases requires careful consideration
of the total design life taking into consideration all reasonably foreseeable load cases. Alternative total design lives
may be used.
The (specified or assumed) design life shall be stated in the Technical Documentation.
If calculation temperatures are below the creep range (see 5.1) no creep design checks are required, and
B.5.1.3 and B.9 do not apply.
If the minimum of the two values:
r)
the product of 1,2 and the creep rupture strength at calculation temperature and for the relevant
lifetime,
s) the product of 1,5 and the 1% creep strain strength at calculation temperature and for the
relevant lifetime
is larger than the 0,2 % proof strength at calculation temperature, no creep design checks are required, and
B.5.1.3 and B.9 do not apply. If the minimum of the two values is not larger than the 0,2 % proof strength at
calculation temperature, creep design checks are required, and B.5.1.3 and B.9 apply.
The designations creep rupture strength and 1 % creep strain strength refer to mean values, as specified in
the material standard, for which a scatter band of experimental results of  20 % is assumed. For larger
scatter bands 1,25 times the minimum band values shall be used instead of mean values.
For interpolation and possible extrapolation of strength values, and for the determination of time to creep
rupture or 1 % creep strain, the procedures given in Clause 19 shall be used.
B.2 Specific definitions
The following definitions are in addition to those in clause 3.
B.2.1
action
imposed thermo-mechanical influence which causes stress and/or strain in a structure, e. g. an imposed
pressure, force, displacement, temperature, see B.6
B.2.2
action type
classification of action based on statistical properties and duration
B.2.3
application rule
generally recognised rule that follows the principles and satisfies their requirements
Note 1 to entry: Alternative design rules, different from the application rules given in this standard, may be used,
provided that it is shown that the alternative rule accords with the relevant principles and is at least equivalent
with regard to reliability, serviceability and durability, see B.5.1.
UNI EN 13445-3:2021
631
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.2.4
characteristic value/function
a characteristic value of an action is a representative value which takes account of the variation of an
action, see B.6.2
Note 1 to entry: A characteristic function of an action is a representative function (of time) for the action,
required for actions for which, in specific design checks, the time-dependence is of importance, e.g.
temperature/pressure transients during start-up or shut-down, see B.6.2.3.
B.2.5
coefficient of variation
measure of statistical dispersion (standard deviation divided by mean value)
B.2.6
combination factor
factor applied to design values of variable actions with stochastic properties if combined with pressure,
or if two or more of these actions are included in one load case, see B.8.2.3
B.2.7
design check
investigation of a component's safety under the influence of specified combinations of actions with
respect to specified limit states, see B.5.1
B.2.8
design model
structural (physical) model used in the determination of effects of actions
B.2.9
effect
response (e.g. stress, strain, displacement, resultant force or moment, equivalent stress resultant) of a
component to a specific action, or combination of actions
B.2.10
limit state
structural condition beyond which the design performance requirements of a component are not
satisfied
Note 1 to entry: Limit states are classified into ultimate and serviceability limit states, see B.4.
B.2.11
load case
a combination of coincident actions. Load cases are classified into normal operating load cases, special
load cases and exceptional load cases, see B.5.1
B.2.12
local stress/strain concentration
stress/strain distribution related to very local geometric or material stress/strain raisers or
temperature fields, which affect the stress or strain distribution only through a fraction of the thickness
Note 1 to entry: Local stress/strain distributions are associated solely with localised types of deformation or
strain, have no significant non-local effect. Examples are stress concentrations at small fillet radii, small
attachments, welds etc.
632
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.2.13
partial safety factor
factor which is applied to a characteristic value of an action or a material parameter in order to obtain
the corresponding design value
Note 1 to entry: It depends on the design check, the action, material parameter, see B.6.3 and B.7.5.
B.2.14
principle
general or definitive statement, for which there is no alternative, unless specifically stated otherwise,
or: Requirement and model, for which no alternative is permitted unless specifically stated, see B.6
B.2.15
structure
combination of all load carrying parts relevant to the component, e.g. the whole vessel, its load carrying
attachments, supports and foundations
B.2.16
(equivalent) stress-concentration-free model
an equivalent idealised model of the structure without local stress/strain raisers
B.2.17
structural strain
strain in a stress-concentration-free model of the structure, i. e. the strain determined in an idealised
model which takes into account the real geometry of the structure with the exception of the local details
which cause only local stress/strain concentrations, see B.7.6
Note 1 to entry: Structural strain includes the effects of gross structural details (e. g. branch connections, conecylinder intersections, vessel-end junctions, thickness discontinuities, presence of attachments, deviations from
design shape with global effect, such as out-of-roundness of cylindrical shells). However it excludes the notch
effects of local structural details, such as small fillet radii, weld toe details, weld profile irregularities, small
(partial penetration) bores, or of local temperature field details.
Note 2 to entry: Finite element shell or beam elements may give structural strain directly.
B.2.18
(relevant) thickness
shortest distance from the critical point, on one surface, to any point on any other surface of the model
B.2.19
total stress / strain
total stress/strain in a design model which includes all stress/strain concentration effects, non-local
and local
B.3 Specific symbols and abbreviations
The following symbols and abbreviations are in addition to those in Clause 4 and in Clause 19 for creep
operation.
UNI EN 13445-3:2021
633
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.3.1 Subscripts
all
allowed
c
creep
d
design
e
related to elastic limit
i
ith value
inf
lower bound
j
jth value
k
kth value
u
related to strain limiting
A
action (general)
G
permanent action
P
pressure action
Q
variable action
sup
upper bound
B.3.2 Symbols
D
fatigue damage (measure)
RM
material strength parameter

partial safety factor
B.4 Failure modes and limit states
The main failure modes are listed in Table B.4-1 with the relevant type of limit state. The latter are classified
according to whether the action is short term, long term or cyclic.
Individual failure modes only are given in Table B.4-1. Combinations of failure modes, e.g. fatigue - plastic
rupture, creep - plastic rupture, creep - fatigue, shall be considered separately.
NOTE 1
The list of failure modes in Tabl B.4-1 is quite general, encompasses also failure modes outside the
scope of this standard.
A limit state is classified as either an ultimate or a serviceability limit state.
634
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
An ultimate limit state is a structural condition (of the component or vessel) associated with burst or
collapse, or with other forms of structural failure which may endanger the safety of people.
NOTE 2
Ultimate limit states include: failure by gross plastic deformation; rupture caused by fatigue; collapse
caused by instability of the vessel or part of it; loss of equilibrium of the vessel or any part of it, considered as a
rigid body, by overturning or displacement; and leakage which affects safety.
NOTE 3
Some states prior to collapse which, for simplicity, are considered in the place of the collapse itself are
also classified and treated as ultimate limit states.
A serviceability limit state is a structural condition (of the component or vessel) beyond which the service
criteria specified for the component are no longer met.
NOTE 4
Serviceability limit states include:
— deformation or deflection which adversely affects the use of the vessel (including the proper
functioning of machines or services), or causes damage to structural or non-structural elements;
— leakage which affects efficient use of the vessel but does not compromise safety nor cause an
unacceptable environmental hazard.
NOTE 5
Depending on the hazard, leakage may create either an ultimate or a serviceability limit state.
UNI EN 13445-3:2021
635
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table B.4-1 — Classification of failure modes and limit states
Failure mode
Short term
Single
Multiple
Application
application
U
U
S, U 1)
U
S
U
U, S 2)
U
U
action type
Long term
Single
Multiple
application
application
Brittle fracture
Ductile rupture 3)
Excessive deformation 1 4)
Excessive deformation 2 5)
Excessive deformation 3 6)
Excessive local strains 7)
Instability 8)
Progressive plastic def. 9)
Alternating plasticity 10)
Creep rupture
U
11)
Creep-Excessive def. 1
S, U 1)
Creep-Excessive def. 2 12)
U
Creep-Excessive def. 3 13)
S
Creep instability
U, S 2)
Erosion, corrosion
S
Environmentally assisted
U
cracking 14)
Creep
U
Creep-Excessive def. 1 11)
S, U 1)
Creep-Excessive def. 2 12)
U
Creep-Excessive def. 3 13)
S
Creep instability
U, S 2)
Erosion, corrosion
S
Environmentally assisted
U
Cracking 14)
Fatigue
Environmentally assisted
fatigue
U indicates ultimate limit state. S indicates service limit state.
1)
In case of risk due to leakage of content (toxic, inflammable, steam, etc.).
2)
In case of sufficient post-instability load carrying capacity.
3)
Unstable gross plastic yielding or unstable crack growth.
4)
Excessive deformations at mechanical joints.
5)
Excessive deformations resulting in unacceptable transfer of load.
6)
Excessive deformations related to service restraints.
7)
Resulting in crack formation or ductile tearing by exhaustion of material ductility.
8)
Elastic, plastic, or elastic-plastic.
9)
Progressive plastic deformations (or ratcheting).
10)
Alternating plasticity (see also Clause 6).
11)
Creep-Excessive deformation at mechanical joints.
12)
Creep-Excessive deformation resulting in unacceptable transfer of load.
13)
Creep-Excessive deformation related to service restraints.
636
Cyclic
U
U
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
14)
Stress corrosion cracking (SCC), Hydrogen induced cracking (HIC), Stress orientated hydrogen induced
cracking (SOHIC).
B.5 Methodology
B.5.1 General, design checks
B.5.1.1 General
To each relevant failure mode, relevant with regard to the scope of this standard, there corresponds a single
design check (DC). Each design check represents one or more failure modes.
The design checks shall be carried out for the following (classes of) load cases, where relevant
— normal operating load cases, where normal conditions apply
— special load cases, where conditions for testing, construction, erection or repair apply
— exceptional load cases, see 5.3.2.2.
In general, each design check comprises various load cases; load cases being combinations of coincident
actions, that can occur simultaneously under reasonably foreseeable conditions.
To each design check a simple principle is stated. For each principle, one or more application rules are given,
to indicate different means by which an assessment can be made. The most relevant application rule or rules
shall be selected. It is permissible to use other application rules, provided they accord with the relevant
principle, and are at least equivalent with regard to safety, reliability and durability.
B.5.1.2 Design checks for calculation temperatures below the creep range
The design checks to be considered are:
— Gross Plastic Deformation Design Check (GPD-DC), see B.8.2;
— Progressive Plastic Deformation Design Check (PD-DC) , see B.8.3;
— Instability Design Check (I-DC) , see B.8.4;
— Fatigue Design Check (F-DC) , see B.8.5;
— Static Equilibrium Design Check (SE-DC), see B.8.6.
NOTE
The design checks are named after the main failure mode they deal with. Some design checks may not
be relevant for a particular design. The list of design checks is not exhaustive. In some cases, it may be necessary
to investigate additional limit states. For example, with austenitic stainless steel, failure by GPD shall be checked
(as an ultimate limit state) but leakage may also need to be checked (as either an ultimate or a serviceability limit
state), see Table B.4-1.
UNI EN 13445-3:2021
637
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.5.1.3 Design checks for calculation temperatures in the creep range
If creep design checks are required, see B.1.4, the design checks which shall be considered, in addition to
those listed in B.5.1.2, are:
— Creep Rupture Design Check (CR-DC), see B.9.4,
— Excessive Creep Strain Design Check (ECS-DC), see B.9.5,
— Creep Fatigue Interaction Design Check (CFI-DC), see B.9.6.
NOTE
For some load cases creep rupture design checks may make corresponding gross plastic deformation
design checks superfluous.
B.5.2 Procedure
The procedure comprises the following stages:
a) At least all of the design checks listed in B.5.1 shall be considered, see NOTE in B.5.1;
b) For each design check all relevant load cases shall be considered;
c) For each design check / load case an appropriate application rule shall be selected, if the principle
is not used directly;
d) For each design check / load case the fulfilment of the design check's principle shall be shown,
directly or by usage of the selected application rule, and by carrying out the following steps:
1) Specification of design check / load case and corresponding actions;
2) Determination of the actions' characteristic values, or characteristic functions;
3)
Calculation of the actions' design values, or design functions;
4) Check of the fulfilment of the principle;
5) Statement confirming whether or not the principle for the load case is fulfilled.
B.6 Actions
B.6.1 Classification
Actions are classified into the following four types:
— permanent actions;
— temperature, pressure, and actions related to them deterministically;
— variable actions other than temperature, pressure and actions related to them deterministically;
— exceptional actions.
638
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Although operating pressures and temperatures are variable actions, they have special characteristics with
regard to their variation in time, random properties, etc. Because there is usually a strong correlation
between operating pressure and temperature, they shall be considered to act simultaneously, and the
pressure - temperature dependence shall be defined appropriately.
NOTE 1
Mechanical, physical, chemical or biological actions may have an influence on the safety of a vessel.
However, in DBA only those which cause stress or strain are considered. Examples of actions considered are:
volume forces (e.g. self-weight), surface forces (pressures, surface loadings, etc.), singular forces (resultants
representing e.g. imposed surface forces), line forces, point forces, temperature changes, displacements imposed
on the vessel at connections, foundations, due to e.g. temperature changes, settlement.
NOTE 2
Examples of permanent actions are: self-weight of a structure and associated fittings, ancillaries and
fixed equipment.
NOTE 3
Examples of variable actions are: imposed displacements, wind or snow loads
NOTE 4
Examples of exceptional actions are: actions on secondary containment due to failure of primary
containment, internal explosions, or exceptional earthquake actions - actions which need not be considered as
normal operating conditions, are not considered to occur under reasonably foreseeable conditions.
NOTE 5
Temperature changes have a dual role in that they may cause stress in the structure and also change its
material properties.
NOTE 6
Environmental attack (whether internal or external) may reduce the safety or serviceability of a vessel.
This should be taken into account in the selection of materials, provision of additional wall thickness (see 5.2.2),
or specification of appropriate material parameters in the design model (see B.7.5).
NOTE 7
Pressure-temperature dependence may be stated either in the form of coincident pairs or in the form
of a functional relationship between fluid pressure and temperature.
With actions which consist of permanent and variable parts, the parts shall be considered individually.
Variable actions may include actions of quite different characteristics, e.g.
— actions which are related to pressure and/or temperature in a deterministic way. These shall be
combined in the pressure/temperature action, and the relationship, exact or approximate, shall be
used;
— actions which are not correlated with pressure or temperature but have well defined (bounded)
extreme values;
— actions, like wind loads, which can be described only as stochastic (i.e. random) processes and are
not correlated with pressure or temperature.
B.6.2 Characteristic values and characteristic functions of actions
The requirements for determining the characteristic values of different types of action are given in Table B.61.
UNI EN 13445-3:2021
639
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table B.6-1 — Characteristic values for different types of action
Action
Permanent
Coefficient
of variation
 0,1 1)
Permanent
> 0,1
3)
Symbol
Characteristic value
G k 2)
Mean of extreme values
G
Upper limit with 95 % probability of
not being exceeded; 4)
Lower limit with 95 % probability of
being exceeded. 4)
Mean of extreme values
k, sup
G k,
in f
Variable
 0,1 1)
Q k 2)
Variable
> 0,1
Q k 2)
Exceptional
-
-
2)
Psup
Pressures and
temperatures
Tsup
P in f
T in f
1)
2)
3)
6)
97% percentile of extreme value in
given period 5)
Shall be individually specified
Reasonably foreseeable highest
pressure
Reasonably foreseeable highest
temperature
Reasonably foreseeable lowest
pressure 6)
Reasonably foreseeable lowest
temperature
The mean of the extreme values may also be used when the difference between the reasonably
foreseeable highest value and the lowest one is not greater than 20% of their arithmetic mean
value.
The subscript k in Table B.6-1 indicates that there are usually several actions in a load case and
they are individually numbered.
Also applies where the actions are likely to vary during the life of the vessel (e.g. some
superimposed permanent loads)
4) If a statistical approach is not possible, the highest and lowest credible values may be used.
5) For variable actions which are bounded, the limit values may be used as characteristic
values.
This value is usually either zero or -1,0 (for vacuum conditions).
The upper characteristic value of the pressure, Psup, may be based on the maximum allowable pressure PS,
the pressure accumulation at a pressure relief device when the pressure relief device starts to discharge, the
pressure increase over the maximum allowable pressure need not be taken into account.
The characteristic values of pressure and temperature describe the pressure-temperature regime that
envelops those pressures and temperatures which can occur under reasonably foreseeable conditions, see
Figure B.6-1.
The following characteristic values shall always be specified:
— the upper characteristic value of the pressure (Psup) ;
— the lower characteristic value of the pressure (Pinf) ;
— the upper characteristic value of the temperature (Tsup) ;
— the lower characteristic value of the temperature (Tinf).
640
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For temperature values which are not environmentally imposed and in cases where a combination of Psup
and Tsup is uneconomic, it may be necessary to specify characteristic pressure - temperature pairs, e.g.
(Psup,i, Tsup,i), (Pinf,i, Tinf,i), which determine an envelope of the (P, T) - regime of the reasonably
foreseeable extreme values, see Figure B.6-1.
P
Psup1
1
Tsup 1
Tinf 5
Tinf 1
Psup 2
2
Psup 5
5
Pinf 3
3
Tsup 2
Tinf 4
Tsup 3
4
Pinf 4
T
Figure B.6-1 — Typical plot of coincident temperatures and pressures
NOTE 1
For permanent actions which give in some combinations with other actions favourable and in others
unfavourable contributions, upper and lower characteristic values are required.
The self-weight of the structure and of non-structural parts may be calculated on the basis of nominal
dimensions and mean unit masses.
For wind, snow, and for earthquake actions, the values specified in relevant regional codes, i.e. country
specific data, may be used.
In load cases where thermal stresses (constant or transient) have an influence on the safety of the structure,
the characteristic values of coincident pressure / temperature shall be the extreme values of operating
pressure and temperature that can reasonably be expected to occur under normal operating conditions over
the life of the vessel.
For actions for which, in specific design checks, the time-dependence is of importance, characteristic
functions, of time or a time-order parameter, are required for the PD- and F- design checks, see also
Clause 17 and Clause 18 (for fatigue assessment). Realistic assessment of these functions is crucial to the
checks' results, especially the fatigue results. Thus, the characteristic functions shall represent an "upper
bound estimate" of the fluctuating actions to be experienced by the structure or part under reasonably
foreseeable conditions during the full design life – in a statistical sense like the characteristic values. For
different design checks different characteristic functions may be specified, taking account of the design
checks' principles.
NOTE 2
The characteristic functions should be specified by the purchaser; if not, the manufacturer should
assume reasonably extreme values.
Used characteristic values and characteristic functions shall be clearly documented.
UNI EN 13445-3:2021
641
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.6.3 Design values and design functions of actions
The design value A d of an action shall be determined by multiplication of its characteristic value with the
relevant partial safety factor of the action, in general terms:
Ad  
A
A
,
(B.6-1)
A is the characteristic value of the action and γA the relevant partial safety factor of the action as given in B.8
for the considered design check.
For exceptional actions the partial safety factors (for the actions) shall be agreed upon by the parties
concerned, but shall not be smaller than one.
NOTE
The partial safety factor 
A
takes account of the following:
—
the possibility of non-conservative deviation of the actions from their characteristic values;
—
the uncertainty of the models which describe the physical phenomena for the action and effect;
—
uncertainty in any stochastic models of the action;
—
whether the action has a favourable or an unfavourable effect: For example, in one load case the action due to
the weight of a component might be opposing the governing one, e.g. pressure, and, therefore, has a
favourable effect. In another, the weight might be acting with the pressure and so has an unfavourable effect.
In the two load cases, the partial safety factor of weight would have a different value. If the governing action
is not obvious, separate load cases are required.
Design functions of actions, required in the progressive plastic deformation and the fatigue design checks,
are identical with the characteristic functions, i.e. the partial safety factors for these actions in the relevant
design checks are equal to 1.
B.7 Design models
B.7.1 General
For the determination of the effects of (design) actions specific (physical) models shall be used and these
depend on the design check. Detail specifications for these specific models are given in Clause B.8 dealing
with the specific design checks, general descriptions and requirements in the following.
Whenever the initial (and weightless) stress state of the model is of importance in a design check, the stressfree state shall be used.
First-order-theory shall be used, i.e. geometrically linear kinematic relations and equilibrium conditions for
the undeformed structure shall be used except for the two following checks.
Instability design checks shall be based on non-linear geometric relations – equilibrium conditions for the
deformed structure and non-linear kinematic relations. Second order theory – linear kinematic relations and
equilibrium conditions for the deformed structure – may be used, if it can be shown to be accurate enough.
642
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
In case of structures and actions resulting in an unfavourable (weakening) effect, geometrically non-linear
effects shall be taken into account in design checks against gross plastic deformation, creep rupture, creep
excessive strain, and fatigue.
NOTE
Examples of structures and actions with such weakening effect are:
— nozzles in cylindrical shells under transverse moment;
— nozzles in cylindrical shells under axial compressive force;
— bends under closing moment;
— cylindrical shells with out-of-roundness or peaking under external pressure.
B.7.2 Geometry
For geometric data nominal values for individual dimensions, rather than minimum values, shall be used,
with the exception of thicknesses for which analysis thicknesses shall be used.
NOTE
In case of sub-models or part-models, the models should encompass all the necessary parts of the
structure to include possible elastic follow-up effects.
B.7.3 Clad components
For clad components the nominal face of the cladding shall be used as surface at which the pressure acts.
Structural strength may be attributed to the cladding in gross plastic deformation design checks, B.8.2, only
in the case of integrally-bonded type and by agreement of the parties concerned.
In instability design checks, B.8.4, no structural strength shall be attributed to the cladding.
In the progressive plastic deformation design checks, B.8.3, and in the fatigue design checks, B.8.5, the
presence of the cladding shall be considered with respect to both the thermal analysis and the stress
analysis. However, when the cladding is of the integrally-bonded type and the nominal thickness of the
cladding is not more than 10 % of the total nominal thickness of the component, the presence of the
cladding may be neglected, i.e. the model based on the base metal geometry.
B.7.4 Constitutive laws
The constitutive law to be used in the model depends on the design check:
— in the gross plastic deformation design check, B.8.2, a linear-elastic ideal-plastic law with Tresca's
yield condition (maximum shear stress condition) and associated flow rule;
UNI EN 13445-3:2021
643
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— in the progressive plastic deformation design check, B.8.3, in the creep rupture design check, B.9.4,
in the creep excessive strain design check, B.9.5, a linear-elastic ideal-plastic law with von Mises'
yield condition (maximum distortion energy condition) and associated flow rule;
— in the fatigue design check, B.8.5, a linear-elastic law;
— in the instability design check, B.8.4, either a linear-elastic or a linear-elastic ideal-plastic law,
depending on the approach.
In the GPD-DC von Mises' yield condition may also be used, but the design material strength parameter
(design yield strength) shall then be modified, see NOTE in B.8.2.1.
In the F-DC, which shall be performed by usage of the requirements of Clause 18, continuing plastification is
accounted for by application of plasticity correction factors, see 18.8.
In the creep-fatigue interaction design check results of F-DC and ECS-DC are used.
B.7.5 Material parameters
B.7.5.1 Material strength parameters
B.7.5.1.1
Short-term characteristic values
The design value of the material strength parameter (design yield strength) of plastic constitutive laws RMd
shall be determined by division of the parameter's characteristic value by the relevant partial safety factor,
in general terms:
RMd = RM / R
(B.7-1)
where
RM
is the characteristic value of the relevant material strength and R the relevant partial safety
factor.
Details for the determination of the characteristic values of the material strengths, and the partial safety
factors, are specified in the sub-clauses of the design checks, B.8.2 to B.8.5.
For exceptional situations, the partial safety factor  R shall be agreed upon by the parties concerned, but
shall not be less than the one for testing situations.
In the determination of these characteristic values RM the minimum specified material strength data shall be
used, i. e. values for ReH, Rp0.2/T, Rp1.0/T, Rm/T , which apply to the materials in the final fabricated condition,
which shall conform with the minimum specified values of the appropriate material specification.
NOTE
4:2021.
These values will generally be achieved when the heat treatment procedures conform with EN 13445-
These minimum values, guaranteed for the delivery condition, may be used unless the heat treatment is
known to lead to lower values.
644
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
If welding gives lower strength values after fabrication and/or heat treatment, these shall be used.
Temperature dependent material strength data, used in the determination of a characteristic strength value,
Rp0.2/T Rp1.0/T and Rm/T, shall be for the reference temperature specified in the relevant sub-clauses of the
design checks / load cases, B.8.2 to B.8.5.
If short-term material strength parameters for load cases with temperatures in the creep range are not
specified in the material standards for the (high) calculation temperatures, extrapolations in temperature
from specified values as in Annex S may be used.
B.7.5.1.2
Long-term characteristic values
For the determination of the long-term characteristic values of
temperatures in the creep range, see B.9.3.
RM
, relevant for load cases with calculation
B.7.5.2 Other material parameters
For the modulus of elasticity, Poisson's ratio, and the coefficient of linear thermal expansion, time invariant
design values may be used. These are obtained from the corresponding instantaneous values for the
material, see Annex O, at a reference temperature which depends on the design check / load case. This
reference temperature shall not be less than
— 0,75 Tc max + 5 K in the gross plastic deformation design check, and where Tc max is the maximum
calculation temperature of the load case;
— 0,25 Tc min + 0,75 Tc max in the progressive plastic deformation and the fatigue design check, and
where Tc min and Tc max are minimum and maximum calculation temperatures in the action cycles
considered;
— Tc max in the instability design check, and where Tc max is the maximum calculation temperature of
the load case.
NOTE
The reference temperature may be space dependent.
B.7.6 Structural strain
In some design checks structural strains are required. Some models may give these directly, e.g. finite
element models using shell or beam elements. In cases where the model does not give structural strain
directly, e.g. finite element models using volume (brick) elements, the value of the quantity of interest at a
critical point (hot spot) shall be determined by quadratic extrapolation, with surface pivot points at distances
of 0,4e, 0,9e, 1,4e from the critical point, see 18.6.1; e is the (relevant) thickness of the structure at the
critical point, see B.2.18.
Denoting the quantity of interest at the critical point by yo, the corresponding one in the pivot point Pi by yi,
yo may be calculated by Equation (B.7-2):
yo = y1 – 1,52 (y2 – y1) + 0,72 (y3 – y2) = 2,52 y1 – 2,24 y2 + 0,72 y3
(B.7-2)
where
UNI EN 13445-3:2021
645
EN 13445-3:2021 (E)
Issue 1 (2021-05)
P1 is the pivot point nearest to the critical one, P2 is the next, etc.
NOTE
In case of doubt, or in case of obviously meaningless extrapolation values, the total stress/strain in any
model which deviates solely in the local stress/strain concentrations may be used.
B.8 Non-creep Design checks
B.8.1 General
All of the design checks specified in the Clause B.8 shall be considered, and all relevant load cases shall be
dealt with.
B.8.2 applies mainly to failure by gross plastic deformation (GPD), in either operation or test, but deals also
with excessive local strains. The other sub-clauses apply as follows: For failure by progressive plastic
deformation (PD), see B.8.3; by instability (I), see B.8.4; by fatigue (F), see B.8.5; and by overturning and
global displacement, i. e. with rigid body motions, static equilibrium (SE), see B.8.6.
B.8.2 Gross Plastic Deformation (GPD)
B.8.2.1 Principle
For each load case, the design value of an action, or of a combination of actions, shall be carried by the
design model with
— linear-elastic ideal-plastic constitutive law
— Tresca's yield condition (maximum shear stress hypothesis) and associated flow rule
— design material strength parameter
— partial safety factor
R
RM
d
as specified in B.8.2.3 c) or B.8.2.4 c)
as specified in B.8.2.3 c) or B.8.2.4 c)
— proportional increase of all actions and a stress-free initial state
with the maximum absolute value of the principal structural strains being less than:
— 5 % in normal operating load cases
— 7% in testing load cases.
NOTE 1
In exceptional load cases the strain limitation does not apply.
NOTE 2
In case of the normal hydraulic test, as specified in EN 13445-5:2021 and negligible action other than
pressure, this check is not required.
Von Mises' yield condition may be used instead of Tresca's, but then the design strength parameter shall be
multiplied by
3 /2
.
With the exception of cases where deformation has a weakening effect, see B.7.1, first-order-theory shall be
used; where deformation has a weakening effect geometrical non-linear effects shall be taken into account.
646
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.8.2.2 Application rule: Lower bound limit approach
If it can be shown that any lower bound limit value of the action or combination of actions, determined with
the design model specified in the principle, is reached without violation of the strain limit, the principle is
fulfilled, if the design value of the action or combination of actions does not exceed that lower bound limit
value.
B.8.2.3 Design checks for normal operating load cases
a) Partial safety factors of actions shall be as given in Table B.8-1.
Table B.8-1 — Partial safety factors for actions and normal operating load cases
Action
Condition
Partial safety factor
Permanent
For actions with an unfavourable effect

