BS EN 14917:2021
BSI Standards Publication
Metal bellows expansion joints
for pressure applications
BS EN 14917:2021
BRITISH STANDARD
National foreword
This British Standard is the UK implementation of EN 14917:2021. It
supersedes BS EN 14917:2009+A1:2012, which is withdrawn.
The UK participation in its preparation was entrusted to Technical
Committee GSE/42, Gas fittings and connections including metal hose
and hose assemblies.
A list of organizations represented on this committee can be obtained on
request to its committee manager.
Contractual and legal considerations
This publication has been prepared in good faith, however no
representation, warranty, assurance or undertaking (express or
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recipient’s own risk.
The recipient is advised to consider seeking professional guidance with
respect to its use of this publication.
This publication is not intended to constitute a contract. Users are
responsible for its correct application.
This publication has been prepared under a mandate given to the
European Standards Organizations by the European Commission and the
European Free Trade Association. It is intended to support requirements
of the EU legislation detailed in the European Foreword. A European
Annex, usually Annex ZA or ZZ, describes how this publication relates to
that EU legislation.
For the Great Britain market (England, Scotland and Wales), if UK
Government has designated this publication for conformity with UKCA
marking (or similar) legislation, it may contain an additional National
Annex. Where such a National Annex exists, it shows the correlation
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of the European text will indicate the relationship to UK regulation
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© The British Standards Institution 2021
Published by BSI Standards Limited 2021
ISBN 978 0 539 06281 6
BS EN 14917:2021
BRITISH STANDARD
ICS 23.040.99
Compliance with a British Standard cannot confer immunity from
legal obligations.
This British Standard was published under the authority of the
Standards Policy and Strategy Committee on 31 August 2021.
Amendments/corrigenda issued since publication
Date
Text affected
EN 14917
EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
July 2021
ICS 23.040.99
BS EN 14917:2021
Supersedes EN 14917:2009+A1:2012
English Version
Metal bellows expansion joints for pressure applications
Compensateurs de dilatation à soufflets métalliques
pour appareils à pression
This European Standard was approved by CEN on 21 June 2021.
Kompensatoren mit metallischen Bälgen für
Druckanwendungen
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.
Ref. No. EN 14917:2021 E
BS EN 14917:2021
EN 14917:2021 (E)
Contents
Page
European foreword....................................................................................................................................................... 7
1
Scope ................................................................................................................................................................. 10
2
Normative references ................................................................................................................................. 10
3
Terms and definitions ................................................................................................................................ 14
4
Classification .................................................................................................................................................. 17
4.1
Classification of expansion joints ........................................................................................................... 17
4.1.1 General ............................................................................................................................................................. 17
4.1.2 Axial................................................................................................................................................................... 17
4.1.3 Angular............................................................................................................................................................. 17
4.1.4 Lateral .............................................................................................................................................................. 17
4.1.5 Universal ......................................................................................................................................................... 17
4.1.6 Pressure balanced designs (axial or universal) ................................................................................ 17
4.2
Classification of the parts of expansion joints ................................................................................... 20
4.2.1 Main pressure-bearing parts (A) ............................................................................................................ 20
4.2.2 Pressure parts other than main pressure-bearing parts (B) ....................................................... 20
4.2.3 Attachments to main pressure-bearing parts and to pressure parts (C)................................. 20
4.2.4 Other parts (D) .............................................................................................................................................. 20
5
Materials.......................................................................................................................................................... 22
5.1
General ............................................................................................................................................................. 22
5.1.1 Materials for pressure-bearing parts ................................................................................................... 22
5.1.2 Materials for parts attached to pressure-bearing parts................................................................. 22
5.1.3 Materials for non-pressure parts ........................................................................................................... 22
5.2
Pressure-bearing parts .............................................................................................................................. 22
5.2.1 Bellows............................................................................................................................................................. 22
5.2.2 Other pressure-bearing parts.................................................................................................................. 22
5.2.3 Ductility ........................................................................................................................................................... 23
5.2.4 Brittle fracture .............................................................................................................................................. 23
5.3
Material documentation ............................................................................................................................ 27
6
Design ............................................................................................................................................................... 28
6.1
General ............................................................................................................................................................. 28
6.1.1 Symbols............................................................................................................................................................ 28
6.1.2 Basic design criteria .................................................................................................................................... 34
6.1.3 Allowable stresses ....................................................................................................................................... 34
6.1.4 Additional loadings...................................................................................................................................... 37
6.2
Bellows design............................................................................................................................................... 38
6.2.1 Purpose ............................................................................................................................................................ 38
6.2.2 Conditions of applicability ........................................................................................................................ 38
6.2.3 Design of U-shaped unreinforced bellows .......................................................................................... 56
6.2.4 Design of U-shaped reinforced bellows................................................................................................ 72
6.2.5 Design of toroidal bellows ........................................................................................................................ 75
6.2.6 Fatigue.............................................................................................................................................................. 82
6.2.7 Bellows under the influence of movements ....................................................................................... 87
6.2.8 Equivalent axial displacement per corrugation................................................................................ 92
6.2.9 Forces and moments on pressurized expansion joints .................................................................. 97
6.2.10 Torsion acting on bellows (unreinforced or reinforced) ............................................................ 108
Internal sleeve............................................................................................................................................. 109
6.3
6.3.1 Scope ...............................................................................................................................................................109
6.3.2 Additional symbols .................................................................................................................................... 109
6.3.3 Flow velocity ................................................................................................................................................ 109
6.3.4 Design conditions....................................................................................................................................... 112
6.4
Hardware ......................................................................................................................................................113
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6.4.1 General .......................................................................................................................................................... 113
6.4.2 Design parameters .................................................................................................................................... 113
6.4.3 Hardware parts .......................................................................................................................................... 115
6.4.4 Permanent joints ....................................................................................................................................... 116
7
Manufacturing............................................................................................................................................. 118
7.1
General .......................................................................................................................................................... 118
7.2
Materials ....................................................................................................................................................... 118
7.2.1 General .......................................................................................................................................................... 118
7.2.2 Material traceability ................................................................................................................................. 118
7.3
Permanent joints ....................................................................................................................................... 119
7.3.1 General .......................................................................................................................................................... 119
7.3.2 Process and personal ............................................................................................................................... 119
7.3.3 Repair and rework during manufacturing ....................................................................................... 120
7.4
Forming of the bellows ............................................................................................................................ 120
7.4.1 Forming processes .................................................................................................................................... 120
7.4.2 Heat treatment............................................................................................................................................ 121
7.5
Tolerances.................................................................................................................................................... 122
7.5.1 General .......................................................................................................................................................... 122
7.5.2 Bellows .......................................................................................................................................................... 122
7.5.3 Expansion joint........................................................................................................................................... 123
7.6
Production tests ......................................................................................................................................... 123
8
Testing, inspection and documentation ............................................................................................ 124
8.1
General .......................................................................................................................................................... 124
8.2
Abbreviations.............................................................................................................................................. 124
8.3
Documents ................................................................................................................................................... 124
8.4
In-process inspection and testing........................................................................................................ 125
8.4.1 General .......................................................................................................................................................... 125
8.4.2 Materials ....................................................................................................................................................... 125
8.4.3 Permanent joints ....................................................................................................................................... 125
8.4.4 Non-destructive testing of welds ......................................................................................................... 127
8.5
NDT methods............................................................................................................................................... 134
8.5.1 Quality level ................................................................................................................................................. 134
8.5.2 Acceptance levels and testing techniques ........................................................................................ 134
8.5.3 Non-destructive testing Personnel qualifications and approval.............................................. 135
8.5.4 Non-destructive testing documentation............................................................................................ 135
8.6
Final assessment and documentation ................................................................................................ 137
8.6.1 General .......................................................................................................................................................... 137
8.6.2 Final inspection .......................................................................................................................................... 138
8.7
Documentation ........................................................................................................................................... 140
8.7.1 Final documentation package ............................................................................................................... 140
8.7.2 Declaration/certification........................................................................................................................ 140
8.7.3 Operating instructions............................................................................................................................. 141
9
Marking and labelling .............................................................................................................................. 141
10
Handling and installation ....................................................................................................................... 141
10.1 General instructions ................................................................................................................................. 141
10.2 Packaging and storage ............................................................................................................................. 142
10.3 Installation ................................................................................................................................................... 142
10.4 Unrestrained expansion joints ............................................................................................................. 142
10.5 Restrained expansions joints ................................................................................................................ 142
Annex A (informative) Categories of expansion joints................................................................................ 143
A.1
General .......................................................................................................................................................... 143
A.2
Determination of expansion joints categories ................................................................................ 143
A.3
Fluid groups................................................................................................................................................. 143
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A.3.1 General ...........................................................................................................................................................143
A.3.2 Group 1...........................................................................................................................................................143
A.3.3 Group 2...........................................................................................................................................................144
A.4
Technical requirements........................................................................................................................... 144
A.4.1 Expansion joints for vessels ................................................................................................................... 144
A.4.2 Expansion joints for piping..................................................................................................................... 144
A.4.3 Sound engineering practice (SEP)........................................................................................................ 145
A.5
Expansion joint category ......................................................................................................................... 145
Annex B (informative) Specification for materials 1.4828, 1.4876, 2.4360 and 2.4858 ................. 147
Annex C (informative) Incorporation of expansion joints into piping or pressure vessels ........... 154
C.1
General ...........................................................................................................................................................154
C.2
Specific symbols and definitions .......................................................................................................... 155
C.3
Application criteria for expansion joints in piping........................................................................ 156
C.3.1 General ...........................................................................................................................................................156
C.3.2 Use of axial expansion joints .................................................................................................................. 156
C.3.3 Use of restraint expansion joints.......................................................................................................... 162
C.3.4 Use of universal expansion joints......................................................................................................... 168
C.3.5 Indeterminate configurations of expansion joints ........................................................................ 170
C.4
Application criteria for expansion joints in pressure vessels ................................................... 173
C.4.1 General ...........................................................................................................................................................173
C.4.2 Axial expansion joint installed in the shell ....................................................................................... 173
C.4.3 Axial expansion joint installed at the floating head ...................................................................... 174
Annex D (informative) Calculation methods for systems of pipes containing expansion joints .. 175
D.1
General ...........................................................................................................................................................175
D.1.1 Preliminary remarks ................................................................................................................................ 175
D.1.2 Determining movement values ............................................................................................................. 175
D.1.3 Thermal expansion.................................................................................................................................... 175
D.2
Approximate calculation of bellows movement ............................................................................. 177
D.2.1 General ...........................................................................................................................................................177
D.2.2 Hinged systems ........................................................................................................................................... 178
D.2.3 Definitions .................................................................................................................................................... 178
D.3
Exact calculation of bellows movement ............................................................................................. 182
D.3.1 Two hinges in a plane system (Z-system).......................................................................................... 182
D.3.2 Two gimbals in a three-dimensional system (Z-system) ............................................................. 183
D.3.3 Three hinges in a plane system (U-system) ...................................................................................... 184
D.3.4 Three hinges in a plane system (L-system) ...................................................................................... 185
D.3.5 Three hinges in a three-dimensional system (Z-system) ............................................................ 187
D.4
Calculation of forces and moments...................................................................................................... 190
Annex E (informative) Explanatory notes on the design of expansion bellows.................................. 191
E.1
General ...........................................................................................................................................................191
E.2
Calculation design ...................................................................................................................................... 191
E.3
Types of bellows ......................................................................................................................................... 192
E.3.1 Corrugation shape...................................................................................................................................... 192
E.3.2 Number of plies........................................................................................................................................... 192
Fatigue life expectancy ............................................................................................................................. 192
E.4
E.5
Instability ......................................................................................................................................................193
E.5.1 General ...........................................................................................................................................................193
E.5.2 Column instability...................................................................................................................................... 193
E.5.3 In-plane instability .................................................................................................................................... 193
E.5.4 Buckling .........................................................................................................................................................193
E.6
Bellows spring rate.................................................................................................................................... 194
Annex F (informative) Procedure for setting-up a design fatigue curve............................................... 196
F.1
General ...........................................................................................................................................................196
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EN 14917:2021 (E)
F.2
Procedure for setting up a design fatigue curve for expansion bellows................................ 196
F.2.1 General .......................................................................................................................................................... 196
F.2.2 Number of tests .......................................................................................................................................... 196
F.2.3 Extrapolation range .................................................................................................................................. 196
F.2.4 Manufacturing methods .......................................................................................................................... 196
F.2.5 Bellows material ........................................................................................................................................ 197
F.3
Tests ............................................................................................................................................................... 197
F.3.1 Movement..................................................................................................................................................... 197
F.3.2 Test pressure............................................................................................................................................... 197
F.3.3 Other test conditions................................................................................................................................ 197
F.3.4 Fatigue test equipment............................................................................................................................ 198
F.4
Evaluation of the test results ................................................................................................................. 199
F.5
Linear regression....................................................................................................................................... 204
Annex G (informative) Polynomial approximations for coefficients Cp, Cf, Cd ................................... 205
G.1
Coefficient Cp............................................................................................................................................... 205
G.2
Coefficient Cf................................................................................................................................................ 206
G.3
Coefficient Cd............................................................................................................................................... 207
G.4
Linear interpolation ................................................................................................................................. 208
Annex H (informative) Required design data and information ............................................................... 210
H.1
Required design conditions ................................................................................................................... 210
H.2
Additional information............................................................................................................................ 210
Annex I (informative) Expansion joints risk analyses................................................................................. 211
Annex J (informative) Additional material properties................................................................................ 212
Annex K (normative) Hardware calculation ................................................................................................... 217
K.1
General .......................................................................................................................................................... 217
K.2
Additional symbols ................................................................................................................................... 217
K.3
Force due to pressure............................................................................................................................... 220
K.4
Tie bar............................................................................................................................................................ 221
K.4.1 General .......................................................................................................................................................... 221
K.4.2 Tie bar in tension ....................................................................................................................................... 221
K.4.3 Tie bar in compression ............................................................................................................................ 222
K.5
Pin ................................................................................................................................................................... 222
K.6
Lug with bore .............................................................................................................................................. 225
K.6.1 General .......................................................................................................................................................... 225
K.6.2 Forces due to pressure............................................................................................................................. 225
K.6.3 Stresses due to reaction force ............................................................................................................... 226
K.7
Gimbal, square and round ...................................................................................................................... 227
K.7.1 General .......................................................................................................................................................... 227
K.7.2 Stresses in bored section ........................................................................................................................ 227
K.7.3 Square type gimbal.................................................................................................................................... 228
K.7.4 Round type gimbal .................................................................................................................................... 231
K.8
Attachment plate........................................................................................................................................ 233
K.8.1 Attachment plate (closed/open) with 2 restraining parts ......................................................... 233
K.8.2 Circular attachment plate with 3 or more tie bars valid up to DN 800 .................................. 241
K.9
Lug-plate connection (hinge/gimbal) ................................................................................................ 244
K.9.1 General .......................................................................................................................................................... 244
K.9.2 Lug-plate for form-lock connection .................................................................................................... 245
K.9.3 Lug-plate for welded buttonhole connection .................................................................................. 248
K.10 Tie bar and lug attachment on flanges............................................................................................... 249
K.10.1 Integral flange............................................................................................................................................. 249
K.10.2 Plate welded on flange............................................................................................................................. 253
K.11 Gusset............................................................................................................................................................. 256
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K.12 Gusset with reinforcing rings................................................................................................................. 256
K.12.1 General ...........................................................................................................................................................256
K.12.2 Basic definitions ......................................................................................................................................... 258
K.12.3 Stresses in the gussets .............................................................................................................................. 259
K.12.4 Stresses in the ring and pipe .................................................................................................................. 259
K.12.5 Stresses in welds a7, a8 and a9 ............................................................................................................. 260
Annex ZA (informative) Relationship between this European Standard and the Essential
Requirements of EU Directive 2014/68/EU ..................................................................................... 262
Bibliography...............................................................................................................................................................264
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EN 14917:2021 (E)
European foreword
This document (EN 14917:2021) has been prepared by Technical Committee CEN/TC 342 “Metal hoses,
hose assemblies, bellows and expansion joints”, the secretariat of which is held by SNV.
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 January 2022, and conflicting national standards shall
be withdrawn at the latest by January 2022.
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 supersedes EN 14917:2009+A1:2012.
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) / Regulation(s).
For relationship with EU Directive(s) / Regulation(s), see informative Annex ZA, which is an integral part
of this document.
Modifications to EN 14917:2009+A1:2012:
— adaptation to Directive 2014/68/EU;
— general revision and correction;
— complete revision and restructuring of Clause 6, i.a.;
— addition of design in the creep range;
— modification of stress calculation for internal pressure capability;
— reformulation of column instability calculation;
— modification of in-plane instability calculation;
— harmonisation of fatigue calculation for all bellows types and introduction of 4 fatigue curves for
different material classes;
— extension of material characteristics for calculating forces and moments on pressurised
expansion joints;
— addition of Annex K for stress calculation of hardware;
— revision of Testing, inspection and documentation;
— revision of material properties in Annex B and Annex J;
— correction of Coefficient Cp .
Any feedback and questions on this document should be directed to the users’ national standards body.
A complete listing of these bodies can be found on the CEN website.
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BS EN 14917:2021
EN 14917:2021 (E)
According to the CEN-CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: 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 the United
Kingdom.
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EN 14917:2021 (E)
Introduction
Metal bellows expansion joints are used as parts in pressure vessels or piping components.
If an expansion joint is designed and manufactured covered by EU-Directive 2014/68/EU a risk
assessment has to be done. The possible risks of an expansion joint and how they have been dealt in this
document are described in Annex I.
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EN 14917:2021 (E)
1 Scope
This document specifies the requirements for design, manufacture and installation of metal bellows
expansion joints with circular cross section for pressure applications with maximum allowable pressure
greater than 0,5 bar.
2 Normative references
The following referenced documents are indispensable for the application 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 764-4:2014, Pressure equipment — Part 4: Establishment of technical delivery conditions for metallic
materials
EN 764-5:2014, Pressure equipment — Part 5: Inspection documentation of metallic materials and
compliance with the material specification
EN 1092-1:2018, Flanges and their joints — Circular flanges for pipes, valves, fittings and accessories, PN
designated — Part 1: Steel flanges
EN 1591-1:2013, Flanges and their joints — Design rules for gasketed circular flange connections — Part 1:
Calculation
EN 1759-1:2004, Flanges and their joints — Circular flanges for pipes, valves, fittings and accessories, Class
designated — Part 1: Steel flanges, NPS 1/2 to 24
EN 10028-1:2017, Flat products made of steels for pressure purposes — Part 1: General requirements
EN 10028-2:2017, Flat products made of steels for pressure purposes — Part 2: Non-alloy and alloy steels
with specified elevated temperature properties
EN 10028-3:2017, Flat products made of steels for pressure purposes — Part 3: Weldable fine grain steels,
normalized
EN 10028-4:2017, Flat products made of steels for pressure purposes — Part 4: Nickel alloy steels with
specified low temperature properties
EN 10028-7:2016, Flat products made of steels for pressure purposes — Part 7: Stainless steels
EN 10204:2004, Metallic products — Types of inspection documents
EN 10216-1:2013, Seamless steel tubes for pressure purposes — Technical delivery conditions — Part 1:
Non-alloy steel tubes with specified room temperature properties
EN 10216-2:2013+A1:2019, Seamless steel tubes for pressure purposes — Technical delivery conditions —
Part 2: Non-alloy and alloy steel tubes with specified elevated temperature properties
EN 10216-3:2013, Seamless steel tubes for pressure purposes — Technical delivery conditions — Part 3:
Alloy fine grain steel tubes
EN 10216-4:2013, Seamless steel tubes for pressure purposes — Technical delivery conditions — Part 4:
Non-alloy and alloy steel tubes with specified low temperature properties
10
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EN 14917:2021 (E)
EN 10216-5:2013, Seamless steel tubes for pressure purposes — Technical delivery conditions — Part 5:
Stainless steel tubes
EN 10217-1:2019, Welded steel tubes for pressure purposes — Technical delivery conditions — Part 1:
Electric welded and submerged arc welded non-alloy steel tubes with specified room temperature properties
EN 10217-2:2019, Welded steel tubes for pressure purposes — Technical delivery conditions — Part 2:
Electric welded non-alloy and alloy steel tubes with specified elevated temperature properties
EN 10217-3:2019, Welded steel tubes for pressure purposes — Technical delivery conditions — Part 3:
Electric welded and submerged arc welded alloy fine grain steel tubes with specified room, elevated and low
temperature properties
EN 10217-4:2019, Welded steel tubes for pressure purposes — Technical delivery conditions — Part 4:
Electric welded non-alloy steel tubes with specified low temperature properties
EN 10217-5:2019, Welded steel tubes for pressure purposes — Technical delivery conditions — Part 5:
Submerged arc welded non-alloy and alloy steel tubes with specified elevated temperature properties
EN 10217-6:2019, Welded steel tubes for pressure purposes — Technical delivery conditions — Part 6:
Submerged arc welded non-alloy steel tubes with specified low temperature properties
EN 10217-7:2014, Welded steel tubes for pressure purposes — Technical delivery conditions — Part 7:
Stainless steel tubes
EN 10222-2:2017, Steel forgings for pressure purposes — Part 2: Ferritic and martensitic steels with
specified elevated temperatures properties
EN 10222-3:2017, Steel forgings for pressure purposes — Part 3: Nickel steels with specified low
temperature properties
EN 10222-4:2017, Steel forgings for pressure purposes — Part 4: Weldable fine grain steels with high proof
strength
EN 10222-5:2017, Steel forgings for pressure purposes — Part 5: Martensitic, austenitic and austeniticferritic stainless steels
EN 10253-2:2007, Butt-welding pipe fittings — Part 2: Non alloy and ferritic alloy steels with specific
inspection requirements
EN 10253-3:2008, Butt-welding pipe fittings — Part 3: Wrought austenitic and austenitic-ferritic (duplex)
stainless steels without specific inspection requirements
EN 10253-4:2008, Butt-welding pipe fittings — Part 4: Wrought austenitic and austenitic-ferritic (duplex)
stainless steels with specific inspection requirements
EN 10269:2013, Steels and nickel alloys for fasteners with specified elevated and/or low temperature
properties
EN 10272:2016, Stainless steel bars for pressure purposes
EN 10273:2016, Hot rolled weldable steel bars for pressure purposes with specified elevated temperature
properties
11
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EN 14917:2021 (E)
EN 13184:2001, Non-destructive testing — Leak testing — Pressure change method
EN 13445-2:2014, Unfired pressure vessels — Part 2: Materials
EN 13445-3:2014, Unfired pressure vessels — Part 3: Design
EN 13480-2:2017, Metallic industrial piping — Part 2: Materials
EN 13480-2:2017/A1:2018, Metallic industrial piping — Part 2: Materials
EN 13480-2:2017/A2:2018, Metallic industrial piping — Part 2: Materials
EN 13480-2:2017/A3:2018, Metallic industrial piping — Part 2: Materials
EN 13480-3:2017, Metallic industrial piping — Part 3: Design and calculation
EN ISO 148-1:2016, Metallic materials — Charpy pendulum impact test — Part 1: Test method
(ISO 148-1:2016)
EN ISO 643:2020, Steels — Micrographic determination of the apparent grain size (ISO 643:2019, Corrected
version 2020-03)
EN ISO 3651-2:1998, Determination of resistance to intergranular corrosion of stainless steels — Part 2:
Ferritic, austenitic and ferritic-austenitic (duplex) stainless steels — Corrosion test in media containing
sulfuric acid (ISO 3651-2:1998)
EN ISO 5817:2014, Welding — Fusion-welded joints in steel, nickel, titanium and their alloys (beam welding
excluded) — Quality levels for imperfections (ISO 5817:2014)
EN ISO 6506-1:2014, Metallic materials — Brinell hardness test — Part 1: Test method (ISO 6506-1:2014)
EN ISO 6892-1:2019, Metallic materials — Tensile testing — Part 1: Method of test at room temperature
(ISO 6892-1:2019)
EN ISO 6892-2:2018, Metallic materials — Tensile testing — Part 2: Method of test at elevated temperature
(ISO 6892-2:2018)
EN ISO 9445-1:2010, Continuously cold-rolled stainless steel — Tolerances on dimensions and form — Part
1: Narrow strip and cut lengths (ISO 9445-1:2009)
EN ISO 9445-2:2010, Continuously cold-rolled stainless steel — Tolerances on dimensions and form — Part
2: Wide strip and plate/sheet (ISO 9445-2:2009)
EN ISO 9606-1:2017, Qualification testing of welders — Fusion welding — Part 1: Steels (ISO 9606-1:2012
including Cor 1:2012 and Cor 2:2013)
EN ISO 9606-4:1999, Approval testing of welders — Fusion welding — Part 4: Nickel and nickel alloys
(ISO 9606-4:1999)
EN ISO 9712:2012, Non-destructive testing — Qualification and Certification of NDT personnel
(ISO 9712:2012)
EN ISO 14732:2013, Welding personnel — Qualification testing of welding operators and weld setters for
mechanized and automatic welding of metallic materials (ISO 14732:2013)
12
BS EN 14917:2021
EN 14917:2021 (E)
EN ISO 15609-1:2019, Specification and qualification of welding procedures for metallic materials —
Welding procedure specification — Part 1: Arc welding (ISO 15609-1:2019)
EN ISO 15609-2:2019, Specification and qualification of welding procedures for metallic materials —
Welding procedure specification — Part 2: Gas welding (ISO 15609-2:2019)
EN ISO 15609-3:2004, Specification and qualification of welding procedures for metallic materials —
Welding procedures specification — Part 3: Electron beam welding (ISO 15609-3:2004)
EN ISO 15609-4:2009, Specification and qualification of welding procedures for metallic materials —
Welding procedure specification — Part 4: Laser beam welding (ISO 15609-4:2009)
EN ISO 15609-5:2011, Specification and qualification of welding procedures for metallic materials —
Welding procedure specification — Part 5: Resistance welding (ISO 15609-5:2011, Corrected version 201112-01)
EN ISO 15609-6:2013, Specification and qualification of welding procedures for metallic materials —
Welding procedure specification — Part 6: Laser-arc hybrid welding (ISO 15609-6:2013)
EN ISO 15610:2003, Specification and qualification of welding procedures for metallic materials —
Qualification based on tested welding consumables (ISO 15610:2003)
EN ISO 15613:2004, Specification and qualification of welding procedures for metallic materials —
Qualification based on pre-production welding test (ISO 15613:2004)
EN ISO 15614-1:2017, 1 Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 1: Arc and gas welding of steels and arc welding of nickel and nickel alloys
(ISO 15614-1:2017, Corrected version 2017-10-01)
EN ISO 15614-2:2005, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 2: Arc welding of aluminium and its alloys (ISO 15614-2:2005)
EN ISO 15614-3:2008, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 3: Fusion welding of non-alloyed and low-alloyed cast irons (ISO 156143:2008)
EN ISO 15614-4:2005, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 4: Finishing welding of aluminium castings (ISO 15614-4:2005)
EN ISO 15614-5:2004, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 5: Arc welding of titanium, zirconium and their alloys (ISO 15614-5:2004)
EN ISO 15614-6:2006, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 6: Arc and gas welding of copper and its alloys (ISO 15614-6:2006)
EN ISO 15614-7:2019; Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 7: Overlay welding (ISO 15614-7:2016)
EN ISO 15614-8:2016, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 8: Welding of tubes to tube-plate joints (ISO 15614-8:2016)
1 As impacted by EN ISO 15614-1:2017/A1:2019.
13
BS EN 14917:2021
EN 14917:2021 (E)
EN ISO 15614-10:2005, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 10: Hyperbaric dry welding (ISO 15614-10:2005)
EN ISO 15614-11:2002, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 11: Electron and laser beam welding (ISO 15614-11:2002)
EN ISO 15614-12:2014, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 12: Spot, seam and projection welding (ISO 15614-12:2014)
EN ISO 15614-13:2012, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 13: Upset (resistance butt) and flash welding (ISO 15614-13:2012)
EN ISO 15614-14:2013, Specification and qualification of welding procedures for metallic materials —
Welding procedure test — Part 14: Laser-arc hybrid welding of steels, nickel and nickel alloys (ISO 1561414:2013)
EN ISO 17635:2016, Non-destructive testing of welds — General rules for metallic materials
(ISO 17635:2016)
EN ISO 20485:2018, Non-destructive testing — Leak testing — Tracer gas method (ISO 20485:2017)
3 Terms and definitions
For the purposes of this document the following terms and definitions apply.
3.1
expansion joint
metal equipment consisting of one or more bellows used to absorb movements such as caused by thermal
or mechanical effects in piping or pressure vessels
Note 1 to entry:
See also Clause 4 Classification.
3.2
bellows
flexible element consisting of one or more corrugations and the end tangents
3.3
corrugation
convolution
flexible unit of a bellows with a leakproof wall consisting of one or more plies
3.4
ply
element of the bellows’ wall usually made from sheet or strip material
3.5
end tangent
straight un-corrugated portion at the ends of a bellows
3.6
reinforcing collar
reinforcing sleeve or ring attached to the end tangent for reinforcement
14
BS EN 14917:2021
EN 14917:2021 (E)
3.7
assisting collar
ring placed around the end tangents to facilitate welding
3.8
reinforcing and equalizing ring
reinforcing member
device fitting snugly in the roots of the corrugations in order to reinforce the bellows against internal
pressure and/or to limit the equivalent axial compression
3.9
internal sleeve
circular element fixed to the inside of the expansion joint which allows a satisfactory flow of medium and
protects the bellows from erosion and flow-induced vibrations
Note 1 to entry:
It is designed so that it does not restrict the movement of the expansion joint.
Note 1 to entry:
See also Clause 4 Classification.
3.10
hardware
restraining parts of expansion joints being able to withstand the relevant forces and moments due to the
effect of pressure thrust and additional loadings
3.11
shipping bar
device that secures the expansion joint in a determined position during the period of shipment, handling
and installation
3.12
classification
classifying expansion joints according to the type of movement they are capable of absorbing or
classifying their parts according to their pressure bearing capacity
3.13
maximum allowable pressure
PS
maximum pressure for which the equipment is designed, as specified by the equipment manufacturer
3.14
maximum/minimum allowable temperature
TS
maximum and minimum temperature for which the equipment is designed, as specified by the equipment
manufacturer
3.15
nominal pressure
PN
designation commonly used for reference purposes for piping components and stock parts, and which
represents in this document the maximum allowable pressure at 20 °C
Note 1 to entry:
Normally defined as a dimensionless alphanumeric number; see EN 1333:2006.
15
BS EN 14917:2021
EN 14917:2021 (E)
3.16
pressure thrust
Fp
axial force due to the effect of pressure on the expansion joint
3.17
neutral position
bellows length in a “stress-free” state
3.18
spring rate
reaction force or moment induced by a unit movement
3.19
cycle
full movement, from an initial point to the given working positions and back to the beginning
3.20
squirm
column or in-plane instability of the bellows under the effect of internal pressure and/or axial force
3.21
category
classification of pressure equipment according to ascending level of hazard
Note 1 to entry:
See Annex A.
3.22
equipment manufacturer
natural or legal person responsible for the values of the parameters PS and TS
Note 1 to entry: This may be the manufacturer or planner of the piping or the pressure vessel for which the
expansion joint is designed or the expansion joint manufacturer if free to set these values.
3.23
expansion joint manufacturer
natural or legal person responsible for the design and the manufacturing of the expansion joint
3.24
creep
time-dependent deformation at elevated temperature under load
3.25
creep range
operating range where creep is expected due to the design temperature and the specified life time of the
equipment
16
BS EN 14917:2021
EN 14917:2021 (E)
4 Classification
4.1 Classification of expansion joints
4.1.1 General
There are four types of expansion joints which are designed according to the type of movements which
can be absorbed. Where pressure balanced or provided with restraining parts, the expansion joints can
in addition absorb the pressure thrust. Common examples are shown in Table 1.
4.1.2 Axial
Unrestrained expansion joint which absorbs mainly axial displacement. It does normally not restrain
pressure thrust - only when pressure balanced (see 4.1.6).
4.1.3 Angular
Restrained expansion joint which absorbs angular rotation and restrains the pressure thrust. It allows
rotation in a single plane when fitted with hinges and multi-plane rotations when fitted with gimbal rings.
4.1.4 Lateral
Restrained expansion joint which absorbs lateral deflection and restrains the pressure thrust. It allows
lateral deflection in a single plane when fitted with hinges and multi-plane deflection when fitted with
double hinges or double gimbals. Multi-plane deflection is also permissible when tie rods with spherical
bearings are used; this design allows also angular rotation perpendicular to the plane containing the tie
bars.
4.1.5 Universal
Unrestrained expansion joint which absorbs all types of movements. It does normally not restrain
pressure thrust – only when pressure balanced (see 4.1.6).
4.1.6 Pressure balanced designs (axial or universal)
A pressure balanced expansion joint accommodates the movements and counteracts the bellows
pressure thrust. An additional bellows is incorporated into the unit and is subject to the line pressure to
generate a force equal and opposite to that on the main bellows. Tying these bellows together neutralises
the pressure load on the unit.
17
18
Lateral
Angular
Axial
Type
Yes
Yes
Yes
Hinge
Gimbal
Two tie bars
spherical
No
No
Yes
Design
Pressure
thrust
restraint
X
X
X
Axial
Table 1 — Types of expansion joints
In-line
pressure
balanced
Non-pressure
balanced
externally
pressurized
Non-pressure
balanced
internally
pressurized
EN 14917:2021 (E)
X
X
X
(X)
(X)
Single
plane
X
(X)
(X)
Multiplane
Angular
Movement
X
(X)
(X)
Single
plane
X
(X)
(X)
Multiplane
Lateral
BS EN 14917:2021
Yes
Yes
No
Yes
Double hinge
Double gimbal
Unrestrained
One or two
bellows
Pressure
balanced
Yes
Yes
Design
Three or
more tie bars
Two tie bars
Pinned
(plane)
NOTE 1 X — Applicable.
NOTE 2 (X) — Limited use.
Universal
Type
Pressure
thrust
restraint
X
X
Axial
X
With two
tie bars
only
X
X
X
Single
plane
X
X
Multiplane
Angular
Movement
X
X
X
X
X
X
Single
plane
X
X
X
X
19
Multiplane
Lateral
EN 14917:2021 (E)
BS EN 14917:2021
BS EN 14917:2021
EN 14917:2021 (E)
4.2 Classification of the parts of expansion joints
4.2.1 Main pressure-bearing parts (A)
Parts and assemblies that envelope the medium under pressure and which according to their design and
their stress level are essential for the pressure-bearing integrity of the equipment, i.e. its failure can result
in a sudden discharge of pressure energy, see Figure 1.
4.2.2 Pressure parts other than main pressure-bearing parts (B)
Parts that are charged by the pressure indirectly and have no direct contact to the medium and parts that
are in contact with the medium but according to their design are not essential for the pressure-bearing
integrity of the equipment, see Figure 1.
4.2.3 Attachments to main pressure-bearing parts and to pressure parts (C)
Parts that are directly welded to A or B parts.
4.2.4 Other parts (D)
Parts that are not A, B or C parts.
20
Figure 1 — Classification of the parts of expansions joint
21
d) — Lateral
c) — Angular
Key
1 pretension or shipping bars
a collars, if reinforcing are A parts (see Table 7)
NOTE
These sketches are diagrammatic only.
b) — Axial non-pressure balanced externally pressurized
a) — Axial non-pressure balanced internally pressurized
EN 14917:2021 (E)
BS EN 14917:2021
BS EN 14917:2021
EN 14917:2021 (E)
5 Materials
5.1 General
5.1.1 Materials for pressure-bearing parts
Materials used for pressure-bearing parts as defined in 4.2.1 and 4.2.2 and shown in Figure 1 shall be free
from surface and internal defects, which impair their suitability. These materials shall be selected to be
compatible with anticipated fabrication techniques and to be suitable for the specified conditions.
5.1.2 Materials for parts attached to pressure-bearing parts
For parts that are attached to pressure-bearing parts as defined in 4.2.3 and shown in Figure 1, the
materials used shall not limit the operating conditions of the pressure-bearing parts to which they are
attached, especially when attached by welding.
5.1.3 Materials for non-pressure parts
All materials used for the manufacture of expansion joints shall be suitable for such application during
the scheduled lifetime unless replacement is foreseen.
5.2 Pressure-bearing parts
5.2.1 Bellows
5.2.1.1 Allowable materials
Only materials shall be used that fulfil the general requirements of 5.1 and that are suitable for the special
forming and welding procedures used for bellows according to the demands of 7.3 and 7.4.
Preferable materials are given in Table 2. The table also gives the minimum and maximum operative
temperature limits for the various materials.
Annex J (informative) gives additional properties for some high temperature materials - like creep
rupture stresses - and physical properties at low temperatures.
Other materials not listed in Table 2 may be used, provided they fulfil the general requirements of 5.1
and are also suitable for the special forming and welding procedures according to 7.3 and 7.4 and
provided they conform to a harmonized standard or comply with an European Approval for Material
(EAM) or have a Particular Material Appraisal (PMA) as defined in EN 764-4:2014.
5.2.1.2 Corrosion
The material selected for the bellows element shall have adequate resistance to all the corrosive agents
likely to be encountered during the lifetime of the system.
Topics of special consideration include pitting corrosion, intergranular corrosion, crevice corrosion and
stress corrosion cracking.
Bellows generally have a wall thickness substantially less than that of the rest of the system with which
they are used. Hence the bellows shall be manufactured from a material having the same or a higher
corrosion resistance than that used in the associated plant.
5.2.2 Other pressure-bearing parts
Allowable materials for other pressure-bearing parts shall be selected from Table 2 or from the standards
given in Table 3 dependent on the application. Materials and temperature limitations of flanges which
are designed according to 6.1 are defined in the appropriate flange standard.
22
BS EN 14917:2021
EN 14917:2021 (E)
The lowest allowable working temperature is depending on the degree of load Gσ which is defined by the
maximum quotient of the stress levels resulting from the calculation of pressure resistance and the
allowable stresses related to the regarded stress components:
=
Gσ max  PΘ