G
 1,2
Permanent
For actions with a favourable effect

G
 0 ,8
Variable
For unbounded variable actions

Q
 1,5
Variable
For bounded variable actions and limit values

Q
 1,0
Pressure
For actions without a natural limit
 P  1,2
Pressure
For actions with a natural limit, e.g. vacuum

P
 1,0

T
 1,0
Temperature a
a
It may be necessary to include also effects caused by constrained temperature induced displacements in a GPD-DC, e.g. when
part-models are used and displacements in one model are imposed on the other model.
For wind, snow, and for earthquake actions country specific data, i.e. values specified in relevant regional
codes shall be used, if they are larger, but consistency with the corresponding characteristic values shall be
checked, such that the overall safety is maintained.
If only part of the pressure is subject to a natural limit, e.g. static head, this part may be multiplied by P =
1,0 and the remainder by P = 1,2.
b) Combination rules shall be as follows:
All permanent actions shall be included in each load case.
Each pressure action shall be combined with the most unfavourable variable action.
Each pressure action shall be combined with the corresponding sum of the variable actions; the design
values of stochastic actions, see B.6-1 and Table B.6-1, may be multiplied by the combination factor  = 0,9,
if these stochastic actions are combined with pressure and/or at least one other stochastic action.
UNI EN 13445-3:2021
647
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE
Since it is most unlikely that all the variable stochastic actions would be at their maximum together,
they may each be multiplied by  = 0,9 when combined with pressure or another stochastic action.
Favourable variable actions shall not be considered.
c) Material strength parameters (RM) and partial safety factors (  R ) shall be as given in Table B.82.
Table B.8-2 — RM and
Material
1
Ferritic steel

R
for normal operating load cases
RM
R
eH
or R p0,2/T

1,25 for
1,5625
Austenitic steel
(30%A5<35%)
R
p1,0/T
R
35%)
(see note)
 R p0,2/T

 R
m/20

R p 1.0/T
p1,0/T
R m/T
2 , 5 R p1.0/T
1,25 for
R
otherwise
R m/T
R p0.2/T
R m/20
p0,2/T
p0,2/T
R m/20
 0 ,4
R p1.0/T
19/12 for
2R
1




for 0,4 <
R m/T
Steel castings
 0 ,8
R m/20
1,25
1,0 for
Austenitic steel ( A 5
R p0,2/T
R
R
p 1 .0 / T
R
 0,5
m /T
 0 ,5

19/24
otherwise
Steel other than austenitic steel as per 6.4 and 6.5
As reference temperature of the temperature dependent material strength parameters a temperature not
less than the maximum calculation temperature of the load case shall be used.
NOTE 1
The reference temperature may be chosen as a function of space, or space-independent
NOTE 2
For austenitic steels, the values defined in Table B.8-2 may result in large deformations, and it is
advisable to check against leakage at bolted connections, bolted ends, etc.
B.8.2.4 Design checks for testing load cases
a) Partial safety factors against actions shall be as given in Table B.8-3.
648
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table B.8-3 ― Partial safety factors for actions and testing load cases
Action
Condition
Partial safety factor
Permanent
For actions with an unfavourable effect

G
 1,2
Permanent
For actions with a favourable effect

G
 0 ,8
Pressure
-
 P  1,0
Variable actions need not be considered.
b) Combination rules shall be as follows:
All permanent design actions shall be included in each load case.
In cases where more than one test is applied, e.g. multi-chamber vessels, each pressure case shall be
included.
c) RM and

R
shall be as given in Table B.8-4.
Table B.8-4 — RM and

R
for testing load cases
RM 2
Material

Ferritic1 steel
R e H o r R p 0 ,2
1,05
Austenitic steel (30 %  A 5 < 35 %)
R p 1 ,0
1,05
Austenitic steel ( A 5  35 %)
1,05 for
R p 1 ,0
2 , 0 R p1,0
Rm
Steel castings
R p 0 ,2
1
Steel other than austenitic steel as per 6.4 and 6.5
2
Values for RM shall be for the test temperature.
R p1.0
Rm
R
 0 , 525
otherwise
1,33
NOTE
The deformations at this material strength may be large for austenitic steels, and it is advisable to
check against leakage.
UNI EN 13445-3:2021
649
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.8.3 Progressive Plastic Deformation (PD)
B.8.3.1 Principle
On repeated application of the action cycles described below, progressive plastic deformation shall not occur
for
— first-order-theory;
— a linear-elastic ideal-plastic constitutive law;
— von Mises' yield condition (maximum distortion energy criterion) and associated flow rule; and
— design strength parameters RMd as specified in B.8.3.4.
NOTE
In this design check all partial safety factors are equal to 1, design values and design functions are
equal to characteristic values and characteristic functions.
B.8.3.2 Application rule 1: Technical adaptation
The principle is fulfilled, if it can be shown that the maximum absolute value of the principal structural
strains is less than 5 % after the application of the number of cycles specified for the considered load case. If
the number is not specified, then a reasonable number, but at least 500 shall be assumed.
NOTE
Total strains in any model which deviates only in the local stress/strain concentrations may be used
instead of structural strains.
B.8.3.3 Application rule 2: Shakedown (SD)
The principle is fulfilled, if the model with stress/strain concentrations shakes down to linear-elastic
behaviour under the action cycles considered
B.8.3.4 Application rule 3: Technical Shakedown
The principle is fulfilled if both of the following conditions are satisfied:
a) The equivalent stress-concentration-free model, see B.2.16, or any model which deviates from the
model with local stress/strain concentrations solely in the local stress/strain concentrations,
shakes down to linear-elastic behaviour under the cyclic action considered,
b) For the (detailed) model, with local stress/strain concentrations, any time-invariant selfequilibrating stress field can be found such that the sum of this stress field and the cyclically
varying stress field determined with the (unbounded) linear-elastic constitutive law for the cyclic
action considered is compatible with the relevant yield condition continuously in a core of the
structure which encompasses at least 80 % of every wall thickness.
NOTE 1
A self-equilibrating stress field is a stress field which satisfies the equilibrium conditions (in the
interior and on the surface) for zero imposed forces, i.e. for zero mass forces in the interior points and for zero
forces in all surface points with the exception of those where displacements are prescribed.
NOTE 2
In surface points where displacements are prescribed self-equilibrating stress fields may correspond
to non-vanishing surface forces.
650
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 3
A stress field is compatible with the relevant yield condition, if the von Mises equivalent stress does at
no time and nowhere exceed the design strength parameter.
B.8.3.5 Application rule 4: Technical shakedown for mechanical actions
This application rule applies for load cases without thermal stresses and without stresses induced by
prescribed displacements.
The principle is fulfilled (without specific proof) for all action cycles within the range of actions allowable
according to the Gross Plastic Deformation Design Check (GPD-DC).
NOTE
There are load cases with prescribed displacements which can be converted via global equilibrium
conditions into cases with prescribed forces, e. g. load cases with prescribed vanishing vertical displacements at
brackets, where the corresponding forces may be determined via the global equilibrium conditions.
B.8.3.6 Design checks
a) Action cycle
Characteristic values of permanent actions, and characteristic values or functions of pressure-temperatures,
shall be combined with the most unfavourable variable action in an action cycle, which shall encompass all
reasonably foreseeable combinations.
NOTE
It is important that characteristic functions are indeed representative of the corresponding action, and
the interested parties should be involved in their specification. The characteristic functions should not only
envelop the trajectories of reasonably foreseeable re-occurring actions in the action space, but be also
representative with regard to the speed of change, i.e. they should also envelop (closely) the corresponding
trajectories in the action-time space. In case of doubt, it can even be necessary to characterise the temperature
function (versus time) by a slow and a fast one, in order to encompass the worst case.
b) Design material strength parameters
1) Steels other than austenitic steels as per 6.4 and 6.5:
RM is given by ReH or Rp0.2/T, at the (time- and space-dependent) calculation temperature, or at a
time-independent temperature which shall not be less than 0,75 Tc max + 0,25 Tc min, where Tc max
and Tc min are the highest and lowest calculation temperatures at each point during whole
action cycle.
2) Austenitic steels as per 6.4 and 6.5:
RM is given by Rp1,0/T, at the (time- and space-dependent) calculation temperature, or at a timeindependent temperature which shall not be less than 0,75 Tc max + 0,25 Tc min, where Tc max and
Tc min are the highest and lowest calculation temperatures at each point during whole action
cycle.
3) Steel castings:
RM is given by ReH or Rp0.2/T, at the (time- and space-dependent) calculation temperature, or at a
time-independent temperature which shall not be less than 0,75 Tc max + 0,25 Tc min, where Tc max
and Tc min are the highest and lowest calculation temperatures at each point during whole
action cycle.
UNI EN 13445-3:2021
651
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.8.4 Instability (I)
B.8.4.1 Principle
For each load case, the design value of an action or of a combination of actions shall be not greater than the
design value of the corresponding buckling strength, obtained, with a limitation on the maximum value of
the principal structural strains of 5 %, with a design model with
— pre-deformations according to the critical (classical / bifurcation) buckling shapes and deviations
according to the allowed ones as per EN 13445-4:2021, or per specification on the drawings;
— a linear-elastic ideal-plastic constitutive law;
— von Mises' yield condition and associated flow rule;
— a design strength parameter as specified in B.8.4.4;
— proportional increase of all actions;
— stress-free initial state.
The design value shall be determined by division of this buckling strength by the relevant partial safety factor
 R as specified in B.8.4.4 and 8.4.5
B.8.4.2 Application rule 1: Experimental results
If relevant experimental results for specific load cases are available, the following application rule may be
used:
The principle is fulfilled, if it the design value of an action or of a combination of actions is not greater than a
lower bound of the expected range of failure values based on experimental observation.
The experiments shall include the effect of shape deviations. The results will normally be correlated by a
theoretical model with an experimentally determined reduction factor. Such a theoretical model will cover
buckling failure in the elastic range and comparison of a calculated stress with yield stress, and may include
the effect of shape imperfections. Tolerances on the design shape shall ensure that imperfections are kept
within the range covered by the experimental data.
B.8.4.3 Application rule 2: Clause 8 (for pressure action)
Fulfilment of the requirements given in clause 8 suffices as a stability check for pressure action.
B.8.4.4 Design checks for normal operating load cases
a) Partial safety factors of actions, and combination rules, shall be as specified in B.8.2.3 (for the
GPD-DC). Additionally, temperature action shall be included in all relevant load cases with a
partial safety factor of 1;
652
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) Material strength parameters shall be as in Table B.8-2 (for the GPD-DC). These values shall be used
directly, without multiplication by a safety factor;
c) The partial safety factor
shall be

R
, for the determination of the design value of the buckling strength,
— 1,25 provided that the pressure test (external) as called for in EN 13445-5:2021 is to be carried
out;
— 1,5 otherwise.
B.8.4.5 Design checks for testing load cases
d) Partial safety factors of actions, and combination rules, shall be as specified in B.8.2.4 (for the
GPD-DC).
e) Material strength parameters shall be as in Table B.8-4 (for the GPD-DC). These values shall be
used directly, without multiplication by a safety factor.
f)
The partial safety factor
shall be 1,1.

R
, for the determination of the design value of the buckling strength,
B.8.5 Cyclic Fatigue failure (F)
B.8.5.1 Principle
The design value of the damage indicator D d , for cyclic fatigue, obtained for all the (cyclic) design functions
of pressure / temperature and variable actions shall not exceed 1 .
B.8.5.2 Application rule
Fulfilment of the requirements given in clause 18 suffices as a check against fatigue failure.
B.8.5.3 Particular requirements
In a design check against fatigue, cladding shall be considered with respect to both thermal analysis and
stress analysis. However, when the cladding is of the integrally-bonded type and the nominal thickness of
the cladding is not more than 10 % of the total thickness of the component, the presence of the cladding
may be neglected, i.e. the model based on the base metal geometry.
B.8.6 Static equilibrium (SE)
B.8.6.1 Principle
The design effect of the destabilising actions shall be smaller than the design effect of the stabilising actions.
B.8.6.2 Design checks
a) Partial safety factors of actions shall be as given in Table B.8-2 and Table B.8-4 (for the GPD-DC).
If characteristic values country specific data) are used, it may be necessary to use different partial
safety factors for the actions, to maintain the overall safety required.
UNI EN 13445-3:2021
653
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For the verification of static equilibrium, stabilising (favourable) actions shall be represented by lower
design values and destabilising (unfavourable) actions by upper design values.
Permanent actions shall be represented by appropriate design values, depending on whether the
stabilising and destabilising effects result from
— the favourable or unfavourable part of a single permanent action and/or
— different permanent actions.
The self-weights of unrelated structural or non-structural elements made of different construction
materials shall be treated as separate permanent actions.
The self-weight of a homogeneous structure shall be treated as a single permanent action.
The self-weight of essentially similar parts of a structure (or of essentially uniform non-structural
elements) shall be treated as separate favourable and unfavourable parts of a single permanent action.
b) Combination rules
For stabilising effects, only those actions, which can reliably be assumed to be present in the situation
considered, shall be included in the relevant combination.
Variable actions shall be applied where they increase the destabilising effects but omitted where they
would increase the stabilising effects.
Account shall be taken of the possibility that non-structural elements might be omitted or removed.
The favourable effect of variable action shall not be taken into account.
Where uncertainty of a value of a geometrical dimension significantly affects the verification of static
equilibrium, this dimension shall be represented in this verification by the most unfavourable value that
it is reasonably possible for it to reach.
B.9 Creep design checks
B.9.1
General
All of the design checks specified in the sub-clauses of this clause shall be considered, in addition to the
design checks specified in B.8. All relevant load cases shall be dealt with.
NOTE
There may be load cases where the creep rupture design check may replace the corresponding gross
plastic deformation design check.
The sub-clauses apply as follows: For creep rupture failure (CR), see B.9.4 and for failure by excessive creep
strain (ECS), see B.9.5.
654
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.9.2 Welded joints
Creep properties of welded joints normally differ essentially from those of the base metal, strain
concentrations may result. Weld joints, where the maximum principal stress closest to the normal to the
weld joint direction exceeds 80 % of the relevant design value of the material creep strength parameter,
shall be included in the model as a separate region, slightly larger than the likely maximum weld joint region
including the heat affected zone.
The design values of the material creep strength parameters of this weld region shall be:
— 80 % of the base metal design values, if the value is not determined by tests according to EN
13445-2:2021, Annex C, except for specific cases where it is known that lower values exist,
— design values determined by tests in EN 13445-2:2021, Annex C,
— not greater than the corresponding design values of the base metal.
It is a pre-condition of the use of this clause that all regions which are creep crack critical are accessible for
in-service inspection and in-service non-destructive testing, and that instructions for appropriate
maintenance and inspection are established and included in the operating instructions.
NOTE 1
Means for tracking creep deformation should be provided, including appropriate design details, such
as dedicated measurement points.
NOTE 2
B.9.3
Recommendations on appropriate maintenance and inspection are given in Annex M.
Material creep strength parameters
In the determination of the characteristic values of the material creep strength parameters RM the mean
specified material creep strength data shall be used which apply to the materials in the final fabricated
condition. These values shall conform to the values specified in the appropriate material specification.
Extrapolations shall be as the ones to be used in Clause 19.
The temperature for which these characteristic values are determined shall be the reference temperature
specified in the relevant sub-clauses of the creep design checks, B.9.4 through B.9.6.
B.9.4
Creep Rupture (CR)
B.9.4.1 Principle
For each creep load case, the design value of an action, or of a combination of actions, shall be carried by the
design model with
— linear-elastic ideal-plastic constitutive law,
— von Mises' yield condition (maximum distortion energy hypothesis) and associated flow rule
UNI EN 13445-3:2021
655
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— material strength parameter
3.
RM
and a partial safety factor
R
as specified in Tables B.9-2 and B.9-
— proportional increase of all actions and a stress-free initial state
with the maximum absolute value of the principal structural strains being less than 5 %.
With the exception of cases where deformation has a weakening effect, see B.7.1, first-order-theory shall be
used; where deformation has a weakening effect, geometrical non-linear effects shall be taken into account.
B.9.4.2 Application rule: Lower bound limit approach
If it can be shown that any lower bound limit value of the action or combination of actions, determined with
the design model specified in the principle, is reached without violation of the strain limit, the principle is
fulfilled, if the design value of the action or combination of actions does not exceed that lower bound limit
value.
B.9.4.3 Design Checks
a) Design checks are required for normal operating load cases only
b) Partial safety factors for actions shall be as given in Table B.9-1
Table B.9-1 — Partial safety factors for actions for CR load cases
Action
Permanent
Condition
For actions with an unfavourable effect
 G  1,2
Permanent
For actions with a favourable effect
 G  0 ,8
Variable
For unbounded variable actions
 Q  1,5
Variable
For bounded variable actions and limit values
 Q  1,0
Pressure
Temperature
a
Partial safety factor
 P  1,2
a
 R  1, 0
It may be necessary to include also effects caused by constrained temperature induced displacements in a CR-DC, e.g.
when part-models are used and displacements in one model are imposed on the other model.
c) Combination rules shall be as follows:
— All permanent actions shall be included in each load case.
— Each pressure action shall be combined with the most unfavourable variable action.
— Each pressure action shall be combined with the corresponding sum of the variable actions; the
design values of stochastic actions, see B.6-1 and Table B.6-1, may be multiplied by the
combination factor  = 0,9, if these stochastic actions are combined with pressure and/or at
least one other stochastic action.
656
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 1
Since it is most unlikely that all the variable stochastic actions would be at their maximum together,
they may each be multiplied by  = 0,9 when combined with pressure or another stochastic action.
Favourable variable actions shall not be considered.
d) Design material creep strength parameters ( RM ) and partial safety factors (  R ) shall be
calculated as specified in Table B.9-2 if there is no lifetime monitoring, or Table B.9-3 if lifetime
monitoring is provided.
NOTE 2
Lifetime monitoring is defined in 19.2.
e) As reference temperature T a temperature not less than the maximum calculation temperature
of the load case shall be used.
NOTE 3
The reference temperature
independent.
T
may be chosen as a function of space, but may also be chosen space -
As reference time t , the lifetime specified for the load case in the creep range for the component, or part,
see B.1.4, shall be used.
Table B.9-2 — RM and
Material

for CR load cases without monitoring
R

RM
1,25
R
Steel
m/ T / t
1
1, 2
R
Steel castings
Material
RM
Steel
R
Steel castings
R
B.9.5
R

R
R
R
m/ T / t
 1,5
p1,0/ T / t
m/ T / t
otherwise
p1,0/ T / t
(19/15)  value for Steel
m/ T / t
Table A.B.9-3 — RM and
if
R

R
for CR load cases with monitoring

R
12 ,5
m/ T / t
m/ T / t
12
(19/15)  value for Steel
Excessive Creep Strain (ECS)
B.9.5.1 Principle
In each point of the structure at which the calculation temperature in any load case is in the creep range, the
accumulated equivalent structural creep strain, accumulated over all design lifetimes in the creep range,
shall not exceed 5 %.
Until agreement on the design creep constitutive laws, based essentially on data in material standards, is
reached, the Principle shall not be used, but the Application Rules shall be used instead.
UNI EN 13445-3:2021
657
EN 13445-3:2021 (E)
Issue 1 (2021-05)
B.9.5.2 Equivalent creep strain
Denoting the components of the creep strain by

c

ij
, the equivalent strain  c is defined by
3
3
2
2

 (2 / 3) 

c
c ij
i  1j  1
(B.9-1)
B.9.5.3 Application Rule 1: Long creep periods (life fraction rule)
B.9.5.3.1
General
This application rule applies for creep load cases of sufficiently long creep periods with essentially timeindependent temperature and with time-independent other relevant actions, such that a calculation with
time-independent upper bounds of all relevant actions gives a reasonably good approximation of the
structure's creep behaviour. The creep periods shall be long enough such that the influence of initial
conditions on the lifetime can be reasonably neglected.
NOTE
models.
In case of doubt, the validity of this pre-supposition should be checked with reasonable constitutive
The principle is fulfilled, if in each point of the structure at which the calculation temperature in any load
case is in the creep range, the accumulated weighted design lifetime in the creep range, accumulated over
all design lifetimes in the creep range, does not exceed unity. The weight function shall be the reciprocal of
the allowable lifetime for the reference stress  ref determined for the relevant load case, see B.9.5.3.3.
B.9.5.3.2
Determination of the creep design temperature
For each interval of a load case in which the calculation temperature is in any point in the creep range the
creep design temperature T d ( x i ) shall be specified such that it bounds the calculation temperature T c
from above
Td(xi)  Tc(xi, t)
This upper bound may be replaced by a lower value provided this value is never exceeded by more than 10 %
over a time not more than 10 % of the load case lifetime in the creep range.
NOTE
This creep design temperature, to be specified for each interval of all load cases in which the
calculation temperature is in the creep range, may be specified as a function of space or as space-independent.
B.9.5.3.3
Determination of the reference stress
B.9.5.3.3.1 Determination of the elastic limit action
A
(k )
e
For each interval of a load case, of duration  t ( k ) , in which the calculation temperature is in the creep range,
the value A e of the action, or the combination of actions, shall be determined that corresponds to the onset
of plastification in structural stresses in the region with calculation temperatures in the creep range in a
design model with
— linear-elastic ideal-plastic constitutive law,
658
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— von Mises' yield condition (maximum distortion energy hypothesis)
— material strength parameters and partial safety factors as described in B.9.5.3.3.2
and
— for proportional increase of all actions, with the exception of temperature, which shall be timeindependent, and
— a stress free initial state.
B.9.5.3.3.2 Material strength parameters and partial safety factors
Material strength parameters shall be as in Table B.9-2, but
— partial safety factors

R
shall be equal to 1,0,
— the reference time shall be the (sufficiently long) interval duration
t
(k )
, see B.9.5.3.3.1
NOTE 1
For structures of more than one material the material strength parameters, and their design values,
will be space-dependent.
NOTE 2
For structures of one material, the material strength parameters, and their design values, may be
space-dependent or space-independent, depending on the choice of the creep design temperature.
B.9.5.3.3.3 Determination of the (strain limiting) limit action
A
(k )
u
.
For each interval, of duration  t (k ) , in which the calculation temperature is in the creep range, the
maximum value of the action, or the combination of actions, shall be determined which can be carried by
the design model with
— linear-elastic ideal-plastic constitutive law,
— von Mises' yield condition (maximum distortion energy hypothesis) and associated flow rule,
— material strength parameters and partial safety factors as in B.9.5.3.3.2
and for
— proportional increase of all actions, with the exception of temperature, which shall be timeindependent,
— stress free initial state,
with a maximum absolute value of the principal structural strains less than 5 %.
B.9.5.3.3.4 Reference stress
For each of these intervals, of duration
UNI EN 13445-3:2021
t
(k )
, the design reference stress is given by
659
EN 13445-3:2021 (E)
Issue 1 (2021-05)

(k )
ref
(k )
(k )
(k )
(k )  (k )
(k )

 A
1  0 ,13 ( A
)/ A
A
RM
/A
u
e
e  d
u
d



where, in addition to
A
(k )
e
,
A
(k )
u
,
RM
(k )
d
(B.9-2)
, as defined above,
A
(k )
d
denotes the design value of the
relevant action, or the relevant combination of actions. These design values shall be determined for actions
other than temperature from specified steady upper bounds of these actions with partial safety factors as in
Table B.9-1. The specified steady upper bounds shall bind the actions at least in the relevant interval.
NOTE
The reference stress may be space-independent but also space-dependent, depending on the choice of
the creep design temperature and on the number of materials, see NOTE 1 and NOTE 2 above. Since the very same
reference time  t (k ) has been chosen, the estimate of creep rupture endurance is space-independent. Therefore,
any convenient position x i may be chosen, e.g. the point of maximum equivalent stress, or the point of maximum
temperature, and reference stress and reference temperature in this point used in the determination of the
weighted lifetime.
B.9.5.3.4
Determination of the weighted lifetime
For each interval of a load case, of duration
the weight function is given by
1/ t
where
t
t
(k )
, in which the calculation temperature is in the creep range,
(k )
all
(k )
all
is the allowable lifetime for a stress equal to

(k )
ref
and a limit strength given by the design
strength parameter specified in B.9.5.3.3.2, i.e. according to Table B.9-2.
The weighted design lifetime, corresponding to this interval in this load case, is given by
t
(k )
B.9.5.3.5
/ t
(k )
all
Creep damage indicator
The creep damage indicator, equal to the accumulated weighted design lifetime, is given by the sum of all
weighted design lifetimes, summed up over all intervals of all load cases where the calculation temperature
is in the creep range, i.e. by
D
c
 ∑ t
(k )
/ t
(k )
all
(B.9-3)
where the sum extends over all intervals of all load cases, and over all specified (design) occurrences of the
load cases, in which the calculation temperature is in the creep range.
B.9.5.4 Application Rule 2: Long, interrupted creep periods
B.9.5.4.1
General
This application rule applies for load cases of sufficiently long creep periods, as in application rule 1, but
which are interrupted by action cycles resulting in responses of negligible creep and without plastification,
see B.9.5.4.2 and B.9.5.4.3.
660
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For such load cases, creep and cyclic periods may be treated separately and the individual interrupted creep
periods may be combined into one total (non-interrupted) creep period.
The principle is fulfilled if the creep and cyclic fatigue design check B.9.6 is fulfilled, with the creep damage
indicator determined for the total creep period by usage of application rule 1.
B.9.5.4.2
Action cycles with negligible creep
Action cycles, which interrupt long creep periods, are considered to be of negligible creep, if the maximum
duration of calculation temperatures in the creep range is less than 100 h.
B.9.5.4.3
Action cycles without plastification
Action cycles, which interrupt long creep periods, are considered to be without plastification, if the
maximum von Mises' equivalent stress of the response of the model, described below, to the cyclic actions
and with initial conditions, described below, does not exceed the short-term design material strength
parameter, described below:
a) The constitutive law of the model shall be linear-elastic with material parameters for a
temperature given in B.7.5.2.
b) The initial stress distribution shall be the one obtained like in the determination of the limit
action B.9.5.3.3.3 for a reference time, required for the determination of the material strength
parameters in B.9.5.3.3.2 given by the total creep period.
c) The short-term design material strength parameter, with which the maximum equivalent stress is
compared, shall be the minimum specified values of
—
R
—
R
p0,2/ T
p1,0/ T
c
c
for ferritic steels,
for austenitic steels,
where
Tc
is the respective temperature at each point and each time.
B.9.5.5 Design checks
Actions, combination rules, reference temperature and reference time for creep periods, shall be as for the
CR-DC, in B.9.4.3, but all partial safety factors for actions shall be equal to 1,0.
B.9.6 Creep and cyclic fatigue (CFI)
For each point of the structure, the sum of the design value of the creep damage indicator, see B.9.5.3, and
the design value of the fatigue damage indicator (for cyclic actions), see B.8.5, shall not exceed unity.
UNI EN 13445-3:2021
661
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex C
(normative)
Design by analysis — Method based on stress categories
C.1 Purpose
This annex gives rules concerning design by analysis using stress classification. It applies to pressure vessels
in all testing groups.
The method described, known as "stress analysis", involves the interpretation of stresses calculated on an
elastic basis at any point in a part of a vessel, and then verification of their admissibility by means of
appropriate assessment criteria.
It applies to pressure vessels in all testing groups.
It may be used:
— as an alternative to design-by-formula (see 5.4.1);
— as a complement to design-by-formula for:
— cases not covered by that route;
— cases involving superposition of environmental actions;
— exceptional cases where the manufacturing tolerances given in EN 13445-4:2021, Clause 6 are
exceeded.
In the last item, any deviation beyond tolerance limits shall be clearly documented.
— as an alternative to the design-by-analysis direct route, according to Annex B.
It may be used for a component or even a part of a component.
In all cases, all relevant requirements of this annex shall be fulfilled for that component or part.
The minimum thickness for pressure loading only, shall not be less than required by Formula (7.4-1) or (7.42) for cylindrical shells, Formula (7.4-4) or (7.4-5) for spherical shells, Formula (7.5-1) for dished ends and
Formula (7.6-2) or (7.6-3) for conical shells.
Fatigue failure is not covered by this annex. When required, fatigue assessment shall be performed
according to Clause 18 or Clause 17, as relevant.
Failure by elastic or elastic-plastic instability (buckling) is not covered by this annex. When the analysis
reveals significant compression stresses, the risk for buckling shall be assessed separately.
Provisions are given in C.8 for vessels or vessel parts working in the creep range.
662
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
For vessels or vessel parts working in the creep range it is necessary that the requirements for loading of
non-cyclic nature given in 5.4.2 or 17.5 respectively are considered to be met (i.e. the number of full
pressure cycles or equivalent full pressure cycles is less than 500 or N eq respectively).
In the present edition of the standard no rule concerning creep/fatigue interaction is given in this Annex. If
this interaction is to be taken into account, the design methods of Annex B may be used.
This Annex is currently limited to sufficiently ductile materials, like the whole standard, but it is, for
components operating in the creep range, also limited to sufficiently creep ductile materials, as defined in
EN 13445-2:2021.
Due to the sensitivity of the method used in the present annex to the competence of the users, until
sufficient in-house experience can be demonstrated, the involvement of an independent body, appropriately
qualified in the fields of design-by-analysis and structural stress analysis, is required in the assessment of the
design (calculations) and the potential definition of particular NDT requirements.
C.2 Specific definitions
The following terms and definitions apply in addition to those given in clause 3.
C.2.1
gross structural discontinuity
structural or material discontinuity which affects the stress or strain distribution across the entire wall
thickness over a region of significant area
Note 1 to entry: Examples of gross structural discontinuities are end-to-cylindrical shell or conical shell-tocylindrical shell junction, flange-to-cylindrical shell junction, an opening in a shell, the junction of two cylindrical
shells of different diameter, thickness or material, or a stiffener-to-shell junction.
C.2.2
local structural discontinuity
a discontinuity which only very locally affects the stress or strain distribution, across a fraction of the
thickness of the wall
Note 1 to entry: Stresses resulting from such a discontinuity can only cause highly localised strains and
consequently have no significant influence on the global behaviour of the wall.
Note 2 to entry: Examples of local structural discontinuities are small radius fillets, weld toes, non penetrated
zones in partial penetration welds.
C.2.3
primary stress
stress which satisfies the laws of equilibrium of applied loads (pressure, forces and moments)
Note 1 to entry: Regarding the mechanical behaviour of a structure, the basic characteristic of a primary stress is,
that in case of high (non admissible) increment of external loads, it is not self-limiting. As plasticity develops, a
stage is reached where no further beneficial redistribution of stress can take place.
UNI EN 13445-3:2021
663
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Note 2 to entry: Regarding primary stresses, distinction is made between membrane stresses (Pm, PL) and
bending stresses (Pb) with respect to their distribution across the cross-section governing the load-bearing
behaviour. Primary membrane stresses (Pm) are defined as the average value of the respective stress components
distributed over the section governing the load-bearing behaviour defined by the supporting line segment (see
C.4.4). Primary bending stresses (Pb) are defined as primary stresses distributed linearly across the considered
section and proportionally to the distance from the neutral axis.
Note 3 to entry: Regarding the distribution of membrane stresses along the wall, distinction is made between
general primary membrane stresses (Pm) and local primary membrane stresses (PL). At discontinuities, primary
membrane stresses in shells are classified as local if the equivalent membrane stress exceeds 1,1 times the
nominal design stress f and if the region in which this value is exceeded remains within the length of 1,0 R  e a in
the meridional direction. Minimum values are imposed on the distance between adjacent regions of local primary
membrane stress (see C.7.2).
Note 4 to entry: General primary membrane stresses are distributed in the structure such that no essential stress
redistribution occurs as a result of yielding. In the case of local primary membrane stresses, yielding will cause
such redistribution.
C.2.4
secondary stress
stress developed by constraints due to geometric discontinuities, by the use of materials of different
elastic modulii under external loads, or by constraints due to differential thermal expansions
Note 1 to entry: With respect to the mechanical behaviour of the structure, the basic characteristic of a secondary
stress is that it is self-limiting, i.e. local flow deformation leads to a limitation of the stress. Secondary stresses lead
to plastic deformation when equalising different local distortions in the case of excess of the yield strength.
Note 2 to entry: Only stresses that are distributed linearly across the cross-section are considered to be
secondary stresses. For non linearly distributed stresses, the secondary stresses are those of the equivalent linear
distribution.
Note 3 to entry: Secondary stresses may be of membrane type (Qm) or bending type (Qb). Yet, in most cases,
distinction between both is not necessary, because criterion C.7.3 requires only consideration of their sum (Qm 
Qb). Satisfaction of another criterion which needs separate consideration of the secondary membrane stress (Qm)
is only necessary when instability phenomena are likely to occur (see note 3 to Table C-2).
C.2.5
peak stress
that part of stress which is additive to the respective primary and secondary stresses, to form the total
stress
Note 1 to entry: Peak stresses do not cause any noticeable distortion and are only important to fatigue and brittle
fracture in conjunction with primary and secondary stresses.
Note 2 to entry: Peak stresses also comprise deviations from nominal stresses at hole edges within tube-hole
fields due to pressure and temperature, in which case the nominal stresses are derived from equilibrium of forces
considerations.
C.3 Specific symbols and abbreviations
The following symbols apply in addition to those in Clause 4:
664
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table C-1 — Symbols, descriptions and units
Symbol
Description
Unit
ij
stress components due to an individual load.
MPa
ij
stress components resulting from superposition of all loads acting
simultaneously (at a given instant)
MPa
1,2,3
principal stresses of the stress state defined by the stress
components ij
MPa
eq
equivalent stress according to the maximum shear stress theory
(Tresca theory) or the maximum distortion energy theory (von Mises
theory)
MPa
ij
stress components differences between two loading conditions
MPa
()1,()2,()3
principal stresses of the stress state defined by the stress
components differences ij
MPa
eq
equivalent stress range according to the maximum shear stress
theory (Tresca theory) or the maximum distortion energy theory
(von Mises theory)
MPa
h
length of the supporting segment
mm
Pm
general primary membrane stress
MPa
PL
local primary membrane stress
MPa
Pb
primary bending stress
MPa
Q
secondary membrane  bending stress.
MPa
Qm
secondary membrane stress
MPa
Qb
secondary bending stress
MPa
F
peak stress
MPa
R
mean radius for the region, measured perpendicular to the shell wall
mm
UNI EN 13445-3:2021
665
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C.4 Representative stresses
C.4.1 Equivalent stress
The equivalent stress eq is a scalar quantity defined in accordance with either the maximum shear stress
theory or the maximum distortion energy theory, from the stress components ij, obtained by summation of
all stresses ij of same category generated by the various loads to be considered simultaneously.
The equivalent stress shall be determined as follows:
— maximum shear stress theory:
a) Calculate the principal stresses 1, 2, 3 of the stress state defined by the stress components ij ;
b) The equivalent stress is given by:
eq  max {1  2,2  3,3  1}
(C.4.1-1)
— maximum distortion energy theory:
The equivalent stress is given by:
 eq 

2
2
2
2
2
2
 
 
  11   22   22   33   33   11  3 ( 
 
 
)
12
23
31
11
22
33
(C.4.1-2)
or alternatively by:
 eq 

2
2
2


  1  2   2  3   3  1
1
2
3
(C.4.1-3)
C.4.2 Equivalent stress range
The equivalent stress range eq is a scalar quantity defined in accordance with the maximum shear stress
theory or the maximum distortion energy theory, from the variation of the stress components ij between
two normal operating conditions.
The equivalent stress range shall be determined as follows:
— maximum shear stress theory:
c) Calculate the values (ij)a and (ij)b of the stress components ij for the two loading conditions a
and b considered;
d) Calculate the stress components differences ij between loading conditions a and b:
ij  (ij)a  (ij)b
(C.4.2-1)
e) Calculate the principal stresses ()1, ()2, ()3 of the stress state defined by the stress
components differences ij.
In the case where the principal directions are the same in both conditions a and b, these principal
stresses may be directly calculated from the difference between the principal stresses of the stress
states defined respectively by the stress components (ij)a and (ij)b:
666
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
()1  (1)a  (1)b
()2  (2)a  (2)b
(C.4.2-2)
()3  (3)a  (3)b
f)
The equivalent stress range between loading conditions a and b is given by:
eq  max {()1  ()2,()2  ()3,()3  ()1}
(C.4.2-3)
— maximum distortion energy theory:
The equivalent stress range between loading conditions a and b is given by:
  eq 

2
2
2
2
2
2
 
 
  11   22   22   33   33   11  3 ( 
 
 
)
12
23
31
11
22
33
(C.4.2-4)
or alternatively by:
  eq 
2
2
2
   1      2      3    1   
2   2   3   3   1
(C.4.2-5)
NOTE
Criterion C.7.3-1 requires that the maximum value of eq be found. When more than one load is
applied which vary independently, and/or when principal directions change, identification of the two load
conditions a and b that maximise eq may be difficult ; a trial and error calculation process may be necessary.
C.4.3 Total stress – elementary stresses
The stress state due to a given load is defined by the six elementary stresses ij determined on an elastic
basis by means of a calculation or experimental method in accordance with the requirements of C.4.5.
These stresses shall be expressed in a set of local coordinates designated O, X1, X2, X3 attached to the
supporting line segment defined in C.4.4.1. Axis X3 is that containing the supporting line segment, the origin
O being located at the mid-point of this segment and x3 the position of any point of this segment measured
from the origin O (see Figure C-1).
The so defined stress system is named "total stress" because it includes all the parts in which stresses have
to be divided in the frame of the method of this annex (i.e. the membrane, bending and peak parts).
The total stress shall be determined, at a given point, for each load which has to be taken into account.
C.4.4 Decomposition of stresses
C.4.4.1 Supporting line segment
The decomposition of the elementary stresses, outlined hereafter, shall be carried out across the wall
thickness along a segment which is referred to as the "supporting line segment".
The supporting line segment, of length h, is the smallest segment joining the two sides of the wall (see
Figure C-1). Outside of gross structural discontinuity regions, the supporting line segment is normal to the
wall mean surface; its length h, is then equal to the analysis thickness of the wall.
UNI EN 13445-3:2021
667
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C.4.4.2 Membrane stress
The membrane stress ij,m is the part of stress, constant along the supporting line segment, which is equal to
the average value of the elementary stresses ij along this supporting line segment:
 
ij

m

1
h
 h
h
2
 ij  d x 3
(C.4.4-1)
2
C.4.4.3 Bending stress
The bending stress ij,b is the part of stress, varying linearly across the thickness of the wall, which is given by
the formula:
 
ij

12x 3
h
b
3

h
 h
2
 ij  x 3  d x 3
(C.4.4-2)
2
For a stress analysis in accordance with this annex, only maximal values of ij,b equal and of opposite sign on
each side of the wall, i.e. at both ends of the supporting line segment, shall be considered. For this case:
 