(
f ; Pm f ; Pm + Pb
) (1, 5 ⋅ f ) 
(1)
The use of low temperatures related to degrees of load less than 1,0 given in Table 3 is allowed if the
following additional demands are fulfilled to achieve similar safety against brittle fracture:
a) The expansion joint manufacturer shall ensure that:
— stress raisers are avoided with regard to design and manufacture;
— no cracks are to be expected under working conditions.
b) The expansion joint manufacturer shall in addition carry out suitable heat treatment after forming
or welding on parts of ferritic materials.
c) Stress relieving after welding is dispensable for ferritic materials belonging to the material groups
1.1 or 1.2 according to CEN ISO/TR 15608:2013 [31] and having a wall thickness not greater than
10 mm.
Other materials may be used provided they fulfil the general requirements of 5.1 and conform to a
harmonized standard or comply with a European Approval for Materials (EAM) or have a Particular
Material Appraisal (PMA) as defined in EN 764-4:2014.
For pressure-bearing parts other than bellows an adequate allowance, protection against corrosion or
other chemical attack shall be incorporated or material having the same or a higher corrosion resistance
than that used in the associated plant have to be used, taking due account of the intended and reasonably
foreseeable use.
5.2.3 Ductility
All materials shall be sufficiently ductile in the delivery state.
Materials used for main pressure-bearing parts (4.2.1) and other pressure-bearing parts (4.2.2) shall at
least have:
— an elongation after rupture of A = 14 % and
— an impact energy of KV = 27 J, measured on an ISO-V test-piece according to EN ISO 148-1:2016 at a
temperature not greater than 20 °C but, not higher than the lowest scheduled design temperature or
at ‒196 °C if the design temperature is less.
Bellows materials after forming shall in addition conform to the requirements given in 7.4.
5.2.4 Brittle fracture
Consideration shall be given to the prevention of brittle fracture, especially for expansion joints that are
subjected to temperatures below – 10 °C:
a) Bellows shall be manufactured from the allowable materials according to 5.2.1.1. If bellows are
manufactured from materials according to Table 2 they shall not be used at temperatures lower than
that given in the column “Minimum” in this table, except the nickel alloys 2.4816 and 2.4856.
23
BS EN 14917:2021
EN 14917:2021 (E)
To enable the use of these nickel alloys at lower temperatures impact energy values shall be specified
and verification procedures shall be agreed to between the material manufacturer and the purchaser
at the time of ordering.
b) Other pressure-bearing parts shall be manufactured from the allowable materials according to 5.2.2
and shall not be used at temperatures below that given in Table 2 and Table 3, except the nickel alloys
2.4816 and 2.4856, see a).
Parts with more than 5 mm thickness from ferritic steel (Group 1) or more than 20 mm thickness
from austenitic stainless steel (Group 8) and from nickel alloys shall pass a Charpy impact test (see
5.2.3) if the impact energy is not already covered by the related material standard.
The measured impact energy shall be:
— KV ≥ 27J for ferritic steels (Group 1);
— KV ≥ 40J for austenitic stainless steel (Group 8) and for nickel alloys or that given in the relating
standard whatever is greater.
Table 2 — Preferable materials for bellows elements and other pressure bearing parts and their
temperature limits (see also Table 3)
Material
Type
Number
Steel name
Minimum
Maximum
1.4301
X5CrNi18–10
– 196 a
550
1.4401
X5CrNiMo17–12–2
– 196 a
550
1.4435
X2CrNiMo18–14–3
1.4306
stainless
austenitic
steels
heat
resistant
austenitic
steels
24
Temperature °C
1.4404
X2CrNi19–11
X2CrNiMo17–12–2
1.4539
X1CrNiMoCuN25–20–5
1.4550
X6CrNiNb18–10
1.4541
X6CrNiTi18–10
1.4571
X6CrNiMoTi17–12–2
1.4876
X10NiCrAlTi32–21
X10NiCrAlTi32–21 (H)
1.4828
X15CrNiSi20–12
– 273 a
– 273 a
– 273 a
– 196 a
– 273 a
– 196 a
– 273 a
– 196
– 196
Document
550
550
550
550
EN 10028-7:2016
550
550
550
900 b
600
900 b
Annex B (1), Annex J
Annex B (2.1), Annex J
Annex B (2.2), Annex J
BS EN 14917:2021
EN 14917:2021 (E)
Material
Type
Nickel
alloys
Document
Number
Steel name
Minimum
Maximum
2.4360
NiCu30Fe
– 196
425
Annex B (3)
– 10
450
Annex J
2.4610
NiMo16Cr16Ti
2.4819
NiMo16Cr15W
– 196
2.4858
NiCr21Mo
– 273
2.4816
2.4856
1.0345
ferritic
steels
Temperature °C
1.0425
1.5415
NiCr15Fe
NiCr15Fe (H) c
NiCr22Mo9Nb
P235GH
P265GH
– 196
– 20
540
400
500
– 20
P460NH
450
– 20 d
P355NH
1.8935
400
400
– 20 d
13CrMo4–5
400
– 20
16Mo3
1.7335
1.0565
– 196
– 20
500
400
400
Annex J
Annex J
Annex J
Annex B (4)
EN 10028-2:2017
(heat resistant steels)
EN 10028-3:2017
(fine grain steels)
a Minimum temperature in accordance with EN 13445-2:2014, Annex B and EN 13480-2:2017,
EN 13480-2:2017/A1:2018, EN 13480-2:2017/A2:2018, EN 13480-2:2017/A3:2018, Annex B.
b Special care should be exercised due to the risk of embrittlement when using the materials at elevated
temperatures above 550 °C.
c Heat resistant type (informative).
d Minimum temperature is possible when the specified minimum impact energy of 27 J can be proved.
25
BS EN 14917:2021
EN 14917:2021 (E)
Table 3 — Material standards for other pressure-bearing parts
Lowest allowable
working temperature in °C
Running
no
Description
European Standard
Degree of load Gσ
0,75 a
0,25 a
tmin b
tmin –
50
tmin –
80
tmin b
tmin –
50
tmin –
80
tmin b
tmin –
50
tmin –
80
tmin b
tmin –
50
tmin –
80
tmin b
tmin –
50
tmin –
80
1,0
1
Non-alloy steel tubes with specified
room temperature properties:
— seamless pipes
— welded pipes
EN 10216-1:2013
EN 10217-1:2019
Non-alloy and alloy steels with
specified properties at elevated
temperatures:
— flat products
EN 10028-2:2017
2
— seamless pipes
EN 10216-2:2013+A1:20
19
— welded pipes (SA-welded)
EN 10217-5:2019
— welded pipes (E-welded)
— steel forgings
— bars
— fasteners
Weldable fine grain mild steels,
normalized:
3
5
26
EN 10222-2:2017
EN 10272:2016,
EN 10273:2016
EN 10269:2013
— flat products
EN 10028-3:2017
(P...NH)
— welded pipes
EN 10217-3:2019
— seamless pipes
— steel forgings
4
EN 10217-2:2019
EN 10216-3:2013
EN 10222-4:2017
Flat
and
long
products
from
weldable
fine
grain
EN 10028-3:2017
mild steels, normalized / normalized
(P…NL1, NL2)
rolled with specified low temperature
properties
Flat products for pressure purpose
from Nickel alloy steels with specified EN 10028-4:2017
low temperature properties
BS EN 14917:2021
EN 14917:2021 (E)
Running
no
Lowest allowable
working temperature in °C
Description
European Standard
Degree of load Gσ
0,75 a
0,25 a
tmin b
tmin –
50
tmin –
80
Forgings for pressure purpose, Nickel
steels with specified low temperature EN 10222-3:2017
properties
tmin b
tmin –
50
tmin –
80
EN 10028-7:2016
EN 10216-5:2013
Austenitic stainless steels according EN 10217-7:2019
to Table 2 with minimum allowable
EN 10222-4:2017
temperature – 196 °C
EN 10253-3:2008
EN 10253-4:2008
– 196
– 255
– 270
1,0
6
7
8
9
a
b
Pipes for pressure purpose, from
non-alloy steels with specified low
temperature properties:
— seamless pipes
EN 10216-4:2013
— welded pipes (SA-welded)
EN 10217-6:2019
— welded pipes (E-welded)
EN 10217-4:2019
Fittings for welding, with specified
EN 10253-2:2007
low temperature properties
tmin b
tmin –
50
tmin –
80
Additional requirements for degrees of load smaller than 1,0, see 5.2.2.
Lowest temperature of the regarded material according to the mentioned standards.
5.3 Material documentation
Materials used for expansion joints shall be delivered with documentation as defined in EN 764-5:2014.
A simplified diagram of the routes for inspection, documentation and compliance with the material
specification is given in Figure 2.
27
BS EN 14917:2021
EN 14917:2021 (E)
Figure 2 — Required material documentation
6 Design
6.1 General
6.1.1 Symbols
The following symbols listed in Table 4 apply.
Table 4 — Symbols
Symbol
A
Ac
Ae
Ar
a
b
28
Description
Unit
elongation at rupture according to EN ISO 6892-1
%
bellows effective area; see Formula (5)
mm2
cross sectional metal area of one corrugation; see Formula (4)
mm2
cross sectional metal area of one bellows reinforcing member; see mm2
Figure 14
factor for calculation of the effective spring rate; see Table 14
factor for calculation of the effective spring rate; see Table 14
—
—
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
Description
Unit
bn
nominal width of material (strip, sheet, plate); see Table 20
Cp,
Cd
Cf, shell coefficients for U-shaped corrugations; see Figures 5, 6 and 7
—
factor correcting σm,b(P) for multi-ply bellows; see Formula (21)
—
C1, C2
cc(d)
cn(P)
cdyn
ĉP
Cr
cw
cσ
Dc
Di
Di,pp
Di,t
Dm
Do
Dn
dp
dH
EB
Ec
Er
e
ec
ep
ep,c
factors used to determine the shell coefficients Cp, Cf, Cd; see Formulae (6), —
(7)
factor correcting σm,b(Δq) for multi-ply bellows; see Formula (22)
dynamic factor for column instability; see Formula (46)
increasing factor for curved bellows under pressure; see 6.2.8.4
correction factor for reinforced bellows; see Formula (23)
stress increasing factor due to circumferential welds; see Formula (133)
stress correction factor; see Formula (211)
mean diameter of end tangent reinforcing collar; see Formula (8)
inside diameter of bellows corrugations; see e.g. Figure 8
inside diameter of pipe end; see e.g. Figure 8
inside diameter of bellows end tangents; see e.g. Figure 8
mean diameter of bellows corrugation; see Formula (9)
—
—
—
—
—
—
mm
mm
mm
outside diameter of bellows corrugation (u-shaped or toroidal); see e.g. mm
Figure 8
inside neutral diameter of original tube or ring-plate before forming; see mm
Formulae (59) and (60) and Figure 4
pin diameter; see Table 18
mm
modulus of elasticity of bellows material, temperature depending
N/mm2 (MPa)
bearing diameter of the hinges, pin or sphere; see 6.2.9.3
modulus of elasticity of collar material, temperature depending
mm
N/mm2 (MPa)
modulus of elasticity of reinforcing member material, temperature N/mm2 (MPa)
depending
bellows nominal thickness; see Formula (10)
mm
nominal thickness of one ply
mm
end tangent reinforcing collar thickness; see Figures 9, 14 and 16
nominal thickness of one ply at crest
mm
mm
29
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
Description
Unit
ep,r
nominal thickness of one ply at root
ep*
equivalent ply thickness (thinning during forming); see Formulae (17), mm
(18) and (19)
e*
epp
Fp
Fw
mm
equivalent bellows wall thickness (thinning during forming); see mm
Formula (20)
wall thickness of the pipe end; see Figure 8
force due to pressure effect (pressure thrust); see Formula (24)
mm
N
f
working force of expansion joints; see Formulae (215), (223), (232) and N
(241)
f20
allowable general membrane stress at room temperature
fT
fcr
allowable general membrane stress at design temperature; see Table 5
N/mm2 (MPa)
allowable general membrane stress at test conditions; see Table 5
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
G
allowable design stress in the creep range; see Formula (2)
Gσ
H
degree of load; see Formula (1)
—
KB
axial spring rate of one bellows; see Formulae (35), (36) and (37)
N/mm
Kf
Ksr
KF
K
KP
Kβ
Kμ
Km,b,
Kθ,l
30
shear modulus; see Formula (255)
width of lug in the bored cross section; see Table 18
correction factor for allowable meridional stresses due to cold work; see
Formulae (38), (39), (40) and (41)
mm
—
correction factor for the normalized equivalent axial displacement due to —
cold work;
see Formulae (43) and (44)
friction factor to calculate the forces or moments due to friction in the mm2 or mm3
bearings of the restraining parts; see Formulae (222), (231), (240) and
(248)
effective spring rate of a bellows; see Formulae (212), (217), (226), (235) N/mm
or
and (244)
Nmm/radian
factor giving additional forces or moments of curved bellows due to the mm or mm2
influence of pressure; see Formulae (220), (221), (229), (230), (238), or
(239) and (247)
mm3/radian
spring rate for the effect of side wall tilting on forces or moments; see N/mm or
Formulae (213), (218), (227), (236) and (245)
Nmm/radian
factor for the effect of friction between the plies on forces or moments; see mm2 or mm3
Formulae (214), (219), (228), (237) and (246)
in-plane instability factors; see Formulae (110) and (111)
—
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
Description
Unit
kp,t
ks
de-rating factor for the pressure at the temperature t; see Formula (3)
—
kl
factor for occasional load; see 6.4.2.2.2
—
L
correction factor for reinforcing collar; see Formula (32)
—
Lc
bellows collar length; see Figures 8, 14 and 16
kt
kc
Lt
stabilizing factor influencing column instability; see Formulae (93) and —
(94)
correction factor for bellows tangent; see Formula (31)
distance of the pin centre to the end of the head of the lug; see Table 18
LT
end tangent length; see Figures 8, 14 and 16
lB
initial corrugated length of a bellows; see Figure 20
lB
lifetime in the creep range; see Table 6
l*
equalised corrugated length of a bellows; see Formula (95)
Mt
torsional moment; see Formulae (256) and (257)
Mwy,
MwΘ
My, MΘ
N
middle distance of the bellows of a double bellows type; see Figure 23
—
mm
mm
mm
h
mm
mm
mm
Nmm
working moment of bellows due to lateral deflexion or angular rotation; Nmm
see Formulae (224), (233), (242) and (249)
elastic moment due to lateral deflection or angular rotation; see Nmm
Formulae (175), (178), (181) and (184)
number of corrugations of one bellows
—
n
specified number of fatigue cycles; see 6.2.6.1
—
np
number of plies
Nalw
Nspe
nB
P a
Pm
Pb
PΘ
PS a
Psc
allowable number of fatigue cycles; see Formulae (169) and (170)
yield exponent for effective spring rate calculation; see Table 14
number of bellows in an expansion joint without intermediate pipe
calculation pressure
primary membrane stress
primary bending stress
primary circumferential membrane stress
maximum allowable pressure; see 3.13
—
—
—
—
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
limiting internal design pressure based on column instability; see N/mm2 (MPa)
Formulae (93), (94) and (96)
31
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
Psi
PT
Description
limiting design pressure based on in-plane instability; see Formulae (100) N/mm2 (MPa)
and (101)
test pressure; see 8.6.2.2
bar
shear stress; see Table 18
N/mm2 (MPa)
Pt, max maximum allowable pressure at temperature t
a
Q
q
Re*
ReH, t
Rm, t
Rm, 20
Rm/TL
/t
Rp0
Rp0,2
Rp1,0
Rp0, t
Rp0,2, t
Rp1,0, t
Rp1,0/
TL/ t
ri
Sb
SL
SFc
sΘ
sb
sd
sr
TS
32
Unit
corrugation length; see Figures 8, 14 and 16
bar
mm
temperature depending local yield strength of bellows material in the as- N/mm2 (MPa)
formed or annealed condition; see Formulae (27), (28) and (29)
minimum specified value of upper yield strength at design temperature
N/mm2 (MPa)
minimum specified value of tensile strength at room temperature
N/mm2 (MPa)
minimum specified value of tensile strength at design temperature
mean creep rupture strength at lifetime TL(h) and design temperature
yield point at room temperature; see Table 14
0,2 % proof strength at room temperature
1 % proof strength at room temperature
yield point at design temperature; see Table 14
minimum specified value of 0,2 % proof strength at design temperature
minimum specified value of 1 % proof strength at design temperature
mean creep strain limit (1 %) at lifetime TL(h) and design temperature
internal radius of crest and root knuckle of U-shaped corrugations;
see Formula (25) and Figures 8 and 14
local secondary bending stress; see Table 18
thickness of the lug in the bored cross section; see Table 18
time-dependent safety factor; see Table 6
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
N/mm2 (MPa)
mm
N/mm2 (MPa)
mm
—
circumferential true strain caused by deformation; see 6.2.2.5.2 and 7.4.1.2 —
bending component of true strain caused by deformation; see 6.2.2.5.2 and —
7.4.1.2
equivalent true strain caused by deformation; see 6.2.2.5.2 and 7.4.1.2
—
maximum / minimum allowable temperature; see 3.14
°C
true strain of rupture; see Formula (272)
—
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
t
tn
w
x
x
y
z
Description
Unit
design temperature
°C
corrugation height, see e.g. Figures 8 and 14
mm
nominal thickness of the material (strip, sheet, plate); see Table 20
applied axial displacement from the neutral position; see 6.2.7
mm
β0
initial side wall angle of the corrugation; see Formula (84)
Δq
Δq*
δ
η
κ
µ
μH
νB
σ (Δq)
σ (P)
σeq
Θ
mm
applied lateral deflection; see Figures 22 and 23
α
ΔL
mm
mean axial displacement; see Formula (97)
joint coefficient; see 8.4.4 and Tables 24, 25, 28
βe,alw
mm
dimensional parameter
Formula (109)
for
in-plane
instability
calculation;
—
see —
degree
maximum allowable side wall angle of the corrugation in the extended degree
position; see Formula (197)
cylindrical length of reinforcing member
mm
normalized equivalent axial displacement; see Formula (45)
—
equivalent axial displacement range per corrugation; see Formula (207)
mm
stress capacity ratio for in-plane instability calculation; see Formula (109) —
factor for the influence of the forming process; see Formula (30)
calculation factor; see Formula (48)
—
1/mm
effective friction factor regarding friction between the plies; see
—
Formula (47)
friction factor regarding friction of hinge bearings; see NOTE 2 in —
connection with Formula (222)
Poisson's ratio of bellows material (for stainless steel ν = 0,3)
—
stress due to pressure P
N/mm2 (MPa)
stress due to equivalent axial displacement range Δq
N/mm2 (MPa)
total equivalent stress range due to the cyclic axial displacement range Δq N/mm2 (MPa)
applied angular rotation; see Figure 24
radians
33
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
Description
Subscripts:
0 initial
B bellows
E end
I intermediate
H hinge
LT Lifetime in the creep range
P pin
T test conditions
a
b bending
c collar, corrugation,
compression
d deformation
e extension
h hardware
i inside
m membrane or meridional
o outside
p ply
Unit
r reinforced bellows
t end tangents, torsion,
toroidal, design temperature
Δ difference
Θ circumferential
Σ sum
μ friction
All pressures for calculation purposes are in N/mm2 (MPa) and pt, max is in bar.
6.1.2 Basic design criteria
6.1.2.1 General
Expansion joints shall be designed to withstand the specified pressure PS at the specified temperature
TS. This combination of pressure and temperature shall as a minimum represent the most critical
foreseeable working conditions.
The specified additional loadings according to 6.1.4 shall be taken into account as well.
NOTE
Annex H gives the main design conditions and information and may be used as a guideline.
6.1.2.2 Bellows
Shall be designed according to 6.2.
6.1.2.3 Flanges
Standard flanges shall conform to EN 1092-1:2018 or EN 1759-1:2004. Alternatively the flanges shall be
calculated according to the methods in EN 13445-3:2014, EN 13480-3:2017, EN 1591-1:2013 or Annex K
in this standard for special hardware flanges.
6.1.2.4 Pipe sections
Shall be designed according to the appropriate standard EN 13445-3:2014 or EN 13480-3:2017.
6.1.2.5 Internal sleeves
Shall be designed according to 6.3.
6.1.2.6 Hardware
Shall be designed according to 6.4.
6.1.3 Allowable stresses
6.1.3.1 General
The design stress shall be the lower of the time-independent stress value defined in Table 5 and the timedependent stress value defined in 6.1.3.3 and shall be determined for each design condition.
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BS EN 14917:2021
EN 14917:2021 (E)
The values of the design stress shall be determined from the material properties as defined in the
standards and specifications given in Table 2 and 3 or from relevant material standards.
These minimum values, specified for delivery conditions of the materials, shall be used for design
purpose, unless fabrication and/or heat treatment is known to lead to lower values. In such cases, the
values to be used shall be agreed by the parties involved.
For the design of main pressure-bearing parts and pressure parts other than bolts the maximum
allowable stresses (general membrane stress for predominantly static loads) shall be determined as
given below.
NOTE
Where materials are used having higher proof stresses and sufficient strains to rupture certified by the
material manufacturer in an Inspection certificate according to EN 10204:2004, type 3.1 or 3.2, the allowable
stresses may be increased. The increase should not be more than 50 % of the difference between the specified values
of the standards and the certified values in the certificate and maximum 15 % of the standard value divided by the
relevant safety factor.
6.1.3.2 Design below the creep range (time-independent)
The allowable stresses are given in Table 5.
Table 5 — Allowable stresses
Material
Austenitic
alloys
steel
and
Design conditions
Test conditions
 R p1,0, t 

f =
 1,5 




 R p1,0,T 

fT = 
 1,05 


 R p1,0, t R m, t 

f = min 
;
 1, 2

3




 R p1,0,T R

m,T 
f T = max 
;
 1,05
2 


 R eH, t

R p0,2, t R
m , 20 
or
;
f = min 
 1,5
2, 4 
1,5



 R p 0,2, T 

fT = 
 1,05 


Ni
— general (30 % < A ≤ 35 %)
ab
— alternatively c if A > 35 %
Ferritic steel d
including
normalized
(normalized rolled) steel
a
Where A < 30 % use allowable stresses for “Ferritic steel”.
c
Shall not be used for the design of bellows.
b
d
For Ni-alloys Rp0,2, t shall be used instead of Rp1,0, t.
Non-alloy or low-alloy cast steel are excluded.
6.1.3.3 Design in the creep range (time-dependent)
Where pressure equipment is operated at elevated temperatures near the creep range available timeindependent allowable stresses shall be used up to the temperature where the time-dependent allowable
stresses are crossed (see Figure 3 a); i.e. “the lower stress value” according to 6.1.3.1.
35
BS EN 14917:2021
EN 14917:2021 (E)
Key
I below the creep range
II creep range
Figure 3 — Allowable stresses at high temperatures
Where the time-independent value for the highest temperature available in the harmonized material
standards does not reach the time-dependent values the time-independent value for the highest
temperature shall be extrapolated up to the temperature where the time-dependent values are crossed;
see Figure 3 b). This extrapolated value is regarded as allowable time-independent stress.
The design stress in the creep range fc to be used for design under static loadings shall be:
f cr =
where
R m,LT,t
R m ,LT,t
SFc
(2)
is the mean value of creep rupture strength, shall be taken from Table J.3 or from harmonized
European standards;
SFc is the safety factor which is depending on the design lifetime LT is given in Table 6.
For welds other than circumferential welds in welded pipes and fittings the creep strength values of the
base material shall be reduced by 20 %, except where ensured creep strength values have been
determined for these bellows, pipes and fittings.
This shall also be taken into consideration for bellows with longitudinal welds welded with filler material;
this reduction is only valid for dimensioning.
If the design lifetime is not specified, the mean creep rupture strength at 100 000 h shall be used.
NOTE
If the creep characteristics determine the thickness, additional creep tests (based on extrapolation using
the Larson-Miller formula) for instance on the welding consumables and the complete weld should be performed.
36
BS EN 14917:2021
EN 14917:2021 (E)
Table 6 — Safety factor related to lifetime
Design life time
Mean
creep
strength
rupture
Safety factor
a
b
LT
100 000 h
R m,LT,t
R m,100 000,t
SFc
With lifetime monitoring system.
1,25
a
1,5 b
200 000 h
R m ,100 000,t
R m,200 000,t
1,5 a
1,25 a
without lifetime monitoring system.
Different approaches are possible when agreed between the involved parties.
6.1.3.4 Test conditions
The designer shall ensure that the stress under proof test conditions, given in 8.6.2.2, shall not exceed the
allowable stresses for test condition according to Table 5. This is also valid for the test pressure in the
creep range where fT shall only be based on the time-independent yield strength values at design
temperature or - if not available - at the highest temperature for which time-independent values are
available in the harmonized European material standards.
NOTE
Pressure resistance can only be demonstrated by the proof test with respect to time-independent failure
risks because of the short test duration. Proof test cannot give information about long term pressure resistance
especially not regarding material damage resulting from design temperatures in the creep range.
6.1.3.5 Design on PN basis
Expansion joints designed on PN basis may be designated for temperatures higher than 20 °C but, not
more than the maximum allowable temperature below the creep range where only time-independent
stresses are allowed to be used (see also 6.1.3.2). In these cases the manufacturers de-rating factor for
pressure, kp,t , which shall be based on the respective material standards, shall be applied according to
the following Formula (3):
p
= PN ⋅ k p,t
t, max
6.1.4 Additional loadings
(3)
Additional loadings that may influence the design of expansion joints, but are not the loads normally
regarded for the design of bellows (see 6.2.2.2), shall also be taken into consideration.
a) Additional loadings present within the expansion joint:
— dead weight of expansion joint components (i.e. intermediate pipe, inner sleeve, restraint
hardware, refractory linings etc.);
— dead weight of flow medium within expansion joint;
— dynamic loading due to flow of medium.
These loadings (normal or occasional) shall be defined by the expansion joint manufacturer.
b) External additional loadings due to adjacent piping or equipment:
37
BS EN 14917:2021
EN 14917:2021 (E)
— unsupported weight of adjacent piping/equipment;
— pipe pre-stressing;
— thermal movement;
— environmental (i.e. snow, wind etc.);
— vibration from adjacent equipment (i.e. pumps, compressors, machines, etc.);
— shock loading (i.e. earth quake, explosion loading, etc.);
— dynamic loading due to flow of medium.
External loadings (normal or occasional) shall be provided by the piping or pressure vessel manufacturer.
These lists are not exhaustive.
6.2 Bellows design
6.2.1 Purpose
This subclause provides rules for design and calculation of bellows subject to internal and external
pressure and cyclic displacement.
They are applicable to the following three types of bellows (single or multiple corrugations):
a) unreinforced nominal U-shaped bellows as shown in Figure 8;
b) reinforced nominal U-shaped bellows as shown in Figure 14;
c) toroidal bellows as shown in Figure 16.
These bellows are part of expansion joints as defined in Clause 4.
NOTE
Attention is drawn to the fact that the design of bellows is complex because strength and flexibility
requirements are generally conflicting. Annex E gives detailed information on this issue.
6.2.2 Conditions of applicability
6.2.2.1 Geometry
— A bellows comprises one or more identical axisymmetric corrugations.
— Each corrugation may have one or more plies of the same thickness and of same material.
Deviant characteristics; e.g. different height of corrugations or different ply-materials, are allowed
provided they are treated analogously to the given calculation method and all eventual additional effects
like stiffness (spring rates) and stability are taken into consideration.
6.2.2.2 Loadings
Loadings mainly regarded for the design of bellows dealt with in 6.2 are static or variable internal
pressure, and cyclic axial, lateral or angular movements.
Specific regard shall be given to cover external pressure (see 6.2.3.4) and bellows torsion (see 6.2.10).
Additional loadings according to 6.1.4 shall be given special consideration.
38
BS EN 14917:2021
EN 14917:2021 (E)
6.2.2.3 Temperature
The requirements are valid for materials at temperatures below the creep range and in the creep range,
as stated in 5.2.1.1 or in the relevant European material standards.
6.2.2.4 Welding seams
6.2.2.4.1 General
Typical welding joints of bellows besides other weld seams in an expansion joint are shown in Figures 31
and 32.
6.2.2.4.2 Longitudinal butt welds W1 and W2
Bellows may include one or several longitudinal butt welds.
a) Bellows without circumferential welds: For longitudinal butt welds W1 no weld joint coefficient z is
applied (z = 1);
b) Bellows with circumferential welds (see 6.2.3.6): the concept of weld joint coefficient z shall be
applied to longitudinal butt welds W2; see 8.4.3.1.
6.2.2.4.3 Circumferential butt welds W3
For bellows with circumferential welds (see 6.2.3.6) and for butt weld bellows attachment as shown in
Table 7 No 3.0, the concept of weld joint coefficient z does not apply to such butt welds.
6.2.2.4.4 Bellows attachment welds
The circumferential attachment welds of single and multi-ply bellows shall be designed according to the
sketches given in Table 7. For butt weld bellows attachment as shown in Table 7, No 3.0, the provision of
6.2.2.4.3 applies.
Table 7 — Bellows attachment welds
Weld type
No
General design
1.1 a
1.2 a
Variants (Combinations of A to D are permitted)
A
B
increased neck reinforcing collar
b
C
D
single
double
Assisting collar
outside lap joint/filled
weld
inside lap joints/fillet
weld
39
BS EN 14917:2021
EN 14917:2021 (E)
Weld type
No
Variants (Combinations of A to D are permitted)
A
B
increased neck reinforcing collar
General design
2.1
2.2
D
single
double
Assisting collar
outs. lap joint/groove weld
3.0 c
4.1 d
4.2
C
inside lap joint/groove
weld
c
butt weld
radial edge weld
(inside or outside)
axial edge weld
(inside or outside)
General: 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.
a
b
c
d
In the case of fillet welds, the weld thickness “a“ shall fulfil following formula: a ≥ 0,7⋅e.
The reinforcing collar shall be fixed axially by welding or mechanical devices.
In the case of butt welds, special tools are necessary for welding of multi-ply bellows.
The diameter of the weld should not exceed the mean diameter of bellows Dm by more than 20 % of the
corrugations height w.
40
BS EN 14917:2021
EN 14917:2021 (E)
6.2.2.5 General factors and coefficients
6.2.2.5.1 General intermediate factors
The following general factors apply in 6.2 Bellows.
Cross sectional metal area of one corrugation:
(
)
)
2 ⋅ w + r ⋅ π - 2  ⋅ e *, for U - shaped bellows
m
 

Ac =  

 
2
r
G
π
⋅
⋅
⋅
 
m
p e * +  2 ⋅ L t, eff + D m - D i - 2 ⋅ rm  ⋅ e  , for toroidal bellows



 
(
Bellows effective area:
D 2 , for U - shaped unreinforced and toroidal bellows
 m
2
Ae = × 
4  D m + r i  , for U - shaped reinforced bellows


(4)
π
Factors used to determine the shell coefficients C p , C f , C d ; see 6.2.2.5.3.
C1 =
C2 =
2 ⋅ rm
w
1, 1
(5)
(6)
2 ⋅ rm
Dm ⋅ e p*
Mean diameter of end tangent reinforcing collar:
Dc = Di,t + 2 ⋅ e + e c
Mean diameter of bellows corrugations:

D + e + w , for U - shaped bellows
Dm =  i
D - e - 2 ⋅ rm , for toroidal bellows

 o
Bellows nominal wall thickness:
e = np ⋅ e p
Minimum ply thickness for:
(7)
(8)
(9)
(10)
— U-shaped bellows made from cylinders:
 D +2⋅w 

e p,o = e p ⋅  i
 D + 2 ⋅η ⋅ w 
 i



Di

e p,i = e p ⋅ 
 D + 2 ⋅η ⋅ w 
 i

-0,75
(11)
(12)
41
BS EN 14917:2021
EN 14917:2021 (E)
— U-shaped bellows made from half-corrugations:
 Do - e p 

e p,o = e p ⋅ 
 Dn,o 


 Di + e p 

e p,i = e p ⋅ 
 Dn,i 


(13)
-0,75
— Toroidal bellows:
 D + 4 ⋅ rm 

e p,o = e p ⋅  i


Di


(14)
-0,75
(15)
e p,i = e p
(16)
Equivalent ply thickness for:
— U-shaped bellows made from cylinders:
- 0,5
- 0,667 

e p∗ =
e p ⋅ (1 - η ) ⋅ 1 + (1 - η ) ⋅ w Di
+ η ⋅ 1 + η ⋅ w Di



(
)
(
)
— U-shaped bellows made from half-corrugations:

e p* =

(e p,c + e p,r ) ⋅ rm ⋅ π4 + e p ⋅ w - rm ⋅  2 - π2 
(
— Toroidal bellows:
w + rm ⋅ π - 2
(
)
e p* = e p ⋅ 0,5 ⋅ 1 + Do Di 


(17)
)
-0,5
Equivalent wall thickness:
e * = np ⋅ e p*
Correction factors for multi-ply bellows ( np > 1 ):
(18)
(19)
(20)
— Correction for bending stress in the sidewall due to pressure:






 ep

1 1
 rm
 1 1

- 
- 1  - 
- 1   ; 1
⋅ ( np - 1) ⋅ 
c n(P) = MIN 1 - 
4
2
r
 Cp

 Cp

 m
 w ⋅ C p





— Correction of corrugation height to reduce bending stress due to movement:
42
(21)
BS EN 14917:2021
EN 14917:2021 (E)

c c(d) = 1 

e 
( np - 1 ) ⋅ wp 
(22)

Correction factor for reinforced bellows:
 w 
w
≥ 2,5;
C r = 0,36 ⋅ ln 
 ; valid for 16 ≥
∆q
 ∆q 
C r = 1, 0 for w ∆q > 16 ; C r = 0,33 for w ∆q < 2,5
(
)
(
)
NOTE Cr = 1 for w/Δq = 16; i.e. very small or no movement.
Axial pressure force (pressure thrust):
FP = Ae ⋅ P
Mean inner radius of crest and root knuckle of a u-shaped corrugation:
(
)
(23)
(24)
ri = ric + rir / 2
(25)
rm = ri + e 2
(26)
Mean radius of crest and root knuckle of a u-shaped corrugation:
Local yield strength after forming and heat treatment:
( ) for as formed bellows
R e* = R p1,0, t ⋅ c * ⋅ s d
m
with the factors c* and m acc. to Table 8 and sd acc. to 6.2.2.5.2.
R e* = R p1,0, t for bellows annealed acc. to Table 8 (without cold work)
R e* = R p1,0, t ⋅ 0, 9 for otherwise annealed bellows
R p1,0, t shall be replaced by R p0,2, t if R p1,0, t is not available or allowed (e.g. Ni-alloys).
(27)
(28)
(29)
For ferritic materials R e* is equal to R eH .
43
BS EN 14917:2021
EN 14917:2021 (E)
Table 8 — Material dependent parameters for cold work calculation
(Strip, sheet)
Alloy
Steel name
(informative)
X5CrNi18–10
1.4306
X2CrNi19–11
1.4401
X5CrNiMo17–12–2
1.4404
X2CrNiMo17–12–2
1.4435
X2CrNiMo18–14–3
1.4539
X1CrNiMoCuN25–
20–5
1.4541
X6CrNiTi18–10
1.4550
X6CrNiNb18–10
1.4571
X6CrNiMoTi17–
12–2
1.4828
X15CrNiSi20–12
1.4876
X10NiCrAlTi32–21
1.4876 (H)
X10NiCrAlTi32–21
44
Condition
Number
1.4301
Stressstrain
Material properties a
Material
304
(minimum values)
Rp0,2
Rp1,0
Rm
A
N/mm N/mm N/mm
2
2
2
%
parameters
bc
c*
m
-
-
230
260
540
40
2,96
0,27
304L
220
250
520
45
2,84
0,27
316
240
270
530
40
2,91
0,27
240
270
530
40
2,91
0,27
240
270
550
40
2,85
0,27
904L
240
270
530
35
2,96
0,27
321
220
250
520
40
2,88
0,27
200
240
520
40
3,00
0,27
240
270
540
40
2,81
0,27
230
270
550
30
3,04
0,27
210
240
500
30
3,15
0,27
170
200
450
30
3,53
0,3
316L
316L
347
316Ti
309
800
800 H
cold
rolled,
solution
annealed
hot rolled,
solution
annealed
cold
rolled,
solution
annealed
solution
annealed
soft
annealed
solution
annealed
BS EN 14917:2021
EN 14917:2021 (E)
(Strip, sheet)
Alloy
Steel name
(informative)
NiCu30Fe
2.4610
NiMo16Cr16Ti
2.4816
NiCr15Fe
2.4816 (H)
NiCr15Fe
2.4819
NiMo16Cr15W
2.4856
NiCr22Mo9Nb
2.4858
a
NiCr21Mo
(minimum values)
Condition
Number
2.4360
Stressstrain
Material properties a
Material
400
C-4
600
600 H
C-276
625, Grade 1
825
Rp0,2
soft
Rm
A
N/mm N/mm N/mm
2
2
2
%
annealed
solution
annealed
soft
annealed
solution
annealed
solution
annealed
soft
annealed
solution
annealed
Rp1,0
parameters
bc
c*
m
-
-
175
200
450
30
3,60
0,3
305
340
700
40
2,68
0,24
200
230
550
30
2,96
0,3
180
210
500
35
3,67
0,31
310
330
730
30
3,30
0,27
400
440
830
35
2,59
0,25
235
265
550
30
3,23
0,29
The parameters c* and m are based on the given material properties.
b c* and m are based on test data. These parameters can be achieved by using minimum 5 experimental
stress-strain curves from tensile tests, generating a mean value curve out of these 5 curves, normalizing
this mean value test curve to Rp0,2, Rp1,0 and Rm from the appropriate EN material standard and fitting
C
the curve to σ = c * ⋅ ε m with c * =
and C = a ⋅ 100 m by defining the parameters a and m to get a
R p1,0
curve close to the normalized mean value test curve.
c For austenitic stainless steels not listed in this table c*=2,8 and m=0,27 may be used if
Rp0,2 ≥ 200 N/mm², Rp1,0 ≥ 240 N/mm² and Rm ≥ 520 N/mm².
Forming factor depending on the forming process:
η=
Dn - Di
2⋅w
(30)
with the neutral diameter Dn as the original inner diameter of the cylinder or of the ring plate before
forming starts. It is depending on the forming process, see Table 9 for information.
45
BS EN 14917:2021
EN 14917:2021 (E)
Table 9 — Typical values of forming factor η (informative)
Forming process for corrugations
1
2
3
Forming factor
From inside to outside with restraining
tools starting from the inner diameter Di
by:
— hydraulic or elastomer forming
— expansion (punching)
— roll-forming
Partly to outside and to inside within two
steps starting from a neutral diameter Dn
by:
— roll-forming
— a combined process (hydraulic /
elastomer or expansion and rollforming)
Partly to outside and to inside within one
step; roll-forming with counter-rotating
rolls (free forming)
Remarks
η
0
0,4 to 0,6
0,5 to 0,8
Restraining tools holding
back the roots of the
corrugations
on
the
diameter of the original
cylinder
Restraining tools holding
back the neutral diameter
Dn during the first step
Crest and root diameter
result from equilibrium of
strains
Correction factors considering the stiffening effect of bellows attachments:
a) Unreinforced and reinforced bellows with nominally U-shaped corrugations:
— Correction factor for bellows tangent:



Lt



k t = min 
 ;1, 0
 1,5 ⋅ ( Di,t + e ) ⋅ e p 

(31)
— Correction factor for the reinforcing collar:



Lc
 ;1, 0 , for collars fixed to the fitting
k c = min 


1,5 ⋅ Dc ⋅ e c 



For different types of attachments see also Table 10.
46
(32)
BS EN 14917:2021
EN 14917:2021 (E)
Table 10 — Stiffening effect of different attachments
Sample
1
2
kt
kt
Figure
Tangent
NOTE
3
kt =
Lt, reduced
4
kt =
Lt, reduced
5
kt =
Sample 3: Pipe end is treated similar to toroidal bellows pipe ends.
Lt, reduced
6
kt
b) Toroidal bellows:
The supporting effect of the attached pipe end is reduced to a length:
 1


Lt,c = min 
( Dc ⋅ e c )  ; Lc 

 3

(33)
 1


Li,c = min 
( Dic ⋅ e ic )  ; 0,5 ⋅ Lm 
 3


(34)
The supporting effect of the intermediate ring is reduced to a length:
Theoretical elastic spring rate for one bellows with N corrugations − temperature dependent on Young’s
modulus E B :
a) Unreinforced bellows with nominally U-shaped corrugations:
3
 e* 
1
p 
KB =
⋅EB ⋅
⋅ Dm ⋅ 
⋅


N
 w  Cf
2 ⋅ 1 - ν B2


π
(
np
)
(35)
b) Reinforced bellows with nominally U-shaped corrugations:
3
 e* 
1
p 
KB =
⋅EB ⋅
⋅ Dm ⋅ 
⋅


2
N
 w - rm  C f
2 ⋅ 1 -νB


π
(
np
)
c) Toroidal bellows:
3
 e* 
1
p 
KB =
⋅EB ⋅
⋅ Dm ⋅ 
⋅ B3
r 
2
N
 m
12 ⋅ 1 - ν B


(
)
np
(36)
(37)
where B3 is given in Formula (155).
47
BS EN 14917:2021
EN 14917:2021 (E)
Correction factor for allowable meridional stresses regarding the influence of cold work:
 R* + 2 ⋅ R* + R*
e,m
e,i

 e,o
Kf = 
2 ⋅ R p1,0
 1, 5


for as formed bellows
for annealed bellows (without cold work)
(38)
where the R e* values are at room temperature and the indices “i”, “m”, and “o” mean inside, middle, and
outside:
( )
m
(
)
( )
m
*
R e,o
= R p1,0 ⋅ c * ⋅ s d,o
*
R e,m
= R p1,0 ⋅ c * ⋅ s d,m
*
R e,i
= R p1,0 ⋅ c * ⋅ s d,i
(39)
m
(40)
and material-dependent basic factors acc. to Table 8 are:
(41)
c*, m.
Correction factor for the normalized equivalent axial displacement regarding the influence of cold work:
K sr
where
 R* +R*

e,i,t
 e,o,t
= 
2 ⋅ R p1,0,t

1


for as formed bellows
for annealed bellows (without cold work)
( )
*
= R p1,0, t ⋅ c * ⋅ s d,o
R e,o,t
( )
*
R e,i,t
= R p1,0, t ⋅ c ∗ ⋅ s d,i
m
(43)
m
Normalized equivalent axial displacement including all movements actually acting on a bellows:
*
∆q =
(
3
4 ⋅ 1 -ν 2
⋅
e p*
) w
2
(42)
⋅
EB
K sr ⋅ R p0,t
⋅
∆q
Cd
with R p0, t acc. to Table 14.
(44)
(45)
Dynamic factor for column instability:
 1
for ∆q * ≤ 1 + n t

-3
n t -1

a t ⋅ ∆q *
- b t ⋅ ∆q *

c dyn,t = 
for ∆q * > 1 + n t

-3 

n
-1
t - b ⋅ ∆q *

2 -  a t ⋅ ∆q *

t






( )
( )
48
( )
( )
(46)
BS EN 14917:2021
EN 14917:2021 (E)
Effective friction factor regarding friction between the plies:

* 
µ = µ 0 ⋅  1 - e - ∆q 

NOTE

A value of μ0 = 0,3 has proved to give realistic results for stainless steel.
Calculation factor used for pressure influence on curved bellows:
κ = 2⋅π ⋅
P
K B ⋅ lB
6.2.2.5.2 Equivalent true strain in bellows corrugations
(47)
(48)
6.2.2.5.2.1 True strain in nominal U-shaped bellows made from cylindrical tubes
The true strain after the forming process is depending on the location – crest or root – in the corrugation
profile.
The true strain at the crest (outside) of the corrugation is given by:
s d,o = 1, 04 ⋅ sΘ2 ,o + 0,31 ⋅ sΘ ,o ⋅ s b,o + 0, 41 ⋅ s b,o 2
where the components of the true strain are:
— circumferential component:
(
)
(49)
 D +2⋅w 
i

sΘ ,o = ln 
 D + 2 ⋅η ⋅ w 
 i

(50)
e p,o 
1 

In 1 +
2 
ri,c 


(51)
(
)
— maximum bending component of the inner ply:
s b,o =
For in-plane instability the mean bending component shall be used.
— maximum bending component of the mean ply:
s b,o =
e p,o
1 
In 1 +
2 
rm - 0, 5 ⋅ e p,o





The true strain at the root (inside) of the corrugation is given by:


1
s d,i = 2 ⋅  sΘ ,i + s b,i 
3


where the components of the true strain are:
(52)
(53)
— circumferential component:
49
BS EN 14917:2021
EN 14917:2021 (E)


Di

sΘ ,i = ln 
 D + 2 ⋅η ⋅ w 
i


(54)
e p,i 
1 

In 1 +
2 
ri,r 


(55)
(
)
— maximum bending component of the outer ply:
s b,i =
For the in-plane instability the mean bending component shall be used.
— maximum bending component of the mean ply:
sb,i =

ep,i
1 
In  1 +


2 
rm - 0,5 ⋅ ep,i 
(56)
The forming factor η which is depending on the forming process is given by Formula (30); see also
Table 6.2.2.5-2 for information.
The true strain at the middle of the corrugation is given by:
sd,m = 1,04 ⋅ sθ ,m
where the circumferential component of the true strain is:
 Di + w 
sθ ,m = ln 

 Di +2 ⋅η ⋅ w 
6.2.2.5.2.2 True strain in bellows made from half-corrugations
(57)
(58)
Half-corrugations for this type of bellows are manufactured from ring plates with a centre hole bending
their outer and inner edges to an S-shaped profile by rolling or other methods. Where a cold forming
process is applied, true strain and cold work shall be taken into consideration.
The original diameter of the ring plate – outside or inside – can be calculated from the ready formed Sshaped profile of the half corrugation as follows; see Figure 4:
— for the outside (crest):
m
π

Dn,o = Do - e p +  - 1  ⋅ 2ri,c + e p + e
2
2

(59)
m

π

Dn,i = Di + e p -  - 1  ⋅ 2ri,r + e p − max  i ; Lt 
 2

2 


(60)


1
s d,o = 2 ⋅  sΘ ,o + s b,o 
3


(61)
— for the inside (root):
(
(
)
)
The true strain at the crest (outside) of the corrugation is given by:
where the components of the true strain are:
50
BS EN 14917:2021
EN 14917:2021 (E)
— circumferential component:
(
)
 D -e 
o
p 
sΘ ,o = ln 
Dn,o 


— bending component:
e 
1 
sb,o = In  1 + p,o 
2 
ri,c 
with ep,o acc. to Formula (11)
(62)
(63)
Figure 4 — Root and crest of a half-corrugation
The true strain at the root (inside) of the corrugation is given by:
sd,i = 1,04 ⋅ sΘ2 ,i + 0,31 ⋅ sΘ ,i ⋅ sb,i + 0, 41 ⋅ sb,i2
where the components of the strain are:
(64)
— circumferential component:
 ( Di + ep ) 
sΘ ,i = ln 

 Dn,i 
— bending component:
e 
1 
sb,i = In  1 + p,i 
2 
ri,r 
with ep,i acc. to Formula (12)
The true strain at the middle of the corrugation is given by:
s d,m = 1, 04 ⋅ sθ ,m
(65)
(66)
(67)
51
BS EN 14917:2021
EN 14917:2021 (E)
where the circumferential component of the true strain is:

Di + w
sθ ,m = ln 
 D i + 2 ⋅η ⋅ w





6.2.2.5.2.3 True strain in toroidal bellows
(68)
The true strain after a cold forming process is depending on the location in the toroidal profile according
to Figure 16.
The true strain at the outside of the torus is given by:
sd,o = 1,04 ⋅ sΘ2 ,o + 0,31 ⋅ sΘ ,o ⋅ sb,o + 0, 41 ⋅ sb,o2
where the components of the true strain are:
— circumferential component:
(69)
 ( Do - ep ) 
sΘ ,o = ln 

 ( Di + ep ) 
(70)
e 
1 
sb,o = In  1 + p,o 
2 
rm 
(71)
— bending component:
The true strain caused by deformation at the two small radii in the root shall be regarded in addition:
— Position (1) related to Rc1:
2
sd,r1 = 1,04 ⋅ sΘ2 ,1 + 0,31 ⋅ sΘ ,1 ⋅ sb,1 + 0, 41 ⋅ sb,1
with the specific components:
 2 ⋅ (Rc1 + e ) 
sΘ ,1 = In 1 +

Di


e 
1 
sb,1 = In 1 + p 
2 
Rc1 
— Position (2) related to Rc2:
2
sd,r2 = 1,04 ⋅ sΘ2 ,2 + 0,31 ⋅ sΘ ,2 ⋅ sb,2 + 0, 41 ⋅ sb,2
with the specific components:
52
(72)
(73)
(74)
(76)
BS EN 14917:2021
EN 14917:2021 (E)

2 ⋅ ( R c2 + e ) 

sΘ ,2 = In 1 +
Di




s b,2 =
ep 
1 

In 1 +
2 
R c2 


The true strain at the middle of the corrugation is given by:
s d,m = 1, 04 ⋅ sθ ,m
where the circumferential component of the true strain is:

Di + w
sθ ,m = ln 
 D i + 2 ⋅η ⋅ w





6.2.2.5.3 Shell coefficients
(77)
(78)
(79)
(80)
The shell coefficients Cp, Cf, and Cd are used for the calculation of stresses and spring rates. They shall be
taken from the following graphs or be calculated by polynomial approximations (see Annex G).
53
BS EN 14917:2021
EN 14917:2021 (E)
Figure 5 — Bending stress coefficient Cp
54
BS EN 14917:2021
EN 14917:2021 (E)
Figure 6 — Spring rate coefficient Cf
55
BS EN 14917:2021
EN 14917:2021 (E)
Figure 7 — Deflection coefficient Cd
6.2.3 Design of U-shaped unreinforced bellows
6.2.3.1 General
This subclause applies to two types of unreinforced bellows having nominally U-shaped corrugations
according to the limitations given in 6.2.3.2.
— Those shown in Figure 8 are generally manufactured by a forming process (e.g. hydraulic forming,
roll forming) without any circumferential welding in the corrugations. This type of bellows is covered
by 6.2.3.2 to 6.2.3.5.
56
BS EN 14917:2021
EN 14917:2021 (E)
— Those shown in Figure 12 are of single ply construction where the corrugations have circumferential
welds at their roots and crests. This type of bellows is covered by requirements of 6.2.3.6.2 to
6.2.3.6.5.
Key
1
2
3
4
5
6
7
end tangent without reinforcing collar
corrugation
corrugation crest
corrugation root
reinforcing collar
end tangent with reinforcing collar
pipe where applicable
Figure 8 — U-shaped unreinforced bellows
6.2.3.2 Limitations
The following conditions shall apply in addition to those listed in 6.2.2:
a) the internal radius of the knuckle ri at the crest and the root of the corrugations shall be nominally
the same.
A variation of ± 10 % between the real radiuses at the crest ric or the root rir in relation to the mean
value ri is permitted (see Figure 9 for definitions of ric and rir).
b) the knuckle radius shall be such that:
ri ≥ 2 ⋅ ep
c) the corrugation height shall be such that:
Di
3
≥ w ≥ 2 ⋅ rm
d) the off-set angle β0 of the sidewalls in the neutral position (see Figure 9) shall be such that:
-15° ≤ β 0 ≤ +15°
(81)
(82)
(83)
57
BS EN 14917:2021
EN 14917:2021 (E)
where