ij

b

6
h
2

h
 h
2
 ij  x 3  d x 3
(C.4.4-3)
2
C.4.4.4 Linearised stress
The linearised stress ij,l is the part of stress resulting from the sum of the membrane plus bending parts:
ij,l  ij,m  ij,b
(C.4.4-4)
C.4.4.5 Nonlinearity stress
The nonlinearity stress ij,nl is the part of stress resulting from the difference between the total stress and
the linearised stress:
ij,nl  ij  ij,l  ij  ij,m  ij,b
(C.4.4-5)
Figure C-2 shows the decomposition of the elementary stresses outlined above. In order to avoid possible
confusion between global and local bending stresses, an example of application of the stress decomposition
to the particular case of longitudinal stresses in a cylindrical shell subjected to an external bending moment
is illustrated in Figure C-3.
668
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1
supporting line segment
2
gross structural discontinuity
Figure C-1 — Supporting line segment and local axes
in which elementary stresses are expressed
UNI EN 13445-3:2021
669
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1
supporting line segment
2
membrane stress ij,m
3
bending stress ij,b
4
nonlinearity stress ij,nl
Figure C-2 — Decomposition of an elementary stress
670
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1
longitudinal stress distribution along the shell cross section
2
longitudinal stress distribution along the thickness of the wall
3
membrane stress:  2 2 ,m 
4
bending stress:  2 2 ,b  
16 M (D e  D i )
4
4
 (D e  D i )
16 M (D e  D i )
4
4
 (D e  D i )
(on each side of the wall)
Figure C-3 — Decomposition of the longitudinal stress on the particular case
of a cylindrical shell subject to an external bending moment M
(for this particular case, the longitudinal stress 22 is a principal stress)
C.4.5 Requirements relating to the methods for determining stresses
C.4.5.1 Assumption of linear elasticity
Elementary stresses shall be determined in accordance with the assumptions of linear elasticity:
— material behaviour is linear elastic in accordance with Hooke´s law;
UNI EN 13445-3:2021
671
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— material is isotropic;
— displacements and strains are small (first order theory).
C.4.5.2 Selection of methods for determining stresses
The choice of the method used for determining stresses is under the responsibility of the manufacturer. This
method may be numerical, analytical or possibly experimental.
The following requirements relate only to methods for determining stresses by calculation.
When the vessel studied is built of components which can be classified as shells and plates, calculation
methods that describe the state of these components using global mechanical parameters (i.e. generalised
deformations and stress resultants in a section, corresponding to linear strain and stress distribution across
the thickness of the wall) are generally acceptable.
This is certainly so for:
— vessels for which a fatigue analysis in accordance with Clause 18 is not required,
— vessels or vessel parts for which such an analysis is required but does not necessitate evaluation of
peak stresses (e.g. all cases where the critical fatigue zones are located in welded joints),
— vessels or vessel parts for which evaluation of peak stresses for use in Clause 18 can be carried out
using suitable stress concentration factors, applied to the linearised stresses derived from these
methods.
The analysis of thick wall vessels or of thick parts of vessels, particularly under thermal loads, may require
the use of refined models (two or three dimensional continuous medium permitting analysis of actual nonlinear stress or strain distributions across the thickness of the wall).
In all cases, accuracy or conservatism of the methods used shall be adequate to ensure a good
representation of the calculated stresses with regard to those required for the analysis. In this respect, the
use of tested and recognised practices is recommended.
C.5 Classification of stresses
Stresses determined by analysis shall be classified in accordance with the different categories whose
definitions are given in C.2. In some cases, interpretation of these definitions may be problematical and, to a
large extent, depends on the analyst’s judgement.
In order to limit this difficulty, Table C-2 prescribes the classification to be used for a certain number of
configurations covering most of the common cases.
Information given in this table refers to stresses calculated in accordance with the requirements of C.4.5.
For the analysis of particular geometrical arrangements or loadings, for which the classifications proposed in
these tables would not be suitable, departure from them is permissible, so long as the alternative
classifications are justified by means of direct reference to the definitions given in C.2.
672
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table C-2 — Classification of stresses in some typical cases
ORIGIN OF STRESS
VESSEL
COMPONENT
Cylindrical,
spherical,
conical,
or toroidal
shell
REGION
UNDER
CONSIDERATION
Region far from any gross
structural discontinuity
or from the point of application of
an external local load
Vicinity of a junction with another
shell, an end, a flange
or of the point of application of an
external local load;
vicinity of an opening (with or
without nozzle) 5) 6)
Central region outside the vicinity
of an opening
or of the point of application of an
external local load
Torispherical
or ellipsoidal
dished end
Central region in the vicinity of an
opening (with or without nozzle) 5)
TYPE OF
STRESS
Mechanical loads
Pressure
and global
loads 2)
ij,m
ij,b
Other
mechanical
loads
ij,b
Qm 3)
Pm
Qb 4)
Pb
ij,m
PL
Qb
Qm
Pb 5)
Qb
Thermal loads 1),
restrained
or imposed
displacements
Qb
ij,m
Pm
Qm 3)
ij,b
Pb
Qb
ij,m
PL
Qm
6)
or of the point of application of an
external local load;
ij,b
Pb 5)
Qb
Qb
peripherical region 7)
Region far from any gross
structural discontinuity;
vicinity of an opening (with or
without nozzle) 5)
Flat end,
plane wall
Vicinity of edges or of a stiffener
Isolated ligament
Perforated wall
(shell or plate)
10)
Ligament in a multiple
and close perforation region
Region far from junction
to vessel wall
Nozzle
Vicinity of the junction to a shell
or a dished end 6)
Vicinity of the junction to a flat end
or plane wall 11)
UNI EN 13445-3:2021
ij,m
Pm
Qm 3)
ij,b
Pb
Qb
ij,m
Pm
Qm
ij,b
Qb
ij,m 9)
ij,b 9)
Qb
PL or Pm 8)
Qm
Pb 5)
Qb
Qb
Qb
ij,m 9)
Pm
Qm
ij,b 9)
Pb
Qb
ij,m
Pm
Qm 3)
ij,b
Qb 4)
PL
ij,m
ij,b
PL
Pb or Qb12)
Qb
Qm
Pb 5)
Qb
ij,m
ij,b
Pb
Qb
Qm
Pb 5)
Qb
673
EN 13445-3:2021 (E)
Issue 1 (2021-05)
1) to 12) : see next page
Footnotes to Table C-2 :
1) The piping loads acting on the vessel due to thermal expansion of the piping system shall be considered as mechanical
loads (to be considered under the heading “other mechanical loads”).
2) Global loads are the global bending moments, axial forces or shear forces defined in Clause 16.
3) For regions far from gross structural discontinuities, the classification of membrane stresses due to thermal loads or to
restrained or imposed displacements in category Qm leads to plastic deformations occurring in these regions during the
early loading cycles, at any point where the equivalent primary  secondary membrane stress is greater than the yield
strength of the material.
With regard to the failure modes covered by the rules of this annex, the strength of the vessel is not affected by these
plastic deformations; however, due to these deformations, the use of stresses calculated on an elastic basis is not correct
in assessing the risk of elastic or elastic-plastic instability (buckling).
Consequently, if there are regions of the vessel where this risk of instability shall be considered and if this risk may be
increased by the redistribution of stresses associated with the plastic deformations mentioned above, such plastic
deformations shall not be permitted.
This condition is met by ensuring that, in the regions far from any gross structural or loading discontinuity, the equivalent
primary  secondary membrane stress (eq)(P+Q)m (equivalent stress corresponding to (ij)Pm or (ij)PL  (ij)Qm)
satisfies the relationship:
(eq)( P+Q)m  1,5 f
(C.5-1)
The appropriate category shall be Pb instead of Qb when the shell is not axisymmetric (example: oblique conical shell,
cylinder of elliptic cross section).
5) The classification of bending stresses into category P ensures that no plastic deformation can occur in the region under
b
4)
consideration during normal service.
If small plastic deformations occurring during the early loading cycles are not detrimental for the vessel (e.g. regarding
functionality or esthetical requirements) the classification into Qb category is permitted because these deformations do
not affect the strength of the region concerned..
6) See Figure C-4.
7) For a torispherical end, although there are two different peripherical discontinuities (spherical shell-toroidal shell and
toroidal shell-cylindrical shell junctions), the stress pattern is generally such that only one single local primary membrane
stress region occurs in the knuckle.
Where the relative dimensions and thicknesses of spherical, toroidal, and cylindrical components are such that two such
regions occur, the classification given here for the "peripherical region" applies in the vicinity of each discontinuity; the
intermediate region is to be classified as "region far from any gross structural discontinuity" and the rules relating to the
spacing of local primary membrane stress regions shall be satisfied.
8)
Pm for a flat wall. PL for a wall which is not flat.
9)
For this particular case, the stress value to be retained is the average value across the ligament width.
The effect of the perforations shall be taken into account in stress calculation.
11) For an opening with nozzle in a flat end or a flat wall, for which the concept of "local primary membrane stress region"
has no meaning, the meridional extent of the local primary membrane stress region which may occur at the nozzle base
shall , for the nozzle, be measured from the outside surface of the end or of the wall.
12) P when the strength of the nozzle is taken into account for the calculation of stresses acting in the flat end or the flat
b
10)
wall; if not, Qb.
The first solution, conservative for the nozzle, is only interesting in practice if taking into account the strength of the
nozzle leads to a significant decrease of the flat end or flat wall thickness.
674
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Key
1
shell
2
3
nozzle
nozzle base region
4
thickness transition regions
5
limits of local primary membrane stress region
NOTE
This figure shows the case of an opening with nozzle in a cylindrical shell. It also applies to the case of
an opening with nozzle in a spherical, conical or toroidal shell or in the central region of a dished end ( Rm is the
circumferential mean curvature radius). It applies as well to the case of an opening without nozzle (for this case
ea,n  0). It does not apply to an opening in a flat end or a flat wall; in such cases, see footnote 11) to Table C-2.
When the level of stress acting in the vicinity of the opening is such that a local primary membrane stress
region occurs, the extent of this region, measured taking account of both sides of the nozzle-shell
discontinuity, shall satisfy the condition:
l s  ln 
R m  e a, s 
r m  e a, n
(C.5-2)
2
Possible thickness transitions which may occur between a reinforced part and an unreinforced part of the
nozzle and/or of the shell do not usually involve local primary membrane stress regions.
Where, for particular geometrical or loading arrangements, such regions occur in the vicinity of these
transitions, the conditions in C.7.2 relating to the spacing between adjacent regions of local primary
membrane stresses shall be met, particularly as regards the spacing from the adjacent local primary
membrane region at nozzle base.
Figure C-4 — Opening in a shell
UNI EN 13445-3:2021
675
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C.6 Stress analysis procedure
The procedure to be followed for a stress analysis is the following:
— Step 1:
For each point of the region under study, calculate the elementary stresses resulting
from each load acting on the vessel wall for each loading condition to be considered.
These calculations shall be carried out in accordance with the requirements C.4.5.
The loading conditions to be considered are:
— the loading conditions of all types (normal operation, exceptional operation, proof test) for
which the stress level may be determinant through assessment criteria C.7.2 (step 7).
— the normal operating conditions between which the stress variation may be determinant
through the assessment criteria C.7.3-1 (step 9).
— Step 2:
Decompose the stresses ij calculated above, in accordance with the requirements of
C.4.4, into:
— membrane stress: ij,m,
— bending stress: ij,b.
The bending stress to be taken into account for the analysis is the stress on both sides of the wall i.e. at the
two ends of the supporting line segment (two equal values with opposite signs).
— Step 3:
In accordance with the directives of C.5, classify these stresses into the different
categories defined in C.2:
— general primary membrane stress (Pm),
— local primary membrane stress (PL),
— primary bending stress (Pb),
— secondary membrane stress (Qm),
— secondary bending stress (Qb).
Following this classification the stress ij,m is designated (ij)Pm, (ij)PL, or (ij)Qm, and the stress ij,b is
designated (ij)Pb or (ij)Qb.
— Step 4:
Calculate the sum of the stresses classified in this way for the set of loads acting
simultaneously in the loading condition under consideration.
Stresses resulting from this summation are designated: (ij)Pm , (ij)PL , (ij)Pb , (ij)Qm , (ij)Qb
— Step 5:
From this, deduce:
g) the primary membrane stress, general or local (depending on the point under consideration):
(ij)Pm or (ij)PL.
676
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
h) the total primary stress (ij)P :
(ij)P  (ij)Pm , or (ij)PL   (ij)Pb
(C.6-1)
the primary  secondary stress (ij)P+Q :
i)
(ij)P+Q  (ij)Pm , or (ij)PL  (ij)Pb  (ij)Qm  (ij)Qb
— Step 6:
(C.6-2)
According to C.4.1 calculate the following equivalent stresses:
— (eq)Pm, equivalent to stresses (ij)Pm, or, depending on point under consideration, (eq)PL,
equivalent to stresses (ij)PL,
— (eq)P, equivalent to stresses (ij)P
— Step 7:
Verify the admissibility of these equivalent stresses with respect to criteria in C.7.2.
— Step 8:
For each set of two normal operating loading conditions which may be determinant,
calculate the range of the primary  secondary stress (ij)P+Q and then, as indicated in C.4.2,
calculate the corresponding equivalent stress range (eq)P+Q .
The set of loading conditions to be retained is that which results in the greatest value of (eq)P+Q.
— Step 9:
Verify the admissibility of the equivalent resulting stress range (eq)P+Q with respect
to criteria C.7.3.
The procedure detailed above concerns assessment against static loading. If a fatigue assessment is
required, the following step shall be added:
— Step 10: Verify the admissibility of the cyclic loads, using the relevant stresses (primary +
secondary stresses in welded joints, primary + secondary + peak stresses in unwelded zones),
according to Clause 17 or Clause 18, as appropriate.
NOTE
The detailed procedure for establishing the characteristics of the stress cycles to be considered is
defined in these clauses.
C.7 Non-creep assessment criteria
C.7.1 General
The whole design shall basically meet the stress criteria given in C.7.2 and C.7.3. These criteria are illustrated
diagrammatically in Table C-3.
Relaxation of criterion C.7.3-1 is possible in some cases, under the conditions given in C.7.4.
When compressive stresses occur, buckling shall be assessed. For external pressure, see applicable rules in
Clause 8.
NOTE
Functional requirements may set limitations on the allowable deformations.
UNI EN 13445-3:2021
677
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table C-3 — Illustration of assessment criteria
Stress Categories
Primary stress
Description
(For practical
examples, see
Table C-2)
General
membrane
stress
Local
membrane
stress
Primary mean
stress calculated
across the wall
thickness without
taking into account
discontinuities and
stress
concentrations.
Primary mean
stress calculated
across the wall
thickness taking
into account large
discontinuities, but
not stress
concentrations.
Caused only by
mechanical loads.
Caused only by
mechanical loads.
Secondary
membrane  bending
stress
Bending
stress
Primary stress
component
proportional to the
distance from the
centroid of the solid
wall section. Does
not include
discontinuities
and stress
concentrations.
Self-equilibrating stress
necessary to satisfy the
continuity of the
structure. Occurs at large
discontinuities, but does
not include stress
concentrations.
Can be caused by both
mechanical loads and
thermal effects.
Caused only by
mechanical loads
Peak stress
a) Addition to
primary or
secondary
stress because
of stress
concentration.
b) Certain thermal
stresses which
may cause
fatigue, but not
distortion.
Q
Symbol
Pm
(eq)Pm  f
(eq. C.7.2-1)
assessment
againts static
loading
F
( Qm  Qb)
2)
(eq)PL  1,5f
(eq)P+Q  3 f
(eq. C.7.2-2)
(eq. C.7.3-1)
_______
= design loads
     = operating loads
fatigue
assessment
(only if
required)
1)
Pb
PL1)
(eq)P  1,5 f
(eq. C.7.2-3)
Assessment 4) based on :
3)
7)
2)
5)
(eq)P+Q
7)
or
max (i)
or
(eq)P+Q+F
6)
7)
PL = Pm does not occur at the point in question.
In assessment criteria given in Formulae (C.7.2-1) to (C.7.2-3), the value of the nominal design stress f shall be that relevant for the
loading condition under consideration (normal operation, exceptional operation, proof test), as defined in clause 6.
2)
3)
If (eq)P+Q is greater than 3f, see C.7.6
4)
Fatigue assessment shall consider all the applied cycles of various types, each of them being characterised by their own relevant stress
range (see footnotes 5 and 6), mean temperature and mean stress (if relevant). Clause 18 (detailed fatigue assessment) should normally
be used.
The primary  secondary stress range (named "structural stress range" in Clause 18 on detailed fatigue assessment) applies to
assessment of welded joints. In that case, either the equivalent stress range (eq)P+Q or the principal stress ranges (i) may be
5)
used.
The primary  secondary  peak stress range, named "total (notch) stress range" in clause 18 on detailed fatigue assessment, applies to
assessment of unwelded parts.
6)
7)
678
It should be observed that, depending on the model used, the computer programs usually give directly the primary 
secondary stresses (P  Q) or the primary  secondary  peak stresses (P  Q  F).
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C.7.2 Limitation of equivalent primary stresses
The equivalent primary membrane stresses shall for all loading conditions satisfy the relationships:
(eq)Pm  f
(C.7.2-1)
(eq)PL  1,5 f
(C.7.2-2)
(eq)P  1,5 f
(C.7.2-3)
The value of f to be retained shall be that consistent with the type of loading condition considered (normal
operation, exceptional operation, proof test), and shall be taken at the calculation temperature of that
condition.
In addition, the following conditions on the spacing between adjacent regions of local primary membrane
stresses shall be satisfied:
— two adjacent regions of local primary membrane stresses which exceed 1,1 times the nominal
design stress f shall be at a distance of at least 2 ,5 R  e a in meridional direction. Here, R is the midsurface radius of curvature and ea the wall analysis thickness;
— Discrete regions of local primary membrane stresses, (e.g. those resulting from concentrated loads
acting on brackets), where the equivalent membrane stress exceeds 1,1 times the nominal design
stress f, shall be spaced so that there is no overlapping of these regions.
C.7.3 Limitation of equivalent stress ranges resulting from primary  secondary stresses
The equivalent stress range resulting from variation of primary  secondary stresses between any two
normal operating conditions shall at all points satisfy the relationship:
(eq)P+Q  3 f
(C.7.3-1)
The value of f to be retained shall be that corresponding to loading conditions of normal operating type, but
as an exception to the corresponding definition given in Clause 6, its determination shall be based on the
yield strength of the material only, i.e.:
—
for steels, other than austenitic steels, as per 6.2 or 6.3: Rp0,2/T
— for austenitic steels as per 6.4 or 6.5: Rp1,0/T
and it shall be taken at the following temperature:
T*  0,75Tmax  0,25Tmin
(C.7.3-2)
where Tmax and Tmin are respectively the higher and the lower of the calculation temperatures of the two normal
operating conditions considered.
UNI EN 13445-3:2021
679
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C.7.4 Alternative to limitation of equivalent stresses and equivalent stress ranges
Deviations from the preceding limitations of equivalent stresses and equivalent stress ranges are possible if
it is proved by other means that the component meets the required safety margin against gross plastic
deformation and progressive plastic deformation stated in Annex B (e.g. by tests on the component, plastic
analysis, or the like).
C.7.5 Limitation of primary stresses in case of tri-axial state of stress
Where the stress analysis leads to a tri-axial state of stress, the following condition shall be satisfied
additionally whenever the smallest tensile principal stress exceeds half the highest tensile principal stress, to
avoid brittle failure caused by the limited ductility in such stress states:
max (1 ; 2 ; 3)  Rp/T
(C.7.5-1)
where Rp/T is the value of the proof strength relevant for determination of f (either Rp0,2/T or Rp1,0/T) at
calculation temperature.
This value can be exceeded if it is shown by a fracture mechanics analysis that higher values can be accepted.
C.7.6 Simplified elastic-plastic analysis
The equivalent stress range resulting from variation of primary  secondary stresses between two normal
operating conditions is allowed to exceed 3f on condition that:
a) (eq)’P+Q  3 f
(C.7.6-1)
where
(eq)’P+Q is the equivalent same stress range, calculated without taking into account bending
stresses of thermal origin;
f
is the same as specified in C.7.3.
b) a detailed fatigue analysis according to Clause 18 is performed. In this analysis, (eq)P+Q shall be
multiplied by the appropriate plasticity correction factor, as determined from that clause
(Detailed assessment of fatigue life);
c) the material is such that Rp < 0,8 Rm, Rp being here the value of the yield strength relevant for
determination of f (either Rp0,2 or Rp1,0) at room temperature;
d) the absence of risk of incremental collapse by thermal stress ratchet in regions of general primary
membrane stress is established according to C.7.7.
680
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
C.7.7 Prevention of incremental collapse resulting from thermal ratcheting
C.7.7.1 General
The "thermal ratcheting" phenomenon is the mechanism of incremental collapse which may occur in certain
conditions under the effect of cyclic thermal loads associated with a permanent pressure action.
It results in a plastic deformation which increases by about the same amount at each cycle and quickly leads
to an unacceptable value.
Meeting the criterion C.7.3-1 guarantees the absence of thermal ratcheting.
C.7.7.3 provides a rule which, for the particular cases of linear or parabolic thermal gradients, enables the
absence of thermal ratcheting to be guaranteed when the condition C.7.3 is not met.
This rule applies to the regions of general primary membrane stress. The absence of thermal ratcheting in
these regions ensures the absence of thermal ratcheting in discontinuity regions.
C.7.7.2 Specific parameters
is the equivalent general primary membrane stress due to pressure alone.
(eq)Pm,P
(eq) (P+Q),Tis the equivalent primary  secondary stress range of the stress due to thermal load
From these particular stresses, the two following dimensionless parameters are defined:
x
(
y 
eq
) Pm, P
1, 5 f
(
eq
) (P  Q ), T
1,5 f
(C.7.7-1)
(C.7.7-2)
The definition of f to be considered shall be that defined in C.7.3, but its value shall be taken at the
maximum calculation temperature reached during the cycle.
C.7.7.3 Assessment criterion
For an axisymmetric shell under constant pressure and subject to a thermal gradient across the thickness of
the wall, there is no risk of failure by incremental collapse due to thermal ratcheting if, in regions of general
primary membrane stress, the following relationships are satisfied:
a) linear thermal gradient:
— for 0,5  x  1 :
y  4(1  x)
(C.7.7-3)
— for 0  x  0,5 :
y  1/x
UNI EN 13445-3:2021
(C.7.7-4)
681
EN 13445-3:2021 (E)
Issue 1 (2021-05)
b) parabolic thermal gradient:
— for 0,615  x  1 :
y  5,21(1  x)
(C.7.7-5)
— for 0  x  0,615 :
y shall take a value lower than that given by the curve defined by the following points:
for x  0,3 0,4 0,5
(C.7.7-6)
y  4,65 3,55 2,70
C.8 Creep assessment criteria
C.8.1 Formulae to be used
In Annex C, stresses which relate to the different stress categories (e.g. membrane, membrane plus bending,
primary plus secondary stresses, etc.) are calculated. Allowable values for these are also specified. For creep
design, the formulae of interest are reproduced below:
(
(
(
)
eq
eq
eq
(
)
)
eq
Pm
PL
P
)
(C.8-1)
 f
(C.8-2)
 1,5  f
(C.8-3)
 1,5  f
P  Q
(C.8-4)
 3 f
NOTE
Subscript P, which means general or local primary membrane plus primary bending stresses is not
mentioned in C.3 where symbols used in Annex C are defined. It is defined through Formula (C.6-1).
Depending on whether the vessel service consists in one or more than one creep load cases, the following
rules in C.8.1 or C.8.2 respectively shall be applied at any point likely to be critical for creep damage.
C.8.2 Assessment criteria for a single creep load case
Formula (C.8-1) to (C.8-4) shall be satisfied at the point under study, using assumed analysis thickness and a
nominal design stress f obtained as explained in 19.5.
To obtain the minimum required thickness, an iterative procedure shall be used.
C.8.3 Assessment criteria for multiple creep load cases
The following procedure shall be applied:
682
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) For each creep load case, the analysis according to Annex C is carried out with the assumed
analysis thickness. The stresses are calculated for the different stress categories (see C.6). The
calculated stresses are then divided by the coefficient applicable to that stress category, as shown
below:

(m)i
 (
(

(L)i

(P)i
eq
)
)
PL

)
eq
(C.8-6)
P
(P  Q)i
(C.8-7)
1,5
(

(C.8-5)
Pm
1,5
(

eq

eq
b) The largest of 
)
P  Q
(C.8-8)
3,0
(m) i
,
(L) i
,
(P) i
,
the fictitious nominal design stress f
Fi
(P  Q) i
shall be determined. For the point under study,
for the creep load case under consideration shall be the
largest of these stresses:
f
Fi


 max  
;
;
;

(m)
i
(L)
i
(P)
i
(P

Q)
i


The allowable time to damage,
fictitious design stress
f
Fi
tD , f
Fi
,T i
(C.8-9)
shall be calculated according to Formula (19-11) for this
at the calculation temperature T i .
c) Steps a) and b) shall be repeated for each load case.
d) The accumulated creep damage resulting, for the point under study, from all applied load cases
shall be determined by the following time-fraction rule:
t
n
i
 1,0

t
i  1 D, f , T
Fi i
(C.8-10)
If more than one material is used in a part or component of the pressure vessel then Formula (C.8-10) shall
f
be applied separately for each region with different material using the fictitious design stress Fi at the
corresponding point and the material creep design curve for the corresponding material.
To obtain the minimum required thickness, an iterative procedure covering the whole procedure of C.8.2 for
all relevant points may be used.
UNI EN 13445-3:2021
683
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex D
(informative)
Verification of the shape of vessels subject to external pressure
D.1 Purpose
This annex gives guidance on the determination of the deviation from design shape of cylinders, cones and
spheres.
D.2 Specific definitions
None.
D.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in Clauses 4 and 8.
L1
is the chord length of a template, see Formula (D-1);
L2
is the chord gauge length determined from Formula (D-4);
Ii
is the ith influence coefficient, see Table D-1;
N
is the number of measuring stations ( 24);
Re
is the radius of an external template;
R m ax
is the maximum radius of a sphere as built measured locally;
Rt
is the radius of an internal template;
Y
is the maximum size of the gap between the template and shell;

i

r
is the ith chord gauge reading;
is the deviation from the mean circle determined by a chord gauge.
D.4 Methods of measurement
Surveying techniques, such as optical, infra-red or laser measurements, may be used to provide accurate
measurements of radius in all geometries, i.e. cylinders, cones or spheres. Other methods for specific
geometries are also described.
D.5 Cylindrical and conical sections
D.5.1 General
The following three methods detailed in D.5.2 to D.5.4 are applicable to cylinders and cones.
684
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
D.5.2 Direct measurement
Radii or differences from a constant radius should be measured at an even number of equally spaced
intervals around the circumference. The number of points should be sufficient to define the profile of the
section but not fewer than 24.
The measurements may be made by surveying techniques, or by swinging an arm internally (see Figure D-1),
or by rotating the vessel about its longitudinal axis and taking external readings. The axis of rotation of the
internal swinging arm or of the vessel should approximate to the true centre of the section under
consideration.
The radial measurements should be made to a precision of about 0,000 1R. From them, the out-ofroundness should be determined using Annex E.
Figure D-1 — Swinging arm
D.5.3 Templates
The vessel should be checked against either an internal or external template as shown in Figure D-2. The
chord length of the template should be as follows:
(D-1)
0 ,9 R  L 1  1,1 R
For an external template, R e should be put approximately equal to 1,01 R. The measured width of the gap
between the vessel and the template should be within the following limits:
(D-2)
R e  1,0 0 2 R  Y  R e  0 ,9 9 8 R
For an internal template, R r should be put approximately equal to 0,99 R. The measured width of the gap
between the vessel and the template should be within the following limits:
0 ,9 9 8 R  R r  Y  1,0 0 2 R  R r
UNI EN 13445-3:2021
(D-3)
685
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure D-2 — Internal and external templates
D.5.4 Chord gauge
D.5.4.1 Method
Chord gauge measurements at no fewer than 24 equally spaced positions on the circumference should be
made to give values of  i , the chord gauge readings or rise (see Figure D-3). It is also possible to use
differences from a constant rise with the same result.
The required length of the chord gauge is given by:
L2 
4  R
(D-4)
N
The readings should be measured to a precision of 0,1 mm.
The departures from the mean circle can be calculated from:
N1
r 

(D-5)
 i  / i r
i 0
where
li
is an influence coefficient. For two values of N, the values for
NOTE 1
I S  INS
NOTE 2
The chord gauge may also be known as a bridge gauge.
e.g.
I 10  I 14
lr
are given in Table D-1.
,with N=24
NOTE 3
Alternatively the departures from the mean circle can be calculated using the method described in
KENDRICK Shape imperfections in cylinders and spheres - their importance in design and methods of
measurement. J. Strain Analysis for Eng. Design, 12, No. 2, April 1977.
686
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The vessel is of adequate circularity if the maximum value of

r
does not exceed 0,005 R.
Figure D-3 — Chord or bridge gauge
Table D.1 — Influence coefficients
r
N = 24
N = 48
r
N = 24
N = 48
r
N = 48
r
N = 48
0
1,76100
3,6185
12
0,60124
-1,3835
24
1,2101
36
-1,3835
1
0,85587
2,6580
13
0,54051
-1,1944
25
1,1791
37
-1,5076
2
0,12834
1,7753
14
0,36793
-0,9544
26
1,0873
38
-1,5538
3
-0,38800
0,9834
15
0,11136
-0,6780
27
0,9385
39
-1,5107
4
-0,68359
0,2923
16
-0,18614
-0,3804
28
0,7385
40
-1,3689
5
-0,77160
-0,2910
17
-0,47097
-0,0763
29
0,4957
41
-1,1210
6
-0,68487
-0,7624
18
-0,68487
0,2201
30
0,2201
42
-0,7624
7
-0,47097
-1,1210
19
-0,77160
0,4957
31
-0,0763
43
-0,2910
8
-0,18614
-1,3689
20
-0,68359
0,7385
32
-0,3804
44
0,2923
9
0,11136
-1,5107
21
-0,38800
0,9385
33
-0,6780
45
0,9834
10
0,36793
-1,5538
22
0,12834
1,0873
34
-0,9544
46
1,7753
11
0,54051
-1,5076
23
0,85587
1,1791
35
-1,1944
47
2,6580
UNI EN 13445-3:2021
687
EN 13445-3:2021 (E)
Issue 1 (2021-05)
D.5.4.2 Example
For a cylinder of mean radius 2 000 mm the following chord gauge readings were obtained at 15° intervals
starting at the crown.