2

 w - 2 ⋅ rm 
4 ⋅ rm 
w - 2 ⋅ rm 

 180





+ 4⋅
-2⋅
β0 =  2 ⋅ 1 ⋅



q 
q
q

 π








(84)
In addition it shall be checked if the side wall angle β0 in the neutral position is limited by the
intended movement which may lead to blocking in the case of compression or to buckling when
extending movement is foreseen (see 6.2.8.2).
e) The corrugation length shall be such that:
(
(
)
)

2 r + e 

q > max  ic

r
e
2
+
 ir



(85)
Figure 9 — Possible configuration shapes in the neutral position
6.2.3.3 Internal pressure capability
6.2.3.3.1 Limitation due to stresses
6.2.3.3.1.1 Circumferential membrane stresses due to pressure
a) End tangent:
The cylindrical end tangent of a pressurized bellows (see Figure 8) will partly be supported by the
fitting to which it is welded.
Where the length of the bellows tangent without any collar but, including a possible cylindrical part
of same thickness of a weld end Lt (see Table 7, No 3.0, General design) fulfils the following
condition no stress calculation is required for the tangent:
Lt ≤ 0, 5 ⋅ Di,t ⋅ e
58
BS EN 14917:2021
EN 14917:2021 (E)
Otherwise the circumferential membrane stress due to pressure of a tangent without a collar is given
by:
σ Θ ,t ( P ) =
D i,t ⋅ k t
2⋅e
⋅P
(86)
When the tangent is reinforced by a collar the circumferential membrane stress due to pressure is
given by:
( ) 12
σ Θ ,t P =
D i,t ⋅ Lt ⋅ E B ⋅ Dc ⋅ k t ⋅ k c
Dc ⋅ e ⋅ Lt ⋅ E B ⋅ k c +  D i,t + e  ⋅ e c ⋅ Lc ⋅ E c ⋅ k t


⋅P
(87)
b) Reinforcing collar:
The circumferential membrane stress due to pressure of the collar is given by:
D i,t ⋅ Lt ⋅ E c ⋅  D i,t + e  ⋅ k t ⋅ k c
1


⋅P
σ Θ ,c ( P ) =
2 D ⋅ e ⋅ L ⋅ E ⋅ k + D + e ⋅ e ⋅ L ⋅ E ⋅ k
 c c
c
t
B
c  i,t
c
t


c) Bellows corrugations:
(88)
— End corrugations
The circumferential membrane stress due to pressure is given by:
σΘ , E (P ) =
where
(
)


1  q + ∆q e ⋅ Dm - Ac  + Lt ⋅ Di,t
⋅
⋅P
Ac + e ⋅ Lt + e c ⋅ Lc
2
e c ⋅ Lc + e ⋅ Lt
shall be replaced by
2 ⋅ e ⋅ Lt
for
e c ⋅ Lc > e ⋅ Lt
(89)
NOTE The influence of a collar shall be limited to a cross section similar to the cross section of the tangent.
— Intermediate corrugations
The circumferential membrane stress due to pressure is given by:
σΘ , I (P ) =
(
)
1 q + ∆q e ⋅ Dm - Ac
⋅
⋅P
Ac
2
where q + ∆qe is the longest occurring corrugation length in operating condition.
(90)
The circumferential membrane stresses of all individual components shall comply with the allowable
stress for the material related to the regarded part:
59
BS EN 14917:2021
EN 14917:2021 (E)
For bellows with W1 welds:
σ Θ ( P ) ≤ f , below the creep range or
σ Θ ( P ) ≤ f cr , in the creep range.
For bellows with W2 welds:
σ Θ ( P ) ≤ z ⋅ f , below the creep range or
σ Θ ( P ) ≤ z ⋅ f cr , in the creep range.
6.2.3.3.1.2 Meridional stresses due to pressure
The meridional membrane stress due to pressure is given by:
σ m, m ( P ) =
w
2 ⋅ e*
⋅P
The meridional bending stress due to pressure is given by:
(91)
2
1 cn(P)  w 
σ m, b ( P ) =
⋅
⋅ Cp ⋅ P
2 np  ep* 
 
(92)
With the correction factor for multi-ply bellows cn(P) according to Formula (21). For one ply cn(P) = 1 .
The meridional membrane and bending stresses shall comply with:
σ m, m ( P ) + σ m, b ( P ) ≤ f ⋅ K f , below the creep range;
 σ (P ) 
σ m, m ( P ) +  m,b  ≤ fcr , in the creep range.
 1,25 
6.2.3.3.2 Limitation due to instability
6.2.3.3.2.1 Column instability
To avoid column instability the different types of expansion joints have to be regarded under different
conditions.
Where expansion joints consists of more than one bellows but, having guided intermediate pipes each
bellows will behave as a single bellows. The guide shall not allow relative lateral and angular movement
between the intermediate pipe and the guide.
a) Internal Pressure – Operating and Test in the work shop
PSC,t =
60
1 2 ⋅ π K B,t
⋅
⋅
⋅ c dyn ⋅ k S ⋅ K Θ
2
2
lB
*
nB
( )
(93)
BS EN 14917:2021
EN 14917:2021 (E)
PSC,T =
1
2 ⋅ π K B,T
⋅
⋅
⋅ c dyn ⋅ k S ⋅ K Θ
2
1, 4
lB
*
nB
( )
with
c
c dyn =  dyn,t
1
(94)
at operating condition acc. to Formula (46)
at test condition (without displacement)

for stabilized bellows (e.g. by pre - compressing to block or
1
kS = 
stress releasing heat treatment
0,5 for non - stabilized bellows (as formed)


at operating / test cond. for axial / universal and test cond. for

1
angular / lateral expansion joints
KΘ = 
 1 - ν 2 at operating condition for angular and lateral expansion joints


)
(

1
nB* = 
n

 B
for expansion joints with guided intermediate pipe
for expansion joints without guided intermediate pipe
and the equalised length of one bellows (after some cycles, if applicable):
(
lB = l B + 0,5 x 1 + x 2
) n1
B
(95)
where x1 and x2 are understood as the initial maximum values of axial displacement for the complete
expansion joint at the extreme positions of a cycle with positive sign for extension and negative sign
for compression. The equalised length lB of each single bellows is shown in Figure 10. In test condition
x1 and x2 are usually 0.
Figure 10 — Corrugated length and axial displacements shown for one bellows (nB = 1)
61
BS EN 14917:2021
EN 14917:2021 (E)
The maximum allowable pressure PS shall not exceed the limiting pressure PSC,t at design
temperature:
PS ≤ PSC,t
The test pressure PT shall not exceed the limiting pressure PSC,T at test conditions:
PT ≤ PSC,T
b) Internal Pressure - Test on site after/during operation
(
)( )
K x,T + K β x,T ⋅ ± x
K B,T
1
2 ⋅π
4
PSC,T =
⋅
⋅
+
×
2 
2
1, 4
nB
x  π ⋅ Dm
*
nB
 lB ±



nB 

( )
(96)
with parameters acc. to a) and:
— the effective spring rate K x, T for one bellows according to Formula (212) at test conditions,
— the factor K β x, T according to Formula (213) at test conditions,
— the mean axial displacement of the expansion joint (see Figure 10)
x = 0, 5 ⋅ x 1 - x 2
The test pressure PT shall not exceed the limiting pressure PSC,T at test conditions:
(97)
PT ≤ PSC,T
c) External Pressure
The axial force induced by axial compression of the bellows may cause column instability without
internal pressure acting on the bellows.
The allowable axial compressing force increased by external pressure Pext acting on the bellows at
the same time is given by:
FSC,t =
FSC,T =
62
2
2
2
2
D
D
1
2π 2
⋅
⋅ m ⋅ K B,t ⋅ c dyn + π ⋅ m ⋅ Pext
2
1, 4 
4
4
x 
 lB  ⋅ nB*

nB 

( )
D
D
1
2π 2
⋅
⋅ m ⋅ K B,T ⋅ c dyn + π ⋅ m ⋅ Pext
2
1, 4 
4
4
x 
 lB  ⋅ nB*


nB 

( )
(98)
(99)
BS EN 14917:2021
EN 14917:2021 (E)
with parameters acc. to a).
The maximum force from axial displacement shall not exceed the allowable force at design
temperature:
(K + K ) ⋅ - nx ≤ F
x,t
β x,t
SC,t
B
The maximum force from axial displacement shall not exceed the allowable force at test conditions:
(K + K ) ⋅ - nx ≤ F
x,T
β x,T
SC,T
B
6.2.3.3.2.2 In-plane instability
The allowable internal pressure to avoid in-plane instability is given by:
Psi ,t =
Psi,T =
*
1+1,5 ⋅ n Re, min,t
⋅
⋅ K ∆β ⋅ K N
2
Kθ ⋅ α
*
1+1,5 ⋅ n Re, min,T
⋅
⋅ K ∆β ⋅ K N
1, 4
Kθ ⋅ α
with the parameters:
(100)
(101)
— The minimum local yield strength at the crest or the root of the corrugation based on Formulae (27),
28, 29):
— for as-formed bellows with cold work:
(
*
R e,min,t
= R p1,0,t ⋅ c * ⋅ s d,min
(
*
R e,min,T
= R p1,0,T ⋅ c * ⋅ s d,min
) at operating condition
m
) at test condition
m
where the minimum true strain is given by:
 s
according to Formula (49)
s d,min = min  d,o
s
 d,i according to Formula (53)
calculated with s b,o and s b,i , according to Formulae (52) and (56) respectively.
— for bellows annealed according to Table 8 (without cold work):
*
R e,min,t
= R p 1,0,t at operating condition
*
R e,min,T
= R p1,0,T at test condition
(102)
(103)
(104)
(105)
(106)
63
BS EN 14917:2021
EN 14917:2021 (E)
— for otherwise annealed bellows:
*
R e,min,t
= R p 1,0,t ⋅ 0, 9 at operating condition
*
R e,min,T
= R p1,0,T ⋅ 0, 9 at test condition
(107)
(108)
R p1,0, t and R p1,0, T shall be replaced by R p0,2, t and R p0,2, T if R p1,0, t and R p1,0, T are not available or allowed
(e.g. Ni-alloys).
For ferritic materials R e* is equal to R eH .
— A stress capacity relation:
K m,b
δ =
with
3⋅ Kθ
(109)
α = 1 + 2⋅δ 2 + 1 - 2⋅δ 2 + 4 ⋅δ 4
— the meridional bending stress capacity:
2

w
1
K m,b =
⋅
2 ⋅ np  e *
 p

 ⋅C
p



(111)
— the circumferential stress capacity:
Kθ =
(110)

1  4 ⋅ rm ⋅ Dm
⋅
-1 

2 
Ac


(112)
q + ∆qc
4 ⋅ rm
(113)
— a factor regarding the deviation of the corrugation length q from the pure u-shape:
K ∆β =
where q + ∆q c is the shortest occurring corrugation length in operating or test condition
— an increasing factor for small number of corrugations:
(
)
(
K N = 1 - 0, 02 ⋅ N -7 + 0, 03 ⋅ N -7
) for 2 ≤ N ≤7; for N > 7: KN = 1
2
and material-dependent basic factors according to Table 8:
c*, m.
64
(114)
BS EN 14917:2021
EN 14917:2021 (E)
The maximum allowable pressure PS shall not exceed the limiting pressure Psi,t at design temperature:
PS ≤ Psi,t
The test pressure PT shall not exceed the limiting pressure Psi,T at test conditions:
PT ≤ Psi, T
6.2.3.4 External pressure capability including vacuum
6.2.3.4.1 General
The limitations in 6.2.3.2 and the stress calculation method in 6.2.3.3 shall be applied accordingly taking
P with a positive sign as the maximum difference between external and internal pressure.
Special care shall also be given to the fact that reinforcing members are no longer supporting tangents
and corrugations. In addition, the pressure area of a corrugation is increased by the corrugation’s metal
area instead of being decreased; i.e. ( q ⋅ Dm + Ac ) in the Formulae (89) and (90).
When a bellows designed for internal pressure within its working conditions is also submitted to vacuum,
the design for this condition shall be performed assuming that only the internal ply resists the pressure.
Thus the pressure stress equations of 6.2.3.3.1 shall be applied with np = 1.
NOTE
The calculation methods can accordingly be applied to bellows which are subjected to vacuum only,
though they are not within the scope of this document.
6.2.3.4.2 Instability due to external pressure
This design shall be performed according to external pressure design rules by replacing the bellows with
an equivalent cylinder.
The dimensions of the equivalent cylinder shall be defined as follows:
— the equivalent thickness eeq is given by:
(
)
I
e eq = 3 12 ⋅ 1 - v 2 ⋅ xx
q
where the moment of inertia for one corrugation cross section is given by:
3


2
 2⋅w - q
I xx = e ⋅ 
+ 0, 4 ⋅ q ⋅ w - 0, 2 ⋅ q 
48




*
(
)
(
)
— the equivalent mean diameter is given by:
Deq = Di + w + 2 ⋅ e eq
(115)
(116)
(117)
65
BS EN 14917:2021
EN 14917:2021 (E)
Figure 11 — Cross section for moment of inertia Ixx
The allowable external pressure Pcir is given by:
Pcir,t =
2 ⋅ E B,t
3
 e eq 

⋅
 Deq 


3
with a safety factor of 3 included and
Pcir,T =
2 ⋅ E B,T
2, 25
 e eq 

⋅
 Deq 


3
(118a)
(118b)
with a safety factor of 2,25.
The external working pressure shall not exceed Pcir:
PS ≤ Pcir
The external test pressure PT shall not exceed Pcir, T:
PT ≤ Pcir, T.
NOTE 1
The moment of inertia Ixx is understood as that of one corrugation cross section relative to the axis
passing through the centre of gravity and parallel to the axis of the bellows (see Figure 11).
NOTE 2
The allowable external design pressure to avoid circumferential instability is based on the behaviour of
an infinitely long cylinder.
NOTE 3
Consideration of the influence of the attached piping may be included if subject to detailed analysis.
6.2.3.5 Stresses due to displacement
6.2.3.5.1 Stresses due to equivalent axial displacement
The following stresses which are the basic stresses for the calculation of fatigue cycles are calculated from
the total equivalent axial displacement range Δq relating to the bellows’ corrugation according to 6.2.7
and 6.2.8.
Meridional membrane stress range:
66
BS EN 14917:2021
EN 14917:2021 (E)
( )
σ m, m ∆q =
( ) ⋅ ∆q
E B,20 ⋅ e p*
2
(119)
2 ⋅ w3 ⋅ Cf
Meridional bending stress range:
( )
σ m, b ∆q =
(
3
2 ⋅ 1 -ν 2
⋅
E B,20 ⋅ e p*
) w ⋅c
Total equivalent stress range:
2
2
c(d) ⋅ C d
(120)
⋅ ∆q
( )
( )
σ eq = 0,7 ⋅ σ m, m ( P ) + σ m, b ( P ) + σ m, m ∆q + σ m, b ∆q 

 

6.2.3.6 Bellows with circumferential welds
(121)
6.2.3.6.1 Scope
This subclause applies to unreinforced namely U-shaped bellows of single ply fabricated from two
symmetrical half-corrugations joined by circumferential butt welds:
— either directly (Figure 12 a));
— or by means of a cylindrical shell (Figure 12 b));
— or by means of short integral cylindrical parts obtained by forming to facilitate welding
(Figure 12 c)). Details are shown in Figure 13.
Each of the half-corrugations consists of one single seamless element or is formed from several elements
joined by meridional butt welding (Figure 12 d)).
67
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 circumferential welds
2 meridional welds
Figure 12 — U-shaped bellows with circumferential welds
6.2.3.6.2 Limitations
Where short integral cylindrical parts on the two half-corrugations are used, they have together a length
mi at the root and me at the crest (see Figure 13).
To avoid special calculation of the circumferential stresses for the cylindrical parts their length mi or me
shall conform to:
mi 
me  ≤ 0, 5 ⋅ Dm ⋅ e p

To be used instead of formulas in 6.2.3.2.


2


4 ⋅ rm
 w − 2 ⋅ rm 
 w − 2 ⋅ rm  
 180



 −2⋅
 ⋅
β0 =  2 ⋅ 1 −
+ 4⋅





q - me - mi 

 q - me - mi 
 q - me - mi   π







q > max 


68
mi 

2
2 
m
m
2(rir + e ) + e + i 
2
2 
2(ric + e ) +
me
+
BS EN 14917:2021
EN 14917:2021 (E)
Figure 13 — U-shaped corrugations with integral cylindrical part
For checking the condition in 6.2.3.2 d) Formula (84) shall be replaced by:


2


4 ⋅ rm
 w − 2 ⋅ rm 
 w − 2 ⋅ rm  
 180

 + 4⋅
 −2⋅
 ⋅
β0 =  2 ⋅ 1 −






q - me - mi

 q - me - mi 
 q - me - mi   π





For checking the condition in 6.2.3.2 f) Formula (85) shall be replaced by:


q > max 


mi 

2
2 
m
m
2(rir + e ) + e + i 
2
2 
2(ric + e ) +
me
+
6.2.3.6.3 Internal pressure capability
6.2.3.6.3.1 Limitation due to stresses
The requirements of 6.2.3.3.1 shall apply with the following modification:
Bellows corrugations:
— End corrugations:
The circumferential membrane stress due to pressure is given by:
σΘ , E (P ) =
(
)
(
) (
)
)
1 q - m i ⋅ D m + me ⋅ w + L t + m i / 2 ⋅ D i + e
⋅
⋅P
2
Ac + e * ⋅ me + Lt + mi / 2
— Intermediate corrugations:
(
(122)
The circumferential membrane stress due to pressure is given by:
69
BS EN 14917:2021
EN 14917:2021 (E)
σΘ , I (P ) =
(
)
(
)
1 q - m i ⋅ D m + me ⋅ w + m i ⋅ D i + e
⋅
⋅P
2
Ac + e * ⋅ me + mi
(
)
(123)
6.2.3.6.3.2 Limitation due to instability
The requirements of 6.2.3.3.2 shall apply with the following modification:
— s d,o according to Formula (61);
— s d,i according to Formula (64).
6.2.3.6.4 External pressure capacity
The requirements of 6.2.3.4 shall apply.
6.2.3.6.5 Stresses due to displacement
6.2.3.6.5.1 General
The equivalent stress range which is the basis for the calculation of the expected number of cycles is
depending on the maximum cyclic stresses due to displacement which may be influenced and increased
by circumferential welds in the knuckles or in the tangent of the corrugation.
The magnitude of stress increase by circumferential welds is depending on the design which is
characterized here by the sell coefficient Cd.
6.2.3.6.5.2 Maximum equivalent stress range
Two areas (1) and (2) have to be regarded.
6.2.3.6.5.3 Shell coefficient Cd < 1,2
The maximum equivalent stress range occurs always in the bellows sidewall (no circumferential weld).
The requirements of 6.2.3.5.1 shall apply and the maximum equivalent stress range is given by:
( )
( )
σ eq = 0,7 ⋅ σ m, m ( P ) + σ m, b ( P ) + σ m, m ∆q + σ m, b ∆q 

 

(124)
where the different stress components are calculated according to the Formulae (91), (92), (119) and
(120) and Δq according to 6.2.7 and 6.2.8.
6.2.3.6.5.4 Shell coefficient Cd ≥ 1,2
The maximum stress range occurs either in the sidewall or in a knuckle or in the tangent.
The requirements of 6.2.3.5.1 shall apply with the following modifications which depend on the three
different locations within the corrugation.
a) Sidewall (no circumferential weld):
The maximum equivalent stress range is given by Formula (124) above.
b) Knuckles where circumferential welds exist:
The maximum equivalent stress range is given by:
70
BS EN 14917:2021
EN 14917:2021 (E)


σ eq = c w ⋅ 0,7 ⋅ σ m, m ( P ) + σ m, b ( P ) + σ v ∆q 




( )
where the effective stress intensity σ v ( ∆q ) is given by:
2
2
σ v ( ∆q ) = σ m ( ∆q )  + σ Θ ( ∆q )  - σ m ( ∆q ) ⋅ σ Θ ( ∆q )




The two stress components σ m ( ∆q ) and σ Θ ( ∆q ) are given below.
i.
The meridional stress component is given by:
( )
( )
( )
σ m ∆q = σ m, m ∆q + σ m, b,k ∆q
where
(125)
(126)
(127)
the meridional membrane stress σ m, m ( ∆q ) is given by Formula (119);
the meridional bending stress σ m,b,k ( ∆q ) in the knuckles is given by:
σ m,b,k ( ∆q ) = σ m, b ( ∆q ) ⋅ f ro
(128)
where the maximum bending stress in the sidewall σ m, b ( ∆q ) − Formula (120) – is reduced up to the
knuckle by the run-out factor f ro :


∆LM + 0,5 ⋅ me 

f ro =  1  ⋅ 1 - w Dm , for the crest
 0, 4 ⋅ D + w ⋅ e * 
m
p 

(
(
)
)


∆LM + 0,5 ⋅ mi 

f ro =  1  ⋅ 1 + w Dm , for the root
 0, 4 ⋅ D - w ⋅ e * 
m
p 

(
)
(
)
Therein the maximum cylindrical length ∆LM of the curved part of the knuckle is given by:
(
)
∆LM = 0,5 ⋅ w ⋅ 1 - 3 C d + 1, 4 ⋅ rm - e p 


(129)
(130)
(131)
Only the factor of the knuckle with a circumferential weld has to be taken into consideration; the
maximum value of f ro shall be used if both knuckles have circumferential welds.
ii. The circumferential stress component due to equivalent axial displacement is given by:
71
BS EN 14917:2021
EN 14917:2021 (E)
σ Θ ( ∆q ) = ν ⋅ σ m ( ∆q ) + 0, 22 ⋅ E B ⋅
c) Tangent
rm
w ⋅ Dm
(132)
⋅ C d ⋅ ∆q
The maximum equivalent stress range near the attachment weld is given by:


σ eq = c w ⋅ 0,7 ⋅ σ m, m ( P ) + σ m, b ( P ) + σ m,b,t ∆q  ,




(133)
 

∆ l M + Lt
 

σ m,b,t ∆q = σ m,b ∆q ⋅ max 0;  1 
  0, 4 ⋅ Dm - w ⋅ e p  

 
(134)
( )
where the reduced meridional bending component σ m,b,t ( ∆q ) is given by:
( )
( )
(
)
and the remaining parameters σ m,b ( ∆q ) and ∆LM are given above.
The stress increasing weld factor c w at the circumferential welds is recommended to be: c w = 2
The maximum value σ eq ( ∆q ) from the locations 1) to 3) shall be taken for the calculation of expected life
cycles.
6.2.4 Design of U-shaped reinforced bellows
6.2.4.1 General
This subclause applies to bellows having nominally U-shaped corrugations with rings to reinforce the
bellows against internal pressure (see Figure 14).
The rings may have a divergent cross section in relation to the drawing but, shall in any case have radii
rir on both sides in contact with the corrugations and a cylindrical area in between in contact with the
intermediate tangents of the bellows (see Figure 15). Where applicable, the relevant equations shall be
adjusted.
The end reinforcing members shall be restrained against the longitudinal annular pressure load of the
bellows. If gussets are used the end reinforcing members shall be calculated similar to toroidal bellows
(see 6.2.5.4.2).
72
BS EN 14917:2021
EN 14917:2021 (E)
Key
1
2
3
4
end tangent corrugation
reinforcing collar
reinforcing ring
corrugation
5
6
7
8
corrugation crest
corrugation root
equalizing ring
end equalizing ring
Figure 14 — U-shaped reinforced bellows
6.2.4.2 Limitations
The conditions listed in 6.2.2 and 6.2.3.2, a) to d) shall apply.
In the case of divergent specific cross section according to Figure 15 q* shall be used instead of q for
6.2.3.2, d) and e):
q* = q - ∆ L
(135)
Figure 15 — Reinforcing member with specific cross section
73
BS EN 14917:2021
EN 14917:2021 (E)
6.2.4.3 Internal pressure capability
6.2.4.3.1 Limitation due to stresses
6.2.4.3.1.1 Circumferential membrane stress due to pressure
a) End tangent:
( )
σ Θ ,t P =
D i ⋅ L t ⋅ E B ⋅ Dc


2 ⋅  Dc ⋅ e ⋅ Lt ⋅ E B +  D i + e  ⋅ e c ⋅ Lc ⋅ E c 




b) Reinforcing collar:
⋅P
D i ⋅ Lt ⋅ E c ⋅  D i + e 


⋅P
σ Θ ,c ( P ) =




2 ⋅  Dc ⋅ e ⋅ Lt ⋅ E B +  D i + e  ⋅ e c ⋅ Lc ⋅ E c 




c) Bellows corrugations:
( ) 12 ⋅ D
σΘ P =
q ⋅ Dm ⋅ Dm,r ⋅ E B
m,r ⋅ Ac ⋅ E B + D m ⋅ Ar ⋅ E r
d) Reinforcing member:
( ) 12 ⋅ D
σΘ , r P =
2
q ⋅ Dm
⋅ Er
(136)
(137)
⋅P
(138)
⋅P
(139)
m r ⋅ Ac ⋅ E B + D m ⋅ Ar ⋅ E r
The circumferential membrane stresses of all individual parts shall comply with the allowable stress for
the material related to the regarded part:
— σ Θ ( P ) ≤ z ⋅ f , below the creep range or
— σ Θ ( P ) ≤ z ⋅ f cr , in the creep range.
NOTE
In the case of reinforced members which are made in sections and joined by fasteners in tension, this
equation assumes that the structure used to retain the fastener does not bend or extend so as to permit the
reinforcing member sections to open gaps.
6.2.4.3.1.2 Meridional stresses due to pressure
a) The meridional membrane stress is given by:
σ m, m ( P ) =
0,76 ⋅ w - rm 
2⋅e*
⋅P
b) The meridional bending stress is given by:
2


0,76  w - rm 
σ m, b ( P ) =
⋅
⋅ Cp ⋅ P
2 ⋅ np  e * 
p


74
(140)
(141)
BS EN 14917:2021
EN 14917:2021 (E)
The meridional membrane and bending stresses shall comply with:
— σ m, m ( P ) + σ m, b ( P ) ≤ f ⋅ K f , below the creep range;
 σ m,b ( P ) 
 ≤ f , in the creep range.
cr
 1, 25 


— σ m, m ( P ) + 
6.2.4.3.2 Limitation due to instability
6.2.4.3.2.1 Column instability
The requirements of 6.2.3.3.2 apply using the smallest possible spring rate which is based on
Formula (36) and given by:
KB =
(
π
)
2 ⋅ 1 - ν B2
3


e p*

 ⋅ 1
⋅EB ⋅
⋅ Dm ⋅


N
 w - 0,33 ⋅ rm  C f


np
(142)
6.2.4.3.2.2 In-plane instability
Reinforced bellows are not subject to in-plane instability.
6.2.4.4 Stresses due to displacement
6.2.4.4.1 Stresses due to equivalent axial displacement
The following stresses which are the basic stresses for the calculation of fatigue cycles are calculated from
the total equivalent axial displacement range Δq of each corrugation according to 6.2.7 and 6.2.8.
Meridional membrane stress range:
( )
σ m, m ∆q =
( )
E B,20 ⋅ e p*
(
2 ⋅ w - rm
2
) ⋅ Cf
(143)
⋅ ∆q
3
Meridional bending stress range:
( )
σ m, b ∆q =
(
2 ⋅ 1 -ν
2
3 ⋅ E B,20 ⋅ e p*
) ⋅ (w - C ⋅ r )
Total equivalent stress range:
r
m
2
2
⋅ 0, 25 ⋅ c c(d)
⋅ Cd
(144)
⋅ ∆q
σ eq = 0,7 ⋅ σ m, m ( P ) + σ m, b ( P ) + σ m, m ( ∆q ) + σ m, b ( ∆q )

6.2.5 Design of toroidal bellows



(145)
6.2.5.1 Scope
This subclause applies to bellows having toroidal corrugations as shown in Figure 16. Each corrugation
consists of a torus with radius r.
75
BS EN 14917:2021
EN 14917:2021 (E)
Two design cases are considered:
I
external collar:
II
welding end collar:
The tangent of the bellows is welded externally to the welding end. The collar is additional item acting
like a reinforcing ring. This collar shall be fixed by reinforcing gussets to balance the bellows pressure
thrust.
The tangent of the bellows is welded internally to the welding end. The extreme part of the welding
end is acting like a reinforcing member, and the pressure thrust is directly balanced by the welding
end itself.
The different design cases are regarded particularly for the calculation.
The general conditions of applicability listed in 6.2.2 apply.
Key
I design with external collar
1
2
3
welding end
gussets
external collar
II
4
5
6
design with welding end collar
corrugation (Torus)
intermediate collar
welding end collar
Figure 16 — Toroidal bellows
6.2.5.2 Limitations
The following conditions of applicability are in addition to those listed in 6.2.2:
76
BS EN 14917:2021
EN 14917:2021 (E)
a) The collar radius Rc shall be designed:
— as small as possible to ensure sufficient movement (movement shall be absorbed by the torus,
not by the root of the corrugation);
— as large as necessary to fulfil the limits of forming given in 7.4 as a function of strain caused by
deformation sd; see 6.2.2.5.
b) The initial gap in neutral position shall conform to:
G p ≤ 0, 8 ⋅ r
(146)
∆q e ≤ r - G p
(147)
∆q c ≤ G p
(148)
c) The maximum extension shall conform to:
d) The maximum compression shall conform to:
6.2.5.3 Determination of symbols and intermediate factors
6.2.5.3.1 Symbols
Symbols applying in addition to that given in 6.1.1 are listed in Table 11.
6.2.5.3.2 Additional factors
The following factors apply in addition to those given in 6.2.2.5:
C c = -0, 2431 + 0, 0168 ⋅ N g + 0,3024 ⋅ N g2
Dic = Di + 2 ⋅ e + e ic
Fg =
)
(

K
1 π
2
⋅  ⋅ Dm
- Di2 ⋅ P + B ⋅ ∆q c 
N g  4
N

Bw =
)
(
2 ⋅ 12 ⋅ 1 - ν 2 ⋅ r 2
Dm ⋅ e p
B1 = 1 + 0, 134 ⋅ B w 2 - 0, 0061 ⋅ B w 3 + 0, 00011 ⋅ B w 4

1
B2 = 
1 + 0, 12 ⋅ B w - 5


(
)
if B w < 5 

if B w ≥ 5


 1 + 0, 0625 ⋅ B 2 if B < 4 


w
w
B3 = 

0,
5
B
if
B
4
⋅
≥
w
w




The characteristics of the three coefficients B1 to B3 are shown in Figure 17.
(149)
(150)
(151)
(152)
(153)
(154)
(155)
77
BS EN 14917:2021
EN 14917:2021 (E)

Ap = 2 ⋅  Ltc + e

(
D





) ⋅ Di +  2m - r i  ⋅ G p + r 2i ⋅ π 
Figure 17 — Calculation coefficients B1, B2, B3
78
(156)
BS EN 14917:2021
EN 14917:2021 (E)
Table 11 — Additional symbols
Symbol
Description
Unit
Ap
pressure area of one corrugation; see Formula (156)
mm2
Atc
effective cross sectional metal area of one bellows reinforcing collar over a virtual
length Leff; see 6.2.5.3.3
mm2
B1
coefficients for the calculation of meridional membrane stress; see Formula (153)
—
Aic
Bw
B2
B3
Cc
Dic
effective cross sectional metal area of the intermediate collar over a virtual length
mm2
Leff; see 6.2.5.3.3
basic calculation coefficients; see Formula (152)
coefficients for the calculation of meridional bending stress; see Formula (154)
coefficients for the calculation of KB; see Formula (155)
factor for the curvature of supported external collar; see Formula (149)
—
—
—
—
mean diameter of bellows intermediate collar; see Formula (148)
mm
axial force per external collar gusset; see Formula (151)
N
eic
intermediate collar thickness (see Figure 16)
Gp
opening length of the torus in neutral position (see Figure 16)
mm
length of intermediate collar (delivery length) (see Figure 16)
mm
Fg
Leff
Lm
Ng
effective length used for the calculation of Atc or Aic ; see Formula (158) and
Figure 18
number of equally spaced gussets per external collar
Rc1, Rc2 end radius of collar (see Figure 16, Y)
Zc
section modulus of external collar about the neutral axis in lateral direction
(perpendicular to the bellows middle axis) used in Formula (160)
6.2.5.3.3 Collar effective length and area
mm
mm
—
mm
mm3
The active part of the collars concerning the meridional bending stress of the collars, Ltc , or Lic , is located
near the bellows attachment and is independent of the bellows tangent length; see Formulae (33) and
(34) and Figure 18.
The effective areas of the reinforcing collar, Atc, and the intermediate collar, Aic, shall be calculated using
the corresponding effective length, Leff and regarding the specific design shape.
The effective length is given by:
Leff = min  Ltc ; Lt or Lic ;0, 5 ⋅ Lm 


(157)
79
BS EN 14917:2021
EN 14917:2021 (E)
Figure 18 — Effective length and area
6.2.5.4 Internal pressure capability
6.2.5.4.1 Limitation due to stresses
6.2.5.4.1.1 Circumferential membrane stress due to pressure
a) Bellows tangent:
σΘ , t (P ) =
Ap ⋅ E B ⋅ D c ⋅ D m
( Ac ⋅ E B ⋅ Dc + 2 ⋅ Atc ⋅ E c ⋅ Dm ) ⋅ ( Di + e )
2⋅
b) Reinforcing collar:
σ Θ ,c ( P ) =
2⋅
Ap ⋅ E c ⋅ D m
( Ac ⋅ E B ⋅ Dc + 2 ⋅ Atc ⋅ E c ⋅ Dm )
⋅P
(158)
⋅P
(159)
c) External reinforcing collar:
When the collar is externally welded to the shell – design I – and supported by gussets (see Figure 16)
additional circumferential bending stress is caused in the external collar due to pressure.
This circumferential bending stress is given by:
F ⋅N ⋅ D
( ) 4 g⋅ π ⋅ Cg ⋅ Zc
σ Θ , b,c P =
c
(160)
c
The sum of stresses shall conform to:
— σ Θ , c ( P ) + σ Θ ,b, c ( P ) ≤ 1, 5 ⋅ z ⋅ f , below the creep range;
— σΘ , c (P ) +
σ Θ ,b,c ( P )
1, 25
d) Intermediate collar:
σ Θ ,ic ( P ) =
80
2⋅
≤ z ⋅ f cr , in the creep range
Ap ⋅ E ic ⋅ Dm
( Ac ⋅ E B ⋅ Dic + 2 ⋅ Aic ⋅ E ic ⋅ Dm )
⋅P
(161)
BS EN 14917:2021
EN 14917:2021 (E)
e) Bellows corrugation (torus) at Dm
σΘ (P ) =
2⋅
(
Ap ⋅ E B ⋅ D c
Ac ⋅ E B ⋅ Dc + 2 ⋅ Atc ⋅ E c ⋅ Dm
)
⋅P
(162)
The circumferential membrane stresses of all individual parts shall comply with the allowable stress for
the material related to the regarded part:
— σ Θ ( P ) ≤ z ⋅ f , below the creep range or
— σ Θ ( P ) ≤ z ⋅ f cr , in the creep range.
6.2.5.4.1.2 Meridional membrane stress due to pressure
The meridional membrane stress in the torus due to pressure is given by:
r  Dm - rm 
⋅P
e *  Dm - 2 ⋅ rm 
σ m,m ( P ) = m ⋅ 
and shall conform to:
(163)
— σ m,m ( P ) ≤ f , below the creep range;
— σ m,m ( P ) ≤ f cr , in the creep range.
6.2.5.4.2 Limitation due to instability
6.2.5.4.2.1 Column instability
The requirements of 6.2.3.3.2.1 shall apply with the following modifications:
— the axial elastic spring rate KB according to Formula (37) shall apply;
— bellows corrugated length lB is replaced by lB,t:
l B,t = N ⋅ 2 ⋅ rm
6.2.5.4.2.2 In-plane instability
(164)
Toroidal bellows are not subject to in-plane instability.
6.2.5.5 Stresses due to Displacement
6.2.5.5.1 Stresses due to equivalent axial displacement
The following stresses which are the basic stresses for the calculation of fatigue cycles are calculated from
the total equivalent axial displacement range Δq of each toroidal corrugation according to 6.2.7.
Meridional membrane stress range:
81
BS EN 14917:2021
EN 14917:2021 (E)
σ m, m ( ∆q ) =
*2
E B,20 ⋅ e p
3
34, 3 ⋅ rm
⋅ B1 ⋅ ∆q
Meridional bending stress range:
( )
σ m, b ∆q =
*
E B,20 ⋅ e p
2
5,72 ⋅ rm
⋅ B 2 ⋅ ∆q
Total equivalent stress range:
σ eq = 3 ⋅ σ m, m ( P ) + σ m, m ( ∆q ) + σ m,b ( ∆q )
6.2.5.6 External pressure
(165)
(166)
(167)
The design of toroidal bellows with external pressure is not covered by this document.
6.2.6 Fatigue
6.2.6.1 General
The specified number of cycles Nspe shall be the number of cycles expected to occur during the operating
life of the bellows. The allowable number of cycles Nalw, as calculated in this subclause, shall always
exceed the specified number of cycles.
If a bellows is submitted to noteworthy different sets of cycles due to pressure or displacement at
different operating conditions, such as those produced by start-up or shutdown, the cumulative effect of
these cycles can be accounted for by linear summation of fatigue damage parameters according to the
Miner’s rule; see 6.2.6.3.
6.2.6.2 Expected and allowable number of cycles
The number of cycles based on a best-fit approach is generally given by:
 A 

Nc = 
 σ eq - B 


C
The parameters A, B, and C for different material classes are given in Table 12.
(168)
The different material classes are specified by the characteristic physical parameters Rp0,2 and Rm which
are mean standard values for each material class and may deviate by a small percentage (see NOTE in
Table 12).
82
BS EN 14917:2021
EN 14917:2021 (E)
Table 12 — Parameters of the fatigue equations
Material
class
1
2
Material type
(main characteristic of the
class)
High strength Nickel alloys
Corrosion resistant Nickel
alloys
3
4
Austenitic stainless steels
(fine grain ferritic steels)
Different alloys
(heat resistant ferritic steels)
Mean material
properties
MPa
Rp0,2
Rm
400
830
220
(410)
530
(530)
310
180
(270)
Max. equiv.
stress
range
MPa
σ eq,max
720
450
(400)
Calculation
parameters
−
A
B
C
4 200
23 000
600
3,1
3 800
20 000
520
3,2
3 100
14 500
390
3,4
2 600
12 500
290
3,4
NOTE Maximum allowable deviation of the listed mean material properties is < 10 %.
Table 13 contains the preferable materials for bellows (see Table 2) related to the four material classes.
The allowable number of fatigue cycles is defined by the design curves and given by:
C
C


 
1  A 
A
 ;
  , for σ > B
N alw = min  ⋅ 
eq



 
B
B
⋅
σ
σ
3
1,
25
  eq
eq





(169)
C


A
 , for B ≥ σ eq > B 1, 25
N alw = 
 1, 25 ⋅ σ eq - B 


(170)
The allowable number of cycles shall always exceed the specified number of cycles:
N spe ≤ N alw
Formula (169) is limited to a minimum of 100 cycles which is achieved when the allowable maximum
equivalent stress range σeq,max is not exceeded; see Table 12.
Formula (170) delivers results for input data down to the endurance strength: σ eq = B 1, 25 . (Calculated
numbers of cycles greater 107 are regarded to be informative only.)
The characteristic of the fatigue curves for the different material classes is shown in Figure 19.
NOTE
The allowable number of cycles is calculated with a reasonable safety (factor 3 on cycles and 1,25 on
stresses) and represents the estimated number of operating cycles within the usual pattern of test results, see also
Annex E.
6.2.6.3 Cumulative fatigue life
The cumulative fatigue life of a bellows submitted to different sets of cycles (pressure/displacement at
various operating conditions) can be determined by linear summation of the fatigue damage parameters
for the specific sets of cycles from the stress range spectrum.
83
BS EN 14917:2021
EN 14917:2021 (E)
The total fatigue damage parameter Df is given by:
k n
n
n
n
n
i
Df = 1 + 2 + 3 + ... + k =
N1 N 2 N3
Nk 1 Ni
∑
where
ni
Ni
are the numbers of cycles of each total stress range σ eq,i applied during the design life;
are the allowable numbers of cycles corresponding to σ eq,i .
The total fatigue damage parameter Df shall comply with:
Df ≤ 1, 0
84
(171)
BS EN 14917:2021
EN 14917:2021 (E)
Key
1
2
3
4
Class 1
Class 2
Class 3
Class 4
Figure 19 — Fatigue curves giving the allowable number of cycles for different material classes
85
BS EN 14917:2021
EN 14917:2021 (E)
Table 13 — Preferable materials for bellows (see Table 2 and Table 8) related to the four
material classes
Material class
1
2
Number
Steel name
Alloy
(informative)
2.4610
C-4
2.4856
2.4819
1.4541
1.4571
1.4301
1.4306
1.4401
1.4404
3
1.4435
1.4539
1.4828
1.4876
2.4858
1.0565
1.8935
1.4550
1.4876 (H)
2.4816
4
2.4360
1.0345
1.0425
1.5415
1.7335
625
C-276
321
316Ti
304
304L
316
316L
316L
904L
309
800
825
Fine grain ferrite
347
800 (H)
600
400
Heat resistant ferritic steel
This subclause gives the allowable number of cycles within a temperature range between low (negative
sign) and elevated temperatures up to the creep range; for higher temperatures see 6.2.6.4.
6.2.6.4 Specific fatigue curves
The manufacturer is allowed to use specific fatigue curves appropriate to his production if they are
established by following the procedure for setting-up a design fatigue curve given in Annex F.
86
BS EN 14917:2021
EN 14917:2021 (E)
6.2.6.5 Allowable number of cycles in the creep range
The allowable number of cycles in the creep range is reduced in relation to that below the creep range;
see Formulae (169), (170). It is depending on the design temperature and the hold time at operating
conditions.
6.2.7 Bellows under the influence of movements
6.2.7.1 General
The purpose of this subclause is to determine the equivalent axial displacement components and the
corresponding elastic forces and moments of bellows subjected at its ends to:
— axial displacements;
— lateral deflections;
— angular rotations.
NOTE 1
See Figure 20 for movements, forces and moments at one bellows.
The following equations give:
— the equivalent axial displacement components Δqx, Δqy, ΔqΘ of a bellows corrugation depending on
the movements of an expansion joint starting from the initial neutral position of the bellows (no prestressing);
— the corresponding forces and moments at the ends of an expansion joint resulting from the elastic
behaviour of the non-pressurized bellows using the elastic spring rate KB of one bellows.
Figure 20 — Bellows principle movements, forces and moments
NOTE 2
The starting point “1” and the working point “2” indicated in the figures are given for the calculation of
the equivalent axial extension respectively compression displacements Δqe and Δqc of a bellows corrugation; see
6.2.8.
NOTE 3
For forces and moments of pressurized expansion joints see 6.2.9.
6.2.7.2 Axial displacement
When the ends of an expansion joint consisting of one or more bellows are subjected to an axial
displacement x; i.e. x1 or x2 (see Figure 21), the equivalent axial displacement of each corrugation of the
bellows is given by:
87
BS EN 14917:2021
EN 14917:2021 (E)
∆q x =
1
⋅x
N ⋅ nB
(172)
where x shall be taken:
— positive for extension
— negative for compression
NOTE
(x > 0);
(x < 0).
Values of x in extension and compression can be different.
Figure 21 — Bellows subjected to an axial displacement x
The corresponding axial force Fx applied to the ends of the expansion joint is given by:
Fx = K B ⋅
x
nB
(173)
where KB is the axial elastic spring rate of one bellows according to Formulae (35) to (40), depending on
the type of bellows.
6.2.7.3 Lateral deflection
6.2.7.3.1 Bellows without intermediate pipe
When the ends of the bellows are subjected to a lateral deflection y; i.e. y1 or y2 (see Figure 22), the
equivalent axial displacement of the strongest loaded corrugation of the bellows is given by:
∆q y = 3 ⋅
Dm
( l B ⋅ nB ± x )
⋅
y
N ⋅ nB
(174)
where y shall be taken as positive for a pre-stressed position “1” and as negative for the working position
“2” if the neutral position is passed; otherwise it shall also be taken as positive; see Figure 22. Where axial
displacement x is pre-existing the appropriate corrugated length is used. Where nB is the number of
bellows which are connected directly or with short rings to each other.
NOTE
Highest values Δqy occur near the bellows ends with extension at the convex side (extrados) and
compression at the opposite side (intrados) of the bent parts. Subjected to pressure the highest curvature is moved
in direction of the bellows middle length; but will not be higher than the initial one. In the middle of the bellows the
equivalent axial movement is always zero; see 6.2.8.
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Figure 22 — Single bellows subjected to lateral deflection y
The corresponding moment My applied to the ends of the bellows is given by:
My =
2
Dm
K
D
3
⋅
⋅ B ⋅ y = m ⋅ K B ⋅ N ⋅ ∆q y
4 l B ⋅ n B ± x nB
4
The corresponding lateral force Fy applied to the ends of the bellows is given by:
Fy =
3
⋅
2
2
Dm
( l B ⋅ nB ± x )
2
⋅
KB
nB
⋅ y = 2 ⋅ My ⋅
1
l B ⋅ nB ± x
6.2.7.3.2 Universal or a lateral type expansion joint with intermediate pipe
(175)
(176)
6.2.7.3.2.1 Expansion joint with unsupported intermediate pipe
The equivalent axial displacement of the strongest loaded corrugation of a bellows whose ends are
subjected to a lateral deflection y; i.e. y1 or y2 (see Figure 23), is given by:
3 D
∆q y = ⋅ m ⋅
2 N ⋅ lB
( ) ⋅ l ⋅y
l ± 0, 5 ⋅ x
1 + 3 ⋅ (l l )
1 + l * lB
*
B
2
*
*
(177)
where y shall be taken positive for a pre-stressed position “1” and as negative for the working position
“2” if the neutral position is passed; otherwise it shall also be taken as positive. Where axial displacement
x is pre-existing the appropriate length is regarded.
NOTE 1
Highest values Δqy occur at the bellows outer ends with extension at the convex side (extrados) and
compression at the opposite side (intrados) of the bent parts. (When pressurized, the maximum curvature of the
bellows centreline shifts with increasing pressure from the ends towards the middle of the bellows and there the
bending may increase by a factor ĉ py ; see 6.2.8).
NOTE 2
Long single bellows or more than one bellows are not recommended for pressurized lateral and
universal expansion joints because of their disproportionate negative influence on stability and fatigue the following
equations do not include more than one bellows on each end. If for special reasons more than one bellows on each
side are used, the relevant parameters (N, lB, l*, KB) may be adapted to get quasi one bellows.
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Figure 23 — Lateral / universal expansion joint with two bellows
and intermediate pipe
The corresponding moment My applied to the ends of the bellows is given by:
( )
( )
2
1 + l * lB
Dm
l*
3
1
My = ⋅
⋅
⋅
⋅ K B ⋅ y = ⋅ Dm ⋅ N ⋅ K B ⋅ ∆q y
2
*
8
lB
4
l ± 0, 5 ⋅ x
1 + 3⋅ l* l
B
(178)
The corresponding lateral force Fy applied to the ends of the bellows is given by:
2
3 D
Fy = ⋅ m ⋅
4 l2
B
M
( ) ⋅
1
1
⋅K ⋅ y = 2⋅
⋅
l
1 ± x 2 ⋅ l  ⋅ 1 + l ± x l 
1 + (l ± x ) l
( )  ( ) 
1 + 3 ⋅ (l l )