0
15
30
45
60
75
 (mm)
70,2
70,6
69,1
67,0
66,2
67,1
 (mm)
6,5
8,4
5,0
-0,6
-4,0
-3,4

90
 (mm)
68,8
69,5
68,8
67,4
67,5
67,7
 (mm)
-0,5
1,1
0,0
-2,2
1,0
-1,2

180
105
120
195
135
210
150
225
240
165
255
 (mm)
68,8
69,1
68,3
67,4
67,5
68,7
 (mm)
1,4
2,7
1,9
0,8
1,0
2,4

270
285
300
315
330
345
 (mm)
69,6
69,1
67,4
65,9
66,1
68,1
 (mm)
2,5
-0,3
-5,0
-7,9
-6,0
0,2
The value of  at  = 0° was obtained by summing:

0
= (70,2) (1,76100) + (70,6) (0,85587) + (69,1) (0,12834) + … + (68,1) (-0,85587) = 6,5
(D-6)
The value of  at  = 105° was obtained by summing :

7
= (70,2) (-0,47097) + (70,6) (-0,68487) + (69,1) (-0,77160) + … + (68,1) (-0,18614) = 1,1
(D-7)
For this example it is seen that the maximum departure from the mean circle is 8,4 mm occurring at  = 15°
and is less than 0,005 R = 10 mm.
D.6 Spheres and spherical sections
To confirm that the local form is within the limit on
R max
set in 8.7.2, a check should be made of the whole
spherical surface using a template having an arc length of
deviation from design shape is no greater than
 R max
0 ,72 
R

2 ,4
R max  e a

 1  e a

and checking that the inward
. Checks may be carried out using a bridge
gauge, or template of the nominal radius and measuring the deviation.
Alternatively, checks may be carried out using templates with a radius of
R m ax
as follows:
1) Internal template. If the template fits on the plate without rocking, the local radius will be equal
to or less than R m a x and therefore acceptable.
688
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
2) External template. If the template fits on the plate without rocking and there is clearance at the
centre of the template, this indicates that the local radius is greater than R m a x and therefore is
unacceptable.
NOTE
In the case of large or site erected vessels, the checks may be made on plates after pressing and before
welding (care should be taken however in the support of plates which would otherwise distort if supported
incorrectly whilst these checks are made). Additionally, after fabrication a check should be made throughout the
length of all seams, using a template of arc length 2 ,4
R m ax  e
, and spanning the welded seam equally on either
side. Where doubt arises concerning the local form away from or along the welded seam, this should be subject to
further verification.
Table D-2 expresses the basic tolerance specified in 8.7 in terms of permissible inward deviations for use
with the above template. Table D-2 also shows the deviation and corresponding penalty on design pressure
for greater tolerances.
Table D-3 gives recommended maximum deviations appropriate to a range of spheres and spherical sections.
Table D-2 — Maximum permissible local deviations from design shape
Expressed as
a radius
Expressed as an
Inwards deviation
from design shape
R m a x 


 R m ax
 1  e
 0 ,7 2 


R

Design pressure
reduction factor
 R m ax 


 1,3 R 
1,30 R
0,216 e
1,00
1,40 R
0,288 e
1,16
1,50 R
0,360 e
1,33
1,60 R
0,432 e
1,51
1,70 R
0,504 e
1,71
1,80 R
0,576 e
1,92
1,90 R
0,648 e
2,14
2,00 R
0,720 e
2,37
2,10 R
0,792 e
2,61
2,20 R
0,864 e
2,86
2,30 R
0,936 e
3,13
2,40 R
1,008 e
3,41
2,50 R
1,080 e
3,70
NOTE
UNI EN 13445-3:2021
2
Intermediate values may be obtained by linear interpolation.
689
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table D-3 — Recommended maximum allowable deviation from design shape for spheres and
spherical sections subject to pressure on convex surface
R
e
Expressed as a
maximum allowable
local radius
R m ax
Expressed as a
maximum allowable
inwards deviation
using a gauge
L  2 ,4 R m a x e
Design pressure
Reduction factor
 R m ax 


 1,3 R 
60
1,30 R
0,216 e
1,00
80
1,35 R
0,252 e
1,08
100
1,40 R
0,288 e
1,16
150
1,50 R
0,360 e
1,33
200
1,55 R
0,396 e
1,42
250
1,60 R
0,432 e
1,51
400
1,70 R
0,504 e
1,71
600
1,80 R
0,576 e
1,92
800
1,85 R
0,612 e
2,03
1 000
1,90 R
0,648 e
2
2,14
NOTE The above values are recommended only.
690
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex E
(normative)
Procedure for calculating the departure from the true circle of cylinders
and cones
E.1 Purpose
This annex provides the means for calculating the departure from the true circle of a cylinder or cone
following measurement of its radius.
E.2 Specific definitions
None.
E.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in Clauses 4 and 8, and Clause D.3.
a 1, b 0 , b1
are coefficients in the lowest series of the Fourier expansion;
R r
is the measurement of radius at position
r
is the number of the measurement (0..(N-1));
r
;
w
r
is the deviation from mean circle at measuring station
w
m ax
is the maximum deviation from the mean circle;
r
;
is the angular interval of the measurements;

E.4 Method
The measurements shall be taken at equally spaced intervals around the circumference and methods for
taking them are described in D.5.1. At least 24 measurements shall be taken. They may be of either inside or
outside radius but this shall be consistent.
The radial measurements shall be corrected for the mean and for the error in positioning the true centre,
see Figure E-1. This is done by finding the coefficients b 0 , b 1 , a 1 , etc., in the Fourier series expansion of the
measurements. Thus:
b0 
a1 
1
N
2
N
r N1

R r
(E-1)
r0
r N1

R r  s in r 
(E-2)
r0
UNI EN 13445-3:2021
691
EN 13445-3:2021 (E)
Issue 1 (2021-05)
2
b1 
N
r N1

R r c o s r 
(E-3)
r0
The departure from the mean circle at each position is given by:
w
r
(E-4)
 R r   b 0  a 1 s in r   b 1 c o s r 
NOTE
A suggested working form based on 24 measurements is given in Table E-1 for calculating the
deviation.
w
m ax
 m ax
w
0
........ w
(N  1 )

(E-5)
For the vessel to be within the 0.5 % tolerance, the following shall apply:
w m ax
R
(E-6)
 0 .0 0 5
If Equation (E-6) is not satisfied, the allowable pressure shall be calculated using Annex F.
Figure E-1 — Radius measurements and the true centre
692
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table E-1 — Working form for the determination of the departure from the mean circle
(1)
Point
no.r
(2)
Reference
(3)
sin
(4)
cos
angle
(5)
Measured
radius
degrees
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
R
0,0000
0,2588
0,5000
0,7071
0,8660
0,9659
1,0000
0,9659
0,8660
0,7071
0,5000
0,2588
0,0000
-0,2588
-0,5000
-0,7071
-0,8660
-0,9659
-1,0000
-0,9659
-0,8660
-0,7071
-0,5000
-0,2588
(7)
(8)
(9)
R r  s in r 
R r c o s r 
a 1 s in r 
b 1 c o s r
column (3)x
column (5)
column (4)x
column (5)
1
0

1
24

1
a 1 s in r 
(11)
+
b
+
+
column (3)x
a1
column (4)x
b1
column (8)+
column (9)
0
 a
1
(12)
Deviation
sin r 
b 1 c o s r
R r
column (10)+


b0

r
 a 1 s in r   b 1 c o s r 

column (5)column (11)
b0
1,0000
0,9659
0,8660
0,7071
0,5000
0,2588
0,0000
-0,2588
-0,5000
-0,7071
-0,8660
-0,9659
-1,0000
-0,9659
-0,8660
-0,7071
-0,5000
-0,2588
0,0000
0,2588
0,5000
0,7071
0,8660
0,9659
+
b
(10)
b 1 c o s r
r
mm
0
15
30
45
60
75
90
105
120
135
150
165
180
195
210
225
240
255
270
285
300
315
330
345
(6)


2

a
3
1

1
12

2

b
1

1
12

3

NOTE Shaded area indicates negative values.
UNI EN 13445-3:2021
693
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex F
(normative)
Allowable external pressure for vessels outside circularity tolerance
F.1 Purpose
This annex provides a procedure to determine the allowable pressure for cylinders with a departure from the true
circle greater than 0,5 % of radius measured from the true centre.
F.2 Specific definitions
None.
F.3 Specific symbols and abbreviations
The following symbols and abbreviations apply in addition to those in Clauses 4 and 8, and D.3 and E.3
an , bn
cyl
cyl
are Fourier series coefficients;
P ra
is the allowable external pressure according the rules in this annex;
Pa
is the allowable pressure for an otherwise similar cylinder within 0,5 % tolerance (see 8.5.2.2);
Pq
is the lower bound estimate of the collapse pressure of cylinder;
n
is the harmonic value used to evaluate  in Equation (8.5.2-6) and in Equation (F-4) .
cyl
F.4 Method
The allowable pressure

P ra  P q  P a  P q
P ra

is determined from the following equation:
0 ,005 R
w
 Pa
(F-1)
max
where
Pq
is the lowest value of P at any location r at which:
P R
ea
 
br
 
e
(F-2)
and
694
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Pq  Pa

(F-3)
br
n cyl  N / 2
E  ea

2 R
2
1   
2

n cyl  2


P
 an
sin
x 
cyl
 P m n cyl   P 





 n cyl


n cyl


 R 
1   

 L 
2

 r    bn
cyl
cos
2
n cyl





r 

(F-4)
where

P m n cyl
 is the value of
Pm
determined using Equation (8.5.2-5) at each value of
n
cyl
and:
an 
When
2
N
N 1

R r  s in
n
cyl
r 

(F-5)
r 0
n  N / 2
bn 
2
N
N 1


R r c o s n c y l  r  

(F-6)
r0
When n  N / 2
bn 
w m ax
1
N
N 1

R r c o s
n
cyl
r 

(F-7)
r 0
is determined in Annex E.
UNI EN 13445-3:2021
695
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex G
(normative)
Alternative design rules for flanges and gasketed flange connections
G.1 Purpose
This annex provides a calculation method for bolted, gasketed circular flange joints. It is applicable to flanges and
bolted domed ends, and is an alternative to the methods in Clauses 11 and 12. Its purpose is to ensure structural
integrity and leak tightness for an assembly comprising two flanges, bolts and a gasket. Flange loadings are shown
in Figure G.3-1. Different types of bolts and gaskets are shown in Figures G.3-2 to G.3-3.
Use of this alternative method is particularly recommended in case a more accurate calculation is imposed by one
of the following circumstances:
a) need of assuring leak tightness in presence of dangerous fluids;
b) multiple design or testing conditions;
c) presence of additional external loads;
d) presence of temperature differences among the different components of the bolted joint;
e) need to avoid overstress of the bolts and/or the gasket.
Using this alternative calculation method a controlled bolting-up method (see Table G.8-2) is recommended and
should be documented by the Manufacturer in the User’s manual.
This annex is based on EN 1591-1:2001, Flanges and their joints — Design rules for gasketed circular flange
connections — Part 1: Calculation method. The new edition of this standard, EN 1591-1:2013, provides a
calculation of a bolted joint considering specified leak rates through the gasket: such calculation is however only
possible if the gasket manufacturer is able to supply sufficient gasket parameters, or if such parameters are the
result of specific testing, carried out in accordance with EN 13555:2014. Therefore, when specified leak rates are
a design requirement and when sufficient gasket data are available, EN 1591-1:2013 shall be used as an
alternative either to this Annex or to Clauses 11 and 12. The use of EN 1591-1:2013 is not applicable in the case
of a bolted joint between a flange and the flanged extension of a heat exchanger tubesheet (see Figures J.12
and J.13) and in the case where a tubesheet is clamped between two flanges (see Figure J.11).
G.2 Specific definitions
The following terms and definitions apply in addition to those in 11.2.
G.2.1
integral flange
flange either integral with or welded to the shell, see Figures G.3-4 to G.3-8
696
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.2.2
blank flange
flat closure connected by bolts, see Figure G.3-9
G.2.3
loose flange
separate flange-ring abutting a stub or collar, see Figure G.3-10
G.2.4
hub
axial extension of a flange-ring, usually connecting flange-ring to shell, see Figures G.3-4 and G.3-5
G.2.5
collar or stub
abutment for a loose flange, see Figure G.3-10
G.2.6
load condition
application of a set of applied simultaneous loads; designated by the identifier I
G.2.7
load change
change of load condition
G.2.8
assembly condition
as defined in 11.2 and designated by I = 0 in this annex
G.2.9
subsequent condition
load condition subsequent to the assembly condition, e.g. working condition, test condition, conditions
arising during start-up and shut-down, designated by I = 1, 2, 3
G.2.10
external loads
forces and/or moments applied to the joint by attached equipment, e.g. weight or thermal expansion of pipes
G.2.11
compliance
inverse of the axial stiffness of the assembly, symbol Y, units mm/N
G.2.12
flexibility modulus
inverse of the stiffness modulus of a component, excluding the elastic constants of the material; axial: symbol
X, units 1/mm; rotational: symbol Z, units 1/mm3
UNI EN 13445-3:2021
697
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.3 Specific symbols and abbreviations
G.3.1 Use of figures
Figures G.3-1 to G.3-10 serve only to illustrate the notation. They are not intended to give all the detail on
different designs. They do not illustrate all possible flange types for which the method is valid.
For some standard flange types, according to EN 1092-1:2018, the relevant Figures are the following:
Figure:
G.3-8
EN 1092-1:
Type:
01
G.3-10 a)
02 + 35
G.3-10 b)
02 + 36 or 37
G.3-9
05
G.3-4 a)
11
G.3-4 c)
21
G.3.2 Subscripts and special marks
G.3.2.1 Subscripts
A
for
Additional (FA, MA)
B
for
Bolt
C
for
Creep of gasket (gC)
D
for
Equivalent cylinder (tapered hub + connected shell; for load limit calculation)
E
for
Equivalent cylinder (tapered hub + connected shell; for flexibility calculation)
F
for
Flange
G
for
Gasket
H
for
Hub
I
for
Load condition identifier (takes values I = 0, 1, 2, ...)
L
for
Loose flange
M
for
Moment
P
for
Pressure
Q
for
Net axial force due to pressure
R
for
Net axial force due to external loads (Resultant)
S
for
Shell, shear
T
for
Shell, modified
X
for
Flange weakest cross section

for
Symbol for change or difference
av
for
average
698
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
d
for
design
e
for
effective
i
for
interim
max
for
maximum
min
for
minimum
nom
for
nominal
opt
for
optimum
req
for
required
s
for
shaft i.e non threaded part of bolt
t
for
theoretical, torque, thread
0
for
zero load condition (I = 0, see subscript I)
G.3.2.2 Special marks
~
is an accent placed above symbols of flange parameters that refers to the second flange of the joint,
which may differ from the first.
G.3.3 Symbols
NOTE
Units are given in brackets; [-] indicates that the quantity is dimensionless.
AB
is the effective total cross-section area of all bolts [mm2], Formula (G.5-53);
AF, AL
is the radial cross-section area of flange ring, loose flange [mm2];
AGe, AGt
is the gasket area, effective, theoretical [mm2], Formulae (G.5-60), (G.5-57);
b0,
is the width of the chamfer or radius on a loose flange [mm], Figure G.3-10;
bF, bL
is the effective width of flange, loose flange [mm], Formulae (G.5-5), (G.5-8), (G.5-9),
(G.5-12);
bGe, bGi, bGt
are the gasket widths (effective, interim, theoretical) [mm], Table G.5-1, Formulae (G.5-59),
(G.5-55);
UNI EN 13445-3:2021
699
EN 13445-3:2021 (E)
Issue 1 (2021-05)
cF, cG cM, cS
are correction factors [-],Formulae (G.5-36), (G.7-8), (G.7-15), to (G.7-18);
d0
is the inside diameter of the flange ring [mm] or outside diameter of the central part of a
blank flange (with thickness e0). In no case is it greater than the inside diameter of the
gasket [mm], Figures G.3-4 to G.3-10.;
d1
is the average diameter of hub, thin end [mm], Figures G.3-4, G.3-5;
d2
is the average diameter of hub, thick end [mm], Figures G.3-4, G.3-5;
d3, d3e
are the bolt circle diameters (real, effective) [mm], Figures G.3-4 to G.3-10;
d4
is the flange outside diameter [mm], Figures G.3-4 to G.3-10;
d5, d5t, d5e
are the diameters of bolt holes (pierced, blind, effective) [mm], Figures G.3-4 to G.3-10,
Formula (G.5-2);
d6
is the inside diameter of a loose flange [mm], Figure G.3-10;
d7
is the diameter of the position of the reaction between a loose flange and a stub or collar
[mm], Figure G.3-1, Formulae (G.5-27) to (G.5-29) and (G.5-63);
d8
is the outside diameter of stub or collar [mm], Figure G.3-10;
d9
is the diameter of a central hole in a blank flange [mm], Figure G.3-9;
dB0, dBe, dBs
are bolt diameters (nominal, effective, waisted) [mm], Figure G.3-2;
dG0, dG1, dG2
are gasket contact diameters (real contact at curved surfaces, theoretical inside, theoretical
outside) [mm], Figure G.3-3;
dGe, dGi, dGt
are gasket calculation diameters (effective, interim, theoretical) [mm] Figure G.3-3,
Table G.5-1;
dE, dF, dL, dS, dX
are average diameters of a part or section (designated by the subscript) [mm],
Formulae (G.5-6), (G.-10), (G.5-13), (G.5-17, (G.5-19), (G.5-21), Figures G.3-4 to G.3-10;
E0
is the compressive modulus of elasticity of the gasket [MPa] at zero compressive stress
Q = 0, see G.9.2;
EB, EF, EG, EL
are the moduli of elasticity (of the part designated by the subscript) at the design
temperature [MPa];
e0
is the wall thickness of central plate of blank flange (inside d0 ) [mm], Figure G.3-9;
e1
is the minimum wall thickness at thin end of hub [mm], Figures G.3-4, G.3-5;
e2
is the wall thickness at thick end of hub [mm], Figures G.3-4, G.3-5;
700
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
eD, eE
is the wall thickness of the equivalent cylinder for load limit and flexibility calculations
respectively [mm], Formulae (G.7-11), (G.5-15), (G.5-18), (G.5-20);
eF , e L
is the effective axial thickness of flange, loose flange [mm], Formulae (G.5-7), (G.5-11),
(G.5-14);
eFb
is the thickness of flange ring at diameter d3 (bolt position) [mm];
eFt
is the thickness of flange ring at diameter dGe (gasket force position), relevant for thermal
expansion [mm];
eG
is the gasket axial thickness [mm], Figure G.3-3;
eP
is the portion of the flange thickness subject to radial pressure loading [mm], Figures G.3-4
to G.3-10;
eQ
is the portion of the flange thickness not subject to radial pressure loading [mm],
Figures G.3-6 to G.3-7;
eS
is the shell thickness [mm], Figures G.3-4 to G.3-10;
eX
is the flange thickness at the weakest section [mm], Figure G.3-9;
FA
is the external axial force [N], Figure G.3-1, tensile force positive, compressive force
negative;
FB
is the total bolt force of all bolts [N], Figure G.3-1;
FG
is the gasket force [N], Figure G.3-1;
F
is the minimum gasket force in assembly condition that guarantees that the required
gasket force is maintained in all subsequent conditions [N], Formula (G.6-10);
FQ
is the axial fluid-pressure force [N], Formula (G.6-1);
FR
is the force resulting from FA and MA [N], Formula (G.6-2);
fB, fE, fF, fL, fS
are nominal design stresses (of the part designated by the subscript) [MPa], at the design
temperature;
gC
is the creep factor for gasket [-],see G.9.2 and Tables G.9-1 to G.9-6;
hG, hH, hL
are lever arms (gasket, hub, loose flange) [mm], Figure G.3-1, Formulae (G.5-24) to (G.526), (G.5-30) to (G.5-32), (G.5-61), (G.5-62);
hP, hQ, hR, hS, hT
are lever arm corrections [mm], Formulae (G.5-22), (G.5-37) to (G.5-40), (G.5-48), (G.5-49);
I
is the load condition identifier [-], for assembly condition I = 0, for subsequent conditions
I = 1, 2, 3...;
UNI EN 13445-3:2021
701
EN 13445-3:2021 (E)
Issue 1 (2021-05)
jM, jS
are sign numbers for moment, shear force (+1 or -1) [-], Formulae (G.7-19), (G.7-20);
K1
is the rate of change of the modulus of elasticity of the gasket with compressive stress after
bolting-up [-], see G.9.2 and Tables G.9-1 to G.9-6;
kQ, kR, kM, kS
are correction factors [-],Formulae (G.5-41) to (G.5-44), (G.7-21),(G.7-22) and Table G.7-1;
lB, le, ls
are bolt axial dimensions [mm], Figures G.3-2 and G.3-5 to G.3-7; le = lB – ls
lH
is the length of hub [mm], Figures G.3-4, G.3-5;
MA
is the external bending moment [Nmm], Figure G.3-1;
Mt
is the bolt assembly torque [Nmm], Formula (G.8-4);
m
is the gasket compression factor [-], see G.9.2 and Tables G.9-1 to G.9-6;
NR
is the number of times that the joint is re-made during the service life of the flanges,
without influence on results for NR  10;
nB
is the number of bolts [-];
P
is the fluid pressure [MPa], internal pressure positive, external negative;
pB
is the pitch between bolts [mm], Formula (G.5-1);
pt
is the bolt thread pitch [mm];
Q
is the mean (existing) effective gasket compressive stress [MPa], Q = FG/AGe
QI,min
is the minimum required compressive stress in gasket for subsequent load condition No. I
[MPa], depending on load parameters, Formula (G.9-4);
Q0,min
is the minimum required compressive stress in gasket for assembly condition (I = 0) [MPa],
see G.9.2 and Tables G.9-1 to G.9-6;
Qmax
is the maximum allowable compressive stress in gasket [MPa] (including safety margins,
which are same for all load conditions), see G.9.2 and Tables G.9-1 to G.9-6;
r2
is the radius of curvature in gasket cross section [mm], Figure G.3-3;
TB, TG, TF, TL
are design temperatures (average for the part designated by the subscript) [oC];
T0
is the temperature of joint at bolting-up [oC] (usually +20 oC);
WF, WL, WX
are resistances (of the part or section designated by the subscript) [Nmm],
Formulae (G.7-10), (G.7-29), (G.7-31), (G.7-33);
702
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
XB, XG
are axial flexibility moduli of bolts, gasket [1/mm], Formulae (G.5-54), (G.5-65);
YG, YQ, YR
are axial compliances of the joint corresponding to loads FG, FQ, FR [mm/N], Formulae (G.65), (G.6-6), (G.6-7);
ZF, ZL
are rotational flexibility moduli of flange, loose flange [1/mm3], Formulae (G.5-45), (G.546), (G.5-50), (G.5-51), (G.5-52);
B, F, G, L
are average thermal expansion coefficients [K-1], averaged between T0 and TB, TG, TF, TL

are intermediate working variables [-],Formulae (G.5-16), (G.5-33) to (G.5-35), (G.5-64),
(G.7-13), (G.7-14), see G.7.1;
U
is the overall axial thermal expansion relative to bolting-up condition [mm], Formula (G.63);
n+, n-
are the scatter values of the initial bolt load for nB bolts above nominal value, below
nominal value [-],Formulae (G.6-15), (G.6-16), see G.8.3; analogeous for nB = 1.
F, L
is the rotation of flange, loose flange, due to applied moment [rad], Formulae (G.8-16),
(G.8-17);

is the coefficient of friction, assumed to be equal for bolts and nuts [-], see G.8.4;

is a diameter ratio for blank flanges [-],Formula (G.5-47);
B, F, G, L, X
are load ratios (of the part or section designated by the subscript) [-],Formulae (G.7-3),
(G.7-7), (G.7-9), (G.7-28), (G.7-30), (G.7-32), (G.7-34);
max
is the reduced maximum allowable load ratio [-],Formula (G.7-2);
G
is the angle of inclination of a sealing face [rad or deg], Figure G.3-3;
S
is the angle of inclination of connected shell wall [rad or deg], shown in Figures G.3-6 and
G.3-7 with sign convention;

is the load ratio of flange ring due to radial force [-], Formula (G.7-23);
Z
is the particular value of  [-], Table G.7-1.
UNI EN 13445-3:2021
703
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Integral flange
b) Loose flange
Figure G.3-1 ― Applied loads and lever arms
704
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Hexagon headed bolt
b) Stud bolt
c) Waisted stud
d) View on ‘Z’
Figure G.3-2 ― Bolt details
UNI EN 13445-3:2021
705
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure G.3-3 — Gasket details
a) Tapered hub with no thickening in the bore
b) Tapered hub with thickening in the bore
706
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Figure G.3-4 — Integral hub-flange on a cylindrical shell (continued on next page)
c) Radiused cylindrical hub
1) shell 2) hub 3) ring
Figure G.3-4 — Integral hub-flange on a cylindrical shell (continued)
1) shell 2) hub 3) ring
Figure G.3-5 — Reverse integral hub-flange on a cylindrical shell
UNI EN 13445-3:2021
707
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Flange at the small end of cone
b) Flange at the large end of cone
1) shell 2) ring
Figure G.3-6 — Flange integral with a conical shell
708
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) Domed cover
b) Insert pad
1) shell 2) ring
Figure G.3-7 — Flange integral with a spherical shell
UNI EN 13445-3:2021
709
EN 13445-3:2021 (E)
Issue 1 (2021-05)
1) shell 2) ring
Figure G.3-8 — Slip-on weld flange
1) plate 2) ring
Figure G.3-9 — Flat closure
710
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
a) With stub flange
b) With collar
1) shell 2) stub / collar 3) loose flange
Figure G.3-10 — Loose flange
UNI EN 13445-3:2021
711
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.4 General
G.4.1 Conditions of applicability
G.4.1.1 Geometry
The method applies when:
—
there are two similar or dissimilar flanges, or one flange and a blank flange;
—
the whole assembly is axisymmetric;
—
there are four or more identical, uniformly distributed bolts;
—
there is a circular gasket, located within the bolt circle on plane surfaces and compressed axially;
—
the flange dimensions met the following conditions:
a)
b)
c)
0 , 2  b F / e F  5 ,0
;

0 ,2  b L / e L  5 ,0
e F  max e 2 ; d B0 ; p B  3 0 ,01 ... 0 ,10   p B / b F

cos  S  1 1  0 ,01  d S / e S 
NOTE 1
and b).
Condition a) need not to be met for a collar in combination with a loose flange, see Figure G.3-10 a)
NOTE 2
Condition b) is to limit non-uniformity of gasket pressure due to spacing of bolts. The values 0,01 and
0,10 are to be applied for soft (non-metallic) and hard (metallic) gaskets respectively. A more precise criterion is
given in G.8.1.
The following configurations are excluded from the scope of the method:
— flanges of essentially non-axisymmetric geometry, e.g. split loose flanges, oval flanges or gusset
reinforced flanges;
— flange joints having metal to metal contact between the flanges or between the flanges and a spacer ring
fitted either inside or outside the gasket or inside or outside the bolts. An example is a spiral wound
gasket on a high pressure application.
G.4.1.2 Material characteristics
Values of nominal design stress for bolts shall be determined as for shells in Clause 6.
Material properties for gaskets may be taken from G.9.
NOTE
For gaskets which undergo large deformation (e.g. soft rubber) the results can be conservative (e.g. required
bolt load too high, allowable fluid pressure too low, etc.) because the method presupposes small deformations.
712
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.4.1.3 Loads
This method applies to the following loads:
— fluid pressure : internal or external;
— external loads : axial forces and bending moment;
— axial thermal expansion of flanges, bolts and gasket;
The following are not taken into account:
— External torsional moments and external shear loads, e.g. due to pipework.
G.4.1.4 Mechanical model
The method is based on the following mechanical model:
— Geometry of both flanges and gasket is axisymmetric. Small deviations such as those due to a finite
number of bolts, are permitted;
— Flange ring cross section on a radial cut remains undeformed. Only circumferential stresses and strains
in the ring are considered. Radial and axial stresses and strains are neglected. This leads to the
conditions in G.4.1.1 a);
— Shell connected to the flange ring is cylindrical. A tapered hub is treated as an equivalent cylindrical
shell. It has a calculated wall thickness which is different for elastic and plastic behaviour but always lies
between the thicknesses of the thin and thick end of the hub. Conical and spherical shells are treated as
equivalent cylindrical shells with same wall thickness as the actual shell; the differences in shape are
explicitly taken into account in the formulae. This simplification leads to the condition in G.4.1.1 c). The
method assumes equal radial deformation and rotation of the flange ring and the shell at their junction;
— Gasket is in contact with the flange faces over an annular area which the method determines. The
effective radial width bGe of the gasket, which may be less than its true width, is calculated for the
assembly condition (I = 0) and assumed to be unchanged for all subsequent load conditions (I = 1, 2...).
The calculation of bGe includes elastic rotations of both flanges, and approximate elastic and plastic
deformations of gasket;
— Modulus of elasticity of gasket material may increase with the compressive stress Q on the gasket. The
method uses a linear model: EG = E0 + K1Q, in which EG is the unloading modulus from the highest value
of gasket stress which is attained (Q);
— Creep of gasket material is taken into account approximately by factor gC ;
— Thermal and mechanical axial deformations of flanges, bolts and gaskets are taken into account;
— Loading of the whole flange connection is axisymmetric. An external bending moment is treated as an
equivalent axial force transmitted by the bolts; see Formula (G.6-2);
UNI EN 13445-3:2021
713
EN 13445-3:2021 (E)
Issue 1 (2021-05)
— Load changes between load conditions cause changes in the bolt and gasket forces. These are calculated
taking account of elastic deformations of all components. The required initial assembly force is
calculated (see G.6.4) to ensure that the required forces on the gasket to ensure leak tightness are
achieved under all conditions (see G.6.3);
— Load limit checks are based on limit loads for each component. Excessive plastic deformations are
prevented. The load limit for gaskets, which depends on Qmax , is an approximation.
The following are not taken into account in the model:
— Bolt bending stiffness and bending strength. Ignoring bolt bending is a conservative simplification.
Calculated tensile stiffness of bolts includes deformation of the bolt threads within a nut or tapped hole,
see Formula (G.5-36);
— Creep of flanges and bolts. This is due to lack of relevant material data for deformation;
— Different radial deformations of the flanges. With two equal flanges this is not relevant as the radial
deformations are the same.
G.5 Parameters
G.5.1 Flange parameters
G.5.1.1 General
Specific flange types shall be treated as follows:
An integral flange is calculated as an equivalent ring with rectangular cross-section, with dimensions bF and eF,
connected at diameter dE to an equivalent shell of constant wall thickness eE.
A blank flange is calculated as an equivalent ring with rectangular cross-section, with dimensions bF and
eF,connected at diameter dE = d0 to a plate of constant thickness e0. It may have a central opening of diameter d9.
If a nozzle is connected at the opening, the nozzle is not taken into account in the calculation.
A loose flange is calculated as an equivalent ring with rectangular cross-section dimensions bL and eL, without
connection to a shell. The stub or collar is treated in the same way as an integral flange.
A screwed flange is calculated as a loose flange with inside diameter equal load transmission diameter equal
average thread diameter
G.5.1.2 Flange ring
G.5.1.2.1
Bolt holes
The pitch between bolts is given by:
pB    d 3 / nB
714
(G.5-1)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The effective diameter of the bolt hole is:
d 5e  d 5 
(G.5-2)
d 5 / pB
With blind bolt holes, the hole diameter is assumed to be:
(G.5-3)
d 5  d 5 t  l 5 t / e Fb
The effective bolt circle diameter is:
2
(G.5-4)
d 3 e  d 3  (1  2 / n B )
NOTE
pB
G.5.1.2.2
and
~
pB
are equal, as well as
d 3e
~
and d 3 e .
Effective dimensions of flange ring
In Figures G.3-4 to G.3-10, the equivalent ring is indicated by chain dotted lines.
The effective thickness eF or eL is the average thickness of the flange ring. It shall be obtained by dividing the
radial gross cross-section area of the ring AF or AL (bolt holes or stud holes ignored) by the radial width of this
section.
NOTE
Since there is a large variety of shapes of cross sections, formulae are not given for calculation of AF or AL
for specific flange types.
For an integral flange and blank flange (see Figures G.3-4 to G.3-9), calculate:
bF  (d 4  d 0 ) / 2  d 5 e
(G.5-5)
d F  (d 4  d 0 ) / 2
(G.5-6)
e F  2  A F /( d 4  d 0 )
(G.5-7)
bL  d L  e L  0
(G.5-8)
For a loose flange with stub or collar (see Figure G.3-10), calculate:
bF  (d 8  d 0 ) / 2
(G.5-9)
d F  (d 8  d 0 ) / 2
(G.5-10)
e F  2  AF / (d 8  d 0 )
(G.5-11)
bL  (d 4  d 6 ) / 2  d 5 e
(G.5-12)
d L  (d 4  d 6 ) / 2
(G.5-13)
e L  2  A L /( d 4  d 6 )
(G.5-14)
G.5.1.3 Connected shell
G.5.1.3.1
Tapered hub
The following shall be calculated:
UNI EN 13445-3:2021
715
EN 13445-3:2021 (E)
Issue 1 (2021-05)


e E  e 1  1 




/ 3



d 1  e1  lH 

 1  l H
(G.5-15)
(G.5-16)
  e 2 / e1
d E  min d 1  e 1  e E ; d 2  e 2  e E   max
G.5.1.3.2
d 1
 e1  e E ; d 2  e 2  e E

(G.5-17)
2
No hub
The effective dimensions are given by:
(G.5-18)
eE  eS
dE  dS
G.5.1.3.3
(G.5-19)
Blank flange (no connected shell)
The effective dimensions are:
eE  0
(G.5-20)
dE  d0
(G.5-21)
NOTE
Formulae (G.5-20), (G.5-21) apply whether the blank flange has an opening (with or without nozzle) or not.
G.5.1.4 Lever arms
NOTE
When the gasket is of flat type (as defined in Table G.5-1), the parameters hP and hG below can be
calculated only when dGe has been determined, i.e. when the calculations in G.5.3.2 have been completed.
G.5.1.4.1
hP 
General
d
Ge
 dE
2  2  d Ge
 d E  / 6  2  eP
2

 d F / d Ge
2
(G.5-22)
NOTE
this formula is a simplified one, which gives appropriate results for normal cases of flanges. For flanges with
extreme dimensions (large flange ring width in comparison to internal diameter and/or thick flange ring in comparison
to internal diameter), the exact Formula (7.11a) of the lever arm hp stated in the CEN technical report CR 13642:1999
can be used :

h p   d Ge  d

s
2

2  d Ge  d
6
s
 e s  cos 
s
2
ds
1


 e s  cos 
2
3


1
2
 2  ep  d p  
2

 d Ge

s

For blank flanges:
eP  0
G.5.1.4.2
Integral flange and blank flange
h G  (d 3 e  d G e ) / 2
(G.5-24)
hH  (d 3 e  d E ) / 2
(G.5-25)
hL  0
(G.5-26)
G.5.1.4.3
Loose flange with stub or collar
d 7 ,min  d 7  d 7 ,max
716
(G.5-23)
(G.5-27)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
d 7 ,min
 d
6
(G.5-28)
 2  b0
 d8
(G.5-29)
h G  (d 7  d G e ) / 2
(G.5-30)
hH  (d 7  d E ) / 2
(G.5-31)
hL  ( d 3 e  d 7 ) / 2
(G.5-32)
d 7 ,max
As the value of d7 is not known in advance, the following hypotheses can be made :
— for the flexibility and force calculations (i.e. up to the end of G.6), take for d7 the value d70 given by
Formula (G.5-63);
NOTE
It follows that hG, hH and hL can vary with each iteration necessary to calculate bGe and dGe (see G.5.3.2).
— for the calculation of load ratios (G.7), the most favourable value between d7min and d7max can be
used, as stated in G.7.6.
G.5.1.5 Flexibility-related flange parameters
NOTE
When the gasket is of flat type, the parameter hQ below can be calculated only when dGe has been
determined, i.e. when the calculations in G.5.3.2 have been performed.
G.5.1.5.1
 
Integral flange, stub or collar
eE  d F
(G.5-33)
b F  d E  cos  S
d E  eE
  0 ,550  cos  S 
(G.5-34)
eF
(G.5-35)
  1  eP / eF  e Q / eF
cF 
1   
 
1     4  1  3    3  
h S  e F  1,10 
eE
dE
UNI EN 13445-3:2021

2
  6  1  2       6     3  
1 2   
1   
2
2

4
(G.5-36)
(G.5-37)
717
EN 13445-3:2021 (E)
Issue 1 (2021-05)
hT  eF 
1  2     
2
(G.5-38)
1   


hQ  hS  k Q  hT  2  d F  eP / d E
2
 0 ,5  tan  S
 d
E
/ d Ge
2
(G.5-39)
(G.5-40)
h R  h S  k R  h T  0 ,5  tan  S
For conical and cylindrical shells:
k Q   0 ,85 / cos  S
(G.5-41)
k R   0 ,15 / cos  S
(G.5-42)
For a spherical shell:
k Q   0 ,35 / cos  S
(G.5-43)
k R   0 ,65 / cos  S
(G.5-44)
For all cases:
ZF 
3  dF  cF
  bF  eF
(G.5-45)
3
(G.5-46)
ZL  0
G.5.1.5.2
Blank flange
(G.5-47)
  d9 / dE
hQ 
hR 
ZF 
2
d E  (1  
8
)

0 ,7  3 ,3  
2
0 ,7  1,3  
2
2
d E  (1  
 dE

d
 Ge




2
2
) 0 ,7  3 ,3  

2
2
4  ( 1   ) 0 ,7  1,3  

(G.5-49)
3 dF
  bF  e F
3
 dF  e0
3

 1 
2
 1,4  2 ,6   
2
(G.5-50)
(G.5-51)
ZL  0
G.5.1.5.3
(G.5-48)
Loose flange with stub or collar
For the stub or collar Formulae (G.5-33) to (G.5-45) shall be used; for the loose flange the following formula shall
be used:
ZL 
718
3 dL
  bL  eL
3
(G.5-52)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.5.2 Bolt parameters
NOTE
The bolt dimensions are shown in Figure G.3-2. Diameters of standardised metric series bolts (in accordance
to EN ISO 4014:2011 and EN ISO 4016:2011) are given in G.8.2.
G.5.2.1 Effective cross-section area of bolts
AB  nB 

4
 min( d Be ; d Bs )
2
(G.5-53)
G.5.2.2 Flexibility modulus of bolts
XB 
 l
le
0 ,8
s



2
2
nB    d
d Be
d B0
 Bs
4




(G.5-54)
The thickness of any washers shall be included in lengths ls and le.
G.5.3 Gasket parameters
NOTE
Clause G.9 gives typical non-mandatory values for material properties. If data for the actual gasket are
available, they should preferably be used.
G.5.3.1 Theoretical width
NOTE
The theoretical gasket width bGt is the maximum gasket width and becomes effective under a very high
force or with very low flange rotation.
b Gt  d G 2  d G 1  / 2
(G.5-55)
d Gt  d G 2  d G 1  / 2
(G.5-56)
A Gt    d Gt  b Gt
(G.5-57)
G.5.3.2 Effective width
NOTE 1
The effective gasket width bGe for many types of gasket depends on the force FG applied to the gasket. It is
determined for the bolting-up condition with FG = FG0 and assumed to be unchanged for subsequent conditions. The
calculation contains an iteration for bGe within an iteration for FG0. The steps are as follows:
1)
An initial value FG0 from Formula (G.5-58) is assumed;
2) From Formulae (G.5-59) to (G.5-64), an iteration is performed to determine bGe to within the required
accuracy;
3) The calculation proceeds to Formula (G.6-13), where the required value for FG0 is checked against the
assumed.
NOTE 2
The value FG0 used for this determination represents the minimum force which should be reached in the
bolting-up condition to meet the leak tightness criteria given in G.6.4.
To start the calculation, an arbitrary value for FG0 may be chosen e.g.:
F G0  A B  f B0 / 3  F R0
UNI EN 13445-3:2021
(G.5-58)
719
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where FR0 is given in G.6.2.2.
An interim gasket width bGi shall be determined from Table G.5-1, starting with the first approximation and
proceeding to the more accurate expressions given.
Effective gasket width and effective gasket area:
b Ge  min b Gi ; b Gt
(G.5-59)

(G.5-60)
A Ge    d Ge  b Ge
NOTE 3
The effective gasket diameter dGe is the diameter where the gasket force acts. It is also determined from
Table G.5-1.
Table G.5-1 ― Effective gasket geometry
Type
Gasket form
Formulae
1
Flat gaskets, soft or
composite materials or
pure metallic, Figure G.33a
First approximation:
More accurately:
b Gi  b Gt
2

e G /(   d Ge  E Gm )


F G0

 


~
~
~
 Z F / E F0  h G0  Z F / E F0
h
   d Ge  Q max 

 G0
b Gi 





E Gm  E 0  0 ,5  K 1  F G0 / A Ge
~
Z F , Z F according to Formula (G.5-45) or (G.5-50)
Always:
2
Metal gaskets with curved
First approximation: b Gi 
surfaces,
More accurately:
simple contact,
Figures G.3-3b, G.3-3c
b Gi 
4
Ring joint metal gasket,
octagonal,
double contact;
Figure G.3-3d





d Ge  d G0
Always: b G i according to Figure G.3-3d
(Projection of contacting surfaces in axial direction.)
Always:
d Ge  d Gt
Metal gaskets with curved
First approximation: b Gi 
surfaces,
More accurately:
double contact,
Figures G.3-3e, G.3-3f
b Gi 
Always:
720
6  r 2  cos  G  b Gt  Q max / E G0
2



F G0
 6  r 2  cos  G  F G0




  d Ge  E G0
   d Ge  Q max 


Always:
3
d Ge  d G2  bGe
12  r 2  cos  G  b Gt  Q max / E G0
2



F G0
 12  r 2  cos  G  F G0




  d Ge  E G0
   d Ge  Q max 







d Ge  d Gt
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Lever arm for integral flange and blank flange:
h G 0  ( d 3 e  d Ge ) / 2
(G.5-61)
Lever arm for loose flange with stub or collar:
h G0  ( d 70  d Ge ) / 2
(G.5-62)


d Ge    d 3 e 

d 70  min  max  d 7 ,min ;
 ; d 7 ,max 
1 




(G.5-63)
 
Z L  E F0
(G.5-64)
Z F  E L0
Formulae (G.5-59) to (G.5-64) are re-evaluated iteratively until bGe is constant within the required precision.
NOTE 4
Agreement within 5 %, is generally enough, but for comparison of the results of different programs a
precision of 0,1 % is recommended.
G.5.3.3 Axial flexibility modulus of gasket
X
G

eG
A Gt

b Gt  e G / 2
b Ge  e G / 2
(G.5-65)
G.6 Forces
G.6.1 General
All potentially critical load cases shall be calculated. The number of load cases depends on the application. (See
also G.6.2.2.2.)
G.6.2 Loads
G.6.2.1 Assembly condition (I = 0)
Fluid pressure (internal or external) is zero; therefore PD = 0.
External loads FA0 and MA0 combine to give a net force FR0 as in G.6.2.2.2 (load case I = 0). All temperatures are
equal to the initial uniform value T0.
G.6.2.2 Subsequent conditions (I = 1, 2, 3...)
G.6.2.2.1
F Q =
G.6.2.2.2
Fluid pressure

4
 d Ge
2
 P
(G.6-1)
Additional external loads
Additional external loads FAI and MAI combine to give a net force FRI as follows:
UNI EN 13445-3:2021
721
EN 13445-3:2021 (E)
Issue 1 (2021-05)
FR  = F A   M
A
(G.6-2)
 4 d 3e
In the case of multiple loads, the loading which gives the most severe conditions shall be selected.
When an external moment occurs, the most severe case may be difficult to predict. On the side of the joint where
the moment induces an additional tensile load (sign + in Formula (G.6-2)) the load limits of the flange or bolts may
govern, or minimum gasket compression. On the side where the moment induces a compressive load (sign - in
Formula (G.6-2)), the load limit of the gasket may govern. Therfore two load conditions (one for each sign in
Formula (G.6-2), using different indices I for each case) shall be systematically checked whenever an external
moment is applied.
G.6.2.2.3
U
Thermal loads

 l B 
B
 (T B   T 0 )  e Ft  
~
~
 e G   G   (T G   T 0 )  e Ft   F 
F
 (T F   T 0 )  e L  
 (T L   T 0 )
L
~
~
~ ~
 (T F   T 0 )  e L   L   (T L   T 0 )
(G.6-3)
where
(G.6-4)
~
~
e Ft  e Ft  e L  e L  e G  l B
The thickness of any washers shall be included in
~
e Ft
and
e Ft
.
NOTE
It is assumed that the temperature and thermal expansion coefficient of the washers are equal to those on
the corresponding flange.
G.6.3 Compliance of the joint
Lever arms are calculated in G.5.1.4, for all cases except loose flanges for which Formula (G.5-62) is to be used.
In general Formulae (G.6-5) to (G.6-7) shall apply for all load conditions (I = 0, 1, 2 ...), with:
—
gC = 1,0 for bolting-up condition (I = 0), even if the gasket characteristics indicate that gC < 1,0 at
ambient temperature ( T   20 o C );
—
EGI calculated using
Q  F G0 / A Ge
~
~ 2
~
/ E F  Z F  hG / E F 
~
~ 2 ~
2
 Z L  hL / E L   Z L  hL / E L   X B / E B 
YG

 Z F  hG
for all I .
2

XG
E G 
 g C

(G.6-5)


~
~
~
~
~
~
Y Q   Z F  h G  h H  h P  h Q  / E F   Z F  h G  h H  h P  h Q / E F  

 Z L  hL
2
~
~ 2 ~
/ E L   Z L  hL / E L   X B / E B 


(G.6-6)

~
~
~
~
~
Y R   Z F  h G  h H  h R  / E F   Z F  h G  h H  h R / E F  

 Z L  hL
2
~
~ 2 ~
/ E L   Z L  hL / E L   X B / E B 

(G.6-7)
NOTE
The evaluation of Formulae (G.6-6), (G.6-7) may be waived for load cases without fluid pressure (resultant
FQ = 0), without external force (FR = 0) respectively.
G.6.4 Minimum forces necessary for the gasket
G.6.4.1 Assembly condition (I = 0)
Minimum force for seating the gasket is given by:
F G0,
722
min
 A Ge  Q 0, min
(G.6-8)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
where Q0,min is taken from G.9.3, Tables G.9-1 to G.9-6, unless more relevant data are available.
NOTE
This force need not be considered when for the subsequent conditions QI,min is determined taking into
account complete leak rate conditions (see G.9.2). In this case, take FG0,min = 0.
G.6.4.2 Subsequent conditions (I = 1, 2, 3...)
Force required to assure leak-tightness under pressure, and no loss of contact at bolts or nuts:
FG 
,min
 max
A Ge
Q
,min
;  F Q   F R 
(G.6-9)

where QI,min is taken from G.9.2, Formula (G.9-4) with mI from G.9.3, Tables G.9-1 to G.9-6, depending on fluid
pressure and temperature of the load case.
G.6.5 Forces in assembly condition (I = 0)
G.6.5.1 Required forces
To guarantee that the force on the gasket in subsequent conditions never falls below FGI,min, the gasket force in
the bolting-up condition shall be at least equal to the following:
F G   max
all   0
F G  ,min
 Y G   F Q   Y Q   F R   Y R   F R0  Y R0

U 
 Y G0
(G.6-10)
Taking into account what is also necessary for seating of the gasket (Formula (G.6-8)), the required gasket force
and the corresponding bolt load are as follows:

F G 0 , r e q  m a x F G 0 , m in ; F G 
F B0, req
 F G0, req  F R0

(G.6-11)
(G.6-12)
If the value FG0,req given by Formula (G.6-11) is higher than the value FG0 assumed up to this step, the calculation
must be repeated from Formula (G.5-59) and using a higher value FG0 until:
F G0, req  F G0
(G.6-13)
If the value FG0,req given by Formula (G.6-11) is lower than the value FG0 assumed up to this step, this value is
acceptable because it is conservative.
The true required force FG0,req is found through a number of iterations until within the required precision is valid:
UNI EN 13445-3:2021
723
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(G.6-14)
F G0, req  F G0
NOTE 1
To cease the described iteration an agreement within 5 % is generally enough, but for comparison of the
results of different programs a precision of 0,1 % is recommended.
NOTE 2
Advices for assemblage (e.g. required torque) are recommended to select for slightely increased forces (e.g.
10 % above the required), tending to better leak tigthness. Limiting are the allowed load ratios calculated in G.7.
G.6.5.2 Accounting for bolt-load scatter at assembly
All bolt-tightening methods involve some degree of inaccuracy.
For an assemblage with nB bolts the resulting scatter values  n  and  n  are defined by Formulae (G.6-15) and
(G.6-16). These are less than the scatter values  1 and  1 for an assemblage with only a single bolt.
Indicative values
 1
and
 1
for single bolts are given in G.8.3.
A reasonable approximation for the influence of nB is given by the following formulae:

nB
4
(G.6-15)

nB
4
(G.6-16)
 n    1  1  3
 n    1  1  3
The design of the flange connection has to be such that the actual bolt load FB0 is within the range
F B0,
min
 F B0  F B0,
(G.6-17)
max
where
F B0, max
 F B 0 ,nom
 1   n 

(G.6-18)
F B0, min
 F B 0 ,nom
 1   n 

(G.6-19)
After bolting-up, the actual bolt force achieved shall not be less than the minimum required bolt force FB0,req i.e.:
(G.6-20)
FB 0 , m in  FB 0 , r e q
The scatter in bolt-tightening shall be taken account of the following way:
a) The nominal bolt assembly force, used to define the bolting up parameters. This is calculated as
follows:
— For a method where bolt load is controlled:
F B0, nom
 F B0, req
1 
n

(G.6-21)
— For a method without control of bolt load:
724
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
The value to be selected for FB0,nom is the average bolt load FB0,av that can be expected in practice for the
method used, independently of FB0,req.
The following condition shall be met, where
F B0, nom
 F B0, av  F B0, req
1 
n
n
shall be based on
 1
= 0,5 :
(G.6-22)

If this is not met, the bolt-tightening method initially chosen is not valid and shall be changed.
NOTE For the common case of manual bolt-tightening, G.8.3 gives an estimate of FB0,av provided that standard
wrenches are used.
b) The maximum forces to be used for the load limit calculation (see G.7) in assemblage condition. This is
given by:
F B 0  F B 0 ,m a x  F B0,
F G0  F G0
,max
 1  
nom
 F B 0 ,max
n
(G.6-23)

(G.6-24)
 F R0
The effective gasket width bGe need not be recalculated.
G.6.6 Forces in subsequent conditions (I = 1, 2, 3...)
The calculation forces in subsequent conditions shall be based on a design assembly gasket force FG0,d given by:
F G0
,d

 max  F G  ;