1 + l * lB
*
B
2
*
*
B
B
y
B
*
B
(179)
6.2.7.3.2.2 Expansion joint with guided intermediate pipe (see Table 1, Lateral, Double hinge)
The equivalent axial displacement of each corrugation of the bellows is given by:
∆q y =
1
⋅
2
Dm
N ⋅ l*
⋅y
(180)
where y shall be taken positive for a pre-stressed position “1” and as negative for the working position
“2” if the neutral position is passed; otherwise it shall also be taken as positive; see Figure 23.
NOTE
Bellows behave exactly like bellows subjected to angular rotation (see 6.2.8).
The corresponding moment My applied to the ends of the bellows is given by:
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Dm
My =
⋅ N ⋅ K B ⋅ ∆q y
4
The corresponding lateral force Fy applied to the ends of the bellows is given by:
Fy =
Dm
2× l*
⋅ N ⋅ K B ⋅ ∆q y = 2 ⋅
6.2.7.4 Angular rotation
My
l*
(181)
(182)
When the ends of the bellows are subjected to an angular rotation Θ (see Figure 24), the equivalent axial
displacement of each corrugation of the bellows is given by:
∆qΘ =
Dm
2 ⋅ N ⋅ nB
⋅Θ
(183)
where Θ , expressed in radians, shall be taken positive for a pre-stressed position “1” and as negative for
the working position “2” if the neutral position is passed; otherwise it shall also be taken as positive; see
Figure 24. Where nB is the number of bellows which are connected directly or with short rings to each
other.
NOTE 1
Equivalent axial displacement ∆qΘ is constant across the whole length of the bellows with extension at
the convex side (extrados) and compression at the opposite side (intrados) as long as the bellows is not charged
with pressure. (If pressurized, the curvature of the bellows centreline is increased in the middle of the bellows by a
factor ĉ pΘ which also increases directly the equivalent axial displacement there; see 6.2.8.4.)
Figure 24 — Bellows subjected to angular rotation θ
The corresponding moment MΘ applied to the ends of the bellows is given by:
MΘ =
K
1
1
2 KB
⋅ Dm
⋅
⋅ Θ = ⋅ Dm ⋅ B ⋅ N ⋅ ∆qΘ
8
nB
4
nB
Where nB is the number of bellows which are connected directly or with short rings to each other.
(184)
NOTE 2
Long single bellows or more than one bellows are not recommended for pressurized angular expansion
joints because of their disproportionate negative influence on stability and fatigue; see 6.2.8.4.2.
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6.2.8 Equivalent axial displacement per corrugation
6.2.8.1 General
The following calculation of the equivalent axial displacement per corrugation is based on the initial
position “1” and the working position “2” for four different possible cases (see Figures 25 to 28):
a) Figure 25 - no cold spring;
b) Figure 26 - cold spring;
c) Figures 27 and 28 working conditions different to a) or b).
These calculations result in maximum values for extension Δqe and for compression Δqc which have to
be checked against the given limits (see 6.2.8.3).
They also lead to the total equivalent displacement Δq which gives the basis for the calculation of the
bellows fatigue (see 6.2.8.4).
Figure 25 — Δq from compression only, with no cold spring
Figure 26 — Δq from extension and compression, with cold spring Δqe
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Figure 27 — Δq from extension only, with cold spring Δqe (working conditions)
Figure 28 — Δq from compression only, with cold spring Δqc (working conditions)
6.2.8.2 Total equivalent axial expansion and compression
The total equivalent axial expansion and compression per corrugation result from all the bellows
movements at the two positions “1” and “2”. The interim values ∆q Σ and ∆q ∆ are calculated from the
given movement components with the correct sign (+ for extension / − for compression).
For the different types of bellows they are given by:
— for single bellows at the ends:
∆q Σ ,1 = ∆q x,1 + ∆q y,1 + ∆qΘ ,1
∆q ∆ ,1 = ∆q x,1 - ∆q y,1 - ∆qΘ ,1
(185)
∆q Σ ,2 = ∆q x,2 + ∆q y,2 + ∆qΘ ,2
∆q ∆ ,2 = ∆q x,2 - ∆q y,2 - ∆qΘ ,2
(186)
∆q Σ ,1 = ∆q x,1 + 0 + cˆPΘ ⋅ ∆qΘ ,1
∆q ∆ ,1 = ∆q x,1 - 0 - cˆPΘ ⋅ ∆qΘ ,1
(187)
— for single bellows in the middle:
∆q Σ ,2 = ∆q x,2 + 0 + cˆPΘ ⋅ ∆qΘ ,2
∆q ∆ ,2 = ∆q x,2 - 0 - cˆPΘ ⋅ ∆qΘ ,2
— for double bellows with unsupported intermediate pipe:
∆q Σ ,1 = ∆q x,1 + cˆPy ⋅ ∆q y,1 + cˆPΘ ⋅ ∆qΘ ,1
∆q Σ ,2 = ∆q x,2 + cˆPy ⋅ ∆q y,2 + cˆPΘ ⋅ ∆qΘ ,2
∆q ∆ ,1 = ∆q x,1 - cˆPy ⋅ ∆q y,1 - cˆPΘ ⋅ ∆qΘ ,1
∆q ∆ ,2 = ∆q x,2 - cˆPy ⋅ ∆q y,2 - cˆPΘ ⋅ ∆qΘ ,2
(188)
(189)
(190)
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— for double bellows with guided intermediate pipe:
∆q Σ ,1 = ∆q x,1 + cˆPΘ ⋅ ∆q y,1 + cˆPΘ ⋅ ∆qΘ ,1
(191)
∆q ∆ ,1 = ∆q x,1 - cˆPΘ ⋅ ∆q y,1 - cˆPΘ ⋅ ∆qΘ ,1
∆q Σ ,2 = ∆q x,2 + cˆPΘ ⋅ ∆q y,2 + cˆPΘ ⋅ ∆qΘ ,2
(192)
∆q ∆ ,2 = ∆q x,2 - cˆPΘ ⋅ ∆q y,2 - cˆPΘ ⋅ ∆qΘ ,2
The pressure depending increasing factors ĉ py and ĉ pΘ are defined in 6.2.8.4 below.
NOTE 1
The values for single bellows are different at the ends and in the middle as in the middle they include
increased bending due to pressure and exclude lateral displacement. Single bellows imply here several bellows in
series.
NOTE 2
Double bellows expansion joints with restraining devices (e.g. tie-rods) will normally not be designed
for axial displacement, except for that caused by the expansion of the intermediate pipe. Angular rotation, if planned,
is limited according to the design (e.g. number of tie-rods, position of hinges).
a) The maximum compression is given now by:
∆q c = min 0; ∆q Σ ,1 ; ∆q ∆ ,1 ; ∆q Σ ,2 ; ∆q ∆ ,2 
(193)
( i c + e ) )
(
( q - ∆L - 2 ( ri r + e ) ) 


(194)


To avoid collision of the corrugations, it shall comply with:
 q - ∆L - 2 r
∆q c ≤ min 
Where ΔL is only valid for reinforced bellows with reinforcing members of specific cross section; see
Figure 15.
b) The maximum extension is given now by:
∆q e = max 0; ∆q Σ ,1 ; ∆q ∆ ,1 ; ∆q Σ ,2 ; ∆q ∆ ,2 

(195)

To avoid buckling of the bellows crest, it shall comply with:
∆q e ≤ ∆q e, alw
where the allowable extension (based on the corrugation in neutral position) is given by:
 w 

∆q e, alw ≤ 0, 1336 ⋅ 
2⋅r 
m 

0,67


⋅ rm ⋅ Di + 2 ⋅ w + e * ⋅ c * ⋅ s d


(
) ( )
m
R p1.0, t 

⋅

R p1.0 

0,5
(
- q - ∆L - 4 ⋅ rm
(196)
)
R p1,0 values shall be replaced by R p0,2 values, if R p1,0 is not available or allowed (e.g. Ni-alloys).
(197)
The corresponding side wall angle at the allowable extension is — for information — given by:
β e, alw = 1, 2 ⋅
94
(

180  ∆q e, alw + q - ∆L - 4 ⋅ rm
⋅
π 
2 ⋅ rm

)  ⋅  w  -1,43
 2⋅r 
m 
 
(198)
BS EN 14917:2021
EN 14917:2021 (E)
6.2.8.3 Total equivalent axial displacement range
The total maximum equivalent axial displacement range Δq giving the stress range for the calculation of
the bellows fatigue is also based on the above equivalent axial displacement components.
In addition to the already used increasing factors ĉ Py and ĉ PΘ a stress correction factor c σ for angular
and lateral movements is regarded (see 6.2.8.4).
This modified equivalent axial displacement per corrugation depending on the different types of bellows
is given by:
— for single bellows at the ends:
(
)
(
)
∆q Σ = ∆q x,1 + c σ ⋅ ( ∆q y,1 + ∆qΘ ,1 ) -  ∆q x,2 + c σ ⋅ ∆q y,2 + ∆qΘ ,2 

(199)
∆q ∆ = ∆q x,1 - c σ ⋅ ( ∆q y,1 + ∆qΘ ,1 ) -  ∆q x,2 - c σ ⋅ ∆q y,2 + ∆qΘ ,2 

— for single bellows in the middle:
(
∆q Σ = ∆q x,1 + c σ ⋅ cˆPΘ ⋅ ∆qΘ ,1 - ∆q x,2 + c σ ⋅ cˆPΘ ⋅ ∆qΘ ,2
(
∆q ∆ = ∆q x,1 - c σ ⋅ cˆPΘ ⋅ ∆qΘ ,1 - ∆q x,2 - c σ ⋅ cˆPΘ ⋅ ∆qΘ ,2
(200)
)
(201)
)
(202)
— for double bellows with unsupported intermediate pipe:
(
)
(
)
(
)
∆q Σ = ∆q x,1 + c σ ⋅ cˆPy ⋅ ∆q y,1 + cˆPΘ ⋅ ∆qΘ ,1 -  ∆q x,2 + c σ ⋅ cˆPy ⋅ ∆q y,2 + cˆPΘ ⋅ ∆qΘ ,2 
(
(203)
)
∆q ∆ = ∆q x,1 - c σ ⋅ cˆPy ⋅ ∆q y,1 + cˆPΘ ⋅ ∆qΘ ,1 -  ∆q x,2 - c σ ⋅ cˆPy ⋅ ∆q y,2 + cˆPΘ ⋅ ∆qΘ ,2 
— for double bellows with guided intermediate pipe:
(
) 
(
(204)
)
∆q Σ = ∆q x,1 + c σ ⋅ cˆPΘ ⋅ ∆q y,1 + ∆qΘ ,1 -  ∆q x,2 + c σ ⋅ cˆPΘ ⋅ ∆q y,2 + ∆qΘ ,2 
(
) 
(
(205)
)
∆q ∆ = ∆q x,1 - c σ ⋅ cˆPΘ ⋅ ∆q y,1 + ∆qΘ ,1 -  ∆q x,2 - c σ ⋅ ˆc PΘ ⋅ ∆q y,2 + ∆qΘ ,2 
(206)
∆q = max  ∆q Σ

(207)
The total maximum equivalent axial displacement range is finally given by:
; ∆q ∆


6.2.8.4 Pressure depending increasing factors and stress correction factor
6.2.8.4.1 General
The influence of pressure on the curvature of the bellows depends on the type of bellows, on their
dimensional design and on the type of movement and results in the increasing factors c PΘ and  .
c Py
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The stress correction factor cσ regards the special behaviour of curved bellows where the bending stress
distribution is not rotationally symmetric like in an axial displaced bellows. In curved bellows the
maximum bending stresses are concentrated in small areas at the convex outside (extrados) and the
concave inside (intrados) of the bellows corrugations. Thus, the adjacent parts of the corrugations are
able to deform slightly which leads to a reduction of the maximum bending stresses.
6.2.8.4.2 Increasing factors for single bellows
Single bellows for:
— angular rotation:
The increasing factor for an angular rotated single bellows is given by:
c PΘ =
κ ⋅ ( lB 2)
(208)
sin κ ⋅ ( lB 2) 
where 0 < κ ⋅ ( lB 2) < π , with κ according to Formula (48).
— lateral deflection:
A lateral deflected single bellows shows no appreciable increase in curvature by the influence of
pressure in the interesting range so no increasing factor is provided.
6.2.8.4.3 Increasing factors for double bellows
a) Double bellows with unsupported intermediate pipe:
— lateral deflection:
The increasing factor for lateral deflection is given by:
ĉ Py = 1
, for
(κ ⋅ l B ) ≤ π 4 and
 


4,8  
3, 5  
 
ĉ Py = max 1; 2, 33 ⋅ 0, 5 + 0, 015 ⋅ κ ⋅ l B
  , for π 4 < κ ⋅ l B ≤ π

 

l * lB  
 

 

(
)
(
)
(209)
2, 0
(210)
with κ according to Formula (48).
NOTE Values for ( l * l B ) should not be greater than 40 to keep the error of the approximation given by
Formula (210) within 5 %.
— angular rotation:
The increasing factor for each of the two bellows is given by Formula (208).
b) Double bellows with guided intermediate pipe
The lateral deflection of such an expansion joint leads to angular rotation of the bellows and results
in an increasing factor ĉ PΘ given by Formula (208).
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6.2.8.4.4 Stress correction factor
The stress correction factor for all curved bellows – angular rotated or lateral deflected – is given by:
(
(
)
)


Cd
2
, if C 2 ≤ 1, 5

 1 -ν ⋅

1 + 1, 9 ⋅ C 1
cσ = 

2
 1 -ν ,
if C 2 > 1, 5




(211)
6.2.9 Forces and moments on pressurized expansion joints
6.2.9.1 General
The calculation of forces and moments applied to the attachments of complete expansion joints – with or
without restraining parts – requires the knowledge of the effective spring rates of the different types of
expansion joints. The effect of pressure and friction on the bellows and on the hinges is taken into
consideration.
The following formulae are given with regard to the units of the parameters as defined in Table 4.
6.2.9.2 Bellows spring rates and influence factors
6.2.9.2.1 Elastic and effective spring rate
Basis for the calculation of working forces and moments is the elastic-plastic component yield curve of
the bellows. The initially elastic spring rate exhibits a nonlinear behaviour when a certain movement is
exceeded. This characteristic is caused by the elastic-plastic material behaviour.
The displacement-force characteristic of an axially extended bellows is shown simplified in Figure 28,
using normalized values x* and F* for the axial displacement and the resulting force, related to the elastic
values xel and Fel; i.e. x* = F* = 1.
Definitions (see Figure 28):
— the elastic spring rate is defined as the slope of the line A – B;
— the effective spring rate is defined as the slope of the line A - C which complies with the decline of the
total hysteresis in the zero-crossing (x* = 0); see also Figure E.2.
(Similar characteristic are existing for lateral deflected or angular rotated bellows.)
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Figure 29 — Displacement-force characteristic of an axial bellows
6.2.9.2.2 Working forces and moments
Working forces and moments of a bellows are based on the effective spring rate; they are however
additionally influenced by the effect of the side wall tilting of the deflected corrugations and, with multiply bellows, by the effect of friction between the plies when the pressurized bellows is deflected.
For lateral and angular expansion joints there are additional influences to be regarded which are caused
by pressure:
— the friction of the hinges, if there are any;
— the force components of curved bellows (lateral and angular expansion joints) and of the angled
restraining anchors.
Details are given below.
For the determination of the forces and moments in piping systems, in most cases the elastic spring rate
or the effective spring rate given by the manufacturer is sufficient.
The following, more precise determination of the working forces and moments is recommended where
expansion joins are attached to sensitive devices or when the below given conditions apply:
— high operating temperatures;
— high operating pressures;
— large displacements.
In these cases, the experience of the manufacturer shall also be taken into account.
NOTE
A quite good approximation of quasi working spring rates can be found by using nominal or maximum
movement and pressure for their calculation.
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Table 14 — Material-dependent parameters for the stress-strain curve (small strain)
Yield point
Material
at room
temperature
ε0
Rp0
b*
n
at design
temperature
304
−
0,001
MPa
MPa
1,54
−
0,1
−
304L
0,001
196
1,56
0,1
316
0,001 1
217
1,52
0,09
316L
0,001 1
217
1,52
0,09
316L
0,001 1
217
1,52
0,09
904L
0,001 1
217
1,52
0,09
321
0,001
196
1,56
0,1
347
0,000 8
168
1,86
0,14
316Ti
0,001 1
217
1,52
0,09
309
0,001
199
1,75
0,13
800
0,000 9
186
1,59
0,1
800 H
0,000 7
144
1,72
0,12
Number
Alloy
Steel name
(informative)
1.4301
X5CrNi18–10
1.4306
X2CrNi19–11
1.4401
X5CrNiMo17–12–
2
1.4404
X2CrNiMo17–12–
2
1.4435
X2CrNiMo18–14–
3
1.4539
X1CrNiMoCuN25–
20–5
1.4541
X6CrNiTi18–10
1.4550
X6CrNiNb18–10
1.4571
X6CrNiMoTi17–
12–2
1.4828
X15CrNiSi20–12
1.4876
X10NiCrAlTi32–
21
1.4876 (H)
X10NiCrAlTi32–
21H
Yield strength parameters
207
at room
temperature
nt
 R p1,0 

= n⋅
 R p1,0, t 


=n
 R p1,0 

= n⋅
 R p1,0, t 


=n
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Yield point
Material
at room
temperature
ε0
Rp0
b*
n
at design
temperature
400
−
0,000 8
MPa
MPa
1,57
−
0,1
−
C-4
0,001 4
281
1,50
0,09
600
0,000 9
175
1,61
0,11
 R p1,0 

= n⋅
 R p1,0, t 


600 H
0,000 8
155
1,68
0,12
C-276
0,001 5
296
1,26
0,05
625, Grade 1 0,001 9
375
1,46
0,09
625, Grade 2 0,001 3
253
1,46
0,08
212
1,53
0,1
Number
Alloy
Steel name
(informative)
2.4360
NiCu30Fe
2.4610
NiMo16Cr16Ti
2.4816
NiCr15Fe
2.4816 (H)
NiCr15Fe
2.4819
NiMo16Cr15W
2.4856
NiCr22Mo9Nb
2.4856 (H)
NiCr22Mo9Nb
2.4858
825
NiCr21Mo
Ferritic steels
At room temperature:
a = 1, 67 - 0,5 ⋅ n
−
−
(
at room
temperature
153
0,001 1
ReH
ln R p0,2 R p1,0
ln  R p0,2 E + 0, 002

( )
R p0 = R p1,0 ⋅ b * ⋅ ε 0
n
 R p0,2 

= n⋅
 R p0,2, t 


=n
0,0
At design temperature:
R p0, t = R p0 ⋅ ( R p0,2, t R p0,2 )
(
nt
a t = 1, 67 - 0,5 ⋅ nt bt = 0, 68 - 0,3 ⋅ nt
;
b = 0, 68 - 0,3 ⋅ n
n=
Yield strength parameters
)
) ( Rp1,0
or
For unlisted materials nt = n .
)
E + 0, 01 

(
; b * = R p1,0 E + 0, 01
)
-n
= R eH, t
1

 n-1
E

; ε0 = 
;


 R p1,0 ⋅ b * 


The equations are based on the well-tried exponential function for the stress-strain curve of
ductile materials in the low strain area, σ = a ⋅ ε , and require 0,2 % and 1,0 % yield strength
values. Valid for ε 0 ≤ ε ≤ 0,015.
b
100
BS EN 14917:2021
EN 14917:2021 (E)
6.2.9.3 Type of expansion joint
6.2.9.3.1 Axial expansion joint
a) Axial effective spring rate of a single bellows:
The axial effective spring rate regarding only the elastic-plastic material behaviour is temperature
depending and given by:
 1


K x, t = K B,t ⋅  
*
 a t ⋅ ∆q
 
( )
for ∆q * ≤ 1 + nt 

-3 
n t -1

*
- b t ⋅ ∆q *
 for ∆q > 1 + nt



( )
(212)
where the parameters are the following:
1) axial elastic spring rate K B,t according to Formulae (35) to (40) calculated with E B,t depending
on the type of bellows;
2) exponent n t depending on the bellows material; see Table 14;
3) factors a t and b t depending on n t ; see formulae in Table 14;
*
4) normalized equivalent axial displacement ∆q according to Formula (45).
b) Additional factors:
The axial working force of a single bellows is influenced by additional factors.
1) Spring rate regarding the effect of the side wall tilting:
K β x,t =
π
24
⋅ E B,t ⋅
e p* ⋅ np  ∆q 


Dm ⋅ N  2 
2) Factor regarding the friction between the plies:
(
K µ x = µ ⋅ π ⋅ Dm ⋅ e p* ⋅ np - 1
)
with the equivalent friction coefficient µ according to Formula (47).
(213)
(214)
c) Axial working force:
The axial working force of an axial expansion joint with one or more bellows is finally given by:
∆x
Fw x, t =  K x, t + K β x, t  ⋅
+Kµx ⋅P

 nB
(215)
where – after some cycles between x1 and x2 – the effective axial displacement Δx related to any axial
displacement x which is starting from the initial neutral position is given by:
101
BS EN 14917:2021
EN 14917:2021 (E)
∆x = x -
x1 + x2
2
6.2.9.3.2 Lateral or universal expansion joint
(216)
6.2.9.3.2.1 General
Additional influences on working forces and moments have to be regarded for lateral and universal
expansion joints besides that on axial expansion joints; i.e. the effect of pressurized curved bellows and
that of the restraining parts.
It shall be taken into consideration that lateral working forces of deflected bellows without intermediate
pipe or with unsupported intermediate pipe may be strongly reduced by internal pressure. In the case
that the values in non-pressurized conditions are higher, those shall be used for piping system design.
Long single bellows or more than one bellows are not recommended for pressurized lateral and universal
expansion joints with intermediate pipe because of their disproportionate negative influence on stability
and fatigue; thus the following equations do not include more than one bellows on each end. If for special
reasons more than one bellows on each side are used, the relevant parameters (N, lB, l*, KB) may be
adapted to get quasi one bellows.
6.2.9.3.2.2 Bellows without intermediate pipe used for lateral deflection
a) Lateral effective spring rate:
The lateral effective spring rate regarding only the elastic-plastic material behaviour is temperature
depending and given by:
2
)
(

3  D
K y, t = ⋅  m  ⋅ 1 - ν 2 ⋅ K x, t

2  l B ⋅ nB 
with the axial effective spring rate K x, t according to Formula (212).
(217)
b) Additional factors:
Working force and working moment of the bellows are influenced by the additional factors 1 to 3.
1) Spring rate regarding the effect of the side wall tilting:
K β y,t =
Dm ⋅ e p * ⋅ np  ∆q 
⋅
⋅

2
6
2 
⋅N 
l ⋅n
E B,t
(B
B
)
2) Factor regarding the effect of friction between the plies:
K µ y,t = µ ⋅
2
2 ⋅ Dm
l B ⋅ nB
(
⋅ e p* ⋅ np - 1
)
with the effective friction coefficient µ according to Formula (47).
102
(218)
(219)
BS EN 14917:2021
EN 14917:2021 (E)
3) Factors regarding the reaction of the curved bellows and of the angled restraining anchor due to
pressure:
i.
the factor for the force is given by:
 1, 2
1 

K Py (f) = - Ae ⋅ 
l ⋅n

l
 B B Rc 
(220)
with the reduced length of the tie rod lRc measured between the contact points of the bearing
sphere and the cones or similar bearing parts.
The last term within the brackets is zero if no restraining parts exist.
ii. the factor for the moment is given by:
(221)
K Py m = - 0, 1 ⋅ Ae
( )
Working force and working moment of the expansion joint are influenced in addition by the
factor 4.
4) Factor for the force due to bearing friction, provided restraining parts are existing:
d
K Fy = µ H ⋅ Ae ⋅ H , with:
lR
i.
the friction coefficient μ H of the hinges;
(222)
ii. the relevant hinge bearing diameter dH (normally the diameter of the bearing sphere);
iii. the length of the tie rod lR measured between the centre points of the bearing spheres.
NOTE
The friction coefficient μ H depends on the type of hinge bearing and is expected to be:
0,005 ≤ μ H ≤ 0,5 where the smallest value is valid for roller bearings and the highest one for steel on steel,
not greased.
c) Lateral working force and working moment of the expansion joint with one or more bellows are
finally given by:
(
)
∆y
Fw y, t =  K y, t + K β y,t  ⋅
+ K Fy + K µ y,t ⋅ P + K Py (f) ⋅ ∆ y ⋅ P

 nB
(223)
M w y, t =
(224)

l B ⋅ nB   
∆y
+ K Fy + K µ y ⋅ P  + K Py(m) ⋅ ∆ y ⋅ P
⋅  K y, t + K β y,t  ⋅
 nB
2


(
)
where – after some cycles between y1 and y2 – the effective lateral deflection Δy related to any lateral
deflection y which is starting from the initial neutral position is given by:
103
BS EN 14917:2021
EN 14917:2021 (E)
∆y = y -
y1 + y2
2
6.2.9.3.2.3 Two bellows with intermediate pipe used for lateral deflection
(225)
(A) Expansion joint with unsupported intermediate pipe (Figure 23)
a) The lateral effective spring rate:
The lateral effective spring rate regarding only the elastic-plastic material behaviour is temperature
depending and given by:
)
(
2
Dm
⋅ 1 -ν 2
3

K y, t = ⋅
⋅ K x,t
2
4 2 
l B ⋅ 1 + 3 ⋅ l * l B 


(226)
)
(
with the axial effective spring rate K x,t according to Formula (212).
b) Additional factors:
Working force and moment of the bellows are influenced by additional factors 1 to 3.
1) Spring rate regarding the effect of the side wall tilting:
Dm ⋅ e p* ⋅ np
1
⋅E ⋅
⋅
K β y,t =
12 B,t
N ⋅ l2
B
1
( l)
1+3⋅ l
*
B
2
 ∆q 
⋅

 2 
2) Factor regarding the effect of friction between the plies:
K µ y,t = µ p ⋅
2
2 ⋅ Dm
(l + l )
B
*
(
⋅ e p* ⋅ np - 1
)
(227)
(228)
with the effective friction coefficient µ according to Formula (47).
3) Factors regarding the reaction of the curved bellows and of the angled restraining anchors due
to pressure:
i.
the factor for the force is given by:
)
(






2,5 ⋅ l * l B - 0,5 

 1, 2 
 - 1 
K Py (f) = - Ae ⋅ 
⋅
2  l
 lB 

*
l
l
1
+
3
⋅

 Rc 
B




(
)
(229)
with the reduced length of the tie rod lRc measured between the contact points of the bearing
sphere with the cones or similar bearing parts.
The last term within the brackets is zero if no restraining parts exist.
104
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EN 14917:2021 (E)
ii. the factor for the moment is given by:
( ) ⋅ 1, 09 - 1,51 + 0, 63 
K
=-A ⋅
( )


l l )
(
l l ) 
1 + 3 ⋅ (l l ) 
(


1 + l * lB
e
Py m
*
B

2
*

*
B
B
2
(230)
Working force and working moment of the expansion joint are influenced in addition by factor
4.
4) Factor for the force from bearing friction, provided restraining parts are existing, is given by:
K Fy = µ H ⋅ Ae ⋅
with:
dH
(231)
lR
the friction coefficient μ H of the hinges (see 6.2.9.3.2.2, NOTE);
i.
ii. the relevant hinge bearing diameter dH (normally the diameter of the bearing sphere);
iii. the length of the tie rod lR measured between the centre points of the bearing spheres.
c) Lateral working force and moment are finally given by:
(
)
(
)
Fw y,t = K y,t + K β y,t ⋅ ∆ y + K Fy + K µ y,t ⋅ P + K Py(f) ⋅ ∆ y ⋅ P
M w y,t =
lB + l *  
⋅ K y,t + K β y,t ⋅ ∆ y + K Fy + K µ y,t ⋅ P  + K Py(m) ⋅ ∆ y ⋅ P


2
(
)
(
)
(232)
(233)
where – after some cycles between y1 and y2 – the effective lateral deflection Δy related to any lateral
deflection y which is starting from the initial neutral position is given by:
∆y = y -
y1 + y2
2
(B) Expansion joint with guided intermediate pipe
(234)
It is assumed that the hinges are positioned over the middle of the bellows (see Figure 30).
a) Lateral effective spring rate:
The lateral effective spring rate regarding only the elastic-plastic material behaviour is temperature
depending and given by:
2
(
)
1 D
K y, t = ⋅ m ⋅ 1 - ν 2 ⋅ K x,t
4 l *2
with the axial effective spring rate K x,t according to Formula (212).
(235)
105
BS EN 14917:2021
EN 14917:2021 (E)
Figure 30 — Expansion joint with guided intermediate pipe
b) Additional factors:
Working force and working moment of the bellows are influenced by the additional factors 1 to 3.
1.
Spring rate regarding the effect of the side wall tilting:
K β y,t =
2.
Dm ⋅ e p* ⋅ np  ∆q 
1
⋅ E B,t ⋅
⋅

36
 2 
N ⋅ l *2
Factor regarding the effect of friction between the plies:
K µy = µ ⋅ 2 ⋅
2
Dm
l
*
(
⋅ e p* ⋅ np - 1
)
with the equivalent friction coefficient µ according to Formula (47).
3.
(236)
(237)
Factor regarding the reaction of the curved bellows and of the angled restraining anchors due to
pressure:
i.
K Py(f) =
the pressure factor for the force is given by:
l
1
⋅ Ae ⋅ B
3
l*
(238)
Ae l B
⋅
6 l*
(239)
ii. the pressure factor for the moment is given by:
K Py m =
( )
Working force and working moment of the expansion joint are influenced in addition by the factor 4.
4.
Factor for the force due to bearing friction, providing restraining parts are existing:
d
K Fy = µ H ⋅ Ae ⋅ H
l*
with:
i
106
the friction coefficient μH of the hinges (see 6.2.9.3.2.2, NOTE);
(240)
BS EN 14917:2021
EN 14917:2021 (E)
ii
the relevant hinge bearing diameter dH (normally the pin diameter);
iii the length of the tie anchor l * measured between the centre points of the hinges.
c) Lateral working force and moment are finally given by:
(
)
(
)
Fw y,t = K y,t + K β y,t ⋅ ∆ y + K Fy + K µ y,t ⋅ P + K Py(f) ⋅ ∆ y ⋅ P
M w y, t =
l*  
⋅ K + K β y,t ⋅ ∆ y + K Fy + K µ y,t ⋅ P  + K Py (m) ⋅ ∆ y ⋅ P

2  y,t
(
)
(
)
(241)
(242)
where – after some cycles between y1 and y2 – the effective lateral deflection Δy related to any lateral
deflection y which is starting from the initial neutral position is given by:
∆y = y -
y1 + y2
2
6.2.9.3.3 Angular expansion joint
(243)
Two additional influences on the working moment have to be regarded for angular expansion joints
besides that for axial expansion joints; i.e. effect of pressurized curved bellows and that of the restraining
parts.
a) Angular effective spring rate of a single bellows:
The angular effective spring rate regarding only the elastic-plastic material behaviour is temperature
depending and given by:
2
)
(
D
K Θ , t = m ⋅ 1 - ν 2 ⋅ K x, t
8
with the effective axial spring rate according to Formula (212).
(244)
b) Additional factors:
The angular working moment of the bellows is influenced by the additional factors 1 to 3:
1.
Spring rate regarding the effect of the side wall tilting:
K βΘ ,t =
2.
E B,t
72
⋅
Dm ⋅ e p* ⋅ np  ∆q 
⋅

N
 2 
Factor regarding the friction between the plies:
(
2
K µΘ ,t = µ ⋅ Dm
⋅ e p* ⋅ np - 1
)
with the effective friction coefficient µ according to Formula (47).
(245)
(246)
107
BS EN 14917:2021
EN 14917:2021 (E)
3. Factor regarding the reaction moment of the curved bellows and the angled restraining anchors
due to pressure:
K PΘ =
Ae
6
⋅ l B ⋅ nB
The angular working moment of the expansion joint is influenced by the additional factor 4:
(247)
4. Factor regarding the moment from the bearing friction:
K FΘ = µ H ⋅ Ae ⋅
with:
i
ii
dH
2
(248)
the friction coefficient μH of the hinges (see 6.2.9.3.2.2, NOTE 2);
the relevant hinge diameter dH (normally the pin diameter).
c) The angular working moment is finally given by:
(
)
(
)
∆Θ
M w Θ , t = K Θ , t + K βΘ , t ⋅
+ K FΘ + K µΘ ⋅ P + K PΘ ⋅ ∆Θ ⋅ P
nB
(249)
where – after some cycles between Θ1 and Θ2 – the effective angular rotation ΔΘ related to any
angular rotation Θ which is starting from the initial neutral position is given by:
∆Θ = Θ -
Θ1 + Θ2
2
6.2.10 Torsion acting on bellows (unreinforced or reinforced)
(250)
The shear stress and deflection of a bellows due a torsional moment Mt acting round its centre-line shall
be calculated using the following equations.
Shear stress, in N/mm2 is given by:
τ =
2 ⋅ Mt
π ⋅ e ⋅ Di2
(251)
with Mt in N mm.
It shall conform to:
τ ≤ 0, 25 ⋅ f
Angle of twist of one bellows, in radians is given by:
Φ =
108
4 ⋅ M t ⋅ ld ⋅ N
π ⋅ G ⋅ e ⋅ Di3
(252)
(253)
BS EN 14917:2021
EN 14917:2021 (E)
with
— the developed length of one corrugation:
(
)
l d = 2 ⋅ w + 2 ⋅ rm ⋅ π - 2 + ∆L
(254)
For ΔL which is only valid for reinforced bellows with reinforcing members of specific cross section
see Figure 15.
— the shear modulus:
G=
(
E
2 ⋅ 1 +ν
)
(255)
Allowable torsional moment of one bellow due to stability is given by:
M t, alw =
2
π ⋅ K B ⋅ Dm
20
with a safety factor 5 included.
The acting torsion moment shall not exceed the allowable torsion moment:
M t ≤ M t, alw
NOTE
Formula (255) is only applicable for straight bellows.
(256)
(257)
6.3 Internal sleeve
6.3.1 Scope
This subclause describes the use and design of internal sleeve.
An internal sleeve shall be used to protect bellows from flow induced vibrations, see 6.3.3.
It may also be used to:
— hold friction losses to a minimum and secure smooth flow;
— protect bellows from erosion where application and design shall be evaluated individually between
user and expansion joints manufacturer.
The internal sleeve shall not be in direct contact with the convolutions; especially not to prevent a bellows
from column instability.
6.3.2 Additional symbols
The following symbols (see Table 15) are used in addition to that of Table 4.
6.3.3 Flow velocity
6.3.3.1 General
This subclause gives limits for flow velocities which, under the aspect of flow induced vibration, can be
tolerated by the bellows without using an internal sleeve.
109
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They were found either by practical experience (Table 16) or by experimentally proved physical
development (Formula (258). Flow energy of the fluid and damping behaviour of the bellows are taken
into account.
The given values include a safety factor of 1,32.
Table 15 — Additional symbols
Symbol
Description
Unit
CL
length factor; see Formula (261)
—
CS
coefficient for non-uniform flow velocity; see Formula (259)
—
Cv
Ct
ES,150
ES,t
Ki
Geff
LS
tS
tS,min
valw
vmax
vu
flow velocity factor; see Formula (262)
temperature factor: see Formula (263)
modulus of elasticity of internal sleeve at 150 °C
modulus of elasticity of internal sleeve at design temperature
influence factor regarding the flow medium; see 6.3.3.2, b)
—
—
N/mm2
(MPa)
N/mm2
(MPa)
—
mass of the bellows including reinforcement and of liquid between kg
the corrugations
length of internal sleeve; see Formula (261)
mm
minimum thickness of internal sleeve (see Table 17)
mm
design thickness of internal sleeve; see Formula (260)
allowable flow velocity; see Table 16 and Formula (258)
local maximum upstream flow velocity; see Formula (259)
upstream flow velocity; see 6.3.3.2, c)
6.3.3.2 Flow velocity limits
mm
m/sec
m/sec
m/sec
Flow velocities higher than that given below can induce resonant vibrations on the bellows corrugations
which may destroy the bellows.
a) Allowable flow velocity from experimental knowledge:
Values for allowable flow velocity are given in Table 16.
110
BS EN 14917:2021
EN 14917:2021 (E)
Table 16 — Allowable flow velocity
Fluid
Gases
Number of
plies
1
2
3
DN
50
100
≥ 150
a
2,5
3,5
4,3
7,5
10,5
13
5
7,0
Liquids
4
5
1
2
Flow velocity valw in m/s a
8,5
3
4
5
5
5,5
1,2
1,7
2,1
2,4
2,7
15
16,5
3,0
4,3
5,3
6,1
6,8
10
11
2,1
3,0
3,6
Velocity values to be interpolated for intermediate nominal diameters DN.
4,2
4,7
b) Allowable flow velocity from calculation:
Flow velocity values higher than that of Table 16 are allowed when they are given by the following
Formula (258):
v alw = 0, 026 ⋅ q ⋅ K i ⋅
KB
G eff
⋅ np
with the influence factor Ki:
(258)
— K i = 1 for liquids;
—
Ki = 2
for gases;
and the effective mass Geff in kg (see also Table 15).
NOTE 1
Flow velocity values may be smaller than that given in Table 16 when highly flexible bellows are
regarded.
The allowable flow velocities without the use of an internal sleeve shall not be greater than:
— 8 m/s for liquids;
— 20 m/s for gases.
c) Upstream velocity
The upstream velocity directly before the expansion joint depends on the system of piping where
build-in devices may cause a non-uniform flow velocity profile over the cross section.
Thus the local maximum upstream velocity is given by:
v max = v u ⋅ C S
where v u is the upstream flow velocity
(259)
111
BS EN 14917:2021
EN 14917:2021 (E)
and C S is given as follows:
— 1,0 for straight pipe system (length ≥ 10 times the pipe dimeter) ;
— 1,5 for systems with one and two elbows;
— 2,0 for systems with three and more elbows;
— 2,5 for systems with other devices; e.g. valves, T-connections.
Other reasons that may limit upstream flow velocities shall be regarded in addition.
The allowable upstream velocity shall conform to:
v max ≤ v alw
An inner sleeve shall be used if higher velocity values are given. But, the use of inner sleeves is not
mandatory if other damping devices are used, provided their effectiveness can be proved.
NOTE 2
steam.
Maximum flow velocities are normally not greater than 10 m/s for water and 300 m/s for gas and
6.3.4 Design conditions
6.3.4.1 General
The internal sleeve shall be designed in such a way that it does not restrict the movement of the expansion
joint.
Drain holes or other means of draining shall be provided for internal sleeves in expansion joints for steam
or liquid service when the flow is vertically upward.
NOTE
The material selected for the internal sleeve is usually similar to that of the inner ply of the bellows.
6.3.4.2 Minimum thickness
The minimum design thickness tS of the internal sleeve for normal applications shall be based on the
minimum thickness tS, min given in Table 17 modified with regard to the additional influences as given
below:
tS = tS, min ⋅ CL ⋅ C v ⋅ C t
where the following factors apply:
— length factor:
1

CL =  L
S

 450
if LS ≤ 450mm 


if LS > 450mm 

— flow velocity factor:
112
(260)
(261)
BS EN 14917:2021
EN 14917:2021 (E)
 1

Cv =  v
max

 30
if vmax ≤ 30m / s 


if vmax > 30m / s 

1

C t =  ES,150
 E
 S, t
if TS ≤ 150°C 


if TS > 150°C 

(262)
— temperature factor:
(263)
with:
—
—
ES,150 the internal sleeve’s modulus of elasticity at 150 °C and
ES, t the internal sleeve’s modulus of elasticity at design temperature TS.
Table 17 — Minimum internal sleeve thickness tS, min
DN
tS, min
50 to 80
0,6
100 to 250
300 to 600
700 to 1 200
1 400 to 1 800
6.4 Hardware
> 1 800
mm
1,0
1,2
1,5
2,0
2,5
6.4.1 General
Hardware shall be understood as being the restraining parts of expansion joints.
Hardware elements that are main pressure-bearing or pressure-bearing parts (see 4.2) shall be able to
withstand the relevant forces and moments due to the effect of pressure and of additional loadings
defined in 6.1.4.
6.4.2 Design parameters
6.4.2.1 Force due to pressure
The pressure acting on the bellows effective area results in a force (pressure thrust) Fp that acts as the
main load on the restraining parts. This force is given by Formula (24).
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6.4.2.2 Design stresses
6.4.2.2.1 Determination of design stresses
Stresses in the different parts of hardware may be determined either by calculation or by experiment.
6.4.3 explains the most relevant load cases of often used designs. An analytical conservative calculation
method for these designs is given in Annex K.
Where different design is used or stresses are needed more in detail or more precise the finite element
method (FEM) may be used. For this design method an appropriate standard like
EN 13445-3:2014 shall be used.
Where in special cases design by experiment is chosen the real build-in situation shall be taken into
consideration; i.e. the influence of the adjacent pipe runs with its supports shall be represented
adequately.
6.4.2.2.2 Limitation of design stresses
The design stresses for pressure bearing parts shall conform to the maximum allowable stresses
according to 6.1.3.1 or 6.1.3.3 taking into consideration the design temperature (see 6.4.2.3).
For design temperatures:
— below the creep range they shall be in accordance with the stress limits in Annex K;
— in the creep range the allowable stress f in Annex K shall be replaced by fcr.
=1 2.
For occasional loads the maximum allowable stresses may be increased by a load factor k l ,
6.4.2.3 Design temperature
6.4.2.3.1 General
The design temperature t of the different hardware parts can be expressed in relation to the fluid
temperature t f and shall not be smaller than stated below (see Table 18).
6.4.2.3.2 Insulated parts
— Parts directly attached to the pipe, e.g. plates or gussets:
t = tf
— Parts not directly connected to the pipe, e.g. loose plates, tie bars, and gimbals:
t = 0, 9 ⋅ t f
6.4.2.3.3 Non-insulated parts
(264)
(265)
— Parts directly connected to a pipe and not or only partly insulated will exhibit a variable temperature
profile depending on the design and application:
0,5 ⋅ t f ≤ t ≤ 1, 0 ⋅ t f
— Parts not directly connected to a non-insulated or insulated pipe:
t = max 80 °C; 0,33 ⋅ t f 


114
(266)
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6.4.2.3.4 Deformation
In addition to the above stress limits, load-dependent deformations which may impair the function of the
expansion joint shall be considered. This is relevant especially for gimbals, attachment plates, gussets and
pipes.
6.4.3 Hardware parts
6.4.3.1 General
Special design criteria shall be regarded for the below mentioned hardware parts independent of the
method used for the determination of design stresses.
6.4.3.2 Tie bar
The tie bar in Table 18 Ref. 1, restrains loads in tension and/or in compression (e.g. case of expansion
joints operating under vacuum).
If it is designed for:
— tension, the effect of thread shall be considered;
— compression, the effect of instability due to the compression shall be considered;
— bending due to frictional effects in the bearings, the effect of thread shall be considered.
6.4.3.3 Pin
The pin in Table 18 Ref. Two transmits load. It is designed for bending, shear and bearing pressure.
6.4.3.4 Lug
The lug in Table 18 Ref. Three is designed for tension and for bearing pressure in the hole.
The load carrying capacity of the bored section of the lug depends on its shape which in turn influences
the relevant stresses (see K.4).
If the limits given in K.4 are exceeded the validity of the calculation shall be proven.
6.4.3.5 Gimbals
A gimbal as shown in Table 18 Ref. Four is either round (ring) or square (case), and carries mainly
longitudinal load in direction of its centreline. It is designed for bending, shear and for bearing pressure
in the hole.
Additional aspects shall be considered:
— torsional moment for round gimbals;
— instability due to the bending (lateral torsional buckling) for square gimbals.
6.4.3.6 Attachment plate
A plate attached to the pipe as shown in Table 18 Ref. Five is either a closed or an intersected plate. The
plate is either directly connected to a pipe by welding or indirectly attached over radial free arresters
forming a floating system (possible only for closed plate). The arresters on the pipe are mainly
longitudinally loaded.
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The plate shall be designed for bending and shear and the influence of the loaded plate on the pipe shall
be regarded with respect to stresses and deformation (see 6.4.2.3.4). The pipe shall be designed for
tension load.
6.4.3.7 Gusset
A gusset as shown in Table 18, Ref. 6, is a plate connected longitudinally along the pipe, it restrains mainly
longitudinal load; a gusset shall be designed for bending and shear and the influence of the loaded gusset
on the pipe shall be regarded with respect to stresses and deformation as described in 6.4.2.3.4 and
6.4.3.6. Additionally gussets can be reinforced by rings. The rings have to be designed for bending as well.
6.4.4 Permanent joints
All welded joints in Table 18, Ref. 7, shall be designed for shear taking into account the joint coefficient z
which shall be chosen according to the type and extent of performed test, see also 8.4.4.
Table 18 — Load cases for hardware parts
Part
2 — Pin
1 — Tie bar
Ref.
Origin of stress
Diagram
Round
Shape
Tubular
Tension
σt
Compression
σc
Bending
σb
Bending
σb
Average
shear
τ
3 — Lug
Mean
bearing pressure
σ Be
116
Tension
σt
Mean
bearing
pressure (hole)
σ Be
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Part
Ref.
Origin of stress
Diagram
4 — Gimbal
Average
shear
τ
Square
A - A Cross section
B - B Bored cross section
Equivalent
& bending
σ= 1, 73 ⋅ τ + σ b
Round
Mean
bearing
pressure (hole)
σ Be
Key
A plate
B pipe
Plate
Equivalent
& bending
σ= 1, 73 ⋅ τ + σ b
Pipe
5 — Attachment plate
Average shear
τ
Tension
σ lm
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Part
Ref.
Origin of stress
Diagram
7 — Permanent
joints
Key
A gusset
B pipe
All welds
Gusset
Equivalent
& bending
1, 73 ⋅ τ + σ b
Pipe
6 — Gusset a
Average shear
τ
Tension
σ lm
Average shear
τ
a For (single) gussets no easy conservative calculation method is available (see K.11). When
calculating them the mentioned stresses shall at least be considered. Gussets connected with
reinforcing rings can be calculated acc. to K.12.
7 Manufacturing
7.1 General
In order to comply with this document the manufacturing methods used shall ensure that the expansion
joint conforms to the design requirements in Clause 6.
7.2 Materials
7.2.1 General
Materials shall be chosen from those given in Clause 5.
The manufacturer shall ensure that the material for non-pressure parts complies with that specified in
the design and/or the drawings.
7.2.2 Material traceability
For verifying the identity of materials used for parts which contribute to pressure resistance, i.e. part A
to B as defined in 4.2, a suitable traceability system shall be established. This system shall as a minimum
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have an appropriate procedure utilizing the documentation received from the supplier as requested in
5.3.
During processing, the identification of the parts shall be maintained. Identification can be maintained by
marking, stamping, a documented system or a combination of these methods, as convenient for the
manufacturer and as defined in the appropriate procedure.
Documentation associated with batches of welding consumables shall be maintained.
7.3 Permanent joints
7.3.1 General
For the purposes of this chapter permanent joints are defined as:
b) welded joints used during the bellows manufacturing process;
c) welded joints used for attaching the bellows to the fittings, refer to Table 7 for examples;
d) welded joints used on other pressure-bearing parts, classified as parts A, B and C in 4.2.
7.3.2 Process and personal
7.3.2.1 General
The welding of the permanent joints shall be executed by a suitable process and by suitable qualified
personal ensuring that the joints and their adjacent zones are free of any surface or internal defects
detrimental to the safety of the expansion joints.
7.3.2.2 Welding procedure
The suitable welding procedure shall be assessed against the requirements of EN ISO 15609-1:2019 1,
EN ISO 15609-2:2019,
EN ISO 15609-3:2004,
EN ISO 15609-4:2009,
EN ISO 15609-5:2011,
EN ISO 15609-6:2013, EN ISO 15613:2004 or EN ISO 15614-1:2017 , EN ISO 15614-2:2005, EN ISO
15614-3:2008, EN ISO 15614-4:2005, EN ISO 15614-5:2004, EN ISO 15614-6:2006, EN ISO 156147:2019, EN ISO 15614-8:2016, EN ISO 15614-10:2005, EN ISO 15614-11:2002, EN ISO 15614-12:2014,
EN ISO 15614-13:2012, EN ISO 15614-1:2013.
Welding procedures for non-pressure joints, e.g. those associated with parts D in Figure 1 may also be in
accordance with EN ISO 15610:2003, EN ISO 15613:2004 or EN ISO 15614-1:2017 1, EN ISO 156142:2005, EN ISO 15614-3:2008, EN ISO 15614-4:2005, EN ISO 15614-5:2004, EN ISO 15614-6:2006, EN
ISO 15614-7:2019, EN ISO 15614-8:2016, EN ISO 15614-10:2005, EN ISO 15614-11:2002, EN ISO 1561412:2014, EN ISO 15614-13:2012, EN ISO 15614-1:2013.
7.3.2.3 Welders and welding operators
Welders using manual processes, shall be qualified according to EN ISO 9606-1:2017 or
EN ISO 9606-4:1999 as appropriate.
Welding operators using mechanised or automated welding processes shall be qualified according to
EN ISO 14732:2013.
The operators and welders shall be qualified before commencing the production of permanent joints.
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7.3.3 Repair and rework during manufacturing
The expansion joint manufacturer shall produce and maintain detailed procedures for repair and
reworks on the expansion joint’s permanent joints as defined in 7.3.1 b) and c). If a permanent joint of
the bellows itself as defined in 7.3.1 a) is reworked this shall be carried out to qualified procedures and
the product proved by appropriate tests.
7.4 Forming of the bellows
7.4.1 Forming processes
7.4.1.1 General
Different forming processes may be applied:
— Bellows as shown in Figure 8 shall be manufactured by cold forming, like hydraulic and elastomeric
processes, roll forming or expanding mandrel forming.
— Bellows as shown in Figure 9 (half-corrugation) shall be manufactured by cold, warm or hot roller
bending.
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.
7.4.1.2 Limitations of the cold forming process
The amount of cold forming is given by the true strain of deformation sd depending on the type of bellows,
the forming process and the regarded location in the bellows corrugation (see 6.2.2.5.2).
a) Maximum equivalent true strain:
The maximum equivalent true strain of deformation for the different types of bellows is given below.
1) U-shaped bellows made from cylindrical tubes:

2
2 
1, 04 ⋅ sΘ

,o + 0, 31 ⋅ sΘ ,o ⋅ s b,o + 0, 41 ⋅ s b,o 


s d = max 



1
2, 0 ⋅  sΘ ,i + ⋅ s b,i 

3






(268)

2
2
1, 04 ⋅ sΘ

,i + 0, 31 ⋅ sΘ ,i ⋅ s b,i + 0, 41 ⋅ s b,i 


s d = max 



1
s
s
⋅
⋅
2,
0
+
 Θ ,o


b,o 
3






(269)

2
2 
 1, 04 ⋅ sΘ ,o + 0,31 ⋅ sΘ ,o ⋅ s b,o + 0, 41 ⋅ s b,o 


2
s d = max 1, 04 ⋅ sΘ2 ,1 + 0,31 ⋅ sΘ ,1 ⋅ s b,1 + 0, 41 ⋅ s b,1



2
2
 1, 04 ⋅ sΘ ,2 + 0,31 ⋅ sΘ ,2 ⋅ s b,2 + 0, 41 ⋅ s b,2 


(270)
2) U-shaped bellows made from half-corrugations:
3) Toroidal bellows:
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b) Allowable equivalent true strain:
The maximum equivalent true strain of deformation is limited by the possible deformation before
rupture may occur in the corrugation.
The allowable maximum equivalent true strain of deformation is given by:
(271)
s d, alw = s r ⋅ k r
where
— the true strain of rupture sr is given by:
(
s r = ln 1 + A / 100
)
(272)
with A the elongation of rupture in %;
— the safety factor kr according to Table 19.
The maximum equivalent true strain shall comply with:
s d, max ≤ s d, alw
Table 19 — Safety factor kr
Ply thickness
mm
Material
Austenitic steels and Ni-alloys a
a
b
ep ≤ 0,7
ep > 0,7
Ferritic and austenitic-ferritic steels b
Materials according to Table 2.
Materials with A ≥ 20 % and
(
R
 eH R p0,2
all
kr
0,9
0,8
0,5
) R  ≤ 0, 81 .
m
7.4.2 Heat treatment
Annealing of bellows after forming is not required if the limits according to 7.4.1.2 are met.
If for exceptional cases, such as:
— brittle fracture;
— corrosion;
— limit of 7.4.1.2 exceeded
annealing is required; it shall be carried out in an inert atmosphere or vacuum after the forming processes
have been completed.
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7.5 Tolerances
7.5.1 General
Dimensional tolerances of bellows and expansion joints depend on the tolerances of the base materials
used and on the manufacturing processes. They are the responsibility of the expansion joint
manufacturer.
This subclause deals with the tolerances that essentially influence the main characteristics of an
expansion joint such as pressure resistance, spring rate, fatigue and its installation.
NOTE
Provided the bellows are manufactured within the given tolerances the resulting tolerances of the
pressure resistance and the fatigue cycles will be covered by the foreseen safety factors and the maximum tolerance
of the calculated spring rate will not be higher than ± 30 %.
7.5.2 Bellows
7.5.2.1 U-shaped bellows without circumferential welds
7.5.2.1.1 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 strip/sheet or plate material shall be in accordance with
Table 20.
Table 20 — Tolerances on material thickness tn
Nominal material width: bn ≤ 2 100
Nominal thickness
tn
< 0,3 a
0,3 ≤ tn < 0,7
≥ 0,7
Tolerance range
Reduced (F) acc. to EN ISO 9445-1:2010, Table 1
Special (S) acc. to EN ISO 9445-2:2010, Table 1 (Method A)
Normal acc. to EN ISO 9445-2:2010, Table 1 (Method A)
a Tolerances are only defined up to nominal material width b < 600 in EN ISO 9445-1:2010. For
n
width ≥ 600 the tolerance range Reduced (F) for nominal width of 250 ≤ w < 600 should be used.
7.5.2.1.2 Corrugation height w
The tolerance on the corrugation height w shall not be greater than ± 5 % for ep up to 0,8 mm and ± 7 %
for ep greater 0,8 mm.
7.5.2.2 U-shaped corrugations and bellows with circumferential welds at their crest or root
7.5.2.2.1 Ply thickness ep
The tolerance of the nominal thickness of the plate material shall be either in accordance with
EN ISO 9445-1:2010 and EN ISO 9445-1:2010, Normal, or not greater than ± 7 % of tn if other standards
are used. If the tolerance is greater than ± 7 % of tn the actual mean thickness of the plate material shall
be taken into account for the calculation.
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7.5.2.2.2 Corrugation height w
The tolerance on the corrugation height w shall not be greater than ± 7 %.
7.5.2.2.3 Bellows tangent
The tolerance on the corrugation bellows tangent shall be in accordance with the related pipe ends.
7.5.2.3 Toroidal bellows
The tolerances on the corrugation dimensions (see Figure 16) shall not be greater than:
— ± 10 % on the corrugation gap Gp in the neutral position;
— ± 8 % on the mean corrugation radius r ;
— ± 10 % on the corrugation circularity ( 100 ⋅ ∆r r ), measured axially and diagonally (≈45°) considering
physical possibility.
NOTE
Higher tolerance on the circularity is acceptable when the additional meridional bending stresses are
regarded for the design (not covered by this document).
7.5.3 Expansion joint
7.5.3.1 Overall length
The overall length of an expansion joint shall be within the tolerance limits defined in Table 21.
NOTE
The tolerances given in the table do not apply to the overall length of axial or universal expansion joints.
Small deviations in the overall length as may occur during handling and transport do not affect the working
capability of the expansion joint.
Table 21 — Overall length tolerances
Overall length in mm
DN
≤ 500
501 to 1 000
1 001 to 4 000
> 4 000
Tolerance in mm
≤ 100
±3
±4
± 6
a
450 to 1 000
±6
±8
±10
a
125 to 400
a
> 1 000
±4
a
To be agreed by the purchaser.
±5
a
± 8
a
a
a
7.5.3.2 End fitting
The tolerances of end fittings (flanges, welding ends, threaded couplings) are given in the relevant
standards.
7.6 Production tests
Production tests shall be carried out as detailed in Clause 8.
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8 Testing, inspection and documentation
8.1 General
The expansion joint manufacturer shall be responsible for design, testing, examinations and certification
specified in 8.3 to 8.7. Where required in the technical specification, additional examination and testing
shall be performed.
8.2 Abbreviations
The following abbreviations apply for 8.4 to 8.5:
— LT Leak testing;
— NDT
Non-destructive testing;
— MT Magnetic particle testing;
— PT Penetrant testing;
— RT Radiographic testing;
— UT Ultrasonic testing;
— VT Visual testing.
NOTE
These abbreviations are taken from EN ISO 9712:2012 and are partially similar to Symbols in 6.1.1.
Therefore they only apply for 8.4 to 8.5 if not indicated otherwise.
8.3 Documents
Documents shall be compiled before fabrication commences according to Table 22.
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Table 22 — List of documents
Object
Design
Category
Documents
I
II
Design calculation reports
Manufacturing and control plans
Qualification of welders
NDT procedures
Pressure test procedure
procedures,
where
Welding procedures qualification records
(WPQR)
a
Yes
Qualification of welding operators
Heat treatment
applicable
External approvals
IV
Drawings and part list
Welding procedures specification (WPS)
Technical schedule
III
Qualification of welders
Qualification of welding operators
No
Qualification of NDT personnel
Approval of deviation of calculating
method, if applicable a
Yes
No
Yes
Deviations can be the application of specific fatigue curves, design in the creep range etc.
8.4 In-process inspection and testing
8.4.1 General
The examinations and tests specified below shall be carried out by personnel trained for the method used.
Written procedures or European standards (where appropriate) shall be available detailing the methods
to be used and the acceptance criteria.
8.4.2 Materials
Materials for all parts and welding consumable shall be checked to verify conformity with the specified
standards, purchase order and Clause 5. The below named material groups are according to
CEN ISO/TR 15608:2013.
8.4.3 Permanent joints
8.4.3.1 General
Typical welded joints of expansion joints are shown in Figures 301 and 32, they are defined as:
— W1 Longitudinal butt weld of bellows without circumferential welds;
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— W2 Longitudinal butt weld of bellows with circumferential welds; longitudinal butt weld of pipe
sections, reinforcing collars, reinforcing and equalizing rings;
— W3 Circumferential butt weld;
— W4 Fillet and edge welds for bellows attachment;
— W5 Fillet weld to connect part A to A and A to B (see 4.2 and Figure 1);
— W6 Fillet weld to connect part B to B (see 4.2 and Figure 1);
— W7 Non-pressure welds associated with part C and D in Figure 1 (these welds are not represented
in Figures 31 and 32).
See also Table 7.
Figure 31 — Typical weld joints of bellows and bellows attachment
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Figure 32 — Typical welded joints of bellows with circumferential welds
8.4.3.2 Welding documents and approvals
For welds W1 to W6 the following shall be checked:
a) for all expansion joints:
— Welding procedure specifications (WPS) are in accordance with EN ISO 15609-1:2019,
EN ISO 15609-2:2019, EN ISO 15609-3:2004, EN ISO 15609-4:2009, EN ISO 15609-5:2011,
EN ISO 15609-6:2013, and are established for all welding activities
b) for expansion joints category II, III, IV in addition:
— Approvals for all WPS shall be in accordance with 7.3.2.2;
— Appropriate and current approvals shall be in accordance with 7.3.2.3.
8.4.3.3 NDT testing
Permanent joints shall be subjected to tests in accordance with the requirements specified in 8.4.4.
8.4.4 Non-destructive testing of welds
8.4.4.1 General requirements and definitions
The tests specified in the paragraphs 8.4.4.3 to 8.4.4.6 are only valid and sufficient on condition that
expansion joints with W3, W4 or W5 welds are subjected to 100 % Leak testing (LT) as specified in
8.4.4.7.
For multi-ply bellows subjected to internal pressure, a venting hole shall be present in the outer plies. It
is usually located in the tangent. The venting hole shall be executed in a way that all plies except the tight
inner ply have a hole and are in contact with the atmosphere.
If it is not possible (e.g. for external pressure) and not practical to have a venting hole or to have only one
ply undrilled, a special LT shall be performed to ensure the tightness of the ply in contact with the medium
under pressure.
If a LT with gas is not possible or practical a hydrostatic pressure test shall be accepted instead.
8.4.4.2 Dissimilar metal welds
The test methods and the extent of testing for welded joints between ferritic and other material (e.g.
austenitic, nickel alloys) shall be that applicable to the higher group of the base materials (material group
according to CEN ISO/TR 15608:2013).
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8.4.4.3 Seam welds of bellows
8.4.4.3.1 Bellows without circumferential welds
8.4.4.3.1.1 Longitudinal butt welds of the bellows W1
This subclause applies to bellows manufactured out of cylinders which are corrugated after longitudinal
butt welding. These longitudinal butt welds shall be subjected to:
— 100 % VT examination before forming the corrugations of the bellows;
— NDT examination in accordance with Table 23 after forming the corrugations of the bellows.
For bellows fabricated in series, these shall be subject to NDT of at least 10 % of the bellows quantity but
not less than 1. Samples shall be taken throughout the production run of manufacture.
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Table 23 — NDT for longitudinal butt welds W1 of bellows without circumferential welds
DN
mm
≤ 1,5
Bellows forming method
Bellows forming method
mm
—
PT a b
in- / outside
≤ 1,00
—
PT a
inside
≤ e p, max
PT a
outside
> e p, max
PT
outside
b
PT a b
in- / outside
e p, max = min 0, 087 D i ; 4 

a
ep
Rolling
> 1,5
≤ e p, max
> 300
Multi-ply
Hydraulic,
elastomer
forming
or similar
method
ep
≤ 300
Single-ply

PT
inside
> 1,00
> e p, max
Hydraulic,
elastomer
forming
or similar
method
Rolling
—
—
—
—
—
—
PT a or b
tight ply
PT a or b
tight ply
e p, max = min 0, 054 D i ; 2, 5