2
3
 ( 1  10 N R )  F B 0 ,max

 F R0 

(G.6-25)
The corresponding subsequent gasket force and bolt load for load limit calculations are:
FG 

F G0, d
 Y G0  F Q   Y Q   F R   Y R   F R0  Y R0
F B   F G   F Q   F R 


U 

YG
(G.6-26)
(G.6-27)
NOTE 1
To prevent leakage, the gasket force in all subsequent conditions shall be at least FGI,min from Formula (G.69). This corresponds to a gasket assembly force equal to FG from Formula (G.6-10). To avoid progressive distortion
due to frequent re-assembly, in some cases the gasket assembly force from Formula (G.6-25) FG0,d should be higher
than FG.
NOTE 2
When progressive distortion does not control, i.e. when FG0,d = FG in Formula (G.6-25), then forces FGI
and FBI , defined by Formulae (G.6-26) and (G.6-27), are those that exist in any condition I  0 for an initial bolt load
equal to the minimum required FB0,req. In subclause G.7, the admissibility of these minimum required forces is
checked. (In contrast, for the assembly condition the admissibility of the maximum possible forces is checked.) Actual
forces in subsequent conditions are above the forces defined by Formulae (G.6-26) and (G.6-27) due to the scatter of
bolting-up method. Nevertheless it is valid to waive the amount of FB0(actual) in excess of FB0,req , since this is a
"passive" ("secondary") force, which dissipates through plastic deformation.
UNI EN 13445-3:2021
725
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 3
When progressive distortion controls, the maximum possible initial bolt load FB0,max is used for
determination of a fictitious gasket force (second term in Formula (G.6-25)). Then a bolt load FB0 > FG + FR0 is
applied and some plastic deformation may occur in subsequent load conditions. The calculation of load limits in G.7
prevents global plastic deformation in all load conditions and serves to limit the accumulation of plastic deformation at
each re-assembly to an acceptable level.
G.7 Load limits
G.7.1 General
Loads on the system shall be within safe limits. These limits are expressed in calculated load ratios. Each load ratio
shall be less or equal to unity for all load conditions:
(I = 0, 1, 2, …)
   1,0 ;
(G.7-1)
The index I for the load condition is omitted in the following for brevity.
For wide flanges a more stringent requirement applies to integral flanges having
flanges having
  d 4 / d 6  2 ,0
   max
  d 4 / d 0  2 ,0
and loose
: Instead of  < 1,0 it shall be:


 min  1,0 ; 0 , 6 


1
5 , 25     1 
2





(G.7-2)
The nominal design stresses in the assembly condition is the same as in the test condition.
NOTE
It is reminded that for assembly condition (I = 0) the forces to be considered are the maximum possible
forces (see G.6.5.2 b).
G.7.2 Bolts
The nominal design stress of bolts here are to be determined by the same rules as used for nominal design stress
of flanges and shells.
The load ratio of bolts shall be limited as follows.
B 
FB
A B  fB

1  C  3 ,2  
2

(G.7-3)
1,0
The term with C takes account of the torque in bolting up. The value C is determined as follows:
For assembly condition after bolting up with torque on the bolts:
If small plastic deformations in the bolts are accepted, which in general is recommended for sufficient ductile
bolt material (minimum rupture elongation A  10 %):
(G.7-4)
C  1  1,000
If strictly elastic behaviour of the bolts is required, which is recommended for not sufficient ductile bolt
material (minimum rupture elongation A < 10 %) and/or for very frequent reassemblages:
726
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
(G.7-5)
C  4 / 3  1,333
For assembly condition after bolting up without torque on the bolts, q.e. with hydraulic tensioner, and for all
subsequent conditions:
(G.7-6)
C  0  0 ,000
Indicative values for the coefficient of friction  are given in G.8.4.
NOTE
It is recommended to observe a minimum load ratio B,min = 0,3 in assembly condition. A smaller load
ratio is in general not good practice, because then the bolts are too thick.
G.7.3 Gasket
The load ratio of the gasket shall be limited as follows.
G 
FG
cG  1 
NOTE

A Gt  c G  Q max
(G.7-7)
1,0
b Gt
(G.7-8)
20  e G
Refer to G.5.3 and to G.9 for gasket characteristics.
G.7.4 Integral flange, stub or collar
Load ratio for flange, stub or collar (for stub or collar max = 1,0):
F 
WF 
F G  h G  F Q  ( h H  h P )  FR  h H
WF

4

 fF  2  b F  e F
2
 max

(G.7-9)
2
 (1  2  opt  Z   Z )  f E  d E  e D

(   1)  l H

e D  e 1  1 
4
4
2
4

(  / 3 )  (d 1  e1 )  lH

2
 c M  jM  k M





R 
(G.7-10)
(G.7-11)
(G.7-12)
f E  min( f F ; f S )
Q 

P dE
(G.7-13)
f E  2  e D  cos  S
FR
(G.7-14)
f E    d E  e D  cos  S
For conical and cylindrical shells:
cM 
1,333  1  0 ,75  ( 0 ,5  
UNI EN 13445-3:2021
Q
 R )
2
  1  ( 0 ,75  
2
Q
 1R
2
)

(G.7-15)
727
EN 13445-3:2021 (E)
Issue 1 (2021-05)

cS 

4

2
1  0 ,75  ( 0 ,5   Q   R )  j S  ( 0 ,5   R  0 ,75   Q


)



(G.7-16)
For a spherical shell:
1,3 3 3  1 
cM 

cS 
4

0 ,7 5  ( 0 , 5   Q   R )
2
  1 
( 0 ,2 5   Q
2
 3  R
2
)



2
1  0 ,7 5  ( 0 ,5   Q   R )  j S  ( 1,5   R  0 ,2 5   Q )


(G.7-17)
(G.7-18)
For all cases:
j M  sign F G  h G  F Q  ( h H  h P )  F R  h H


1
(G.7-19)
jS  1
(G.7-20)
 1,0  k M   1,0
(G.7-21)
0 ,0  k S  1,0
(G.7-22)
NOTE 1
(j
The values of jS, kM, kS to be used are defined in the calculation sequence described following Table G.7-1.
S
,k
M
, k
S
)



  ( 0 ,5  



opt

max

0

min
f E  d E  e D  cos  S
fF  2  b F  e F
Q
  R )  tan  S 
 j M  ( 2  e P / e F  1);

 Q  2  eP
dE
 jS  k S 
e D  c M  c S  (1  j S  k M ) 


3
d E  cos  S


(-1,0  opt  +1,0)
    1,  1,  1 
   0, 0, 0 
    1,  1,  1 
(G.7-23)
(G.7-24)
(G.7-25)
(G.7-26)
(G.7-27)
The value Z in Formula (G.7-10) depends on jM and opt as given in Table G.7-1.
728
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table G.7-1 ― Determination of Z
Range of  o p t
kM

max
(kM

0
( kM

opt
0

opt
  min

min

0
jM
jM  1
jM  1
  opt
  opt
  max
  opt

Z
 1 )

Z
 1 )

Z

Z
  (  1, k ,  1)
M
kM  1
0
  opt
  max
 
opt
( kM
 1 )

Z
  min
(kM
 1 )

Z
  opt

Z
kM  1
  (  1, k ,  1)
M
The sequence of calculation shall be as follows:
a) Calculate eD from Formula (G.7-11)¸  having previously been calculated by Formula (G.5-16);
b) Calculate fE ,  Q ,  R , c M from Formulae (G.7-12), (G.7-13), (G.7-14), (G.7-15) or (G.7-17). If the value in
the root of cM is negative the hub is overloaded and must be redesigned;
c) Calculate
c S ( j   1) ;
S
c S ( j   1) ;
S
jM;opt, 0, max, min from Formulae (G.7-16) or (G.7-18), (G.7-19),
(G.7-24) to (G.7-27). If max < -1,0 or min > +1,0 the ring is overloaded and the flange shall be
redesigned;
d) Determine kM and Z according to Table G.7-1. When that table gives kM < +1 or kM > -1, the value of
kM shall be determined so that WF from Formula (G.7-10) is maximum (see step e) which follows). The
value Z associated with kM is given by Formula (G.7-23);
e) Calculate WF, F from Formula (G.7-10), (G.7-9).
NOTE 2
In the typical case of a flange with a cylindrical shell (  S
tensile force ( F R
 0
), the following is valid:
case is simplified to:  Z
jM  1 ; 
0
 0
), loaded by internal pressure (P > 0) and a
 0  min(  opt ;  max )
. The determination of Z in this
 min(  opt ;  max )
NOTE 3
In the case of a flange with an unusually thin section eX < e2 the additional check of Formula (G.7-30) is
recommended for the integral flange.
G.7.5 Blank flange
The load ratio for a blank flange shall be determined as follows:

F
 F  h  F  (1   3 )  d
G
Q
Ge
 B
 max 
3
 F B  h G  F Q  (1   )  d Ge
UNI EN 13445-3:2021
6  F R  (1   )  d Ge
6 ; F R  (1   )  d Ge
2 ; 1

 1, 0

2  WF

(G.7-28)
729
EN 13445-3:2021 (E)
Issue 1 (2021-05)
WF 

4

 fF  2  b F  e F
2
 d 0  (1   )  e 0
2

(G.7-29)
If there is a potentially critical section where eX < eF (see Figure G.3-9), then the additional load ratio shall be
calculated thus:

X

WX 
FB  ( d 3  d
2 W

4
X
)

(G.7-30)
1,0
X

 fF  ( d 4  2  d 5 e  d X )  e F
2
 d X eX
2

(G.7-31)
G.7.6 Loose flange with stub or collar
Load ratio for loose flange:
L 
WL 
FB  h L

2
(G.7-32)
 max

WL
 fL  b L  e L
2
(G.7-33)
The load ratio for a stub or collar can be evaluated arbitrarily from G.7.4 (always with max = 1,0 or from
Formula (G.7-34). The more favourable result (i.e. the smaller of the F values) is valid. Formula (G.7-34) only
applies to flat gaskets with (dG2 - d7) > 0.
F 
F Q  FR  h H

4


2
 d E  f E  min e E ; e F
2
  min f
 e F ; Q max  d G 2  d 7
2
F
2
4


1,0
(G.7-34)
The lever arms hG, hH, hL may be determined by variation of the diameter d7 in such a way that Formulae (G.7-32)
to (G.7-34) and Formulae (G.7-9) to (G.7-27) all give the most favourable result, i.e. max(F, L) is a minimum.
In the case of FQ + FR > 0 the most favourable result is generally obtained near d7,min according to
Formula (G.5-28). In contrast, in the assembly condition (with FQ = 0 and FR = 0) the optimum is near d7,max
according to Formula (G.5-29).
NOTE
The diameter d7 may be different in all load conditions. In assembly condition (I = 0) the calculation of load
limits may be performed with d7  d70 (Formula (G.5-63)).
G.8 Supplements to the method
G.8.1 Requirement for limitation of non-uniformity of gasket stress
To limit the non-uniformity of gasket stress with widely spaced bolts, it is required that:
eF  p B  3
730
E Gm  b Ge  p B
E
F
 eG  bF

1  
10
G0

2
(G.8-1)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
EGm is given in Table G.5-1, G0 by Formula (G.7-7) for I = 0 with
F G0  F B 0 ,nom  1   n 

(G.8-2)
F R0
For a loose flange eL, bL, EL are used instead of eF, bF, EF.
G.8.2 Dimensions of standard metric bolts
Table G.8-1 ― Metric bolts diameters (dimensions in millimetres)
dB0
Bolt size
see NOTE 1
dBe
see NOTE 2
dBs
see NOTE 3
see NOTE 4
M 6
6
5,06
-
5,3
M 8
8
6,83
-
7,1
M 10
10
8,59
-
9,0
M 12
12
10,36
8,5
10,8
M 14
14
12,12
10,0
M 16
16
14,12
12,0
M 18
18
15,65
13,0
M 20
20
17,65
15,0
M 22
22
19,65
17,0
M 24
24
21,19
18,0
M 27
27
24,19
20,5
M 30
30
26,72
23,0
M 33
33
29,72
25,5
M 36
36
32,25
27,5
M 39
39
35,25
30,5
M 42
42
37,78
32,5
M 45
45
40,78
35,5
M 48
48
43,31
37,5
M 52
52
47,31
41,0
M 56
56
50,84
44,0
52,4
M 64
64
58,37
51,0
60,0
M 726
72
66,37
58,5
68,0
M 806
80
74,37
66,0
76,0
M 906
90
84,37
75,0
86,0
M1006
100
94,37
84,0
96,0
14.6
18,3
22,0
27,7
33,3
39,0
44,7
NOTE 1
For M6 ... M64 the pitch is that of the normal series in accordance to ISO 261:1998.
NOTE 2
The values dBe correspond to the following definitions:
dBe = (dB2 + dB3)/2 (see Figure G.3-2); dBe = dB0 - 0,9382pt
NOTE 3
Diameter of waisted stud.
NOTE 4
Body diameter for rolled thread.
UNI EN 13445-3:2021
731
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.8.3 Scatter of bolting-up methods
G.8.3.1 Scatter values
Table G.8-2 ― Indicative values of 1+ and 1- for Formulae (G.6-15), (G.6-16)
Bolting-up (tightening) method
Measuring method
Factors affecting scatter
Scatter
value 1-
Scatter
value 1+
Wrench
Operator feel, uncontrolled
Friction, Stiffness,
Qualification
0,3 +
0 ,5  
0,3 +
0 ,5  
Impact wrench
Friction, Stiffness,
Calibration
0,2 +
0 ,5  
0,2 +
0 ,5  
Torque wrench = Wrench with
measuring of torque (only)
Friction, Calibration,
Lubrication
0,1 +
0 ,5  
0,1 +
0 ,5  
Hydraulic tensioner.
Measuring of hydraulic pressure
Stiffness, Bolt length,
Calibration
0,20
0,40
Wrench or hydraulic tensioner.
Measuring of bolt elongation
Stiffness, Bolt length,
Calibration
0,15
0,15
Wrench. Measuring of turn of nut
(nearly to bolt yield)
Stiffness, Friction,
Calibration
0,10
0,10
Wrench. Measuring of torque and
turn of nut (nearly to bolt yield)
Calibration
0,07
0,07
NOTE 1 Very experienced operators can achieve scatter less than the given values (e.g. 1+ = 0,15 instead
of 1+ = 0,20 using torque wrench in a case  = 0,20); for inexperienced operators scatter can be greater
than that shown.
NOTE 2 Tabulated scatter values are for a single bolt; the scatter of the total bolt load will be less, for
statistical reasons, see G.6.5.2.
With hydraulic tensioner 1+ and 1- are not equal, due to the fact that an additional load is
applied to the bolt while turning the nut to contact, prior to load transfer to the nut.
NOTE 3
NOTE 4
 is the coefficient of friction between bolt and nut, see G.8.4.
G.8.3.2 Manual tightening
Estimate of average initial bolt force achieved by manual tightening using standard ring wrenches (without
additional lever arm and without hammer impacts):
Average bolt force:
F B 0 ,av  A B 
1000
dB0
NOTE 1
Units in Formula (G.8-3) are strictly AB in [mm2], dB0 in [mm] and FB0,av in [N].
NOTE 2
Such uncontrolled tightening is not recommended.
732
(G.8-3)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.8.4 Assembly using a torque wrench
The nominal torque applied to tighten a bolt shall be calculated from:
M
t, nom
 k B  F B 0 ,nom
(G.8-4)
nB
(G.8-5)
k B  1,2    d B 0
The friction coefficient in Formula (G.8-5)  is an average value, which accounts for friction of bolt threads and
nut or head face. (In the following it is slightely increased against real values to cover some effects of thread
pitch.) The values given below for  are typical indicative values; the highest values being for austenitic steels.
For smooth, lubricated surfaces:
(G.8-6)
  0 ,10 ... 0 ,15
For average, ”normal” conditions:
(G.8-7)
  0 ,1 5 . ..0 , 2 5
For rough, dry surfaces:
(G.8-8)
  0 , 2 0 .. .0 , 3 5
NOTE 1
A simple torque wrench without a torque multiplier device delivers a maximum about
NOTE 2
Explanations to Formula (G.8-5):
M t,nom
 1000
Nm
.
The general formula for kB is:
k B  p t ( 2   )   t  d t ( 2  cos  )   n  d n 2
(G.8-9)
where
dn
is the mean contact diameter under nut or bolt head;
dt
is the mean contact diameter on thread;
n
is the friction coefficient under nut or bolt head;
t
is the friction coefficient on thread;
pt
is the thread pitch;

is the half thread-angle:
In Formula (G.8-9), the first term is due to inclination of the thread helix angle, the second is due to friction
between threads and the third is due to friction under the nut or bolt head.
For threads of ISO triangular profile, kB is:
k B  0 ,159  p t  0 ,577   t  d B 2  0 ,500   n  d n
(G.8-10)
where dB2 is the mean thread diameter (see Figure G.3-2).
An approximate calculation may be made with
    
n
UNIt EN 13445-3:2021
(assumption)
733
EN 13445-3:2021 (E)
Issue 1 (2021-05)
pt  0,1dB0
(average relation)
dB2  0,9dB0
(average relation)
dn  1,3dB0
(average relation)
where dB0 is the nominal diameter (see Figure G.3-2).
This leads to the following simplified formula, which gives a good estimate of kB and may be used instead of
Formula (G.8-5):
(G.8-11)
k B  0 ,16  p t  1,17    d B0
A more rough approximation of this formula leads to Formula (G.8-5).
k B  1,2    d B 0
NOTE 3
M
Explanation to the twisting moment in a bolt shank, used in Formula (G.7-3):
tB, nom

p t
(2   )   t  d
( 2  cos  )  F B0,
t
nom
nB
(G.8-12)
With the same approximations as those used for Formula (G.8-5) it may be found
M
tB, nom

0 ,16
 p t  0 ,52    d B0
  F B0, nom
(G.8-13)
nB
or again more simply
M
tB, nom

0 ,55
  n  d B0
  F B0, nom
(G.8-14)
nB
This Formula (G.8-14) introduced into EN 1591-1:2001 Formula (71) yield the following primary form of the
finally simplified (and by C modified) Formula (G.7-3):
B 
FB
A B  fB


3  0 ,55  d B0
1 3  

min d Be; d Bs







2
(G.8-15)
G.8.5 Flange rotations
G.8.5.1 General
NOTE
The flange rotations that can be expected in practice are dependent on the bolt force applied at bolting-up,
which is itself subject to variation. The method permits some (small) plastic deformation, both at bolting-up and in
subsequent conditions. Therefore
— only lower and upper bounds to the rotations are evaluated, assuming minimum and maximum possible
values of initial bolt load;
—
only the elastic parts of the rotations are calculated.
G.8.5.2 Use of flange rotation
The maximum calculated flange rotation shall be less than the acceptable value specified for the gasket, where
this is available.
NOTE
734
~
~
Measured values of  F   F respectively  L   L can be used to control the bolt load during assembly.
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.8.5.3 Calculation of flange rotations
The elastic rotation of each flange, stub or collar may be calculated from the following Formula (G.8-16) and for
loose flanges from Formula (G.8-17):
 F  Z F E F   F G  h G  F Q  h H  h P  h Q   F R  h H  h R
(G.8-16)

(G.8-17)
 L  Z L E L   F B  h L
The preceding formulae are applicable to all load conditions (I = 0, 1, 2...), provided appropriate values of EF, EL
and FB, FG, FQ, FR for each condition are applied:
FQI, FRI
are values according to Formulae (G.6-1), (G.6-2)
FBI, FGI
are respectively minimum possible values (to calculate minimum rotations) or maximum
possible values (to calculate maximum rotations).
They are given by the following formulae:
Assembly condition (I = 0):
F B0 ,min
 F B0 ,nom
 (1  
n
)
(G.8-18)
F B0 ,max
 F B0 ,nom
 (1  
n
)
(G.8-19)
F G0
,min
F G0
,max
(G.8-20)
 F B0 ,min  F R0
 F B0 ,max
(G.8-21)
 F R0
Subsequent conditions (I = 1, 2...):
NOTE The minimum and maximum values are obtained from Formulae (G.6-26) and (G.6-27) by replacing FG0,d
with FG0,min and FG0,max respectively, i.e.
F G  ,min
F G  ,max
FB 
,min
FB 
,max


F G0 ,min
 Y G0  F Q   Y Q   F R   Y Q   F R0  Y R 0
F G0 ,max
 FG 
,min
 FG 
,max

 Y G0  F Q   Y Q   F R   Y Q   F R 0  Y R 0
 F Q   F R 
U 

 / Y G 
U 
 / Y G 
(G.8-23)
(G.8-24)

 F Q   F R 
(G.8-22)