The test shall be performed on the longitudinal welds at the outside crest, to the maximum extent possible
considering physical accessibility.
The test shall be performed on the longitudinal welds at the inside root of the corrugations, to the
maximum extent possible considering physical accessibility.
8.4.4.3.2 Bellows incorporating circumferential welds
8.4.4.3.2.1 General
This subclause deals with bellows and corrugations manufactured out of half-corrugations
circumferentially welded at their crest and/or root as detailed in 6.2.3.7.
8.4.4.3.2.2 Longitudinal butt welds W2
The type of NDT required and its extent shall be determined taking into account the appropriate joint
coefficient z in accordance with Table 24.
If radial butt welds are present on the original flat ring plates, they shall be tested before forming by RT
or UT.
After forming the half-corrugations and welding them together, the longitudinal butt welds of the
corrugations shall be subjected again to RT or UT examinations to the same extent as before forming.
In addition VT and PT or MT examinations shall be performed on the outside surface of the longitudinal
welds of the corrugations, to the maximum extent possible considering physical accessibility.
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8.4.4.3.2.3 Circumferential butt welds W3
The type of NDT required and its extent shall be determined in accordance with Table 26 taking into
account the material group, the category and the wall thickness.
8.4.4.4 Pipe welds
8.4.4.4.1 Longitudinal butt welds W2 in pipe sections
The weld joint coefficient z shall be selected in accordance with Table 24.
The type of NDT and its extent shall be determined taking into account the joint coefficient z in accordance
with Table 25.
Table 24 — Limitations of joint coefficient for longitudinal butt welds W2
Piping
Unlimited
Joint coefficient z
Fluid Gr. 2
TS −10 °C to 300 °C
PS ≤ 20 bar
Gr. 1.1, 1.2, 8.1, ≤ 16 mm
PS·V ≤ 20 000 bar·L, when t > 100 °C
PS·V ≤ 50 000 bar·L, when t ≤ 100 °C
0,7 a
Gr. 1.1, 8.1, epp ≤ 50 mm
Gr. 1.2, epp ≤ 30 mm
Gr. 9.1, 9.2, epp ≤ 30 mm
Gr. 8.2, 10, epp ≤ 16 mm
Unlimited
Unlimited
a
Vessel
0,85
Unlimited
1
When z = 0,7 is chosen in applications for vessels a higher test pressure shall apply. Test
pressure PT = max(2,0·PS ; 1,25·PS·f20/f).
Table 25 — Extent of NDT on longitudinal butt welds W2 in pipe sections and in bellows with
circumferential welds
Joint coefficient z
0,7
0,85
a
1
Extent %
VT
100
PT or MT
RT or UT
0
0
10
100
10 a
100
An extent of 25 % shall be used for material groups 8.2, 9.1, 9.2 and
10 in applications for vessels.
8.4.4.4.2 Circumferential butt welds W3 in pipe sections and in bellows with circumferential
welds
The type of NDT and its extent shall be determined taking into account the material group, PED Category
and wall thickness in accordance with Table 26.
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Material Group
1.1, 1.2, 8.1
PED Cat.
Table 26 — Extent of NDT for circumferential welds W3
I
II
III
IV
I
1.3, 1.4, 2.1, 2.2, 4.1, 4.2, 8.2, 8.3,
9.1, 9.2, 9.3, 10.1, 10.2
II
III
IV
I
3.1, 3.2, 3.3, 5.1, 5.2, 5.3, 5.4, 6.1,
6.2, 6.3, 6.4, 7.1, 7.2, 11,
all other not mentioned
a
b
II
III
IV
Extent %
Thickness
mm
All
VT
100
≤ 30
> 30
≤ 30
> 30
RT a
or
UT a
0
5b
0
5b
0
10 b
5b
10 b
0
10 b
> 30
≤ 30
PT a
or
MT a
100
5b
10 b
5b
10 b
5b
≤ 30
> 30
10 b
> 30
25 b
10 b
≤ 30
≤ 30
> 30
≤ 30
> 30
100
≤ 30
> 30
25 b
25 b
100
100
100
100
10 b
10 b
10 b
10 b
25 b
25 b
25 b
25 b
25 b
25 b
25 b
25 b
100
100
100
100
These test can be omitted when the longitudinal stress at design conditions is lower than 20 % of
the yield strength and not higher than 50 N/mm2.
If the percentage is less than 100 % at least one complete weld shall be examined.
8.4.4.5 Bellows attachment welds W4
The type of NDT and its extent shall be determined taking into account the material group and PED
Category in accordance with Table 27.
Circumferential root and crest welds in bellows are covered by 8.4.4.4.2.
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EN 14917:2021 (E)
Material Group
1.1, 1.2, 8.1
1.3, 1.4, 2.1, 2.2, 4.1, 4.2, 8.2, 8.3, 9.1,
9.2, 9.3, 10.1, 10.2
3.1, 3.2, 3.3, 5.1, 5.2, 5.3, 5.4, 6.1, 6.2,
6.3, 6.4, 7.1, 7.2, 11, all other not
mentioned
a
b
PED Cat.
Table 27 — Extent of NDT for bellows attachment welds W4
I
II
III
IV
I
II
III
IV
I
II
III
IV
Extent %
VT
100
100
100
PT a
or
MT a
0
0
10 b
100
10 b
10 b
25 b
100
25 b
25 b
25 b
100
This test can be omitted when the von Mises stress at design conditions is lower
than 20 % of the yield strength and not higher than 50 N/mm2.
If the percentage is less than 100 % at least one complete weld shall be examined.
8.4.4.6 Hardware Fillet welds W5 and W6
8.4.4.6.1 General
The type of NDT and its extent shall be determined taking into account the material group and PED
Category in accordance with Table 28.
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Table 28 — Extent of NDT for fillet welds W5 and W6
Extend %
VT
I
1.1, 1.2, 8.1
1.3, 1.4, 2.1, 2.2, 4.1, 4.2, 8.2, 8.3,
9.1, 9.2, 9.3, 10.1, 10.2
3.1, 3.2, 3.3, 5.1, 5.2, 5.3, 5.4, 6.1, 6.2, 6.3, 6.4,
7.1, 7.2, 11, all other not mentioned
a
II
W6
PT a
or
Mt a
0
100
0
III
IV
10
I
10
II
100
10
III
IV
10
I
25
II
III
IV
100
25
100
Joint
coefficient z
Material Group
PED Cat.
W5
Extend %
VT
PT
or
Mt
0,7
0
1
0
0,85
0,7
0,85
1
0
100
0,7
0
0
0
0
0,85
10
0,7
0
1
10
0,85
10
0,7
0
1
0,85
1
10
100
0,7
10
10
0
0,85
25
0,7
0
1
25
0,85
25
0,7
0
1
0,85
1
0,7
0,85
1
25
100
25
25
0
100
100
This test can be omitted when the welding shear stress at design conditions is lower than 20 % of
the yield strength and not higher than 50 N/mm2.
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8.4.4.6.2 Non pressure raised welds
Weldings which are not contributing to tightness or restraining pressure thrust shall be subjected to
100 % visual testing.
8.4.4.7 Leak testing
After completion of weldings contributing to tightness, the expansion joint shall be subjected to Leak test
in accordance with 8.5.2.
8.5 NDT methods
8.5.1 Quality level
The general quality level shall be in accordance with Table 29a and b.
Table 29a — Quality level for bellows according to EN ISO 5817:2014 depending of service
conditions and test methods
Service conditions
Surface imperfections and
imperfections in joint geometry
Standard, Fatigue
Creep
Internal
imperfections
VT
PT and MT
RT and UT
B
B
C
B
B
B
Table 29b — Quality level for other parts than bellows according to EN ISO 5817:2014
depending of service conditions and test methods
Service conditions
Surface imperfections and
imperfections in joint geometry
Standard
Creep
Internal
imperfections
VT
PT and MT
RT and UT
C
C
C
B
8.5.2 Acceptance levels and testing techniques
B
B
Depending on the quality level of Table 29 acceptance levels and testing techniques shall be selected
according to EN ISO 17635:2016, Annex A.
Leak testing shall be in accordance with Table 30.
Table 30 — Leak test acceptance criteria and methods
Methods
Acceptance criteria
EN 1779 Criteria for method
The leakage rate shall be agreed
EN 1593 Bubble emission technique
EN ISO 20485:2018 Tracer gas method
between all parties involved. a
EN 13184:2001 Pressure charge method
a
134
For bubble testing methods according to EN 1593 and EN 1779:1999, Table A.2
technique C1 and C2, the maximum detectable leak rate is 10−4 Pa m3/s.
BS EN 14917:2021
EN 14917:2021 (E)
8.5.3 Non-destructive testing Personnel qualifications and approval
NDT personnel shall be qualified according to EN ISO 9712:2012 to at least level 1 under supervision of
personnel qualified to level 2 or 3 who shall also be responsible for the evaluation of the results.
Visual testing shall be performed by personnel with sufficient knowledge and experience in relation to
the relevant standards and specifications. A certification according to EN ISO 9712:2012 is not required.
8.5.4 Non-destructive testing documentation
All NDT activities (except VT) shall be documented in reports prepared in accordance with the standards
referred to in EN ISO 17635:2016.
Table 31 — Additional acceptance criteria for surface imperfections
Identification of surface imperfections
EN ISO
6520-1
Reference
number
100
2017
Designation
Cracks (all)
Surface pores
Maximum permitted imperfections
EN ISO 5817, quality level
Additional requirements a
1.1
Not permitted
—
1.3
4011–4013
Lack of fusion (all)
2.12
5011–5012
Undercut
1.7
402
Lack of penetration
Expansion joint Category
EN ISO
5817
Reference
number
2.13
I
C
II
B
III, IV
B1
Not permitted
C
Not permitted
C
B2
Shrinkage groove
1.8
C
C
B
503
Excessive convexity
1.10
C
C
C
Overlap
1.13
504
506
507
509
511
Excessive weld metal
Excess penetration
Linear misalignment
Sagging
Incompletely fillet groove
1.9
1.11
C
C
3.1
B
1.14
B
1.14
B
C
C
Not permitted
If a full penetration weld is
required
2 t ≥ 16 mm:
h ≤ 0,5 mm
for
imperfections
6 mm ≤ t < 16 mm:
h ≤ 0,5 mm
for
imperfections
t < 6 mm:
h < 0;3 mm
for
imperfections
—
short
short
short
B
Smooth transition is required:
Weld toe angle ≥ 120°
B
—
B
B
B
B
B
— diameter = 2 mm
and
— depth = 1 mm
with additional conditions that:
— it does not occur at a stop or
restart
— it is not systematic on the
same
weld for pressure welds or
load
carrying attachment welds.
—
5013
502
1 When occurring at the surface,
B
Same as 502
—
—
—
—
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Identification of surface imperfections
EN ISO
6520-1
Reference
number
512
515
516
517
601
602
603
604
605
606
a
Designation
EN ISO
5817
Reference
number
Excessive asymmetry of
fillet welds
1.16
Root porosity
1.18
Root concavity
Poor restart
Stray flash
Spatter
1.17
1.19
1.22
Expansion joint Category
I
II
D
B
D
B
Not permitted
Not permitted
Not permitted
Not permitted
Torn surface
–
Not permitted
Chipping mark
–
Grinding mark
Under flushing
–
–
III, IV
EN ISO 5817, quality level
1.23
Symbols according to EN ISO 5817:2014.
136
Maximum permitted imperfections
Not permitted
D
B
Additional requirements a
—
Short
imperfections:
permitted.
—
not
—
Shall be removed, e.g. by grinding
plus MT or PT or ensure that no
cracks is left.
NOTE
In the special case of
circumferential welded fins which
are attached to tubes by a
mechanised welding process,
spatter shall be minimized, but any
produced may remain, regardless
of the material or heat treatment
involved.
Shall be ground, a
transition is required.
smooth
Any local under flushing shall be
related
to
the
design
characteristics
(calculated
thickness
+
corrosion
allowance = minimum thickness
for base material)
(Thickness shall be measured by
ultrasonic method)
BS EN 14917:2021
EN 14917:2021 (E)
Table 32 — Additional requirements for acceptance criteria for internal
imperfections detected by RT
Identification of imperfections
EN ISO
6520-1
Reference
number
100
2011–2012
2013
2014
2015–2016
Designation
Cracks (all)
Maximum permitted imperfections
Expansion joint Category
EN ISO
5817
I
II
III, IV
Reference
number EN ISO 5817, quality level
1.1
Gas pore
2.3
2.4
2.5
2.6
C
Not permitted
B
B
Additional requirements a
—
For No 2012, the distance between
two pores shall be greater than
twice the diameter of the bigger
one, and not less than 4 mm (to
ensure that there is no chance of
having a lack of fusion).
For No 2014 same as for uniformly
distributed pores.
202
2024
300
301
302
303
3042
304
4011–4013
402
a
—
Shrinkage cavity (all)
Solid
inclusion
Slag
inclusions
(all)
Flux
inclusions
(all)
Oxide inclusions
Metallic
(copper)
Metallic
(all others)
inclusions
inclusions
Lack of fusion (all)
Lack of penetration
Multiple imperfections in
any cross section
2.7
2.8
For No 2015 and 2016 l = 0,3 t,
maximum 5 mm, and d = 2 mm
Not permitted
—
1)
1) d = 0,3 t, maximum 3 mm and
depending of the application:
2.11
Not permitted
—
2.12
Not permitted
2.9
2)
2.10
2.13
4.1
1 < t ≤ 25 mm
In case of several line at slag
inclusions with a distance between
2 of them less than twice the
longest of them, the total length is
to be considered as a defect.
B
Not permitted
Symbols according to EN ISO 5817:2014 d = maximum size of pore.
B
2) Same as for gas
No 2011–2012–2013
—
B
pore
If a full penetration weld is
required
—
8.6 Final assessment and documentation
8.6.1 General
Prior to final certification, the manufacturer shall carry out a final assessment to verify that the expansion
joint has been manufactured in compliance with all specified requirements. The required documentation
shall be compiled.
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8.6.2 Final inspection
8.6.2.1 Visual inspection
An external and internal visual inspection shall be carried out prior to completion of any external coating,
to the maximum extent possible, to verify that dimensions and execution comply with the construction
drawings.
8.6.2.2 Proof test
8.6.2.2.1 Testing conditions
The expansion joint shall be proof tested in the manufacturer's shop by testing the main pressure bearing
parts as classified in Clause 4.
For category I expansion joints, this proof test may be performed on a statistical basis (e.g. at least 10 %
but not less than 1).
The proof test shall be a hydrostatic pressure test, except where the hydrostatic pressure test is harmful
or impractical. In these instances, a pneumatic pressure test or other tests shall be performed.
The proof test shall always be carried out, under controlled conditions, with appropriate safety
precautions and equipment, and in such a way that the persons responsible for the test are able to make
adequate inspections of all pressurized parts.
NOTE
To avoid instability during testing, special consideration should be given to the fixation of the end
connections of the samples in the test equipment.
8.6.2.2.2 On site and spool testing
Where the proof test is not practicable at the manufacturer shop, due to the size or mode of manufacture,
the complete expansion joint shall be proof tested on site after installation on the piping system or vessel.
When spools with expansion joints are tested outside the final piping, special care shall be taken that
guiding and fixing is similar to the final installation.
(Spool means: prefabricated assembly of components which forms part of a piping system.)
8.6.2.2.3 Hydrostatic pressure test
The hydrostatic pressure test shall be performed at room temperature; normally the test medium should
be water.
The test pressure shall be not less than the greater of the two values determined by the following:
PT = 1, 25 ⋅ PS ⋅
f 20
f
PT = 1, 43 ⋅ PS
or
PT = 1, 43 ⋅ PN
for expansion joints designed on PN basis (see 6.1.2.2).
(273)
(274)
(275)
The ratio f 20 f used shall be the lowest ratio of all pressure bearing parts and of the bellows reinforcing
parts.
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If different values of PT are required they shall be agreed between the parties involved.
The expansion joint shall hold at test pressure for a sufficient period to allow the examination, for at least
5 min.
The hydrostatic pressure test shall be passed if no leakage or visible plastic deformation is observed, in
particular in the bellows section.
NOTE
The manufacturer is responsible to avoid corrosion during hydrostatic pressure tests. Therefore it is
recommended to control the halide concentration of the water for hydrostatic tests of expansion joints (bellows
included) made of austenitic stainless steels. An adequate limit for the halide concentration is 0,005 %.
8.6.2.2.4 Pneumatic pressure test
Pneumatic pressure test shall only be permitted in cases where a hydrostatic pressure test is detrimental
to the expansion joint or is not practical.
The conditions of testing shall be established and agreed between all parties concerned.
The requirements of 8.6.2.2.1 and 8.6.2.2.2 shall be fulfilled.
Due to the hazard involved in pressure testing using a compressible medium, special consideration shall
be given to factors such as:
a) maintaining during the test the highest practicable standards of safety and ensuring that only
personnel involved in the testing have access to the testing area, that if the testing is not performed
in a special room the region in the immediate vicinity of the testing area is sealed off and warning
signs used highlighting the danger zone and prohibited area;
b) NDT main pressure bearing parts by MT or PT the inner surface of the welds which have not been
subjected to 100 % volumetric testing as required for the longitudinal seams. If the inner surface is
not accessible UT shall be performed before the pressure test. The amount of testing shall be 10 % of
all circumferential welds including all butt joints of the pipe sections;
c) resistance of the expansion joint materials to fast fracture and the absolute necessity of avoiding
brittle fracture;
d) metal temperature, which shall be at least 25 °C above the reference temperature at which brittle
fracture might occur;
e) the extent of remote monitoring provided during the test.
The test pressure shall be in accordance with 8.6.2.2.3.
The pressure shall be gradually increased to a value of 50 % of the required test pressure PT. Thereafter
the pressure shall be increased in steps of approximately 10 % of the required test pressure until the test
pressure PT is reached.
The pressure shall be then reduced to the inspection pressure Pi:
Pi = PS ⋅
Pi = PN
f 20
f
for design on PS / TS basis
for design on PN basis (see 6.1.2.2)
(276)
The expansion joint shall be held at inspection pressure Pi for a sufficient period to allow the examination,
for at least 5 min.
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The pneumatic pressure test shall be passed if no leakage or visible plastic deformation is observed in
particular way in the bellows sections.
8.6.2.2.5 Other tests
In cases where a hydrostatic or pneumatic pressure test would be detrimental or impractical they shall
be substituted by appropriate NDT (100 % RT and/or UT and 100 % PT and/or MT) subject to agreement
between the parties involved.
Consideration shall be given to final testing at an early stage in the design phase, so that arrangements
can be made to ensure that the individual component receive an appropriate test.
8.6.2.2.6 Documentation of the proof test
The essential data of the proof test shall be confirmed in a test certificate. Where the proof test is not
carried out using water, the test medium shall be recorded.
8.7 Documentation
8.7.1 Final documentation package
The final documentation package shall contain the documents specified in Table 33 and shall be provided
to the customer only on request.
Table 33 — Final documentation
No
Documents
1
Design
3
Approvals
2
4
5
6
7
8
b
Expansion joint category
I
II-IV
X
X
X
Technical schedule
8.3
Materials certificate
8.4.2
Xa
Report of proof test
8.6.2.2.6
X
Report of NDT
Declaration of conformity
Operating instructions
NOTE X: to be included.
a
Subclause
8.5.4
8.7.2
8.7.3
−
X
Xb
X
X
X
X
X
X
Xb
X
Dependent on the manufacturer's decision.
It is recommended to send the original to the customer (in some countries, this is mandatory).
Copy shall be stored for ten years by the manufacturer.
8.7.2 Declaration/certification
On satisfactory completion of final assessment and documentation, the manufacturer shall issue
depending on the category of the expansion joints, a declaration of conformity, appropriate to the
conformity assessment procedure applied.
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EN 14917:2021 (E)
8.7.3 Operating instructions
When placed on the market, expansion joints shall be accompanied with instructions for the user,
containing all the necessary safety information relating to handling, packing, storage, installation and
putting into service according to Clause 10.
If relevant, instructions shall include necessary information for maintenance including checks by the user.
Instructions shall also cover information affixed to the expansion joints in accordance with Clause 9,
Marking and labelling, and shall be accompanied, where appropriate, by the technical documents,
drawings and diagrams necessary for a full understanding of these.
9 Marking and labelling
The marking of the expansion joint shall be durable and be by a nameplate or other permanent means
(e.g. by electrochemical etching). The minimum marking shall be:
a) manufacturer’s name, trademark or sign;
b) year of manufacture;
c) manufacturer’s type of expansion joint (based on 4);
d) identification number for the traceability (batch and/or serial number);
e) Nominal size DN;
f)
pressure/temperature:
— PS/TS (min./max.), for design on PS/TS basis;
— PN/t-range, for design on PN basis.
For the second alternative the manufacturer shall provide de-rating factors depending on the design.
These factors may be fixed to the expansion joint by a tag;
g) nominal or specified movement;
h) the correct flow direction − as appropriate − shall be indicated by an arrow (separate from the name
plate).
10 Handling and installation
10.1 General instructions
Handling and installation of expansion joints need particular care and shall be carried out by experienced
staff.
Damage to expansion joints, especially the bellows, shall be avoided, in order that the full pressure
reliability and service life is achieved.
The manufacturer’s authorization shall be obtained before any repairs are carried out.
The installation procedure shall regard the instructions according to 10.3 up to 10.5 and if relevant,
details of installation shall be clarified between the installer and the expansion joint manufacturer before
any installation attempt is made.
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10.2 Packaging and storage
Suitable packaging shall be provided for expansion joints, to ensure that there is protection during
transport and storage from the effects caused by dirt or aggressive atmospheres.
Transport safety devices or pretension or shipping bars shall not be removed before installation.
10.3 Installation
Care shall be taken to ensure that lifting chains or other lifting devices do not damage the bellows or the
bellows outer cover.
Care shall be taken to ensure that the expansion joints are installed at the correct location and the right
way round, indicated by the flow direction arrow.
A check shall be carried out to ensure that the service data on the identification plate matches the
operating data.
Expansion joints shall be installed at the correct length and any cold spring (pre-stressing) shall be
considered according to the design (see also Annexes C and D).
During installation the bellows shall not be stretched, compressed, bent or twisted, unless such
movements are within the design envelope.
Gaskets and seals shall be positioned correctly.
A check shall be made to ensure that no foreign objects or media inside or outside of corrugations will
affect the working of the bellows.
During welding no electrical current shall be conducted through the bellows.
The expansion joint shall not be used for an earthing connection.
After installation transport safety devices and pretension bars shall be removed.
Anchors and pipe guides shall be firmly installed prior to pressure testing.
Consideration shall be given to the inclination of the expansion joint in order to provide for drainage.
10.4 Unrestrained expansion joints
Unrestrained expansion joints (axial or universal) under pressure will exert a considerable axial force on
the pipeline, i.e. anchors. It is essential that checks are carried out when the expansion joint is first
pressurized to ensure that there is no unforeseen stretching of the bellows. If unforeseen movement is
apparent then the pipe guides or anchors shall be examined to ensure that they have been installed
correctly and sufficiently designed for the duty.
The distance between the bellows and the first support as well as the distances between the supports
shall be such that any buckling of the pipework is avoided (see Annex C). Only one expansion joint shall
be installed between each set of anchors.
Only axial pipe guides or anchors shall be used adjacent to an unrestrained expansion joint.
10.5 Restrained expansions joints
Special instructions (see Annex C) shall be observed for the installation of restrained expansion joints
(angular or lateral). It is important that the direction of the pipe movement is perpendicular to the axis
of the pins.
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EN 14917:2021 (E)
Annex A
(informative)
Categories of expansion joints
A.1 General
The following expositions offer guidance for the determination of the appropriate category of expansion
joints incorporated in pressure vessels or piping systems. They are exactly related to the PED2) but, are
specific to the regarded expansion joints.
In the case a discrepancy to the PED may occur the PED is binding.
NOTE
The category of an expansion joint should be identical to that of the vessel or the piping where it is
installed and it is dependent on the specification determined by the manufacturer of the vessel or the piping. The
category of an expansion joint scheduled for a vessel is defined using all relevant parameters of the vessel which
are only known to the vessel manufacturer.
A.2 Determination of expansion joints categories
Expansion joints used as parts of pressure vessels or piping components are to be regarded as pressure
equipment according to PED, Article 2. Components (bellows,…) forming an expansion joint used as part
of a pressure vessel should be considered as components of the pressure vessel.
According to PED, Article 13, pressure equipment referred to in Article 4 (1) shall be classified by
category in accordance with PED, Annex II according to ascending level of hazard. The categories are
dependent on PS, V (volume) or DN according to their use in vessels respectively piping and on the fluid
group (see A.3).
According to PED, Article 4 (1) (a) to 4 (1) (d) the technical requirements of the different pressure
equipment which must satisfy the essential requirement set out in PED, Annex I are defined in detail (see
A.4).
According to PED, Annex II the categories are defined by using the relevant conformity assessment tables
given there (see A.5).
A.3 Fluid groups
A.3.1 General
For the purposes of classification the fluids shall be divided into two groups in accordance with PED,
Article 13 (1) (a) and 13 (1) (b), see A.3.2 and A.3.3.
A.3.2 Group 1
Group 1 comprises dangerous fluids3) defined as:
— explosive;
2) Pressure Equipment Directive 2014/68/EU of the European Parliament and of the Council [1].
3) A dangerous fluid is a substance or preparation covered by the definitions in Article 2 (2) of the PED.
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EN 14917:2021 (E)
— extremely flammable;
— highly flammable;
— flammable (where the maximum allowable temperature is above flashpoint);
— very toxic;
— toxic;
— oxidising.
A.3.3 Group 2
Group 2 comprises all other fluids not referred to in A.3.2.
A.4 Technical requirements
A.4.1 Expansion joints for vessels
The category for an expansion joints used as part of a pressure vessel is determined by the volume of the
vessel where it is built in.
Where a vessel is composed of a number of chambers, it shall be classified in the highest category
applicable to the individual chambers. Where a chamber contains several fluids, classification shall be on
the basis of the fluid which requires the highest category.
a) Vessels for gases, liquefied gases, gases dissolved under pressure, vapours and also those liquids
whose vapour pressure at the maximum allowable temperature is greater than 0,5 bar above normal
atmospheric pressure (1 013 mbar) within the following limits:
1) for fluids in Group 1 with a volume greater than 1 L and a product of PS and V greater than
25 bar L, or with a pressure PS greater than 200;
2) for fluids in Group 2, with a volume greater than 1 L and a product of PS and V greater than
50 bar L, or with a pressure PS greater than 1 000 bar.
b) Vessels for liquids having a vapour pressure at the maximum allowable temperature of not more
than 0,5 bar above normal atmospheric pressure (1 013 mbar) within the following limits:
1) for fluids in Group 1 with a volume greater than 1 L and a product of PS and V greater than
200 bar L, or with a pressure PS greater than 500 bar;
2) for fluids in Group 2 with a pressure PS greater than 10 bar and a product of PS and V greater
than 10 000 bar L, or with a pressure PS greater than 1 000 bar.
A.4.2 Expansion joints for piping
The category of an expansion joints used as a piping component is normally determined using the
diameter (DN) of the pipe to which it is connected. In a case where the diameter of the expansion joint
dependent on the designed type, e.g. a pressure balanced axial expansion joint (see Table 1) is much
greater than the pipe diameter and a higher risk is expected the category should be determined using this
greater diameter.
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a) Piping for gases, liquefied gases, gases dissolved under pressure, vapours and those liquids whose
vapour pressure at the maximum allowable temperature is greater than 0,5 bar above normal
atmospheric pressure (1 013 mbar) within the following limits:
1) for fluids in Group 1 with a DN greater than 25;
2) for fluids in Group 2 with a DN greater than 32 and a product of PS and DN greater than 1 000
bar.
b) Piping for liquids having a vapour pressure at the maximum allowable temperature of not more than
0,5 bar above normal atmospheric pressure (1 013 mbar), within the following limits:
1) for fluids in Group 1 with a DN greater than 25 and a product of PS and DN greater than 2 000
bar;
2) for fluids in Group 2 with a PS greater than 10 bar, a DN greater than 200 and a product of PS
and DN greater than 5 000 bar.
A.4.3 Sound engineering practice (SEP)
According to PED, Article 4, section 3, expansion joints below or equal to the limits in A.4.1 and A.4.2
respectively must be designed and manufactured in accordance with the sound engineering practice of a
Member State in order to ensure safe use. The expansion joints must be accompanied by adequate
instructions for use and must bear markings to permit identification of the manufacturer or of his
authorized representative established within the Community. Such expansion joints must not bear a CE
marking.
A.5 Expansion joint category
The assessment figures (based on the assessment tables in Annex II of the PED) to classify the expansion
joints incorporated in vessels or in piping by categories in accordance with the above requirements are
listed in Table A.1.
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Table A.1 — Expansion joint classification
Expansion joint
incorporated in
Vessel
Piping
Fluid
Gas
Liquid
Gas
Liquid
Group
PED, Annex II,
Article 3
corresponding
Table
1
1
1
3
2
2
1
2
1
2
2
4
6
7
8
9
Exceptionally, expansion joints intended to contain an unstable gas and falling within categories I and II
on the basis of PED, Annex II, Article 3, Table 1 must be classified in category III.
Exceptionally, expansion joints used in vessels intended for generating warm water (PED, Annex II,
Article 3, Table 4) at temperature greater than 110 °C which are manually fed with solid fuels and have a
PS · V greater than 50 bar L must subject either to an EC design examination (PED Module B) or full
quality assurance (PED Module H).
Exceptionally, expansion joints intended for unstable gas and falling within categories I and II on the basis
of PED, Annex II, Article 3, Table 6 must be classified in category III.
Exceptionally, expansion joints containing fluids at a temperature greater than 350 °C and falling within
categories II on the basis of PED, Annex II, Article 3, Table 7 must be classified in category III.
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EN 14917:2021 (E)
Annex B
(informative)
Specification for materials 1.4828, 1.4876, 2.4360 and 2.4858
This annex specifies the two heat resistant austenitic steels 1.4828 and 1.4876, the nickel copper alloy
2.4360 and the nickel alloy 2.4858 which are often used for the manufacturing of expansion joints for
special application.
There are no harmonized or harmonized supporting standards or European Approvals for Materials
available for these materials. This annex therefore specifies the materials for the application in expansion
joints design and manufacturing.
This specification is mainly based on former standards; i.e. SEW 470 [3] and three VdTÜV material sheets
(WB 412 [4], WB 263 [5] and WB 432/1 [6]) which have proved its worth for practical use, but are not
harmonized according to the PED [1].
NOTE
Material manufacturers' names given in [9] to [23] are only informative.
This specification is based in addition on material manufacturer’s technical documentation and the
experiences of material and expansion joint manufacturers. The most reliable conservative values are
used.
The materials specification is listed in the following tables:
•
Table B.1 — Material designation and chemical composition,
•
Table B.3 — Temperature dependent material properties,
•
•
Table B.2 — Production requirements,
Table B.4 — Testing and material documentation requirements.
The properties of Table B.3 shall be used for the design of expansion joints.
The testing requirements in Table B.4 are defined similar to the analogous European standards
EN 10028-1:2017 and EN 10028-7:2016 and take account of the guiding principles for the contents of
EAM drafts [32].
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Table B.1 — Material designation and chemical composition
Material designation
Position
Material number
Name
International destination
Type
Alloy
1
2.1 / 2.2
3
4
1.4828
1.4876 a
2.4360
2.4858
NICu30Fe
NiCr21Mo
Ni-Cu-alloy
Ni-alloy
X15CrNiSi20–12
309
(approximately)
X10NiCrAlTi32–21
800 / 800 H
Heat resistant austenitic steel
400
825
Chemical composition by weight in %
SEW 470 [3],
[13], [14]
VdTÜV WB 412
[4],
[15], [16]
VdTÜV WB 263
[5],
[17], [18]
VdTÜV WB 432/1
[6],
[19], [20]
Ladle analysis
Ni
11,0 to 13,0
30,0 to 34,0 c
≥ 63 c
38,0 to 46,0 c
Cu
–
≤ 0,75
28,0 to 34,0
1,5 to 3,0
≤ 1,0
≤ 1,0
0,15 to 0,6 d
≤ 0,5
≤ 1,0
≤ 0,5
References b
Document
Manufacturer
Cr
Mo
Co
Ti
Al
Mn
–
–
≤ 2,0
≤ 1,5
–
P
≤ 0,045
N
≤ 0,11
Fe
–
0,15 to 0,6 d
1,5 to 2,5
S
19,0 to 23,0
–
Si
C
148
19,0 to 21,0
–
–
19,5 to 23,5
2,5 to 3,5
≤ 1,0
–
0,6 to 1,2
≤ 2,0
≤ 1,0
≤ 0,2
≤ 0,5
≤ 0,2
0,04 to 0,1
≤ 0,16
≤ 0,025
≤ 0,03
≤ 0,02
≤ 0,02
≤ 0,01
balance
1,0 to 2,5
balance
≤ 0,03
–
–
–
≤ 0,02
–
balance
BS EN 14917:2021
EN 14917:2021 (E)
Material designation
Position
Material number
Name
International destination
Type
Alloy
1
2.1 / 2.2
3
4
1.4828
1.4876 a
2.4360
2.4858
NICu30Fe
NiCr21Mo
Ni-Cu-alloy
Ni-alloy
X15CrNiSi20–12
309
(approximately)
X10NiCrAlTi32–21
800 / 800 H
Heat resistant austenitic steel
400
825
Chemical composition by weight in %
SEW 470 [3],
[13], [14]
VdTÜV WB 412
[4],
[15], [16]
VdTÜV WB 263
[5],
[17], [18]
VdTÜV WB 432/1
[6],
[19], [20]
Product analysis
Ni
10,85 to 13,15
29,85 to 34,15 c
≥ 62,55 c
37,8 to 46,2 c
Cu
–
≤ 0,8
27,8 to 34,2
1,4 to 3,1
≤ 1,05
≤ 1,0
0,10 to 0,65 d
≤ 0,5
References b
Document
Manufacturer
Cr
Mo
Co
Ti
Al
Mn
c
d
–
–
0,10 to 0,65 d
≤ 2,04
–
–
19,3 to 23,7
2,4 to 3,6
≤ 1,0
–
0,55 to 1,25
≤ 1,54
≤ 2,04
≤ 1,05
≤ 0,21
0,03 to 0,11
≤ 0,17
≤ 0,025
≤ 0,035
≤ 0,025
≤ 0,023
≤ 0,015
balance
0,95 to 2,55
balance
–
P
≤ 0,050
N
≤ 0,13
Fe
18,8 to 23,2
–
1,4 to 2,6
S
b
–
Si
C
a
18,8 to 21,2
balance
≤ 1,05
≤ 0,035
–
soft-annealed alloy (≤600 °C) and solution-annealed alloy (H) (≤900 °C)
≤ 0,53
–
–
≤ 0,25
≤ 0,55
≤ 0,03
–
[3] to [6] and [13] to [20] see Bibliography
including max 1 % Co
Al + Ti ≤ 0,7 %
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Table B.2 — Production requirements
Position
Material number
1
2.1 / 2.2
3
4
1.4828
1.4876
2.4360
2.4858
Production
Melting process
Electro arc, induction furnace or vacuum or argon (AOD process)
Quality requirement
Free from surface and internal defects which might impair their usability
Strip,
cold
Sheet, hot rolled
Product and production method
Strip
Sheet
Maximum thickness in mm
Heat treatment
Temperature of product
Holding
time
recommended
a,
Cooling medium
°C
Temperature
min./max.
range
d,
hot
3,5
50
soft-annealed /
solution anneal.
(H)
1 050 to 1 150
900 to 980 /
1 100 to 1 150 (H)
water or air
sufficient fast
water or air
rolled
3,5
50
soft-annealed
all 700 to 800
or 800 to 900
at - 196 °C
Welding
KV
KV
only
1.4828)
3,0
20
soft-annealed
920 to 980
≥ 6 / ≤ 50 µm
> 5 / ≤ 60 µm ≤ 5
/ ≤ 70 µm (H)
≥ 6 / ≤ 50 µm
≥ 6 / ≤ 50 µm
°C
- 196 to 900
- 196 to 600
- 196 to 900 (H)
- 196 to 425
- 270 to 540
J
60 f
80
80
60
≤ 30 to 50
223
138
192 (H)
air
117 c
Minimum e impact energy in transverse direction (Charpy ISO – V according to EN ISO 148-1:2016)
at room temp.
–
60 to 180
respect. 30 - 120
HB
Application temperature
solution-annealed
and quenched
(or
≤ 10 to 100 / ≤ 10
to 150
min
Grain size b [grain size index / mean
diameter]
Hardness, maximum
6 (8)
30
rolled
J
60 f
60 g
80 g
≤ 30 to 50
water or air
200 (strip)
165 (sheet)
50 g
Materials have proven suitable for fusion welding by all recognized welding
processes.
The requirements of 7.3 shall be fulfilled.
Consultation with the material manufacturer is recommended when choosing
welding process and/or filler metal.
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EN 14917:2021 (E)
Position
Material number
1
2.1 / 2.2
3
4
1.4828
1.4876
2.4360
2.4858
Materials have proven suitable for cold and hot forming of bellows by the processes
described in 7.4. The requirements of 7.4 shall be fulfilled.
Forming
Marking
Strip/plate to be marked (normally by permanent ink or vibro-etching) following
EN 10028-1:2017 with the minimum information:
manufacturers identification mark, cast/melt number, batch number,
a
b
c
material grade or number.
depending on thickness
mandatory for 1.4876 (H); optional for other materials
depending on Rp 0,2 value according to [17]
d minimum temperature values according to the proved behaviour of austenitic steels (1.4828, 1.4876) respectively of nickel
alloys (2.4360, 2.4858) supported by manufacturers and users experience; maximum temperature values according to VdTÜV
WB respectively manufacturers technical documentation (see Table B.1)
e minimum value KV in J calculated from for mean toughness values KV by reduction of 30 % (factor 0,7) and from mean
toughness values ak (J/cm2) by factor 0,8 × 0,7 = 0,56 (approximate)
f
g
minimum KV values according to comparable heat resistant austenitic steels of EN 10028-7:2016
defined by relation of values given by [15], [17], [19]
Table B.3 — Temperature dependent material properties
Material
Number
(Position)
1.4828 (1)
solutionannealed,
e ≤ 30 mm
1.4876 (2.1)
soft-annealed,
e ≤ 50 mm
1.4876 (H)
(2.2)
solutionannealed,
e ≤ 50 mm
(2.1), (2.2)
Property a
MPa
Temperature in °C
20
100
200
300
400
270
245
220
205
190
Rp0,2
230
Rm
550
Rp1,0
205
470
180
430
160
410
150
400
425
500
140
180
370
540 d
600
130
170
320
E/105 e
2,00
1,90
1,85
1,75
1,70
1,60
1,55
Rp1,0
240
205
180
165
150
145
135
Rp0,2
Rm
Rp0,2
Rp1,0
Rm
E/105
210
500
170
200
450
2,00
185
425
140
160
425
1,95
160
400
115
145
390
95
130
380
85
125
360
80
135
115
105
100
1,88
1,82
1,75
1,65
400
390
380
360
Elongation
after
rupture
at 20 °C
Density
A min
ρ
%
values
g/cm3
30
7,9
30
7,9
115
300
75
95
Source b c
of
[3],
[13], [14,]
[28]
EN 10028-7:
2016
[4],
[15], [16]
300
1,61
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EN 14917:2021 (E)
Material
Number
(Position)
2.4360 (3)
soft-annealed,
e ≤ 50 mm
2.4858 (4)
softannealed,
e ≤ 20 mm
a
b
c
d
e
g
h
Property a
MPa
Temperature in °C
20
100
200
300
400
Rp0,2
175
E/105
1,82
1,80
1,77
1,70
1,65
Rp1,0 g
265
235
205
195
185
Rm
Rp0,2 g
Rm g
E/105 h
450
235
550
1,96
150
420
205
530
1,92
135
390
180
515
1,87
130
380
170
500
1,81
130
370
160
490
1,74
425
130
370
1,60
500
—
—
—
152
177
480
1,68
NOTE Linear interpolation is permitted for intermediate values.
minimum values for R
p0,2
,R
540 d 600
—
—
—
—
—
151
175
475
1,65
—
Elongation
after
rupture
at 20 °C
Density
A min
ρ
Source b c
of
values
%
g/cm3
30
8,8
[18]
30
8,1
[19], [20]
[5],
—
—
—
—
R
p1,0, m
[3] to [6]: VdTÜV-WB, see Bibliography
[13] to [16] and [18] to [20]: Material manufacturers, see Bibliography
higher temperatures are not recommended by the manufacturers (risk of phase structural reduction of properties)
values taken from EN 10028-7:2016, Annex A (informative values for austenitic steels)
values for 500 °C and 540 °C extrapolated similar to manufacturers values
values taken from manufacturers technical information [20]
152
[6],
BS EN 14917:2021
EN 14917:2021 (E)
Table B.4 — Testing and material documentation requirements
Position
Material number
1
2.1 / 2.2
3
4
1.4828
1.4876 / 1.4876 (H)
2.4360
2.4858
Testing (following EN 10028-1:2017 and EN 10028-7:2016)
Ladle analysis (B.1)
1 per heat
Material identification
All items
Product analysis (B.1)
Plate
at ≤ 5 m long
Tensile
tests
RT (20 °C)
according
to
EN ISO 6892-1:2019
Tensile
1 per heat if required and specified by the purchaser at the time of ordering
tests
> 5 m long
Coil strip
1 transverse test per plate at one end
1 transverse test per plate at each end
1 transverse test per plate at each end of the coil; longitudinal for coil width
< 200 mm
at
elevated
1 transverse test per heat from the product with the largest thickness;
a
temperatures
according
to longitudinal for coil width < 200 mm
EN ISO 6892-2:2018
Impact
transverse (B.2)
according to
EN ISO 148-1:2016
Grain
size
EN ISO 643:2020
test, at
RT 3 tests per product with thickness > 20 mm; for thickness ≤ 20 mm only if required
(20 °C)
and specified by the purchaser at the time of ordering
at – 196 °C
according
Hardness test (HB) according to
EN ISO 6506-1:2014
Intergranular corrosion resistance
according to EN ISO 3651-2:1998
Visual inspection
Dimensional inspection
Material documentation
3 tests per product if required and specified by the purchaser at the time of ordering
to 1 test per heat and heat treatment lot - mandatory for 1.4876 (H); optional for other
materials (to specify be the purchaser at the time of ordering)
1 test per heat and heat treatment lot if required and specified by the purchaser at
the time of ordering
1 per heat and heat treatment lot if required and specified by the purchaser at the
time of ordering
all items
all items (dimensional tolerances shall be agreed between material manufacturer
and purchaser at the time of ordering; see also Table 20).
The material manufacturer shall supply documentation affirming compliance with the specification of this annex.
a
The documentation shall follow the requirements of 5.3.
Not necessary for products with design temperatures ≤ 50 °C.
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EN 14917:2021 (E)
Annex C
(informative)
Incorporation of expansion joints into piping or pressure vessels
C.1 General
The use of expansion joints in piping systems or vessels allows the reduction of stresses resulting
typically from impeded thermal expansion.
However, the use of expansion joints is not a substitute for a stress analysis of the system.
a) Piping
Expansion joints are generally installed in piping systems to encourage the “free” extension of long pipe
runs due to thermal expansion. The thermal expansion of short offsets and branches is mostly controlled
by the natural inherent flexibility of the pipe.
By locating expansion joints in close proximity to connected equipment, it is also possible to reduce forces
and moments created by the expansion of the piping or by vibrations which can bring unacceptable loads
onto the equipment.
Expansion joints should be treated as components in piping. The designer should consider all the loadings
that are likely to be expected under design conditions, including any occasionally occurring operating
conditions as well as exceptional conditions, to ensure that the piping system can be operated in an
acceptable, predictable and controlled manner at all times.
Expansion joints should be considered to be an advantageous means for constructing complex plants
which cannot always be achieved where the displacements are only accommodated by the natural
inherent flexibility of the piping. In addition, the requirements of the applicable regulations can often only
be met when the stresses and forces arising at some points in the piping system are reduced by the
installation of expansion joints.
To minimize complexity, expansion joints should in principle be located at a place where in a pipe plane
simple movements occur. For this, the system is divided into sections. The designer should also locate the
expansion joints so as not to torsion the bellows and to minimize the torsional moments on the bellows.
Where necessary, the torsional loading has to be limited by external devices or measures.
The type of expansion joint used in piping systems is dependent on the direction of the pipes in the
system, on their size, on the operating conditions and movements to be accommodated.
b) Pressure vessels
In vessels, particularly in heat exchangers, high forces which may arise from impeded thermal expansion
can be reduced by making use of the flexibility of axial expansion joints. The tube bundles are thus
relieved from too high axial forces which could result in buckling of the tubes. On account of the lower
stresses, the individual components and the connecting weld seams can be designed with smaller
dimensions.
Depending on the type of heat exchanger expansion joints are located either in the vessel shell or at the
connection of the floating head.
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EN 14917:2021 (E)
C.2 Specific symbols and definitions
The following symbols are used in the figures of this clause.
FP
DA
Pg
Main anchor (fixed point)
IA
Directional anchor
Gi
Planar pipe guide
Sp
Intermediate anchor
Axial pipe guide (i = 1,2,3,or n)
Spring support
Table C.1 — Selection criteria for expansion joint types
Ordinary Axial Expansion Joints a
Restraint Expansion Joints (lateral or angular)
Movements
Small / medium axial displacement up to 200 mm. — Lateral expansion joint
Small lateral deflection and/or angular rotation in Medium / large lateral deflection greater 200 mm
addition.
perpendicular to the centerline.
Large pipe extension requires subdivision of the — Angular expansion joint
pipeline by intermediate anchors and installation Angular rotation in one or all planes compensates
of several axial expansion joints.
large pipe extension by means of hinge systems.
Pipeline routing
Straight pipe run.
Pipe run with changes in direction (two- or threePipe runs with changes in direction have to be dimensional).
subdivided in straight portions by main anchors. Straight pipe run has to be rerouted to achieve “L”
or “Z” bend-systems.
Anchors and guides
Strong main anchors and additional guides are Relatively light anchors and guides are sufficient
required to resist the pressure thrust and to which have only to resist the reaction forces of the
expansion joints and the friction forces of the
prevent expansion joints from squirming.
guides.
Installation space
Low space requirement as outer diameters are Higher space requirement due to greater external
not much greater than the pipe diameter.
dimensions of the restraining parts.
Additional pipe offsets due to necessary rerouting
of the pipe run.
Assembly
Simple installation and pre-tensioning.
Anchors to be fixed before pressure testing.
Careful installation required with regard to the
position of pivots and tie bars to achieve correct
pre-tension and system moving.
Pressure testing possible before anchors are
fixed.
155
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EN 14917:2021 (E)
Ordinary Axial Expansion Joints a
Restraint Expansion Joints (lateral or angular)
Cost comparison
Lower price per unit (several axial expansion Higher price per unit (minimum 2 angular
joints are required for long pipe runs).
expansion joints are required).
Higher cost for anchors and guides.
Lower cost for anchors and guides.
Recommendation
Recommended for small movement, lower Recommended for large movement, high pressure
pressure thrust, and straight pipe runs.
thrust, and pipe runs with changes in direction
a Bellows internally pressurized, not pressure balanced.
C.3 Application criteria for expansion joints in piping
C.3.1 General
The simplest form of compensation in piping is undertaken by using axial expansion joints. However, the
option for using axial expansion joints is limited by the amount of the pressure thrust which can load the
fixed points excessively. In such cases, the use of pressure balanced axial expansion joints can be an
alternate solution.
Often hinge systems applying restrained expansion joints are the best alternative in this case.
An overview of the selection criteria regarding ordinary axial and restraint expansion joints is given in
Table 1.
C.3.2 Use of axial expansion joints
C.3.2.1 General
Axial expansion joints accommodate axial displacement directly by compression or extension. They also
allow for lateral deflection and/or angular rotation to a limited extent.
Axial displacement of internally pressurized axial expansion joints is limited as they tend to become
instable with too great a length.
The use of axial expansion joints with externally pressurized bellows permit larger displacement since
external pressure tends to stabilize the bellows. It is assumed that the greater space requirements are
acceptable and no lateral or angular movement is required.
Ordinary axial expansion joints (not pressure balanced) have a relatively small outside diameter but,
generate the pressure thrust when pressurized which must be absorbed by the main anchors.
Pressure balanced axial expansion joints restrain the pressure thrust but, have remarkable greater
outside diameters.
An approximate orientation for the selection of the appropriate type of axial expansion joint is given in
Figure C.1 where in addition the alternative option on restraint expansion joints in hinge systems is
shown.
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EN 14917:2021 (E)
C.3.2.2 Axial expansion joints, non-pressure balanced
C.3.2.2.1
General
Ordinary axial expansion joints require pipe anchors (fixed points) designed to carry the whole pressure
thrust and all frictional forces from the axial guides. This limits the use of this type of axial expansion
joints as for large diameters and high pressures the pressure thrust becomes too high to be realized.
When a straight pipe run is compensated by ordinary axial expansion joints it tends to buckle. On the one
hand, the bellows itself tends to lateral displacement under the influence of internal pressure, on the
other the pipe can buckle due to the axial working force of the bellows and, to a much greater extent, due
to the pressure thrust, which causes it to act like a straight beam subjected to a compressive axial force.
Apart from proper supporting of the piping for its weight and external forces, it is of vital importance that
correct guiding of the pipe is maintained to ensure the proper functioning of the expansion joints.
By using appropriate guides, which comply with the instructions given below, the risk of buckling can be
avoided:
Key
A
B
C
1
2
ordinary axial expansion joints recommended
restraint or pressure balanced expansion joints preferred
restraint or pressure balanced expansion joints required
light anchors (10 kN to 20 kN depending on DN; e.g. pipes in buildings or on pipe bridges)
heavy anchors (40 kN to 400 kN depending on DN; e.g. earth covered in-duct laid pipelines)
Figure C.1 — Application limits for axial expansion joints
C.3.2.2.2
Important instructions
The following instructions should be regarded to guarantee the proper working of pipe systems with nonpressure balanced axial expansion joints:
157
BS EN 14917:2021
EN 14917:2021 (E)
1.
The piping system should be divided in straight sub-sections by means of anchors, guides or
restraining tie rods to have only one expansion joint per straight section of pipe run between fix
points (see Figure C.2).
Figure C.2 — Axial expansion joints not restraining the pressure thrust
2.
3.
4.
The expansion joint should be positioned close to the anchor followed by an axial pipe guide or
between two pipe guides positioned as near as possible to the expansion joint.
Main anchors and other restraining devices should be designed for the full pressure thrust from the
bellows effective area, plus the bellows working force. Additionally, the forces generated by the
friction of the pipe guides should be considered (see also 3.2.2.3).
When, on the same straight pipe run, an axial expansion joint is located beside a reducer, the loads
on the small diameter anchor should take into account the full pressure thrust of the expansion joint
and, additionally, the possible offset l of the pressure thrust if the reducer is eccentric (see
Figure C.3).
Figure C.3 — Single axial expansion joint located on the large diameter side of a reducer
5.
6.
7.
The pipe should be guided in such a way that no damaging lateral or angular movements will occur,
which are not anticipated and not considered in the pipe stress analysis or in the expansion joint
design. For small diameters, the guides should be spaced in such a way as to avoid buckling of the
line (see C.3.2.2.3).
To allow free movements of the pipe, the guiding devices of the system should be designed to
minimize friction and the risk of sticking in the guides by tilting.
The use of axial expansion joints in a pipe run containing an offset (see Figure C.4) should be avoided.
Pressure thrust and friction forces in the supports will introduce a moment in the piping which may
result in overstressing of piping and guides and in the destruction of the system.
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Figure C.4 — Single axial expansion joint on a pipe run containing an offset
C.3.2.2.3
Spacing of pipe guides
The positioning of pipe guides as specified below should be observed (see also Figure C.1).
a) Distances of the first two pipe guides near an ordinary axial expansion joint are given as follows:
— first pipe guide G1 to the expansion joint:
L1 ≤ 4⋅DN;
— second pipe guide G2 to G1:
L2 ≤ 14⋅DN;
b) Maximum distance between two further pipe guides:
The further pipe guides are mainly applied to control the run of the pipeline.
Straight long pipes with small diameter and high internal pressure tend to buckle. Thus a maximum
distance between the pipe guides should not be exceeded to prevent the pipeline from instability.
The maximum allowable distance Lg is influenced by several forces as the pressure thrust, friction
forces from the guides and the axial working force of the expansion joint.
The maximum allowable distance is given by:
Lg ≤
E⋅J
π
⋅
β Fi ⋅ S S
where
E
J
J=
(C.1)
is the modulus of elasticity of the pipe material;
is the moment of inertia of the pipe cross section:
π
⋅ e ⋅ D3
8 p mp
with
(C.2)
e p and Dmp being wall thickness and mean diameter of the pipe.
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b
is the guiding factor for the relevant pipe guides.
The guiding factor β means: 1,0 if both ends are simply supported; 0,7 if one end is simply supported, the
other end axially guided; 0,5, if both ends are axially guided. A perfect guidance cannot be achieved by
ordinary axial pipe guides because of the necessary clearances between the pipe and the guide. They
should be regarded as “simple supports” (β = 1,0).
— Fi
is the axial buckling force consisting of the components which act on the pipe simultaneously:
Fi = Fp - FB + Ff
where
(C.3)
the pressure thrust Fp is given by Formula (24);
the bellows reaction force FB is depending on the regarded situation; i.e. operating or testing, and is
as a conservative value given by: FB = K B ⋅ x ;
the friction force FF generated by the pipe guides is given by: FF = ± Σ ( µ ⋅ FN ) , where the friction
factor μ is depending on the type of guide. The load FN on a single guide is mainly depending on the
weight of the pipe section carried by this guide;
SS is the safety factor (recommended value: SS = 3).
Additional remarks:
The bellows elastic axial spring rate KB is given by the expansion joint manufacturer or may be calculated
by Formulae (35) to (40) for different types of bellows. The axial displacement x of the bellows has a
negative sign for compression and a positive one for extension. A more precise calculation of the axial
working force is given in 6.2.9.3.1.
For a complete calculation of the total axial friction force, all possible individual forces acting on each
guide within a section of straight pipe run should be taken into consideration. These friction forces will
occur during movement of the system, primarily when temperature is changed or for other reasons.
The resulting load FN which comprises mainly weight loads is taken from the stress analysis of the pipe
system and is given by the pipe manufacturer.
The friction coefficient of the guides is approximately: 0,1 ≤ μ ≤ 0,5, where the smallest value is given for
roller supports, a mean value for stainless steel on PTFE, and the largest value for C-steel on C-steel. They
can be asked for by the pipe supports manufacturer.
A quick overlook of the maximum allowable spacing Lg (in m) for a standardized straight pipe run is
given in Figure C.5.
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The graph is based on the following conditions:
— pipeline: Steel with E = 210 000 N/mm2; e p = T and D m p in accordance with EN 1092-1:2018,
flange type 11;
— pressure: Test pressure PT = 1,43 PN in bar;
— pipe guides: simply supported (β = 1,0); no movement;
— expansion joint: multi-ply in neutral position; i.e. no working force;
— the applied safety factor is: SS = 3.
Figure C.5— Maximum allowable space of guides
C.3.2.3 Axial expansion, pressure balanced
C.3.2.3.1
General
Pressure balanced expansion joints are restraining the pressure thrust but, allow axial displacement.
They are designed with several bellows, the pressure thrust of which is absorbed by means of tie devices
interconnecting the bellows (see also 4.1.6).
This type of axial expansion joints is loading the anchors only by the working force of the expansion joints
and by the friction forces of the pipe guides.
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C.3.2.3.2
In-line pressure balanced axial expansion joints
In a straight pipe run in-line pressure balanced axial expansion joints can be located between two main
or intermediate anchors. These expansion joints can also accommodate the axial movements without
loading the anchors with the pressure thrust. This is undertaken by using bellows and interconnecting
devices between line bellows and outboard bellows which will be subjected to the line pressure. Each
bellows should be designed to absorb the full axial movement (Figure C.6).
Figure C.6 — Axial in-line pressure balanced expansion joints
C.3.2.3.3
Corner-relieved axial expansion joints (pressure balanced)
If a change of direction exists in a pipe run, pressure balanced axial expansion joints located at a change
of direction (elbow or tee type) can be used to absorb the movement without charging the anchors or end
connections with high forces of the pressure thrust. This is undertaken by using an additional equalising
bellows subjected to the line pressure and interconnecting devices between line bellows and equalising
bellows. Each bellows should be designed to absorb the full axial movement (Figure C.7 and C.8).
Figure C.7 — Pressure balanced axial expansion joint (elbow type)
Figure C.8 — Pressure balanced axial expansion joint (tee type)
C.3.3 Use of restraint expansion joints
C.3.3.1 General
Restrained expansion joints; i.e. angular and lateral expansion joints, are able to absorb angular rotation
or lateral deflexion which is perpendicular to the centreline. They are equipped with restraining parts
(hard ware) that can absorb the pressure thrust and additional loads that may occur in the pipe system.
Both types of expansion joints require a pipe run with changes in direction. The different possibilities of
compensation systems are explained below.
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Where the location of pipe legs or the direction of movement is addressed to describe the following
systems, they refer to the situation in the mentioned figure.
C.3.3.2 Angular expansion joints
Angular expansion joints are designed to absorb angular rotation. When they are fitted with hinges, they
allow rotation in a single plane only. When they are fitted with gimbal rings, they allow rotation in any
plane. Usually a set of two or three angular expansion joints between two fixed points or anchors are used
to compensate the movements of a pipe system.
The restraining parts should be designed to restrain the full pressure thrust and any other external
loadings about which the expansion joints manufacturer should be informed by the designer of the piping
system.
The design of anchors, guides and supports should include the working moment of the expansion joints
due to the angular stiffness of the bellows and the friction in the hinge bearings of the restraining parts.
There should be not more than three angular expansion joints installed between two fixed points.
C.3.3.2.1
Plane systems
C.3.3.2.1.1 The two-hinge system
The system with two angular expansion joints (see Figure C.9) is not only subject to thermal expansion
of the upper pipe run but also to a vertical component f of the upper expansion joint’s movement. This
component results from the movement of the expansion joint on the circular arc and from the extension
of the intermediate pipe between the two expansion joints which shows in the opposite direction. Details
may be calculated according to D.3.
The upper pipe run should be able to accommodate this vertical movement; i.e. the “flexible” leg can be
chosen to be sufficiently long that the lateral force and the bending moment are sustained by the piping
and the fixed point.
If this is not possible a two-hinge system is not permissible and a tree-hinge system is recommended.
Figure C.9 — Two hinge angular expansion joints in a plane system
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C.3.3.2.1.2 The three-hinge system
The system with three angular expansion joints (see Figure C.10) is subject to thermal expansion of the
upper pipe run and also to that of the vertical pipe run.
Pipes and guides are only loaded by the working moments of the expansion joints and by the weight if
the piping components.
Figure C.10 — Three hinge angular expansion joints in a plane system
C.3.3.2.2
Three-dimensional systems
C.3.3.2.2.1 The two-hinge system
This system with two gimbal angular expansion joints (see Figure C.11) is only possible if the upper pipe
is flexible enough to accommodate the vertical movement component as described under C.3.3.2.1.1.
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Figure C.11 — Two gimbal angular expansion joints in a three-dimensional system
C.3.3.2.2.2 The tree-hinge system
This often used system (Figure C.12) absorbs movement in any direction of the horizontal pipes by the
gimbal angular expansion joints while the hinge angular expansion joint takes the vertical movement
resulting from the reduction of the vertical distance between the gimbals.
Figure C.12 — Two gimbal and one hinge angular expansion joint in a three-dimensional system
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C.3.3.3 Lateral expansion joints
C.3.3.3.1
General
Lateral expansion joints are used in a similar way as two angular expansion joints. The only general
difference is that the thermal expansion between the restraining bars remains inside the expansion joints.
The relevant compression or extension has to be included in the fatigue life calculation of the bellows.
Where they are designed with spherically seated tie rods or with tie bars in universal joints they may be
used in plane or in three-dimensional systems.
C.3.3.3.2
The two-hinge system
Where a lateral expansion joint with two tie rods is regarded it can be used in a plain or in a treedimensional pipe system.
The movements shown in Figure C.13 are possible – especially a small angular rotation of the lower pipe
leg – provided that one of the horizontal pipe legs is able to absorb the vertical movement component.
The piping connected at the bottom should be guided in such a manner that the expansion joint is not
subject to torsion.
Figure C.13 — Lateral expansion joint with two tie rods in a three-dimensional system
Where a lateral expansion joint with three or more tie rods is regarded it can be used in a plain or in a
tree-dimensional pipe system.
The movements shown in Figure C.14 are possible provided that one of the horizontal pipe legs is able to
absorb the vertical movement component.
The lower flange of the expansion joint is horizontally guided by the tie rods; i.e. no angular rotation is
allowed.
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Figure C.14 — Lateral expansion joint with three or more tie rods in a three-dimensional system
C.3.3.3.3
The tree-hinge system
A lateral expansion joint with two tie rods in connection with one hinge angular expansion joint can be
used in a three-dimensional pipe system where the vertical movement component is too high to be
absorbed by the upper horizontal pipe leg.
The angulation of the upper pipe leg can be absorbed by the upper flange of the lateral expansion joint.
The orientation of the plane that contains the tie rods is important and should be as shown in Figure C.15.
Figure C.15 — Lateral expansion joint with two tie rods and one hinge angular expansion joint
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C.3.3.3.4
Double gimbal lateral expansion joints
Lateral expansion joints with gimbal rings or universal joints are used in a similar way as to two gimbal
angular expansion joints (see C.3.3.2.2). The only difference is that the thermal expansion between the
restraining rods is compensated within the expansion joints. The relevant compression or extension has
to be included into the fatigue life calculation of the bellows.
C.3.4 Use of universal expansion joints
C.3.4.1 General
Universal expansion joints are used to accommodate thermal expansions and/or mechanical movements
of a piping system in all directions.
C.3.4.2 Unrestrained universal expansion joint
The use of unrestrained universal expansion joints is limited to piping systems without or with extremely
low pressure. The pressure thrust should be so small that it has no negative influence on the stability of
the expansion joint or on the geometry of the piping.
All movements and their combinations shown in Figure C.16 are basically possible.
Figure C.16 — Unrestrained universal expansion joint (possible movements)
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C.3.4.3 Restrained universal expansion joints, pressure balanced
C.3.4.3.1
General
Restrained universal expansion joints are always pressure balanced. They restrain the pressure thrust
but, allow movements in any direction. The restraining hard ware should be designed with at least tree
tie rods to prevent the outer flanges from angulating and the bellows from buckling.
C.3.4.3.2
Corner-restrained universal expansion joint, elbow type
Key
1 process vessel
Figure C.17 — Pressure balanced universal expansion joint at a process vessel
C.3.4.3.3
Corner-restrained universal expansion joint, tee type
Key
1 turbine
Figure C.18 —Pressure balanced universal expansion at a turbine
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C.3.4.3.4
In-line restraint universal expansion joint
Key
1 process vessel
Figure C.19 — Pressure balanced universal expansion joint between two process vessels
C.3.5 Indeterminate configurations of expansion joints
C.3.5.1 General
Indeterminate configurations of expansion joints should be avoided as they may lead to uncertainties
with respect to the distribution of the movements among the different expansion joints. A reduced fatigue
life of individual expansion joints would be the negative consequence.
C.3.5.2 Strait piping section with axial expansion joints
The use of two or more axial expansion joints in a piping section will create an indeterminate
configuration.
The amount of displacement imposed on each expansion joint is not clearly defined, as the spool between
the two bellows can move freely to one side or the other depending on the friction in the pipe supports
and the differences in stiffness between the bellows (Figure C.20).
Such a configuration is only permitted if an intermediate anchor is installed in the middle.
Key
a intermediate anchor is missing here
Figure C.20 — Indeterminate piping systems with axial expansion joints (incorrect installation!)
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C.3.5.3 Plane U-bend system with angular expansion joints
No more than three angular expansion joints should be used between two fixed points or anchors in a Ubend system in order not to create any risk of uncertain movement distribution in the system.
The shown configuration with four angular expansion joints (Figure C.21) and no intermediate guide “A”
is theoretically able to take arbitrary positions according to the friction in the hinges and the difference
of stiffness between the expansion joints.
A defined system is given by the installation of a lateral guide “A” at the top of the U- bend.
Figure C.21 — Four angular expansion joints in a U- bend system
C.3.5.4 Three dimensional systems with three gimbal angular expansion points
In the system according to Figure C.22 the position of the upper elbow is not clearly determined; only the
stiffness of the bellows keeps the elbow in position. The use of three gimbals between two fixed points or
anchors is therefore not recommended.
There should be no more than two gimbals located between two fixed points. The upper angular
expansion joint should be of the hinge-type.
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Key
a should be a hinge angular expansion joint
Figure C.22 — Gimbal angular expansion joints in a three-dimensional system
(Incorrect installation!)
C.3.5.5 Three-dimensional system with lateral expansion joints
The use of lateral expansion joints with spherically seated tie rods can be critical in a three-dimensional
piping system, as rotation around the longitudinal axis of the expansion joint is theoretically possible
(Figure C.23).
The torsional load which may be produced in the bellows due to the piping arrangement should be
checked, particularly with respect to combined movements, i.e. angular and torsional movements, which
can induce instability (squirm) of the bellows. This arrangement is used in some applications, but it
requires particular care with respect to the pipe dimensions and the guides.
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Figure C.23 —Lateral expansion joint with spherically seated tie rods in a three-dimensional
system
C.4 Application criteria for expansion joints in pressure vessels
C.4.1 General
Expansion joints in combination with pressure vessels are mainly used in piping systems which are
connected to the vessels as described in C.3.4.3.
Expansion joints installed directly in heat exchangers can demonstrate, in principle, the two possible
ways how to use expansion joints in pressure vessels.
Different temperatures and the resulting difference in thermal expansion of the shell and the internal
tube bundle could lead to high stresses or instability due to impeded thermal expansion. Axial expansion
joints are able to avoid that problem.
C.4.2 Axial expansion joint installed in the shell
The small thermal expansion which is common for heat exchangers on account of their limited length
generally requires only short expansion joints with a few corrugations.
When choosing a thick-walled axial bellows manufactured of half-corrugations, a single corrugation will
often be sufficient. The high lateral stiffness of this corrugation prevents lateral offset of the shell parts
located on the right and left sides of the expansion joint. No special guide is necessary.
The robustness of this design can be an advantage. But, the distinctly larger diameter as compared with
that of the shell has to be taken into consideration for transport and installation in the plant; see
Figure C.24 a).
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Figure C.24 — Axial expansion joint in the vessel shell
If a multi-ply design is chosen the corrugation height will be considerably smaller; thus the outside
diameter of the bellows is only slightly greater than that of the vessel shell. These less robust bellows
should be protected against external damage.
If only one multi-ply corrugation is necessary to accommodate the movement, lateral guide of the shell
parts may be unnecessary, as the lateral stiffness of the corrugation is sufficient as a guide. Otherwise,
guides should be provided on the inside; see Figure C.24 b).
Where the pressure is high and reinforced bellows are needed, the reinforcing members may be designed
in such manner that they as well provide a protection for the bellows.
C.4.3 Axial expansion joint installed at the floating head
In a floating head heat exchanger axial expansion joints with relatively small diameters are used; see
Figure C.25.
Different media and different pressures can occur both inside and outside of the tube bundle.
This should be considered as well in the design calculation as in the selection of materials for the wetted
plies of the bellows. Particular attention should be paid to the possibility of corrosion effects.
Figure C.25 — Axial expansion joint at the floating head
Multi-ply bellows used for this application are usually not supplied with a venting hole, and should
therefore be checked for tightness with particular care by the expansion joint manufacturer.
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Annex D
(informative)
Calculation methods for systems of pipes containing expansion joints
D.1 General
D.1.1 Preliminary remarks
If expansion joints are installed in a system of pipes, the elasticity of the system is fundamentally altered.
This can be explained in simplified terms by imagining the expansion joints to be hinges and the pipe
between the hinge points to be rigid.
This annex deals with selected systems which have to be limited by adequate dimensioned anchors (see
also Annex C).
In order to meet reliable operating conditions, more complex pipe systems should be designed with the
aid of computer stress program.
D.1.2 Determining movement values
The following types of relative movement can be absorbed by the expansion joints (examples):
— thermal expansion;
— pressure stretch;
— vibrations;
— compensation of misalignment;
— foundation settlement;
— offset for installation purpose (e.g. installation or demounting of valves).
The highest movement values are generally caused by thermal expansion; this is discussed separately
and in detail in this annex.
D.1.3 Thermal expansion
The linear thermal expansion Δt of metal components, referring to a temperature range, can be
determined by means of the material-related expansion coefficient (see Figure D.1):
∆ t = L ⋅ α ⋅ ∆t
where
L
α
is the length in m (e.g. pipe section between two main fixed points);
is the mean thermal expansion coefficient in mm/mK (see Table D.1);
Δ t is the temperature difference in K (difference between design temperature and installation
temperature).
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Table D.1 — Mean thermal expansion coefficient α in mm/mK
Material
Temperature range from 20 °C to
100 °C
200 °C
300 °C
400 °C
500 °C
Ferritic steels
0,012 5
0,013
0,013 6
0,014 1
0,014 5
Copper
0,015 5
0,016
0,016 5
0,017
0,017 5
Austenitic steels
Aluminium alloy (AlMg3)
176
0,016
0,023 7
0,016 5
0,024 5
0,017
0,025 3
0,017 5
0,026 3
0,018
0,027 2
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Key
Y thermal expansion Δt in mm/m
X
1
2
3
4
temperature difference Δt in K (reference to 20 °C)
aluminium
austenitic stainless steels (1.4541)
copper
carbon steels
Figure D.1 — Thermal expansion of metals
D.2 Approximate calculation of bellows movement
D.2.1 General
From the various possible relative movements, of which the heat expansion delivers the largest amount,
the actual movements of the individual pipe lengths can be calculated. If axial, universal or lateral
expansion joints are used to compensate movement, these movements will correspond to the related
possible movements of the expansion joints. If the compensation takes place via hinge-systems the
movement values will be converted into angular rotation.
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D.2.2 Hinged systems
The conversion of the movement values Δ into angular rotation can be closely approximated using the
diagram below (Figure D.2). The conversion is precise if it is used for a simple double hinge system with
two hinges one after the other in an offset of the pipe system. With other systems the angular rotations
are calculated approximately but with a limited deviation. For a more accurate calculation that can, in
certain cases be more useful, the equations given in C.3 should be used.
The relevant movement value Δ should first be determined for the particular hinge system in accordance
with the figures under No. 1 to No. 5 of Table D.2. The angular rotation Θ of the expansion joint may then
be taken from the graph (Figure D.2), together with hinge distances A and B.
The hinge distances A and B when selected should be as large as permitted by the overall construction,
and should be such as to ensure small angular rotation of the expansion joints and − above all − the
smallest possible forces and moments in the pipe system. The smallest possible distance should be
selected for C.
The determined angular rotations are actual angular rotations of the pre-stressed system under
operating conditions, and are also valid for the cold system when installed with cold spring. If the system
is to be operated without cold spring the angles obtained will be roughly twice as large, and
correspondingly larger expansion joints will be necessary.
D.2.3 Definitions
D.2.3.1 Distances
A — Main distance
U- and Z-systems:
projected distance between the hinges in or at the pipe offset
L-system:
distance between the hinges in the same pipe run
all systems (except U-system):
distance from relaxing element to offset
B — Secondary distance (three-hinge system only)
U-system:
projected distance between basic and crown hinge
all systems (except U-system):
projected distance between hinges at the bend
C — Bend distance (three-hinge systems only)
U-system:
D.2.3.2 Hinges
not existing
K1 first (outer) hinge in pipe section A
K2 second hinge in pipe section A (U-system: second basic hinge)
K3 third (outer) hinge, relaxing hinge (U-system: crown hinge); three-hinge systems only
D.2.3.3 Movements in pipe runs
Δ 1 first main movement: movement in first main run assigned to K1
Δ 2 second main movement: movement in second main run
Δ 3 secondary movement: movement of pipe offset (relevant only for Z-system)
178
2
1
No.
Double gimbal in a three-dimensional Zsystem
Double hinge in a plane Z-system
Hinge system
Substitute system
Θ2 = Θ1
(
)
1
⋅ ∆ 1 2 + ∆ 22
2
)
)
Θ 1 = f ∆ , A find from Figure D.2
∆=
Θ2 = Θ1
(
(
179
Bending angle in degrees with
50 % cold spring
1
⋅ ∆1 + ∆2
2
Θ 1 = f ∆ , A find from Figure D.2.2
∆=
Table D.2 — Calculation of the bending angles in hinge systems
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BS EN 14917:2021
180
4
3
No.
Hinge system
Three hinges in plane L-system
Three hinges in plane U-system
EN 14917:2021 (E)
Substitute system
(
(
Θ2 = Θ1 + Θ3
Θ 1 = f ∆ A , A 
(
) find from Figure D.2
Θ3 = f (∆ B , B ) 

∆A =
C
1 
⋅ ∆ 2 + ∆ 1 
B
2 
1
∆B = ⋅∆1
2
Θ2 = Θ1
Θ3 = 2 ⋅ Θ1
)
) find from Figure D.2
1
∆1 +∆2
4
Θ1 = f ∆ , A
∆=
Bending angle in degrees with
50 % cold spring
BS EN 14917:2021
5
No.
Two gimbals and one hinge in a threedimensional Z-system
Hinge system
Substitute system
Θ2 = Θ1 + Θ3
(
) find from Figure D.2
Θ3 = f (∆ B , B ) 

Θ 1 = f ∆ A , A 
C
1 
⋅  ∆ 1 2 + ∆ 2 2 + ∆ 3⋅ 
B
2 
1
∆B = ⋅∆3
2
∆A =
181
Bending angle in degrees with
50 % cold spring
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Key
Θ angular rotation
Figure D.2 — Angular rotation in hinge systems
D.3 Exact calculation of bellows movement
D.3.1 Two hinges in a plane system (Z-system)
The simplest system is the two hinge system. It is often implemented as a prefabricated unit in the form
of a lateral expansion joint. If two angular expansion joint are used, the hinge distance A should be defined
prior to the calculation (Figure D.3).
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Figure D.3 — Two hinges in a plane system (Z-system)
Angular rotation:
— with 50 % cold spring
Θ = arcsin
∆
2⋅ A
— without cold spring
Θ = arcsin
∆
A
Height of arch:
(D.1)
(D.2)
The circular movement of the hinged joint K2 causes the vertical hinge distance A to be reduced by the
“height of arch” fy.
f y = A ⋅ (1 - cos Θ )
(D.3)
This reduction, which occurs both in the pre-tensioned state and during operation, and in addition the
thermal expansion in the “working leg” (K1 – K2), will be compensated by elastic bending of the
compensated pipe section.
When sizing and positioning guides and supports, it is thus important to ensure that the flexibility of the
pipe run is not impaired. If the pipe is horizontal, roller supports that are also movable laterally are
recommended.
D.3.2 Two gimbals in a three-dimensional system (Z-system)
If an additional movement from a second plane has to be compensated in a three-dimensional system, a
two gimbals system which is movable in all planes should be determined (see Figure D.4).
Figure D.4 — Two gimbals in a three-dimensional system (Z-system)
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Resulting movement
The resulting movement Δres is given by:
∆ res = ∆ 12 + ∆ 22
(D.4)
From the resulting movement Δ res thus the resulting angular rotation Θ res can be calculated similar to
Formula (D.1):
Θres = Θ1 = Θ2 = arcsin
∆ res
2⋅ A
where Θ 1 and Θ 2 are the angular rotations of the gimbals K1 and K2.
(D.5)
D.3.3 Three hinges in a plane system (U-system)
The U-system can be considered a combination of two double-hinge systems (Figure D.5); with the two
expansion joints at the crown of the U-system being combined to from a single expansion joint. Suitable
hinge distances A and B should be defined for the configuration. The distance B, which should be as short
as possible, is generally derived from two times the radius of a 90° pipe bend plus half the total length of
each of the expansion joints K1 and K2.
Figure D.5 a) — The U-system in operating
position
Figure D.5 b) — The U-system in cold spring
position
Figure D.5 — The U-system
Calculation of the auxiliary parameters:
— with 50 % cold spring:
F =B±
1
⋅ ∆1 + ∆2
4
)
F =B±
1
⋅ ∆1 + ∆2
2
)
(
— without cold spring:
D=
184
(
A2 + B 2
(D.6)
(D.7)
(D.8)
BS EN 14917:2021
EN 14917:2021 (E)
B

D
(D.9)
ψ 1 = arcsin 
F 

D
(D.10)
ψ 2 = arcsin 
Angular rotations:
Θ1 = Θ2 = ψ 1 - ψ 2
(D.11)
Θ3 = 2 ⋅ Θ1
(D.12)
Height of arch:
f y = D2 - F 2 - A
(D.13)
U-systems should, if possible, be planned with 50 % cold spring. The expansion joints will then operate
with roughly the same angular rotation either side of the neutral position. The angular rotations for the
operational condition are calculated according to the above equations with the negative sign.
The plus sign in the Formula (D.6) respectively Formula (D.7) has to be used if low temperature
application (contraction) occurs or in order to calculate the exact angular rotation for the cold spring
position.
D.3.4 Three hinges in a plane system (L-system)
D.3.4.1 General
The method used to compute the L-system is fundamentally different from that used to calculate the
systems described so far. Full compensation is guaranteed with this system, in contrast to the two-hinge
system (Figure D.6).
To achieve the optimum angles; the hinge distances A and B in the configuration should be as large as
possible and C as small as possible. C is generally derived from the radius of the 90° pipe bend plus half
the total length of the expansion joint K3.
Figure D.6 a) — L-system in
operating condition
Figure D.6 b) — L-system in
cold spring condition
Figure D.6 — L-system
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D.3.4.2 Calculation of auxiliary parameters and angular rotations
Parameters F and G:
— with 50 % cold spring:
F=B
1
⋅∆ 2
2
G=C + A
(D.14)
1
⋅∆1
2
(D.15)
— without cold spring:
(D.16)
F=B∆2
(D.17)
G=C + A ∆1
Parameters D, E in mm:
D = B2 + C 2
(D.18)
E = F 2 + G2
Parameters
ξ 2 , ξ 3 , ψ 1 , ψ 3 , ϕ 1 , ϕ 3 in deg
C 

B
ξ 3 = arctan 
ξ 2 = 90° - ξ 3
F 

G
ψ 3 = arctan 
ψ 1 = 90° - ψ 3
 A2 + E 2 - D 2 

ϕ 1 = arccos 
 2⋅ E ⋅ A 


 A2 + D 2 - E 2 

ϕ 2 = arccos 
 2⋅ A ⋅ D 


 E 2 + D 2 - A2 

ϕ 3 = arccos 
 2⋅ E ⋅ D 


186
(D.19)
:
(D.20)
(D.21)
(D.22)
(D.23)
(D.24)
(D.25)
(D.26)
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EN 14917:2021 (E)
Angular rotations:
Θ 1 = ϕ 1 + ψ 1 - 90°
(D.27)
Θ 3 = ξ + ϕ 3 + ψ 3 - 90°
(D.29)
(D.28)
Θ 2 = 180° - ξ 2 - ϕ 2
3
Like the U-system, the L-systems should, if possible, be planned with 50 % cold spring. If unsuitable hinge
distances are selected, the angular rotation at operating condition may deviate considerably from that at
cold spring condition. It is therefore advisable to calculate the angular rotations of both positions; i.e. cold
spring and operating position.
The angular rotation for the operational condition of the system can be calculated according to the
specified Formulae (D.16) and (D.17) with the negative sign. The plus sign has to be used if low
temperature application (contraction) occurs or in order to calculate the exact angular rotation for the
cold spring position.
D.3.4.3 Limitation of movement
It should also be remembered that movements in hinge system with defined distances A, B and C should
not exceed the limit for geometric compatibility; this applies both to the cold spring and to the operating
position.
The following condition should be fulfilled:
with
A + D ≥ 1, 05 E
(D.30)
2
(D.31)
D=
E=
B2 + C
( B + V2 ) + (C + A + V1 )
2
2
D.3.5 Three hinges in a three-dimensional system (Z-system)
(D.32)
D.3.5.1 General
If movements in all three directions have to be absorbed in a three-dimensional system a plane 3-hinge
L-system can likewise be used as a basis for the calculation. Then a double-hinge system, perpendicular
to the basis system, is superposed to cope with the additional movement Δ1. The reduction in the initial
hinge distance A by the height of arch f (see below) is fully compensated by expansion joint K3
(Figure D.7).
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Figure D.7 — The three-dimensional system (z-system)
The three-dimensional system is thus designed by using gimbals for the expansion joints K1 and K2,
which are flexible in all planes, whilst for the expansion joint K3 a simple hinge is used which needs only
to be movable in one plane.
D.3.5.2 Calculation of auxiliary parameters induced by the additional movement Δ1
Angular rotation in one direction only resulting from Δ1:
— with 50 % cold spring:
Θ 1* = Θ 2* = arcsin
∆1
2⋅ A
— without cold spring:
Θ 1* = Θ 2* = arcsin
∆1
A
Parameter A* (theoretical hinge distance for a plane system):
( )
A * = A ⋅ cos Θ 1*
Parameters F and G:
— with 50 % cold spring:
F=B
1
⋅∆ 2
2
G=
C + A∗ 
1
⋅∆ 3
2
— without cold spring:
F =B∆2
188
(D.33)
(D.34)
(D.35)
(D.36)
(D.37)
(D.38)
BS EN 14917:2021
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G= C + A ∗  ∆ 3
(D.39)
D = B2 + C 2
(D.40)
D.3.5.3 Calculation of auxiliary parameters and angular rotations in a plane system with the
theoretical hinge distance A*:
E = F 2 + G2
(D.41)
C 
 
(D.42)
ξ3 = arctan  
B
ξ2 = 90° - ξ3
1
2
(D.43)
F 

G
(D.44)
ψ 3 = arctan 
ψ 1 = 90° - ψ 3
 A*2 + E 2 - D2 
ϕ1 = arccos 

*
 2 ⋅ E ⋅ A

 A*2 + D2 - E 2 
ϕ2 = arccos 

*
 2 ⋅ A ⋅ D 
 E 2 + D2 - A*2 
ϕ3 = arccos 

 2 ⋅ E ⋅ D 
D.3.5.4 Angular rotations
Angular rotations in the main plane of movement:
(D.45)
(D.46)
(D.47)
(D.48)
Θ3 = ξ3 + ϕ3 -ψ 3 - 90°
(D.49)
Θ2 = 180° - ξ2 - ϕ2
(D.51)
Θ1 = ϕ1 +ψ 1 - 90°
(D.50)
Resulting angular rotations of the expansion joints K2 and K3:

Θ1, res = arccos  A* ⋅ cos


Θ2, res = arccos  A* ⋅ cos

Θ1 
A 
Θ2 
A 
(D.52)
(D.53)
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D.4 Calculation of forces and moments
Forces and moments in systems of pipes with expansion joints incorporated will be calculated normally
with proven computer programs. These programs should regard the expansion joints in a proper way
which means that their behaviour in the system should be as realistic as possible.
Axial expansion joints are regarded as axial springs and angular expansion joints normally as a
combination of hinges and torsion springs. The spring constants should be calculated from the equations
given in 6.2.9.
The stiffness of the restraining parts of the expansion joints depending on the direction of the loading
should also be regarded as well as the allowable limits for the amount of external loading on the
restraining parts.
To get reliable results the following assumptions for the calculation should apply in addition:
— the piping system and the expansion joints are properly supported and guided;
— the weight of the piping system and the fluid contained is carried by sufficiently designed supports
and hangers;
— the friction forces caused by guides, supports, and other hardware extraneous to the piping are
regarded;
— forces and moments due to pipe flexibility are regarded.
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Annex E
(informative)
Explanatory notes on the design of expansion bellows
E.1 General
This document was originally based on information given in the 7th edition (1998) of EJMA Standards
(Standards of the Expansion Joint Manufacturers Association, Inc). It was complimented by the knowhow and experience of the European manufacturers and users and by latest state-of-the-art knowledge.
The bellows designed according to this standard comply with the demands of the PED (Directive
2014/68/EU of the European Parliament and of the Council).
Highly reliable and safe design of bellows can be achieved by using the calculation method of this
document; i.e. experimental design by series of tests, including burst tests, is superfluous.
E.2 Calculation design
Main criteria that are regarded for the calculation of a designed bellows are:
1.
Pressure capacity
The pressure capacity (internal or external pressure) with regard to stresses is ensured by the calculation
of maximum pressure stresses which are limited to allowable values for the used material at operating
and test conditions.
The pressure capacity with regard to stability by calculating allowable values for design and test pressure
to avoid column instability and in-plane instability due to internal pressure and buckling of the
corrugations due to external pressure.
2.
Fatigue live
3.
Reliability of calculation design
The specified fatigue live is ensured by calculating the expected fatigue cycles which are mainly
depending on the equivalent stress range due to cyclic movement and pressure load and on the bellows
material. The allowable fatigue cycles result from the expected fatigue cycles divided by a safety factor
which takes into account the spread of the numerous test results.
The design of expansion bellows is extremely complex because of the conflicting requirements that are
demanded on the bellows function.
A sufficient pressure capacity on the one hand demands high wall thickness and small corrugation height
and on the other hand a high flexibility for the absorption of movement conversely requires low wall
thickness and deep corrugations.
Numerous variables are available to fulfil the demanded design criteria, such as type of bellows,
dimensions of the corrugations, number of corrugations, number of plies, reinforcing members, and
bellows materials.
The design equations of this standard have proved in practice to deliver very reliable results although
they are based on several simplifying assumptions, like uniform equivalent ply thickness, isotropic
material, elastic shell theory.
The reliability of the design is in addition based on controlled manufacturing processes with extensive
in-process and final inspection and testing.
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This document is paying a particular attention to the forming and welding processes including the
allowable deviations (tolerances) from the nominal geometry which are affecting the physical behaviour
of the bellows.
E.3 Types of bellows
E.3.1 Corrugation shape
This document deals with three different types of bellows relating to the shape of corrugation:
— unreinforced bellows;
— reinforced bellows;
— toroidal bellows.
These three types have different advantages which are important for their application.
Unreinforced bellows have nominally U-shaped corrugations and provide great flexibility to absorb
movements but, have in contrary a limited pressure resistance.
Reinforced bellows have as well U-shaped corrugations which are reinforced by rings placed in the roots
of the corrugations. These reinforcing members absorb most of the circumferential stresses generated
by the internal pressure and thus lead to greater pressure capacity. Movement is however reduced
because the reinforcing members obstruct flexibility.
Toroidal bellows which are normally supported by reinforcing members or pipe ends provided a very
high pressure capacity as there are mainly meridional stresses and no remarkable bending stresses
induced in the toroid by the internal pressure. As however, flexibility is limited this type of bellows is
used only for high pressures and small movements.
E.3.2 Number of plies
Every type of bellows may be designed with one or more plies.
Multi-ply design provides in relation to a single ply design a significantly higher pressure capacity without
increasing the rigidity of the bellows by a large factor. This effect leads to high movement capability with
relatively small dimensions (bellows length, corrugation height). This design is often used for U-shaped
bellows to avoid reinforcing members.
In a multi-ply bellows the plies are interacting due to geometrical and frictional effects, which have
significant influences on pressure capacity, flexibility, movement and fatigue life.
The design method given in this document is taking into consideration these effects. It is based on a big
series of test results provided by the European manufacturers and has proved to deliver good results up
to more than 20 plies.
E.4 Fatigue life expectancy
Fatigue life depends on the maximum equivalent stress range to which the bellows is submitted during
each complete operational cycle. The cyclic stress range due to deflection generally affects the fatigue
more than a pulsing stress range due to variable pressure.
Accordingly, the cycles to fatigue will be reduced if the deflection is increased and vice versa.
In addition to the shape of the corrugations, the fatigue life is affected by the type of material used for the
bellows and by the manufacturing process. The cold work hardening of austenitic steel for instance,
induced during the forming process of the corrugations, generally improves the fatigue life.
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Stress releasing heat treatment which does not reduce the cold work is also not decreasing the cycle life.
If however, the annealing temperature is increased up to a value where solution annealing takes place
fatigue life is reduced by a marked degree.
Design fatigue curves are given for four material classes which cover Ni-alloys, austenitic stainless steels,
and ferritic steels. They result in an allowable number of cycles with a safety factor 3 included. For highcycle fatigue a safety factor 1,25 on the stress range is applied.
An overly conservative assumption of specified cycles is therefore not recommended because it would
tend to increase the number of corrugations and lead to bellows more prone to squirm.
For materials not mentioned in the standard but, suitable for bellows (forming, welding) specific fatigue
curves may be established from actual fatigue tests on a series of bellows according to Annex F.
E.5 Instability
E.5.1 General
Excessive pressure or an axial compressing force may cause a bellows to become unstable. Instability is
detrimental to bellows performance and can greatly reduce its pressure capacity, fatigue life and
flexibility. Three types of instability are theoretically possible and have to be avoided.
The calculation methods in this document predict allowable pressure and axial force to a safe limit by
applying sufficient high safety factors.
E.5.2 Column instability
Column instability (squirm) is defined as a gross lateral shift of the bellows centre line and can occur
under high internal pressure and/or a great axial compressive load due to bellows stiffness. It generally
appears with bellows which have a relatively large length-to-diameter ratio and is comparable to the
buckling of a straight column under compressive load (see Figure E.1).
Column instability is considered to have occurred if under internal pressure an initially symmetrical
bellows deforms, resulting in lack of parallelism or uneven spacing of adjacent corrugations at any point
on the circumference. This deformation is regarded as unacceptable squirm when the maximum of
corrugation pitch under internal pressure to the initial corrugation pitch exceeds a relation of 1,15 for
unreinforced or 1,20 for reinforced bellows (ASME Section III, Division 1, ND-3649.4).
E.5.3 In-plane instability
In-plane instability is defined as a local bending and rotation of one or more corrugations such that the
plane of these corrugations is there no longer perpendicular to the axis of the bellows, which remains
more or less in line (see Figure E.2).
This type of instability generally appears when bellows with relatively high corrugations and a small
length-to-diameter ratio are associated with high pressure stresses originating plastic hinges at the root
or the crest of the corrugations.
E.5.4 Buckling
When a bellows is subject to excessive external pressure instability (buckling) may occur. The limiting
pressure can be verified by regarding the bellows as a portion of a cylindrical shell with similar behaviour.
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Figure E.1 — Column squirm
Figure E.2— In-plane squirm
E.6 Bellows spring rate
The axial force required to deflect a bellows depends on the material (Young’s modulus, Yield point) and
especially on its geometry, i.e. ply thickness, number of plies, corrugation height and number of
corrugations.
The graph below (Figure E.3) gives exemplary curves of force-to-axial displacement, Fx = f(x).
Starting from the point A the bellow will at first behave elastically and thus the first part of the curve AB
shows a straight line. The second part BC shows the bellows deflecting in the plastic range up to the
maximum effective force at the point C.
When the force is now released the decreasing curve CD shows again a linear behaviour parallel to the
section AB and ends with a residual displacement in the point D.
Figure E.3 — Hysteresis showing axial spring rate of a bellows
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If the direction of the force is now changed, a somewhat different behaviour can be registered and will,
at the end of the complete cycle of applying forces and movement in both directions, result in a repeatable
hysteresis. The effective spring rate for the maximum displacement is given by the slope of the straight
line AC.
It can be imagined that the effective spring rate changes when the total displacement is reduced.
If for multi-ply bellows friction appears between the plies depending on the number of plies and the
amount of pressure the vertical spread of the hysteresis branches will be greater but, the slope of the
curves (a) and (b) will remain the same. For very small movements the elastic spring rate may due to the
frictional effects between the plies be higher than calculated.
The elastic spring rate of the bellows, AB, can be determined analytically with reasonable accuracy; i.e.
with a tolerance of less than ± 30 % based on the manufacturing tolerance limits required in this
document.
The calculation of displacement forces and moments related to different movements should for practical
purpose be based on the effective spring rate AC which is calculated for the maximum design movement
added by the frictional effects.
This should be regarded by the expansion joint manufacturer when providing the effective spring rate of
an expansion joint to the pipe manufacturer.
However, spring rates related to the actual movement may be useful for critical applications.
Table E.1 gives conversion equations for lateral and angular spring rates depending on the axial spring
rate KB.
Table E.1 — Conversion of elastic spring rates
Type of bellows
Single bellows
Double bellows
with unsupported intermediate
pipe
Double bellows
with guided intermediate pipe
Lateral spring rate
Angular spring rate
N/mm
Nmm/rad
3 Dm2
Ky = ⋅ 2 ⋅ KB
2 lB
3 D 2
K y = ⋅ 2 m *2 ⋅ K B
4 lB + 3l
1 Dm2
K y = ⋅ *2 ⋅ K B
4 l
KΘ =
Dm2
⋅ KB
8
KΘ =
Dm
⋅ KB
8
KΘ =
Dm
⋅ KB
8
2
2
a
a
a Gives value for each bellows and is only relevant for universal expansion joints and for lateral expansion joints
with two tie-rods with spherical bearings or hinges and only in the plane of the tie rods and perpendicular to the
bellows centreline.
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Annex F
(informative)
Procedure for setting-up a design fatigue curve
F.1General
This annex defines the procedure by which a specific bellows design fatigue curve may be developed to
be used according to this document.
The necessity for a specific design fatigue curve may be the use of a material not in accordance with the
definitions of 6.2.6 or the adaptation to an individual manufacturer.
F.2Procedure for setting up a design fatigue curve for expansion bellows
F.2.1 General
To set up a specific fatigue curve fatigue tests should be carried out with a minimum of 25 expansion joint
bellows.
The tests should represent the intended application range of the design fatigue curve, respectively the
production program.
F.2.2 Number of tests
At least 5 different bellows designs, each with 5 identical bellows, are to be selected for the fatigue tests.
F.2.3 Extrapolation range
The dimensions of the bellows tested determine the extrapolation range of the design fatigue curve
within the limits given in Table F.1.
Table F.1 — Tested (index t) and permitted (index d) design dimensions
Dimensions
Inner diameter, Di
Ply thickness, ep
Number of plies, np
a
Calculation coefficients, C1, C2 a
Permissible range
0,5 Di,t,min ≤ Di,d ≤ 2,0 Di,t,max; Di,t < 1 000
0,5 Di,t,max ≤ Di,d ≤ unlimited; Di,t ≥ 1 000
0,5 ep,t ≤ ep,d ≤ 1,5 ep,t
1 ≤ np,d ≤ np,t,max
0,5 Ci,t,min ≤ Ci,d ≤ 1,5 Ci,t,max
C1 and C2 are factors given by Formulae (6) and (7), used to determine the coefficients Cp, Cf, Cd.
F.2.4 Manufacturing methods
At least 2 bellows designs are to be tested for each of the various manufacturing methods (hydro forming,
roll-forming, etc.).
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F.2.5 Bellows material
All bellows designs have to be made of the same material in identical metallurgical conditions (as-formed,
annealed, etc.). The material should be the same for each ply.
The design fatigue curve applies to the bellows material used. The application to bellows made of the
same type of material with similar or higher yield strength is permitted.
F.3Tests
F.3.1 Movement
Each bellows design is to undergo fatigue tests with 5 different axial movements.
The movements are derived from graduated values for the equivalent stress range.
(Example
of
800 N/mm2).
distribution:
σeq = 3 000 N/mm2,
2 000 N/mm2,
1 500 N/mm2,
1 000 N/mm2,
The movements for equivalent stresses are calculated using the nominal values of the bellows geometry
and the guaranteed material properties.
The application range of the design fatigue curve is limited to an extrapolation of − 10 % of the minimum
cycle number and 200 % of the maximum cycle number.
F.3.2 Test pressure
F.3.2.1 Constant internal pressure
Each bellows design is to be tested with a constant internal pressure. The test should be carried out at
the maximum allowable pressure according to 6.1.2.1. To be sure that the equivalent fatigue stress is
mainly due to cyclic displacement, and not to the constant pressure, the stress level due to movement
should be high enough to get a pressure component stress which is not higher than 30 % of the equivalent
fatigue stress:
σ eq = 0,7 ⋅ σ m,m ( P ) + σ m,b ( P ) + σ m,m ( ∆q ) + σ m,b ( ∆q )
where
and
( )
(F.1)
( )
0,7 ⋅ σ m, m P + σ m, b P  ≤ 30 % ⋅ σ eq


σ m,m ( ∆q ) + σ m,b ( ∆q )  ≥ 70 % ⋅ σ eq
.
Each of the 5 bellows should be designed so as to determine the maximum allowable pressure PS at 20 °C
complying with the requirements of 6.1.2.1.
F.3.3 Other test conditions
The general conditions for the fatigue tests are as follows:
a) test medium:
b) test temperature:
liquid or gas, preferably water or air;
room temperature (approx. 20 °C);
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c) test frequency: recommendation: The chosen test frequency should avoid dynamic and inertia
effects which causes unequal movements per corrugation;
d) measurement accuracy:
— movement: ± 1 % or ± 0,5 mm, whichever is greater;
— test pressure: ± 5 %.
The movement and the test pressure should be monitored throughout the test with calibrated measuring
instruments. The criterion for the number of cycles to failure is leakage, which may be detected by the
drop of the test pressure.
To minimize possible erratic points, the following characteristics should be checked prior to testing:
a) geometry:
— Di, Do (or circumference π⋅Do), with Do the outside diameter;
— ri+e the external radius, ri the internal radius and, q the pitch of the corrugations (mean values);
b) mechanical properties:
Re, Rm, A % in longitudinal and transverse directions (keep one coupon of the original plate and of
the weld for possible checking after the tests).
Out of tolerance bellows should be rejected and replaced.
NOTE
bellows.
Before the fatigue test, a pressure test as defined in 8.6.2.2 should be carried out for each expansion
F.3.4 Fatigue test equipment
The test equipment should provide a periodically changing, symmetrical alternating movement of the
expansion bellows with or without internal pressure.
The movement should be symmetrical about the stress-free mid-position of the bellows. In the midposition, the bellows is at its nominal length.
A movement cycle or stress cycle comprises movement from the mid-position to an end position, the
movement in the other direction to the other end position and return to the mid-position.
The principal arrangement of the bellows and the bellows movement during the axial fatigue tests is
shown in Figure F.1.
The test can equally be carried out in a vertical or horizontal axis.
The axial pressure thrust is to be restrained by the test equipment.
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Key
1 surge vessel
Figure F.1 — Axial fatigue test arrangement
F.4Evaluation of the test results
To evaluate the formula for the specific fatigue curve the following steps should be carried out.
Step 1: calculate the best fit curve Nm = f (σ eq ) for all the pairs of n test results, Nm, i; σ eq, i, (i = 1 to n)
on the base of the following formula:
C
 Am  m
Nm = 
 , where Bm = 1,7 ⋅ Rp 0,2 , ( respectively 1,7 ⋅ Re )
 σ eq - Bm 
(F.2)
with Nm the number of measured cycles to failure and σeq the related calculated equivalent stress; see
Formulae (121), (145) or (167) according to tested type of bellows.
The best fit curve can be found by the aid of available computer programs or by known mathematical
methods applicable, when Formula (F.2) is transformed to a linear formula, see F.5.
Step 2: calculate a number of j Nm-values from the best fit curve (see step 1, above) for m (at least five)
stress levels σ eq,j (j = 1 to m) preferable the stress levels realized in the tests (intersection points, see
Figure F.2).
Step 3: determine new pairs of values, N; σeq, on the base of step 2 applying the following equations (see
Figure F.3):
 Nm , j 
N j* = 
 ; σ eq, j
 3 
(F.3)
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 σ eq , j 
Nm , j ; σ j* = 

 1,25 
(F.4)
Step 4: select those pairs of values (*) from the above calculated values that represent the “worst case”
and determine the step 4 curve by finding the best fit curve by using an equation similar to the above one
(F.2):
C*
 A* 
N* =  *
, where B * = 1,36 ⋅ Rp 0,2 , ( respectively 1,36 ⋅ Re )
* 
 σ eq - B 
(F.5)
Step 5: to setup the final design curve, make sure that at least 98 % of the test results lie above or on the
step 4 curve; this is the criterion the design curve has to fulfil. If necessary the design curve is determined
by shifting the step 4 curve parallel to the x-axis in the direction of smaller N-values until the 98 %
condition is met using the following formula:
C
 A 
Nalw = 
 ,
 σ eq - B 
*
with A = A ⋅ K
1 C*
(F.6)
*
, B = B and C = C *
where K is determined by the quotient of two N-values, one lying where the design curve should pass and
the second lying on the step 4 curve, both having the same stress level σ eq (see Figure F.4).
NOTE
The final design curve is valid for bellows with the number of plies used in the tests. For different number
of plies use the Formula (22) analogously.
200
BS EN 14917:2021
EN 14917:2021 (E)
Key
possible measured data
best fit curve
intersection points
Figure F.2 — Best fit curve
201
BS EN 14917:2021
EN 14917:2021 (E)
Key
best fit curve
intersection points
N* = N/3
S* = S/1,25
Step 4 curve
202
Figure F.3 — Determination of Step 4 curve
BS EN 14917:2021
EN 14917:2021 (E)
Key
possible measured data
intersection points
Step 4 curve
design curve
Figure F.4 — Determination of Step 5 curve (Design curve)
203
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EN 14917:2021 (E)
F.5Linear regression
A best fit curve can be evaluated by transforming the generalized Formula (F.2):

A 

Nm = 
 σ eq - B 


C
with the variables Nm and σeq into a linear form by taking the logarithms of both sides.
By this procedure:
(
)
(
lnN m = C lnA - ln σ eq - B  = C ⋅ lnA - C ⋅ ln σ eq - B


)
(F.7)
(F.8)
and by introducing the new variables Y = In Nm, X = In (σeq – B) and the constants a = C · In A, b = C the
equation will become that of a straight line:
Y =a-b⋅X
(F.9)
By the method of linear regression (minimum sum of error squares) the constants a and b can now be
detected when a value for B is inserted, see F.4. This can be done by a computer program or by the
following equations.
n
∑
a=
i =1
∑
i =1
X i2 -
n
∑
i =1
n
∑ Xi
Yi X i
 n

2 
n
Xi - 
X i 
i = 1

i =1


n
∑
n
b=-
n
Yi
n
∑
i =1
Yi X i -
∑
n
∑
i =1
Yi
∑
∑
2
n
∑ Xi
2
The missing factors A and C for the Equation (F.7) are now to be calculated as follows:
A = e a/b
C =b
and inserted into the Formula (F.7) which results in the desired best fit curve.
204
(F.10)
i =1
 n

2 
n
Xi - 
X i 
i = 1

i =1


n
i =1
(F.11)
(F.12)
(F.13)
BS EN 14917:2021
EN 14917:2021 (E)
Annex G
(informative)
Polynomial approximations for coefficients Cp, Cf, Cd
G.1 Coefficient Cp
Cp = α0 + α1 ⋅ C1 + α2 ⋅ C12 + α3 ⋅ C13 + α 4 ⋅ C14 + α5 ⋅ C15
Coefficients αi are given in Table G.1 and Table G.2.
C2
Table G.1 — Polynomial coefficients αi for the determination of Cp when C1 ≤ 0,3
α0
α1
α2
α3
α4
α5
0,2
1,0
− 0,369 0
− 1,755 3
2,663 7
0,0
0,0
0,6
1,0
− 2,638 6
19,168
− 71,341
92,161
0,0
7,017 9
− 4,981 6
10,941
− 39,484
0,4
0,8
1
1,2
1,4
1,6
2
2,5
3
3,5
4
1,0
1,0
− 0,714 9
0,106
− 3,063 7
0,333 1
− 2,869 7
− 1,759 5
1,0
− 3,144 6
7,936 4
1,0
− 3,071 8
1,0
1,0
1,0
1,0
1,0
1,0
1,0
− 3,205 3
− 3,304
− 3,071 8
− 3,071 8
− 3,071 8
− 3,071 8
6,148 3
6,148 3
6,148 3
6,148 3
6,148 3
− 0,585
0,0
0,0
112,75
− 512,24
682,12
81,396
− 380,2
577,63
− 22,656
24,013
34,166
16,743
0,0
− 12,809
− 12,809
− 12,809
− 12,809
− 12,809
0,0
66,119
16,743
16,743
16,743
16,743
0,0
0,0
0,0
0,0
0,0
0,0
205
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EN 14917:2021 (E)
C2
Table G.2 — Polynomial coefficients αi for the determination of Cp when C1 > 0,3
α0
α1
α2
α3
α4
α5
0,2
0,714 2
2,128 3
− 10,046
16,319
− 11,688
3,121 5
0,6
0,477 3
3,663 8
− 15,066
24,734
− 18,461
5,194 3
0,4
0,8
0,573 8
0,46
3,239 9
2,887 2
− 13,891
− 12,701
22,801
22,867
− 0,196 6
1,4
0,485 4
− 0,077 9
0,981 1
− 3,98
10,568
− 14,839
10,475
− 2,913 9
− 3,688
6,467 6
− 5,459 1
1,778 6
0,0
− 4,095 1
6,910 6
− 5,608 6
1,754
1,6
2
2,5
3
3,5
4
0,490 7
− 0,313 1
− 0,22
0,11
− 7,416 5
1,100 5
− 3,780 3
1,158 7
G.2 Coefficient Cf
0,0
0,197 7
1,468 8
1,073
0,022 6
5,783 5
0,505 5
0,466 5
− 4,292 9
− 18,763
4,697 1
1
1,2
1,936 4
− 16,871
19,558
6,429 2
Cf = β0 + β1 ⋅ C1 + β2 ⋅ C12 + β3 ⋅ C13 + β4 ⋅ C14 + β5 ⋅ C15
Coefficients βi are given in Table G.3.
206
0,124 9
0,0
− 26,669
− 5,285 8
3,692 7
− 1,135 6
0,0
0,0
0,0
0,0
18,146
1,676 9
0,0
0,0
− 4,872 2
0,0
0,0
BS EN 14917:2021
EN 14917:2021 (E)
C2
Table G.3 — Polynomial coefficients βi for the determination of Cf
β0
β1
β2
β3
β4
β5
0,2
1,006
2,375
− 3,977
8,297
− 8,394
3,194
0,6
1,003
1,993
− 5,055
12,896
− 14,429
5,897
0,997
0,621
− 0,907
2,429
− 2,901
3,622
− 3,467
0,4
0,8
1
1,2
1,4
1,007
1,003
1
1,338
0,112
− 1,717
− 1,41
− 0,285
− 1,309
1,002
− 1,061
− 0,715
1,001
2,5
1
− 0,494
− 1,31
3
0,999
− 1,521
4
1
− 2,007
3,5
− 1,818
1
1,6
2
1,82
0,998
G.3 Coefficient Cd
− 1,896
− 1,879
− 0,829
− 0,039
1,839
1,62
2,981
1,908
3,483
4,959
3,103
4,116
− 2,43
0,02
− 0,55
− 3,044
1,013
− 4,569
− 3,016
1,361
1,191
1,543
0,99
− 4,36
1,555
1,852
− 0,664
2,121
− 2,215
− 0,538
− 0,261
− 2,047
0,87
0,77
0,249
Cd = γ 0 + γ 1 ⋅ C1 + γ 2 ⋅ C12 + γ 3 ⋅ C13 + γ 4 ⋅ C14 + γ 5 ⋅ C15
Coefficients γ i are given in Table G.4.
207
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EN 14917:2021 (E)
Table G.4 — Polynomial coefficients γi for the determination of Cd
C2
γ0
0,4
0,999
0,8
1,005
0,2
0,6
1
1,2
2,5
3,5
4,564
− 1,645
1,003
2,189
− 3,192
5,928
− 5,576
2,07
1,001
0,953
3,924
− 8,773
10,444
− 4,749
1,296
− 0,087
1,31
1,263
0,602
0,909
− 13,929
2,11
− 3,625
1,135
1
− 0,133
− 0,46
1
− 0,545
1,001
0,122
− 2,407
5,184
0,309
1
4
γ5
− 4,414
1
3
γ4
1,685
0,999
2
γ3
1,151
0,998
1,6
γ2
1
1,002
1,4
γ1
− 0,178
− 0,323
− 1,118
3,73
− 0,704
− 0,179
G.4 Linear interpolation
13,828
5,166
− 1,04
0,351
− 0,955
2,273
0,942
1,596
− 1,521
− 0,42
1,457
− 1,561
0,577
− 0,462
0,946
− 4,453
− 1,038
0,181
− 0,706
− 4,83
− 2,312
− 0,115
0,877
2,055
0,474
The previous tables contain tabulated values for the polynomial interpolation of Cp, Cf and Cd.
The boxes below are used to organize data for one-dimensional interpolation.
C1 =
C2 =
2 ⋅ rm
w
2 ⋅ rm
1,1 ⋅ Dm ⋅ ep*
Figure G.1 — Values for linear interpolation
J and L are the values surrounding C2 and A and B are values accompanying C1 for J and L.
208
0,71
0,08
BS EN 14917:2021
EN 14917:2021 (E)
C - L
C p , C f , Cd = B + ( A - B )  2