(G.8-25)
G.9 Gasket properties
G.9.1 General
The purpose of this sub-clause is to present gasket property values for use in this method.
NOTE
Data in this clause is variously based on measurement, experience or estimation. Although currently
regarded as the best available information for generic materials, it is only provided for general guidance. The values are
non-mandatory. Validated data if available should be used in preference.
G.9.2 Specific symbols and abbreviations
NOTE 1
The following list gives partially repetitions from G.3.3 for convenience, partially additionally explanations.
UNI EN 13445-3:2021
735
EN 13445-3:2021 (E)
Issue 1 (2021-05)
EG
E0
K1
is the unloading compression modulus of the gasket for a gasket compressive stress
is the the value of E G extrapolated from measured values of
stress Q  0 , [Mpa], see Tables G.9-1 to G.9-6.
is the coefficient which determines rate of change of
Tables G.9-1 to G.9-6.
EG
EG
Q  0
, [Mpa]
back to zero gasket compressive
with compressive stress [-], see
NOTE 2
Gasket unloading compression modulus E G is assumed to vary linearly with the maximum compressive
stress Q ( m a x ) to which the gasket has been subjected previously
(G.9-1)
E G  E 0  K 1  Q ( m ax )
Observation:
Q (m a x )
here is not the limit value
Q max
but the maximum actual value
simplification, the method recommends calculation of
NOTE 3
The measurement of
EG
EG
using
is made along a chord from
Q (max)
 Q ( 0 )
Q  Q (m a x )
to
Q
. As a conservative
for all I.
Q  ( 0 . 3 ... 0 . 2 )  Q (max)
on a stress-strain
curve of the gasket, obtained at unloading.
gC
is the creep factor for gasket [-], see Tables G.9-1 to G.9-6.
NOTE 4
The creep factor g C is an empirical factor which adjusts the compression modulus
approximately, for any additional compressive displacement U G due to gasket creep. It is defined as:
EG
to account,
(G.9-2)
g G  U G (t 0 ) / U G (t   )
and applied as follows:
E G(includin
736
g creep)
 g C  E G(excludin
g creep)
(G.9-3)
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
NOTE 5
For measurements of
U
G (t   )
, suitable times such as 1 000 hr are acceptable.
Iis the load condition identifier [-]:
I = 0 is the assembly condition;
I = 1, 2, 3, ... are subsequent conditions, including hydrotest, and all service conditions which could be
significant.
m
is the gasket compression factor [-], see Tables G.9-1 to G.9-6. It defines by Formula (G.9-4) an
approximate value of QI,min if better data are not available.
NOTE 6
m  serves a similar purpose to ´m´ in ASME and other design codes (including BS 5500 and CODAP) but,
due to the different way in which the effective gasket width is calculated, it is not the same and direct comparisions
should be avoided.
QI,min is the minimum required gasket compressive stress [Mpa] for a subsequent load condition No. I = 1, 2, 3, …
It is in general then greater then higher the requirements for leak tightness (then less the permitted leak
rate [mg/(ms)]) and then higher the fluid pressure P [Mpa] for these load condition No. I. It depends also
from the temperature and the type of the fluid.
Further there is an important influence of the initially maximum gasket compressive stress Q(max) ,
which normally is the gasket compressive stress in assemblage condition Q0: then greater Q(max) then
less Q,min. These influences are investigated (measured) for some examples, but up to day sufficient
general data are not available. Therefore at the moment the following nearly classical method may be
applied: Realize a minimum gasket compressive stress for assembly condition Q0,min (for a sufficient
initial seating of the gasket) and then assume Q,min as follows:
Q  ,min  m   P 
(G.9-4)
Q0,min is the minimum required gasket compressive stress [Mpa] for assembly condition I = 0; it is not required
if all QI,min are based on leak tightness criteria.
Qmax
is the maximum allowable compressive stress in the gasket [Mpa] for any condition;
NOTE 7
The parameters Q0,min and Qmax define a range of gasket stress between which the gasket behaves in a
consistent reliable manner. Below the lower limit Q0,min the leak-rate may be untypical, high and variable; above the
upper limit Qmax various gasket properties may be untypical and the gasket may suffer permanent damage. If
empirical formulae are fitted to measured gasket properties (e.g. curves of load – compression or stress – tightness) the
range defines limits of validity of the formulae.
NOTE 8
Q0,min is used to define an absolute minimum value of assembly gasket force as follows, which is effectively
a definition of Q0,min:
F G0, min
 A Ge  Q 0, min
(G.9-5)
(see Formula (G.6-8))
NOTE 9
Parameter Q0,min serves, in part, a similar purpose to ´y´ in ASME and other design codes (including
BS 5500 and CODAP) but differs as follows
:
UNI EN 13445-3:2021
737
EN 13445-3:2021 (E)
Issue 1 (2021-05)
f)
Due to the different ways in which the effective gasket width is calculated in the ASME Code and in this method,
the value of Q0,min is not the same as that of y.
g)
Q0,min also serves to define the lower limit of validity of empirical formulae where used to calculate gasket
properties.
NOTE 10 Qmax is used in the following way: Given a maximum possible area Agt and with an adjustment for plastic
yield, based on maximum possible gasket width bGt and initial gasket thickness eG0 , the maximum permitted gasket
force FG is subject to the condition:
F G  A G t  Q m a x   1  b G t / ( 2 0  e G 0 )
(G.9-6)
(see Formulae (G.7-7), (G.7-8))
G.9.3 Tables for gasket properties
All tabulated gasket properties are informative only (see G.9.1). Application of other validated values is permitted.
NOTE 1
The theoretically possible absolute minimum mI = 0,5 is not applicable for practical purposes, because some
safety against failure is necessary.
NOTE 2
The majority of tabulated mI values is intended to correspond to a nitrogen gas leak rate of about 1 ml/min
(at standard ambient temperature and pressure) for a fluid pressure P = 40 bar, gasket outside diameter dG2 = 90 mm,
and gasket inside diameter dG1 = 50 mm.
NOTE 3
There are only a few types of gaskets for which thermal expansion coefficients G have been measured, and
that are not given in Tables G.9-1 to G.9-6. If no values G are available, calculation with the assumption G  F or an
other logical estimation of G is acceptable, because normally the effect of G is very small.
738
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table G.9-1 ― Non-metallic flat gaskets (soft), also with metal insertion
Gasket type and
material
Rubber
1)
PTFE
T
°C
Q0,min
MPa
Qmax
MPa
E0
MPa
K1
m
gC
0...20
0,5
28
200
10
0,9
0,9
100
18
200
10
0,9
0.9
150
12
200
10
0,9
0.9
50
600
20
1,3
0,9
35
500
20
1,3
0,7
0...20
10
100
200
Expanded PTFE
(ePTFE)
20
400
20
1,3
0,5
150
500
40
1,3
1,0
100
150
1 500
35
1,3
0,9
200
150
2 500
30
1,3
0,8
0…20
12
Expanded graphite
without metal insertion
0...20
100
200
300
10
100
100
95
90
1
1
1
1
26
26
26
26
1,3
1,3
1,3
1,3
1,0
1,0
1,0
1,0
Expanded graphite
with perforated metal
insertion
0...20
100
200
300
15
150
145
140
130
1
1
1
1
31
31
31
31
1,3
1,3
1,3
1,3
1,0
1,0
1,0
1,0
Expanded graphite
with adhesive flat metal
insertion
0...20
100
200
300
10
100
90
80
70
1
1
1
1
28
28
28
28
1,3
1,3
1,3
1,3
0,9
0,9
0,9
0,9
Expanded grafite and
metallic sheets
laminated in thin layers
withstanding high
stresses
0…20
15
270
1
33
1,3
1,0
100
250
1
33
1,3
1,0
200
230
1
33
1,3
1,0
300
210
1
33
1,3
1,0
Non-asbestos fibre
with binder, eG < 1mm
0...20
100
200
40
100
90
70
500
500
500
20
20
20
1,6
1,6
1,6
-
Non-asbestos fibre
with binder, eG  1mm
0...20
100
200
35
80
70
60
500
500
500
20
20
20
1,6
1,6
1,6
-
1)
Gasket thickness eG used in calculation shall be the thickness under load.
NOTE
A dash indicates no values available.
UNI EN 13445-3:2021
739
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table G.9-2 ― Grooved steel gaskets with soft layers on both sides
Gasket type
T
Q0,min
Qmax
E0
and material
°C
MPa
MPa
MPa
PTFE layers on soft steel 0...20
or soft iron
100
200
300
10
350
330
290
250
16 000
16 000
16 000
16 000
PTFE layers on stainless
steel
0...20
100
200
300
10
500
480
450
420
16 000
16 000
16 000
16 000
Graphite layers on soft
steel or soft iron
0...20
100
200
300
15
350
330
290
250
16 000
16 000
16 000
16 000
0...20
Graphite layers on low
alloy heat resistant steel
100
200
300
400
500
15
400
390
360
320
270
220
16 000
16 000
16 000
16 000
16 000
16 000
Graphite layers on
stainless steel
0...20
100
200
300
400
500
15
500
480
450
420
390
350
16 000
16 000
16 000
16 000
16 000
16 000
Silver layers on heat
resistant stainless steel
0...20
100
200
300
400
500
600
125
600
570
540
500
460
400
250
20 000
20 000
20 000
20 000
20 000
20 000
20 000
K1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
m
gC
1,3
1,3
1,3
1,3
0,9
0,8
0,7
0,6
1,3
1,3
1,3
1,3
0,9
0,8
0,7
0,6
1,3
1,3
1,3
1,3
1,0
1,0
1,0
1,0
1,3
1,3
1,3
1,3
1,3
1,3
1,0
1,0
1,0
1,0
0,9
0,8
1,3
1,3
1,3
1,3
1,3
1,3
1,0
1,0
1,0
1,0
0,9
0,8
1,8
1,8
1,8
1,8
1,8
1,8
1,8
1,0
1,0
1,0
1,0
1,0
0,9
0,8
NOTE
The K1 values have no significant influence on the results for these type of gaskets so that K1 = 0
may be used for the calculation in this Annex.
740
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table G.9-3 ― Spiral wound gaskets with soft filler
Gasket type and
material
PTFE filler,
one side ringsupported
PTFE filler,
both sides ringsupported
Graphite filler,
one side ringsupported
Graphite filler,
both sides ringsupported
NOTE 1
K1
m
gC
6 000
6 000
0
0
1,6
1,6
0,9
0,8
90
6 000
0
1,6
0,7
80
6 000
0
1,6
0,6
180
6 000
0
1,6
0,9
100
170
6 000
0
1,6
0,8
200
160
6 000
0
1,6
0,7
300
150
6 000
0
1,6
0,6
110
8 000
0
1,6
1,0
100
110
8 000
0
1,6
1,0
200
100
8 000
0
1,6
1,0
300
90
8 000
0
1,6
1,0
400
80
8 000
0
1,6
0,9
300
10 000
0
1,6
1,0
100
280
10 000
0
1,6
1,0
200
250
10 000
0
1,6
1,0
300
220
10 000
0
1,6
1,0
400
180
10 000
0
1,6
0,9
T
Q0,min
Qmax
E0
°C
MPa
MPa
MPa
0...20
100
20
110
100
200
300
0...20
0...20
0...20
20
20
50
Modern philosophy is to use 2 rings: centering ring and outer ring.
NOTE 2 The K1 values have no significant influence on the results for these type of gaskets so that K1 = 0
may be used for the calculation in this Annex.
UNI EN 13445-3:2021
741
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table G.9-4 ― Solid metal gaskets
K1
m
gC
70 000
65 000
60 000
50 000
0
0
0
0
2,0
2,0
2,0
2,0
1,0
0,9
0,8
0,7
210
190
155
110
50
115 000
110 000
105 000
95 000
85 000
0
0
0
0
0
2,0
2,0
2,0
2,0
2,0
1,0
1,0
1,0
0,9
0,7
380
340
280
220
160
100
440
210 000
205 000
195 000
185 000
175 000
165 000
210 000
0
0
0
0
0
0
0
2,0
2,0
2,0
2,0
2,0
2,0
2,0
1,0
1,0
1,0
1,0
0,9
0,7
1,0
100
200
410
360
205 000
195 000
0
0
2,0
2,0
1,0
1,0
300
300
185 000
0
2,0
1,0
400
(500)
220
140
175 000
165 000
0
0
2,0
2,0
0,9
0,7
Gasket type and
T
Q0,min
Qmax
E0
material
°C
MPa
MPa
MPa
Aluminium (Al) (soft)
0…20
100
200
300
50
100
85
60
20
Copper (Cu) or brass
(soft)
0…20
100
200
300
(400)
100
Iron (Fe) (soft)
0...20
100
200
300
400
(500)
0...20
175
Steel (soft)
200
Steel, low alloy,
heat resistant
0...20
100
200
300
400
500
225
495
490
460
420
370
310
210 000
205 000
195 000
185 000
175 000
165 000
0
0
0
0
0
0
2,0
2,0
2,0
2,0
2,0
2,0
1,0
1,0
1,0
1,0
1,0
0,9
Stainless steel
0...20
100
250
550
525
200 000
195 000
0
0
2,0
2,0
1,0
1,0
200
495
188 000
0
2,0
1,0
300
400
460
425
180 000
170 000
0
0
2,0
2,0
1,0
0,9
500
(600)
370
300
160 000
150 000
0
0
2,0
2,0
0,8
0,7
660
630
600
560
510
445
360
210 000
205 000
200 000
194 000
188 000
180 000
170 000
0
0
0
0
0
0
0
2,0
2,0
2,0
2,0
2,0
2,0
2,0
1,0
1,0
1,0
1,0
1,0
0,9
0,8
Stainless steel,
heat resistant
0...20
100
200
300
400
500
600
300
NOTE
The K1 values have no significant influence on the results for these type of gaskets so that K1 = 0
may be used for the calculation in this Annex.
742
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table G.9-5 ― Covered metal-jacketed gaskets
Gasket type and
material
K1
m
gC
1
1
1
1
69
69
69
69
1,3
1,3
1,3
1,3
1,0
0,9
0,8
0,7
150
150
150
150
1
1
1
1
69
69
69
69
1,3
1,3
1,3
1,3
1,0
0,9
0,8
0,7
20
300
300
300
300
300
300
1
1
1
1
1
1
48
48
48
48
48
48
1,3
1,3
1,3
1,3
1,3
1,3
1,0
1,0
1,0
1,0
1,0
1,0
20
300
300
300
300
300
300
1
1
1
1
1
1
48
48
48
48
48
48
1,3
1,3
1,3
1,3
1,3
1,3
1,0
1,0
1,0
1,0
1,0
1,0
T
Q0,min
Qmax
E0
°C
MPa
MPa
MPa
Stainless steel jacket
with expanded PTFE
filler and covering
0...20
100
200
(300)
10
150
150
150
150
Nickel alloy jacket
with expanded PTFE
filler and covering
0...20
100
200
(300)
10
Soft iron or soft steel
jacket
with graphite filler and
covering
0...20
100
200
300
400
(500)
Low alloy steel (4 % to
6 % chrome) or
stainless steel jacket
with graphite filler and
covering
0...20
100
200
300
400
500
UNI EN 13445-3:2021
743
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Table G.9-6 ― Metal-jacketed gaskets
Gasket type and
material
744
K1
m
gC
500
800
1 100
1 400
25
25
25
25
1,6
1,6
1,6
1,6
1,0
1,0
1,0
1,0
150
140
130
120
100
600
900
1 200
1 500
1 800
25
25
25
25
25
1,8
1,8
1,8
1,8
1,8
1,0
1,0
1,0
1,0
1,0
80
180
170
160
150
140
120
800
1 100
1 400
1 700
2 000
2 300
25
25
25
25
25
25
2,0
2,0
2,0
2,0
2,0
2,0
1,0
1,0
1,0
1,0
1,0
1,0
100
250
240
220
200
180
140
800
1 100
1 400
1 700
2 000
2 300
25
25
25
25
25
25
2,2
2,2
2,2
2,2
2,2
2,2
1,0
1,0
1,0
1,0
1,0
1,0
T
Q0,min
Qmax
E0
°C
MPa
MPa
MPa
Aluminium (soft) jacket
with graphite filler
0...20
100
200
(300)
50
135
120
90
60
Copper or brass (soft)
jacket
with graphite filler
0...20
100
200
300
(400)
60
Soft iron or soft steel
jacket
with graphite filler
0...20
100
200
300
400
(500)
Low alloy steel (4 % to
6 % chrome) or
stainless steel jacket
with graphite filler
0...20
100
200
300
400
500
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
G.10 Bibliography
[1]
CR 13642, Flanges and their joints ― Design rules for gasketed circular flange connections ―
Background information
[2]
Wesstrom, D.B.; Bergh, S.E., "Effect of Internal Pressure on Stresses and Strains in Bolted-Flanged
Connections"; Transactions of the ASME, July 1951, pp.553-568
[3]
Richtlinienkatalog Festigkeitsberechnungen (RKF), Behälter und Apparate; Teil 1, BR-A13, "Behälterund Apparateelemente. Flanschverbindungen"; Institut für Chemieanlagen, Dresden 1971; VEB
Komplette Chemieanlagen Dresden, 1979;
[4]
DIN 2505, "Berechnung von Flanschverbindungen"; Entwurf November 1972; Entwurf April 1990.
[5]
TGL 20360, "Flanschverbindungen. Berechnung auf Festigkeit und Dichtigkeit"; Februar 1977
[6]
TGL 32903/13, "Behälter und Apparate ― Festigkeitsberechnung ― Flanschverbindungen";
Dezember 1983.
[7]
Wölfel, J.; Räbisch, W., "Berechnung und Standardisierung von Flanschverbindungen"; Chemische
Technik, Leipzig, 1975, S.470-478.
[8]
Wölfel, J., "Berechnung der Dichtigkeit
Maschinenbautechnik, Berlin, 1985, S.244-247.
UNI EN 13445-3:2021
und
Festigkeit
von
Flanschverbindungen";
745
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex H
(informative)
Gasket factors m and y
Table H.1 gives a list of many commonly used gasket materials and contact facings with suggested design values
of m and y that have generally proved satisfactory in actual service when using the methods of Clause 11. The
design values and other details given in this table are suggested only and are not mandatory. Data from the
manufacturer should be used if available.
Table H.1 — Gasket factors m and y
Gasket material
Gasket
factor m
Minimum
design
seating
stress y
Sketches
Dimension w
(minimum)
MPa
Rubber without fabric or a high percentage of
asbestos1) fibre:
mm
-
0,50
0
-
1,00
1,4
-
(3.2 mm thick
2,0
11,0
-
(1,6 mm thick
2,75
25,5
-
(0,8 mm thick
3,50
44,8
-
Rubber with cotton fabric insertion
1,25
2,8
- below 75 IRH (International Rubber
Hardness Degrees);
- 75 IRH or higher.
Asbestos1) with a suitable binder for the
operating conditions
Rubber with asbestos1) fabric
(3-ply
2,25
15,2
insertion, with or without wire
(2-ply
2,50
20,0
-
reinforcement
(1-ply
2,75
25,5
-
1,75
7,6
10
Vegetable fibre
746
Spiral-wound metal
(Carbon
2,50
asbestos1) filled
(Stainless or
(Monel
3,00
69,0
-
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Gasket material
Gasket
factor m
Minimum
design
seating
stress y
Sketches
Dimension w
(minimum)
MPa
mm
Corrugated metal,
Soft aluminium
2,50
20,0
-
asbestos1) inserted
Soft copper or
brass
2,75
25,5
-
Iron or soft steel
3,00
31,0
-
Corrugated metal,
Monel or 4 % to
6 % chrome
3,25
37,9
-
jacketed asbestos1) filled
Stainless steels
3,50
44,8
-
Corrugated metal
Soft aluminium
2,75
25,5
-
Soft copper or
brass
3,00
31,0
-
Iron or soft steel
3,25
37,9
-
Monel or 4 % to
6 % chrome
3,50
44,8
-
Stainless steels
3,75
52,4
-
Soft aluminium
3,25
37,9
-
Flat metal jacketed
Soft copper or
brass
3,50
44,8
-
asbestos1) filled
Iron or soft steel
3,75
52,4
-
Monel
3,50
55,1
-
4 % to 6 %
chrome
3,75
62,0
-
Stainless steels
3,75
62,0
-
Soft aluminium
3,25
37,9
-
Soft copper or
brass
3,50
44,8
-
Iron or soft steel
3,75
52,4
-
Monel or 4 % to
6 % chrome
3,75
62,0
-
Stainless steels
4,25
69,5
10
or
Grooved metal
UNI EN 13445-3:2021
747
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Gasket material
Gasket
factor m
Minimum
design
seating
stress y
Sketches
Dimension w
(minimum)
MPa
Solid flat metal
Ring joint2)
Soft aluminium
4,00
60,6
-
Soft copper or
brass
4,75
89,5
6
Iron or soft steel
5,50
124
-
Monel or 4 % to
6 % chrome
6,00
150
-
Stainless steels
6,50
179
-
Iron or soft steel
5,50
124
-
Monel or 4 % to
6 % chrome
6,00
150
-
Stainless steels
6,50
179
-
0,7
-
1,4
-
Rubber O-rings:
below 75° IRH
0 to 0,25
between 75° and 85° IRH
-
Rubber square section rings:
below 75° IRH
mm
0 to 0,25
1,0
-
2,8
-
between 75° and 85° IRH
-
Rubber T-section rings:
-
below 75° IRH
between 75° and 85° IRH
0 to 0,25
1,0
-
2,8
1) New non-asbestos bonded fibre sheet gaskets are not necessarily direct substitutes for asbestos based
materials. In particular, pressure, temperature and bolt load limitations may be applied. Use within the
manufacturer's current recommendations.
2) b = w/8.
748
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex I
(normative)
Additional information on heat exchanger tubesheet design
I.1 Loading cases for fixed tubesheet heat exchangers
I.1.1 Purpose
This annex provides information for the determination of the loading cases to be considered for the design of
fixed tubesheet heat exchangers in support to 13.5.4.1. Two procedures are proposed for this determination:
 a general procedure, covered in I.1.4, which explains how to obtain all the loading cases which may
govern the design;
 a simplified procedure, covered in I.1.5, which enables to limit the number of loading cases to be studied.
It can only be used for normal operating conditions.
I.1.2 Specific definitions
No specific definitions.
I.1.3 Specific symbols
No specific symbols.
I.1.4 General procedure
This rule applies to all types of loading conditions mentioned in 13.5.4.1: normal operating conditions,
exceptional operating conditions, pressure test conditions.
The loading cases, and their related parameters, are determined by the following procedure:
a) List all the loading conditions which may govern the design of the exchanger during normal operating
conditions, exceptional operating conditions, pressure test conditions.
For each of these loading conditions, account for the 7 possible loading cases listed in 13.5.4.1;
b) For each of these loading cases record, as shown in table I.1.4-1:
— The design pressure on tube-side P t  and shell-side P s  ;
— The differential thermal expansion   ;
— The design temperatures of the tubesheet T  , the tubes T t  , the shell T s  and the channel T c  ;
UNI EN 13445-3:2021
749
EN 13445-3:2021 (E)
Issue 1 (2021-05)
c) For each of these loading cases which may govern the design, the calculations shall be performed using
the values of the mechanical properties (elastic modulus, nominal design stress, expansion coefficient,
etc.) at the design temperature of each component. See Table I.1.4-1.
Table I.1.4-1 — Table for loading conditions
Condition
Normal
operating
conditions
Exceptional
operating
conditions
Pressure
test
conditions
1
2

n
n+1
n+2

n+p
n+p+1
n+p+2

n+p+q

Ps
Pt
T
P t,1
P s,1

P t,2
P s,2



P t, n
P s, n
P t, n  1
P s, n  1

P t, n  2
P s, n  2


np


P t, n  p
P s, n  p
Tt
Ts
Tc
T1
T t,1
T
2
T2
T t,2
T



n
Tn
T t, n
n 1
T n 1
T t, n  1
T s, n  1
T c, n  1
n2
Tn2
T t, n  2
T s, n  2
T c, n  2

1
T
s,2
T c,2

T
s, n



T np
T t, n  p
T s, n  p

P t, n  p  1
P s, n  p  1
P t, n  p  2
P s, n  p  2



P t, n  p  q
P s, n  p  q
T npq
0
s,1
T n  p 1
T
T np2
T
t, n  p  1
T
t, n  p  2
T s, n  p  2

T
t, n  p  q
s, n  p  1
c,1

T
c, n

T
c, n  p
T c, n  p  1
T c, n  p  2


T s, n  p  q
T c, n  p  q
Design of a heat exchanger including (n + p + q) loading conditions:
― n normal operating conditions: 1 to n,
― p exceptional conditions: (n + 1) to (n + p),
―
q pressure test conditions: (n + p + 1) to (n + p + q).
I.1.5 Simplified procedure for normal operating conditions
This rule applies only to normal operating conditions. It permits to study a restricted number of loading cases,
thanks to a generic treatment enveloping all loading cases, as follows:
a) List all the normal loading cases as detailed in I.1.4a;
b) For each of these loading cases, record (see Table I.1.4-1):
— The design pressure on tube-side P t  and shell-side P s  ;
— The differential thermal expansion   ;
— The design temperatures of the tubesheet T  , the tubes T t  , the shell T s  and the channel T c  ;
c) For each of these loading cases, determine:
— The extreme values (with their algebraic signs) between which P t  , P s  and vary:
750
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
 P t  P t, max
P t, min
 P s  P s, max
P s, min

min
 
max
which are given by:
 P t,1 , P t,2 ,  , P t, n  
P t, min
 min
P s, min
 min

min
 P s,1 , P s,2 ,  , P s, n  
  1 ,  2 ,  ,  n  
 min
P t, max
 max
 P t,1 , P t,2 ,  , P t, n  
P s, max
 max
 P s,1 , P s,2 ,  , P s, n  

max
 max
  1 ,  2 ,  ,  n  
— The maximum value of the design temperature of each component of the exchanger:
,
T max
T
,
t, max
T s, max
,
T c, max
which are given by:
T max
T s, max
 max
 max
 T 1 , T 2 ,  , T n  
T t, max
 max
 T s,1 , T s,2 ,  , T s, n  
 T t,1 , T t,2 ,  , T t, n  
T c, max
 max
 T c,1 , T c,2 ,  , T c, n  
d) The enveloping loading conditions to be considered are the 8 following loading cases shown in
Table I.1.5-1:
Table I.1.5-1 — Enveloping loading conditions
Loading
Pt

Ps
Tt
T
Ts
Tc
case
E0
P t, min
P s, min

min
E1
P t, max
P s, min

min
E2
P t, min
P s, max

min
E3
P t, max
P s, max

min
E4
P t, min
P s, min

max
E5
P t, max
P s, min

max
E6
P t, min
P s, max

max
E7
P t, max
P s, max

max
T max
T
t, max
T s, max
T c, max
As some of these 8 loading cases may not exist in practice, this simplified procedure may result in higher
thicknesses than those obtained using the general procedure of I.1.4.
UNI EN 13445-3:2021
751
EN 13445-3:2021 (E)
Issue 1 (2021-05)
I.2 Calculation of floating tubesheet heat exchanger using 13.5
I.2.1 Purpose
This annex provides information for calculating floating tubesheet heat exchangers by using the rules of 13.5
relative to fixed tubesheet heat exchangers.
I.2.2 2.2
Specific definitions
No specific definitions.
I.2.3 Specific symbols
No specific symbols.
I.2.4 Design method
For mechanical design, a floating tubesheet heat exchanger is treated as a special case of fixed tubesheet heat
exchanger where the shell has:
 no axial rigidity
:
K
s
 0
, which implies:
 no expansion bellows :
K
J
 
, which implies: J = 1
K
s, t
 0
This leads to:
(I.2-1)
Pe  Ps  Pt  P
with all stress formulae for tubesheets, tubes, shell and channel remaining unchanged.
Accordingly, the rules of 13.5 can be applied to design floating tubesheet heat exchangers by replacing
given in 13.6.4.1.
752
Pe
by P
UNI EN 13445-3:2021
EN 13445-3:2021 (E)
Issue 1 (2021-05)
Annex J
(normative)
Alternative method for the design of heat exchanger tubesheets
J.1 Purpose
This annex specifies alternative rules to those in Clause 13 for the design of shell and tube heat exchanger
tubesheets. They apply to heat exchangers of the following types:
— U-tube type, see Figure J.1; also to exchangers with capped tubes and one tubesheet only and
exchangers with curved tubes and a number of separate tubesheets;
— immersed floating head; see Figures J.2 a) and J.2 b);
— externally sealed floating head; see Figure J.3;
— internally sealed floating head; see Figure J.4;
— fixed tubesheet with expansion bellows; see Figure J.5;
— fixed tubesheet without expansion bellows; see Figure J.6.
J.2 Specific definitions
The following terms and definitions are in addition to those in Clause 3.
J.2.1
outer tube limit
circle which encloses all the tubes
J.2.2
load ratio
calculated load or moment applied to a component divided by the allowable load or moment
J.3 Specific symbols and abbreviations
J.3.1 General
The following symbols and abbreviations are in addition to those in Clause 4.
Figures J.1 to J.6 illustrate the six main types of shell and tube heat exchanger. Figures J.7 to J.13 cover
specific details. All Figures illustrate general charact