 J-L 
EXAMPLE
C2 = 1,05
Given: C1 = 0,45 and C2 = 1,05; find: Cp, Cf and Cd
J
L
1,0
1,2
C1 = 0,45
A
B
0,548
0,503
Cp = 0,537
C1 = 0,45
A
B
1,220
0,976
Cf = 1,159
C1 = 0,45
A
B
1,766
1,539
Cd = 1,709
209
BS EN 14917:2021
EN 14917:2021 (E)
Annex H
(informative)
Required design data and information
H.1 Required design conditions
The required design data listed in Table H.1 should be given by the piping or pressure vessel
manufacturer to the expansion joint manufacturer.
Table H.1 — Required design data
Number
Object
Subclause
reference
1
Type of expansion joint
4.1
3
Nominal size DN or relevant diameters
6.2
Minimum and maximum allowable temperature TS
3.14
2
4
5
6
7
8
9
10
11
12
End connections (material, size, standards)
Maximum allowable pressure PS
Displacements
Number of cycles Nspe
—
3.13
6.2.7
6.2.6.1
Material of the bellows (compatible with medium and 5.2.1.1
working conditions)
Additional design conditions
6.1.4
Flow velocity
6.3.3
Nature of fluid: gas or liquid
Category according to Directive 2014/68/EU
H.2 Additional information
6.3
3.21
Additional information that may affect the design should be given by piping or pressure vessel
manufacturer.
210
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EN 14917:2021 (E)
Annex I
(informative)
Expansion joints risk analyses
The possible risks of an expansion joint and how they have been dealt in this document are described in
the Table I.1.
Table I.1 — Risk analysis list
N°
Risk
Adopted precaution
Clause reference
Material
1
2
3
4
5
6
7
8
9
10
Corrosion
5.2.1.2,
5.2.2
5.2.1.1,
Suitability of chosen material 5.2.2,
for forming and welding
5.2.3,
5.2.4
Internal
erosion/wearing
5
due to the medium velocity
Deformation and/or rupture
with loss of fluid and
structural integrity caused by
5
PS and TS
Rupture due to fatigue caused
by cycling movements
Design
6.1.2,
6.3
6
Damages
caused
by
overcoming the design limits
PS, TS, movements and cycles
Leakage from seam welds of
bellows and from welds of
pressure containment parts
Damages caused during
handling and transport
Damages caused by incorrect
installation and use
Fabrication
7.3,
7.4
Control
8.3, 8.7.1
7
8.3, 8.4,
8.6.2.2,
8.7.1
10.2
Explosion or escape of the
medium
during
disassembling
if
not
depressurised or previously
discharged
State of risk a
8.3,
8.4.2,
8.7.1
7
7
Other
8.4.4,
8.6.2.2,
8.7.1
Eliminated
8.7.3, 9
Not eliminated
b
Eliminated
8.7.3, 10
8.7.3, 9,
10
8.7.3, 10
Partially
eliminated b
Not
eliminated b
Not
eliminated b
a State of the risk when the expansion joint is placed on the market.
b Not under the responsibility of the expansion joint manufacturer.
211
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EN 14917:2021 (E)
Annex J
(informative)
Additional material properties
Table J.1 — Material numbers and names
European
material
number
1.4828
International
designation
Alloy
309
Steel name
X15CrNiSi20–12
1.4876
800 / 800 H
X10NiCrAlTi32–21
2.4610
C-4
NiMo16Cr16Ti
2.4819
C-276
NiMo16Cr15W
2.4858
825
NiCr21Mo
2.4360
2.4816
2.4856
400
600
625
NiCu30Fe
NiCr15Fe
NiCr22Mo9Nb
Tables J.2 to J.4 give mechanical properties of several materials for design reasons.
The mechanical properties at elevated temperatures in Table J.2 are taken from VdTÜV material sheets
and are partly interpolated or completed on the basis of reliable documents published by material
manufacturers.
Table J.3 gives mechanical properties at elevated temperatures for the materials specified in Annex B.
The verification of mechanical properties that are not content of the VdTÜV material sheets is only made
by agreement between the purchaser and the manufacturer at the time of enquiry and order.
212
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EN 14917:2021 (E)
Table J.2 — Temperature-dependent material properties
Material
Property a
MPa
2.4610
NiMo16Cr16Ti
solution
annealed,
e ≤ 5 mm
2.4816
NiCr15Fe
(soft)
annealed,
e ≤ 50 mm
2.4816 (H)
NiCr15Fe
solution
annealed,
e ≤ 50 mm
2.4819
NiMo16Cr15W
solution
annealed,
e ≤ 5 mm
2.4856
NiCr22Mo9Nb
(soft)
annealed,
e ≤ 3 mm
NOTE
Temperature in °C
20
100
200
300
400
450
500
340
315
285
270
260
—
—
Rp0,2
305
Rm
700
to
900
Rp1,0
285
—
255
—
245
—
225
—
E/105
2,11 2,07 c 2,02 1,95 c 1,88
Rm
550
to
750
Rp0,2
Elongation
at rupture
at 20 °C
200
—
—
—
—
—
—
180
165
155
150
145
520
500
485
480
475
—
170
160
150
150
145
—
480
460
445
440
435
—
310
280
240
220
195
—
—
Rm
730
to
1 000
—
—
—
—
—
—
Rp0,2
400
350
320
300
280
270
—
700
685
670
660
—
2,14 2,09 2,05 2,00 1,94 1,90 c 1,87
Rm
500
to
700
180
E/105
2,14 2,09 2,05 2,00 1,94 1,90 c 1,87
Rp1,0
330
Rp0,2
E/105
Rm
E/105
305
275
245
230
—
ρ in
Source
of values b
A min in %
g/cm3
40
8,6
[21] d, [33]
8,5
[10], [34]
30
8,9
[22], [35]
35
8,47
[12] d, [36]
—
E/105
Rp0,2
Density
—
30
35
2,08 2,04 2,00 1,95 1,88 1,85 c 1,82
830
to
740
1 000
2,09 2,02 c 1,95 1,9 c 1,85 1,81 c
Linear interpolation is permitted for intermediate values.
—
213
BS EN 14917:2021
EN 14917:2021 (E)
Material
a
b
c
d
Property a
MPa
Temperature in °C
20
100
Minimum values for Rp0,2 and Rp1,0
200
300
400
450
[…] see Bibliography.
Interpolated values (italic).
Only density is based on material manufacturers documentation.
214
500
Elongation
at rupture
at 20 °C
Density
A min in %
ρ in
g/cm3
Source
of values b
BS EN 14917:2021
EN 14917:2021 (E)
Table J.3 — Creep rupture stress (100 000 h)
European
Material number
Steel name
Alloy
1.4828
X15CrNiSi20–12
Source b
SEW 470 [3]
Temperature in °C
309
550
90
600
65
580
620
640
660
680
700
720
WB 434 [7]
36
26
16
14
840
5,5
880
900
134
45
7,5
860
157
55
800
820
c
800 H* a
171
75
12,5
780
b
WB 412 [4]
85
740
760
a
800 H
Typical creep rupture stress c Rm,100 000 in
MPa
560
NOTE
1.4876
X10NiCrAlTi32–21
see [4]
11
9
see [7]
6,5
5
4
3
Linear interpolation is allowed for intermediate values.
Variation with higher creep rupture stresses, see Table J.4.
[…] see Bibliography.
Interpolated values (italic).
215
BS EN 14917:2021
EN 14917:2021 (E)
Table J.4 — Low temperatures yield strength
Approximate temperature depending increasing factor KLT a
Material number
Temperature in °C
- 100
- 196
- 270
1,0
1,3
1,6
—
EN 10028-7:2016 / Annex F
1,8
based on 1.4301
1,0
no low
available
1.4404
1,0
1.4541
1,0
1.4301
1.4306, 1.4401, 1.4435
1.4550, 1.4571, 1.4539
1.4828, 1.4876,
2.4610, 2.4819, 2.4858
2.4360
2.4816, 2.4856
NOTE
a
216
Source / remarks
20
1,0
1,0
1,0
1,0
1,0
1,4
1,0
1,3
1,0
1,0
1,3
1,1
1,7
1,9
1,0
1,0
1,0
1,0
1,6
1,0
1,6
1,2
—
1,3
Linear interpolation is allowed for intermediate values.
based on 1.4541
temperature
[15], [9], [11]
(KLT = Rp 0,2 t / Rp 0,2, 20)
KLT = Rp1,0 t / Rp1,0, 20 or KLT = Rp0,2 t / Rp 0,2, 20, if Rp 1,0 not available.
values
BS EN 14917:2021
EN 14917:2021 (E)
Annex K
(normative)
Hardware calculation
K.1 General
The formulas of the analytical calculation method described in this Annex originates from the Elastic
Beam Theory. It is simplified and covers typical hardware configurations under static load applications
only (in terms of pressure and external loads). In some cases, as for the circular attachment plate (K.8.2),
an improved procedure was developed by combining the equations of circular plate theory with
cylindrical shell theory.
When a more precise or in detail stress calculation is requested, different stress evaluations are possible,
see 6.4.2.2.1.
Dynamic applications (pulsating pressure, intermittent flow and strong vibrations) require special
considerations and calculation method which are not included in the standard.
K.2 Additional symbols
The following symbols listed in Table K.1 are additional to the symbols of Table 4 and apply for the
Annex K.
Table K.1 — Additional symbols
Symbol
Description
Unit
Abolt
resistant cross section of one bolt of flange
mm2
a, a1 to a10
B
throat dimension of welded joint
mm
Bs
bending stiffness of the circular plate; see Formula (K.79)
ATB
b, b0, b1, bFe
bc
bk
CBR
CF1
CnTB
c
D
Dp
resistant cross section of one tie bar
external dimension of plate in general
lever arm of force
span distance in round or square gimbal ring; see Figures K.5 and K.6
distance of gravity centre of the arc; see Formula (K.110) and Figure K.14
spring rate of the pipe reaction to the circular plate; see Formula (K.82)
thickness of plate welded on flange; see Figure K.15
increasing factor for circular plate calculation; see Formula (K.85)
mm2
mm
-
mm
mm
mm
N/mm
mm
-
effective length of pipe carrying jointly in reinforcing rings configuration mm
see Figure K.16
external diameter of flange
external pipe diameter
mm
mm
217
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
Description
Unit
dB
bolt hole diameter in the flange
mm
dh
hole diameter of lug and gimbal ring; see Figures K.5 and K.6
mm
df
dp
dTB
E, E1, E2
Eg,t
El,t
Epipe,t
Eplate,t
Ep,t
ETB,t
F1
F2
Fc
Fe
FR
Ge
internal diameter of flange
pin diameter; see Figures K.2 and K.4
tie-rod hole diameter; see Figure K.14
dimensions of section in gusset with reinforcing rings; see Figure K.16
modulus of elasticity at temperature of gimbal
modulus of elasticity at temperature of lug
modulus of elasticity at temperature of pipe
modulus of elasticity at temperature of plate
modulus of elasticity at temperature of pin
modulus of elasticity at temperature of tie bar
force acting on each restraining part; see Formula (K.1) and Figure K.1
component force of angular rotation; see Formula (K.10) and Figure K.1
compression force on each tie bar
force acting on sections of connection see Figures K.10 and K.11
resultant force acting on pin; see Formula (K.11) and Figure K.1
mm
mm
mm
mm
N/mm2
N/mm2
N/mm2
N/mm2
N/mm2
N/mm2
N
N
N
N
N
G
shear modulus used in square gimbal ring: 0,385 Egt
g1
H
clearance between lugs or lug/gimbal; see Figure K.2
mm
HG
h
height of gusset in reinforcing rings configuration; see Figure K.16
mm
h1
height in gusset section with reinforcing rings; see Figure K.16
I, It
JTB
J
Jr
218
N/mm3
distance from gravity centre of resistant section with reinforcing rings; see mm
Figure K.16
width of lug in the bored section; see Figure K.3
lug plate dimension in connecting section; see Figures K.8, K.11 and K.12
moment of inertia of square gimbal ring; see Formulas (K.34) and (K.35)
mm
mm
mm
mm4
moment of inertia of the min. effective or resistant cross section of one tie mm4
bar
lever arm of F2 ;see Figures K.8, K.10 and K.11
mm
moment of inertia of the cross section with reinforcing rings; see Formula mm4
(K.135) and Figure K.16
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
Description
k2
cross section factor for lug; see Formulae (K.21) and (K.24)
k4, k5, k6
factors for circular plate; see Formulae (K.77), (K.78) and (K.79)
k3
kg0, kg1
K
L
La
Lc
LF
LF1
LF2
lbs
lp
cross section factor for gimbals; see Formula (K.30)
Unit
-
factors to calculate moment of inertia of square gimbal ring; see Formulae (K.36) and (K.37)
diameter of bolt circle of flange
mm
width of gimbal ring in the corner connection; see Figure K.5
mm
width of resistant section of attachment plate; see Figure K.7
mm
distance of the hole centreline to the end of the head of the lug; see mm
Figure K.3
width of gimbal ring in bored cross section; see Figures K.5 and K.6
width of resistant section of flange; see Figures K.13
width of resistant section of welded plate on flange; see Figure K.15
mm
mm
mm
minimum length of the pipe from plate to pipe edge at the bellow side; see mm
Formula (K.86), Figures K.7 and K.8
width of resistant section for connection in plate; see Figure K.10
mm
lp,0,lpφ, lp,90° width of resistant section around the pipe of attachment plate; see mm
Figure K.7
lw
contact width to the pipe in circular plate (weld included); see Formula mm
(K.83) and Figure K.10
MBra
bending moments in circular plate; see Formula (K.75)
nbolt
number of bolts in flange
M, Mb, MB, MP bending moment in general
Nmm
Mt
Nmm
nTB
QG
QTB
torsional moment in general
number of restraining part
critical instability force for square gimbal ring; see Formula (K.33)
R
limiting compression force on each tie bar; see Formula (K.9)
Sc
thickness of gimbal ring; see Figures K.2, K.3, K.5 and K.6
SF
SL, SL1
SR
mean pipe radius 0,5(Dp-s)
thickness of attachment plate or thickness of flange
thickness of lugs in the bored cross section; see Figures K.2 and K.3
thickness of reinforcing ring; see Figure K.16
Nmm
n°
n°
N
N
mm
mm
mm
mm
mm
219
BS EN 14917:2021
EN 14917:2021 (E)
Symbol
S
ug
Description
Unit
minimum thickness of pipe (nominal thickness less tolerance and corrosion mm
allowance when applicable)
W
lug plate dimension in form-lock connection; see Figures K.8 and K.11
mm
WLF1
moment of resistance of integral flange; see Formula (K.104)
mm3
WLF2
Wg
Wp
Wt
Wr
WTB
xg
moment of resistance in general
moment of resistance of plate welded on flange; see Formula (K.116)
mm3
mm3
moment of resistance in bored cross section in gimbal ring; see Formula mm3
(K.29)
moment of resistance of pin; see Formula (K.15)
mm3
moment of resistance of gusset with reinforcing ring; see Figure K.16
mm3
torsional modulus in general
mm3
moment of resistance of the min. effective or resistant cross section of one mm3
tie bar
Y
lug plate dimension in form-lock connection; see Figure K.11
mm
αk
calculation parameter for circular plate; see Formula (K.84)
-
αw
βk
εk
γ
λ
ν
σ
σBe
σb
τ
φbolt
lever arm of force F2 ; see Figures K.11 and K.12
angle for open plate; see Figure K.7
calculation parameter for circular plate; see Formula (K.80)
calculation parameter for circular plate; see Formula (K.81)
angle between gussets with reinforcing rings; see Figure K.16
slenderness factor; see Formula (K.7)
Poisson’s ratio for plate
stress in general
bearing pressure; see Formulae (K.16, K.17 and K.18)
bending stress in general
shear stress in general
angle between two bolt holes; see Figures K.13, K.14 and K.15
K.3 Force due to pressure
mm
rad
-
rad
-
N/mm2
N/mm2
N/mm2
N/mm2
deg
The force acting on the restraining parts depends on the pressure thrust Fp . The force F1 acting on each
restraining part (tie bar, pin, lug, etc.) depends on the number of restraining parts nTB and is given in
general by:
220
BS EN 14917:2021
EN 14917:2021 (E)
Fp
F1 =
nTB
and for hinge and gimbal joints:
Fp
F1 =
2
K.4 Tie bar
(K.1)
(K.2)
K.4.1 General
A basic drawing of a tie bar and the origin of the most relevant stresses are shown in Table 18 Ref. 1.
NOTE
Allowable design stresses (f) for bolt materials that are used for tie-rods shall be according to 6.1.2.3.2
and 6.1.2.3.3.
K.4.2 Tie bar in tension
The tension stress is given by:
σt =
F1
ATB
and shall comply with:
(K.3)
σt ≤ f
NOTE
For threaded round bar ATB is the cross resistant section of thread from relevant standard.
The bending stress due to the friction of pin or sphere is calculated by:
σ bTB =
Mb
WTB
and shall comply with:
(K.4)
σ bTB ≤ 1,5 ⋅ f
with the bending moment:
and
M b = F1 ⋅ µ H ⋅ 0,5 ⋅ d H
(K.5)
μH is the friction coefficient of pin or sphere (see 6.2.9.3.2.2, NOTE 2);
dH is the relevant bearing diameter;
WTB
is the modulus of resistance of the min. effective or resistant cross section of one tie bar;
for threaded bar WTB shall be calculated with the diameter obtained from the cross resistant section
ATB.
221
BS EN 14917:2021
EN 14917:2021 (E)
The combined stress of tension and bending is:
σ = σ t + σ bTB
and shall comply with:
(K.6)
σ ≤ 1,5 ⋅ f
K.4.3 Tie bar in compression
This case may happen when negative pressure or additional load are present.
The slenderness factor λ of a tie bar is given by:
λ=
lR
( J TB / ATB )0,5
— For a slenderness factor λ ≤ 20:
(K.7)
Under these condition, the tie bar shall be verified under compression. The compression stress is:
σ =
Fc
ATB
and shall comply with:
(K.8)
σ ≤ f
— For a slenderness factor λ > 20:
In this case, the tie bar shall be verified against buckling. The limiting the compression force (Euler
with safety factor 4) is given by:
Q TB = 0, 25 ⋅
π 2 ⋅ E TB,t ⋅ J TB
lR 2
The compression force FC shall not exceed:
(K.9)
Fc ≤ Q TB
K.5 Pin
Pins according to Table 18 Ref. 2 and Figure K.2 shall comply the following.
— Resulting force:
The force distribution for a pin is shown in Figure K.1. The force F1 is given by Formula K.1. Force
F2, if rotation Θ is applicable, is:
F2 = F1 ⋅ tan (0,5 ⋅Θ)
222
(K.10)
BS EN 14917:2021
EN 14917:2021 (E)
The resulting force can be calculated according to:
FR = F12 + F22 or FR = F1 1 +(tan (0,5 ⋅ Θ))2
(K.11)
Figure K.1 — Force distribution on pin
Key
a external lug
b intermediate lug
c gimbal
Figure K.2 — Pin for connection of lugs
— The shear stress due to FR is given by:
τ=
2 ⋅ FR
π ⋅ dp 2
and shall comply with:
(K.12)
τ ≤ 0,6 ⋅ f
— The bending stress due to FR is given by:
223
BS EN 14917:2021
EN 14917:2021 (E)
σb =
Mb
Wp
(K.13)
and shall comply with:
σ b ≤ 1, 25 ⋅ f
The bending moment is given by:
Mb =
(
FR ⋅ S L + 2 ⋅ S L1 + 4 g1
)
8
or
and the moment of resistance by:
Wp =
Mb =
(
FR ⋅ S c + 2 ⋅ S L1 + 4 g1
)
8
π ⋅ d p3
32
— Bearing pressure on pin/hole of the lug or gimbal due to FR shall satisfy:
(K.14)
(K.15)
Lug with thickness SL:
σ Be =
FR
dp ⋅ S L
Lug with thickness SL1:
σ Be =
FR
d p ⋅ 2 ⋅ S L1
and shall comply with:
(K.16)
(K.17)
σ Be ≤ 1,3 ⋅ f
where f is referred to the smallest value between pin and lugs materials.
A gimbal with thickness Sc:
σ Be =
FR
dp ⋅ S c
shall comply with:
σ Be ≤ 1,3 ⋅ f
224
(where f is referred to the smallest value between pin and gimbal materials)
(K.18)
BS EN 14917:2021
EN 14917:2021 (E)
K.6 Lug with bore
K.6.1 General
The load carrying capacity of a lug with a bore is depending on the shape of the lug in the area adjacent
to the bore and on the dimensions in relation to the bore diameter. Two types of lugs are to be regarded,
having different calculation approaches (Figure K.4).
K.6.2 Forces due to pressure
For the reaction force acting on the lugs, the following assumptions are made (see Figure K.3):
— FR acts on the intermediate lug with thickness SL or for gimbal Sc (see Formula (K.11))
— 0,5·FR acts on the external lug with thickness SL1
Key
a pin diameter
b hole diameter
c gimbal
Figure K.3 — Lug with bore
225
BS EN 14917:2021
EN 14917:2021 (E)
a) Lug with H / dh ≤ 2
Figure K.4 — Types of lugs
b) Lug with H / dh > 2
K.6.3 Stresses due to reaction force
The calculation is valid for the following limitations:
— relation to width and bore diameter: 1, 8 ≤ H / d h ≤ 4 ;
— for lugs with H / d
h
≤ 2 (see Figure K.4 a);
— for lugs with H / d > 2 (see Figure K.4 b);
h
— relation to the distance of bore centreline to the end of the head of lug and width:
L / ( 0,5H ) ≥ 0, 9 and k 2 ≤ 1 ;
— relation to to the distance of bore centreline to the end of the head of lug and bore diameter:
L / d ≥ 0, 9 and k 2 ≤ 1, 4 .
NOTE
h
If the above limits are exceeded, the validity of the calculation shall be proven.
The equivalent stress σ L and σ L1 in an intermediate and external lug is given by:
σL =
FR
k 2 ⋅ AL
σ L1 =
where
(K.19)
0, 5 ⋅ FR
k 2 ⋅ AL1
for lugs with H / d
(
(K.20)
h
)
≤ 2:
k 2 = 0, 7 ⋅ L 0, 5 ⋅ H ≤ 1
(
)
AL = H - d h ⋅ S L
226
(K.21)
(K.22)
BS EN 14917:2021
EN 14917:2021 (E)
(
)
AL1 = H - d h ⋅ S L1
for lug with
H /d
h
>2
k 2 = 0, 7 ⋅ L d h ≤ 1, 4
:
AL = d p ⋅ S L
(K.23)
(K.24)
(K.25)
AL1 = d p ⋅ S L1
The equivalent stress shall comply with:
(K.26)
σ L and σ L1 ≤ f
For bearing pressure in pin/hole in lugs see Formulae (K.16) and (K.17).
K.7 Gimbal, square and round
K.7.1 General
Gimbals according to Table 18 Ref. 4 and Figures K.5 and K.6 shall comply the following.
K.7.2 Stresses in bored section
— The bending stress due to F1 is given by:
σb =
Mb
Wg
where the bending moment is given by:
F ⋅b
Mb = 1 c
4
and the moment of resistance by:
Wg =
(
S c ⋅ Lc 3 - d h 3
)
6 ⋅ Lc
The bending stress shall comply with:
(K.27)
(K.28)
(K.29)
σ b ≤ k3 ⋅ f
The safety factor is given by:
(
)
k 3 = 1,5 ⋅
3
1 - ( d h / Lc )
1 - d h / Lc
2
(K.30)
227
BS EN 14917:2021
EN 14917:2021 (E)
— The shear stress is:
τ=
0,5 ⋅ F1
( Lc - d h ) ⋅ S c
and shall comply with:
(K.31)
τ ≤ 0, 6 ⋅ f
— The combined stress:
σ = 1,73 ⋅ τ + σ b
shall comply with:
σ ≤ 1,5 ⋅ f
— For bearing pressure in pin/hole in lugs and gimbal see Formulae (K.17) and (K.18)
K.7.3 Square type gimbal
K.7.3.1 General
The shape and size of a square type gimbal is given in Figure K.5.
228
(K.32)
BS EN 14917:2021
EN 14917:2021 (E)
Figure K.5 — Square type gimbal
K.7.3.2 Instability
The critical instability force due to the ratio of Lc/Sc is given by:
QG =
16, 93
bc2
⋅ E g,t ⋅ I ⋅ G e ⋅ I t
(K.33)
229
BS EN 14917:2021
EN 14917:2021 (E)
where
Eg,t: Modulus of elasticity at temperature of gimbal
Ge: Shear modulus
Ge = 0,385 Eg,t for material with ν = 0,3.
NOTE
The moments of inertia are:
Lc + La ) ⋅ S c 3
(
I=
24
(
)
k g0 ⋅ Lc + La ⋅ S c 3
It =
2
where
k g0 =
k g1 =


1  0, 63 0, 052 
1+

3 
k g1
k g15 


( Lc + La )
2 ⋅ Sc
The limiting force shall comply with:
QG
5
≥ F1
K.7.3.3 Stresses in the corner connection
(K.34)
(K.35)
(K.36)
(K.37)
(K.38)
a) Welding connection according to Figure K.5-1)
The Shear stress in welds a1 and a2 is given by:
τw =
0,5 ⋅ F1
(
La ⋅ a1 + a2
)
and shall comply with:
τ w ≤ z ⋅ 0, 6 ⋅ f
b) Connection according to Figure K.5-2)
This case may happen when negative pressure or additional load are present.
— The Shear stress is given by:
230
(K.39)
BS EN 14917:2021
EN 14917:2021 (E)
τc =
0,5 ⋅ F1
1
L ⋅S
3 a c
and shall comply with:
(K.40)
τ c ≤ 0, 6 ⋅ f
— The bending stress is:
σb =
1,5 ⋅ F1
1 
 La 
3 
2
— The combined stresses is given by:
σ = 1,73 ⋅ τ c + σ b
and shall comply with:
(K.41)
(K.42)
σ ≤ 1,5 ⋅ f
c) Connection according to Figure K.5-3)
— The Shear stress is given by:
τc =
F1
La ⋅ S c
and shall comply with:
(K.43)
τ c ≤ 0, 6 ⋅ f
— The bending stress is:
σb =
1,5 ⋅ F1
(0,5 ⋅ La )
2
— The combined stresses is given by:
σ = 1,73 ⋅ τ c + σ b
and shall comply with:
(K.44)
(K.45)
σ ≤ 1,5 ⋅ f
K.7.4 Round type gimbal
The shape and size of a round type gimbal is given in Figure K.6.
231
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 torsion in 45° (rectangular section)
Figure K.6 — Round type gimbal
Stress calculation in 45° for full rectangular cross section (see Figure K.6):
NOTE
used.
When the cross section in 45° is not rectangular, appropriate dimensions and torsional modulus shall be
— The shear stress due to torsion is:
τt =
Mt
Wt
where the torsional moment is given by:
Mt =
0, 414 ⋅ F1 ⋅ bc
4
and the moment of resistance by:
Wt =
232
(K.46)
(K.47)
S c 2 ⋅ Lc
3 + 1, 8
Sc
Lc
(K.48)
BS EN 14917:2021
EN 14917:2021 (E)
— The shear stress due to F1 is given by:
τ F1 =
0,5 ⋅ F1
Lc ⋅ S c
— The total combined shear stress is:
τ = τ t + 1,5 ⋅ τ F1
and shall comply with:
(K.49)
(K.50)
τ ≤ 0, 9 ⋅ f
K.8 Attachment plate
K.8.1 Attachment plate (closed/open) with 2 restraining parts
K.8.1.1 General
Attachment plates (closed/open) according to Table 18 Ref. 5 and Figure K.7 shall comply the following.
The following calculation method is valid for close and open plate with αw ≤ 20°. For open plate with
αw > 20° different method shall be used (e.g. FEM).
NOTE
The force 0,5 Fp is transferred to the plate by tie bars or lugs. For lugs additional check in connecting
section shall be performed according to procedure described in K.8.1.1.3 and K.8.1.1.4).
233
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 closed plate αw = 0°
open plate αw = max 20°
2
3
section 3
Figure K.7 — Attachment plate with 2 restraining parts
K.8.1.2 Stress in plate for section 3
— The bending stress in section 3 is given by:
σb =
1
3 ⋅ Fp ⋅ b
LF ⋅ S F 2
— The shear stress is given by:
τ
1
=
0,5 ⋅ Fp
LF ⋅ S F
and shall comply with:
(K.51)
(K.52)
τ 1 ≤ 0, 6 ⋅ f
— The combined stress is given by:
σ = 1,73 ⋅ τ 1 + σ b1
and shall comply with:
234
(K.53)
BS EN 14917:2021
EN 14917:2021 (E)
σ ≤ 1,5 ⋅ f
K.8.1.3 Stress in sections for form-lock connection (lugs for hinge/gimbal)
The shape and size of sections for form-lock connection is given in Figure K.8.
NOTE 1
NOTE 2
In form-lock type connection, eventual welds to fix the lugs (e.g. tag) are not considered.
The force F1 is equal to 0,5·Fp and for F2 see Formula (K.10)
235
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 resistant sections
2 half resistant section
Figure K.8 — Sections for form-lock connection
a) Stresses due to F1 and moment caused by F2.
— The bending stress is:
236
BS EN 14917:2021
EN 14917:2021 (E)
σ bF1 =
(
)
6 ⋅ 0,5 ⋅ F1 + Fe ⋅ b
lp ⋅ S F2
— The shear stress is given by:
τ F1 =
(0, 5 ⋅ F1 + Fe )
lp ⋅ S F
where
Fe =
and
F2 ⋅ J
2 ⋅ bFe
bFe =
h + ug
2
J = Y + 0,5 ⋅ S F
and shall comply with:
(K.54)
(K.55)
(K.56)
(K.57)
(K.58)
τ F1 ≤ 0, 6 ⋅ f
b) Stresses due to F2, only a half section is considered.
— The bending stress due to F2 is given by:
σ bF =
2
6 ⋅ F2 ⋅ b
lp2 ⋅ S F
— The shear stress is:
τF =
2
F2
lp ⋅ S F
and shall comply with:
(K.59)
(K.60)
τ F2 ≤ 0, 6 ⋅ f
— Shear stress due to the torsional moment caused by Fe is:
τt =
Mt
Wt
where the torsional moment is given by:
(K.61)
237
BS EN 14917:2021
EN 14917:2021 (E)
M t = Fe ⋅ g
(K.62)
and the lever arm of Fe:
(
g = 0, 5 ⋅ l p - u g
)
The torsional modulus (mm3) is:
Wt =
(K.63)
S F2 ⋅ lp
3 + 1, 8
SF
lp
The shear stress shall comply with:
(K.64)
τ t ≤ 0, 6 ⋅ f
c) The total combined stress in resistant sections is given by:
σ = 1, 73 ⋅ τ F2 2 + (τ t + τ F1 ) + σ bF1 2 + σ bF2 2
2
and shall comply with:
σ ≤ 1,5 ⋅ f
K.8.1.4 Stress in sections for welded buttonhole connection (lugs for hinge/gimbal)
The shape and size of sections for welded buttonhole connection is given in Figure K.9.
238
(K.65)
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 resistant sections
2 half resistant section
Figure K.9 — Sections for welded buttonhole connection
239
BS EN 14917:2021
EN 14917:2021 (E)
The force F1 is equal to 0,5·Fp and for F2 see Formula (K.10).
NOTE
a) Stresses due to F1 plus moment caused by F2.
— The bending stress is given by:
σ bF1 =
(
where Fe is:
Fe =
)
6 ⋅ 0,5 ⋅ F1 + Fe ⋅ b
lp ⋅ S F2
F2 ⋅ J
0,5 ⋅ l p
and shall comply with:
(K.66)
(K.67)
τ F1 ≤ 0, 6 ⋅ f
— The shear stress is given by:
τ F1 =
(0, 5 ⋅ F1 + Fe )
lp ⋅ S F
and shall comply with:
τ F1 ≤ 0, 6 ⋅ f
b) Stresses due to F2.
(K.68)
— The bending stress, considered only one section lp (Conservative approach):
σ bF =
2
6 ⋅ F2 ⋅ b
S F ⋅ lp2
— The shear stress is given by:
τF =
2
F2
2 ⋅ lp ⋅ S F
and shall comply with:
(K.69)
(K.70)
τ F2 ≤ 0, 6 ⋅ f
c) The total combined stress in resistant sections is:
σ = 1, 73 ⋅ τ F1 2 + τ F2 2 + σ bF1 2 + σ bF2 2
240
(K.71)
BS EN 14917:2021
EN 14917:2021 (E)
and shall comply with:
σ ≤ 1,5 ⋅ f
K.8.1.5 Stress in the pipe
The tension stress in the pipe is given by:
σ lm =
Fp
( Dp - s ) ⋅ π ⋅ s
and shall comply with:
(K.72)
σ lm ≤ f
The pipe sections shall be designed according to the appropriate standard EN 13445-3:2014 or
EN 13480-3:2017.
For open plate with αW > 20° different method shall be used (e.g. FEM).
When closed plate is employed the secondary stresses due to thermal gradient at high temperature shall
be properly taken into account, floating plate is suggested.
K.8.1.6 Stress in the weld plate/pipe
Considering 0,5·Fp acting on 2 welds (the shear force in the welds will be maximal at φ = 90°) the
longitudinal shear stress is given by:
τ a3 =
(
0,5 ⋅ Fp
)
4 r ⋅ π - α W ⋅ 2 ⋅ a3
and shall comply with:
(K.73)
τ a3 ≤ z ⋅ 0, 6 ⋅ f
NOTE
See NOTEs 2 and 3 in K.8.1.3.
K.8.2 Circular attachment plate with 3 or more tie bars valid up to DN 800
K.8.2.1 General
The shape and size of circular attachment plate is given in Figure K.10.
This calculation method is valid as long as the force due to tie rods reaction can reasonably be considered
uniform distributed along the circumference; outside this assumption and for different shapes other than
circular other alternative methods (e.g. FEM) shall be used.
241
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 pipe side
2 bellows side
3 N° of tie-bars nTB
Figure K.10 — Circular plate with 3 or more tie bars
K.8.2.2 Stress in the plate
The stress in the plate is given by:
σ plate =
6 ⋅ M BRa
S F2
(K.74)
with the bending moment:


Fp ⋅ k 4 ⋅ C nTB


M BRa = - B s ⋅ - 1 - ν ×
+ 2 ⋅ 1 + ν ⋅ Fp ⋅ k 5 ⋅ C nTB + 3 + ν ⋅ Fp ⋅ k 6 ⋅ C

2
nTB 

0, 5 ⋅ Dp


(
where
Bs =
)
(
(
)
)
(
)
E plate,t ⋅ S F 3
(
12 ⋅ 1 - ν 2
(K.76)
)
(
)
(
)
(
)
(
) (
2 
2
 



1 β k ⋅ 1 - ε k ⋅ 1 - ν  ⋅ 2 ⋅ 1 + ν ⋅ ln β k + 3 + ν  - β k ⋅ 1 + ν ⋅ 1 - ε k ⋅ 3 + ν  0, 5 ⋅ Dp
k4 = - ⋅
⋅
8
π ⋅ Bs
1 - ν ⋅ 1 - ε k ⋅ 1 + ν  + β k 2 ⋅ 1 + ν ⋅ 1 + ε k ⋅ 1 - ν 




(
242
(K.75)
)
(
)
(
)
(
)
)
2
(K.77)
BS EN 14917:2021
EN 14917:2021 (E)
(
)
(
)
(
(
)
(
)
2 


 

1 1 - ν ⋅ 1 - ε k ⋅ 3 + ν  + β k ⋅ 1 + ε k ⋅ 1 - ν  ⋅ 2 ⋅ 1 + ν ⋅ lnβ k + 3 + ν 
1
⋅
⋅
k5 =
2
⋅
16
Bs
π




1 -ν ⋅ 1 - ε k ⋅ 1 +ν + β k ⋅ 1 +ν ⋅ 1 + ε k ⋅ 1 -ν




(
k6 = -
βk =
εk =
)
(
)
)
(
)
0,125
π ⋅ Bs
(K.79)
b0
0,5 ⋅ Dp
(K.80)
Bs
C BR ⋅ 0,5 ⋅ Dp
C BR =
E pipe,t ⋅ s 3 ⋅ α k
6
(
⋅ 2 ⋅ α k ⋅ lw + α k 2 ⋅ lw 2 + 2
)
l w = S F + 2, 82 ⋅ a3
αk =
4
(K.78)
3
(r ⋅ s )




Dp - s 

2 ⋅ b0


π 
 180° 


 nTB ⋅ sin 




 nTB 


C nTB =




D
s
2 ⋅ b0
p



π 
 8 ⋅ sin  180° 


 8 


and shall comply with:
(K.81)
(K.82)
(K.83)
(K.84)
(K.85)
σ plate ≤ 1, 5 ⋅ f
The length of the pipe from plate to the bellow side shall be (See Figures K.7 and K.8):
l bs ≥ 1, 2 ⋅ 2 ⋅ r ⋅ s
K.8.2.3 Stress in the pipe
(K.86)
The stress in the pipe is given by:
σ lm =
Fp
( Dp - s ) ⋅ π ⋅ s
(K.87)
243
BS EN 14917:2021
EN 14917:2021 (E)
and shall comply with:
σ lm ≤ f
NOTE 1
The pipe sections shall be designed according to the appropriate standard EN 13445-3:2014 or
EN 13480-3:2017.
NOTE 2
The secondary stresses due to thermal gradient at high temperature shall be properly taken into
account, floating plate is suggested.
K.8.2.4 Stress in the weld plate/pipe
The stress in welds around the pipe is given by:
τ a3 =
Fp
π ⋅ D p ⋅ 2 ⋅ a3
and shall comply with:
τ a3 ≤ z ⋅ 0, 6 ⋅ f
NOTE
See NOTE 2 in K.8.2.3.
K.9 Lug-plate connection (hinge/gimbal)
K.9.1 General
Lug plates connection according to Figures K.11 and K.12 shall comply the following.
NOTE 1
NOTE 2
244
In the below formulae use: SL = min (SL; 2 · SL1).
The force F1 is equal to 0,5·Fp and for F2 see Formula (K.10).
(K.88)
BS EN 14917:2021
EN 14917:2021 (E)
K.9.2 Lug-plate for form-lock connection
K.9.2.1 General
Key
1 bearing area
2 half section 2
3 Section 1
Figure K.11 — Lug-plate for form-lock connection
K.9.2.2 Stresses in Section 1
a) Stress due to F1
The tension stress due to F1 is given by:
245
BS EN 14917:2021
EN 14917:2021 (E)
σ tSL =
F1
h ⋅ SL
(K.89)
b) Stress due to F2
1) The bending stress due to F2 is given by:
σ bSL =
6 ⋅ F2 ⋅ Y
h2 ⋅ S L
2) And the shear stress by:
F2
τ SL =
h ⋅ SL
which shall comply with:
(K.90)
(K.91)
τ SL ≤ 0, 6 ⋅ f
c) Combined stress due to F1 and F2:
The combined bending and shear stresses are:
σ = 1,73 ⋅ τ SL + σ tSL + σ bSL
and shall comply with:
(K.92)
σ ≤ 1,5 ⋅ f
K.9.2.3 Stresses in Section 2
Stresses due to F1 and F2
a) The bending stress due to F1 and F2 is given by:
σ bSL =
(
SL ⋅ xg2
where
Fe =
and
246
F2 ⋅ J
2 ⋅ bFe
bFe =
)
3 ⋅ 0,5 ⋅ F1 + Fe ⋅ u g
h + ug
2
(K.93)
(K.94)
(K.95)
BS EN 14917:2021
EN 14917:2021 (E)
b) The shear stress due to F1 and F2 is given by:
τ SL =
0,5 ⋅ F1 + Fe
SL ⋅ xg
and shall comply with:
(K.96)
τ SL ≤ 0, 6 ⋅ f
c) Combined stress due to F1 and F2:
σ = 1,73 ⋅ τ SL + σ bSL
and shall comply with:
(K.97)
σ ≤ 1,5 ⋅ f
247
BS EN 14917:2021
EN 14917:2021 (E)
K.9.3 Lug-plate for welded buttonhole connection
K.9.3.1 General
Figure K.12 — Lug-plate for welded buttonhole connection
248
BS EN 14917:2021
EN 14917:2021 (E)
K.9.3.2 Weld between lug plate and attachment plate
The shear stresses of the weld between lug plate / attachment plate shall comply the following:
a) The shear stress due to F1 is given by:



2 ⋅ h + S ⋅ 2 ⋅ a 2 ⋅ h + 2 ⋅ S

2
a
⋅
⋅
L
4
L1
4

τ F1 = max 
(
F1
;
)
(
F1
)
and shall comply with:
(K.98)
τ F1 ≤ z ⋅ 0, 6 ⋅ f
— The shear stress due to F2 is given by:



2 ⋅ h + S ⋅ 2 ⋅ a 2 ⋅ h + 2 ⋅ S

2
a
⋅
⋅
L
4
L1
4

τ F2 = max 
(
F2
;
)
(
F2
)
and shall comply with:
(K.99)
τ F1 ≤ z ⋅ 0, 6 ⋅ f
τ MF2 =
where
Fe =
Fe
2 ⋅ a4 ⋅ h
(
F2 ⋅ Y + 0,5 ⋅ S F
(K.100)
)
0,707 ⋅ a 4 + 0,5 ⋅ S F
— The combined shear stress is given by:
τ a = τ F1 2 + (τ F2 + τ MF2 )
2
and shall comply with:
(K.101)
(K.102)
τ a ≤ z ⋅ 0, 6 ⋅ f
K.10 Tie bar and lug attachment on flanges
K.10.1 Integral flange
K.10.1.1 Stress in flange with 2 tie bars or lugs
The shape and size of a flange with 2 tie bars or lugs is given in Figure K.13.
NOTE
The force 0,5 Fp is transferred to the plate by tie bars or lugs. For lugs additional check in connecting
section shall be performed according to procedure described in K.8.1.1.3 and K.8.1.1.4).
249
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 Section 1
Figure K.13 — Flange with 2 tie bars
a) Stresses in section 1
— The bending stress due to 0,5 Fp is given by:
σ b1 =
0,5 ⋅ Fp ⋅ b
WLF1
with the moment of resistance:
WLF1 =
S F 2 ⋅ ( LF1 - 2 ⋅ d B )
6
— The shear stress due to 0,5 Fp is given by:
τ1 =
0,5 ⋅ Fp
S F ⋅ ( LF1 - 2 ⋅ d B )
and shall comply with:
(K.103)
(K.104)
(K.105)
τ 1 ≤ 0, 6 ⋅ f
— The combined bending and shear stress is given by:
σ = 1,73 ⋅ τ 1 + σ b1
250
(K.106)
BS EN 14917:2021
EN 14917:2021 (E)
and shall comply with:
σ ≤ 1,5 ⋅ f
b) Verification of the flange bolt with maximum load
The tension stress on bolt is given by:
σ bolt =
where
Fbolt
k bo ⋅ Abolt
Abolt
(K.107)
is the cross resistant section of the flange bolt
kbo is the effect of thread (see K.4-1)
Fbolt =
with:
ϕ bolt =
0,5 ⋅ Fp
2
(
⋅ cos 90° - ϕ bolt
)
360
in deg with nbolt = number of bolts
nbolt
The tension stress of the flange bolt shall comply with:
σ bolt ≤ f
NOTE 1
NOTE 2
.
(K.108)
(K.109)
The maximum allowable design stress (f) for bolting materials shall be min (Rp 0,2, t/3; Rm 20/4).
Additional stress for prestressing the gasket has to be considered in addition to Formula (K.107).
K.10.1.2 Stress in flange with more than 2 tie bars
The shape and size of a flange with more than 2 tie bars is given in Figure K.14.
NOTE
method.
Different shapes other than circular (triangle, square, etc.) are possible if verified by reliable calculation
251
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 Section 1
2 N° nTB application points of F1
Figure K.14 — Circular flange with more than 2 tie bars
The distance of gravity centre of the arc K where half force Fp (equal to 0,5·nTB·F1) is applied for the
equilibrium of the moments is given by:
bk =
K
π
a) The bending stress in section 1 is:
σ b1 =
Mb
W
where the bending moment is:





 F1 ⋅ nTB  
2 ⋅ b0
⋅
- bk 
Mb = 


2
 π 


 

 nTB ⋅ sin 




 nTB 


and the moment of resistance is:
W =
252
(B - df ) ⋅ S F2
6
(K.110)
(K.111)
(K.112)
(K.113)
BS EN 14917:2021
EN 14917:2021 (E)
If applicable the influence of the tie-rod hole(s) dTB on the value of W shall be taken into account.
See below example for nTB = 5:
B - d f - d TB ) ⋅ S F 2
(
W =
6
The bending stress shall comply with:
(K.114)
σ b1 ≤ 1,5 ⋅ f
b) Verification of the flange bolt with maximum load
The proof is according to the procedure described in K.10.1.1 b).
K.10.2 Plate welded on flange
K.10.2.1 Stress in plate welded on flange with 2 tie bars
The shape and size of plates welded on a flange for installing 2 tie bars is given in Figure K.15.
253
BS EN 14917:2021
EN 14917:2021 (E)
Key
1 Section 1
a weld details
NOTE 1
NOTE 2
Figure K.15 — Plate welded on flange
More plates welded other than two are possible if verified by a reliable calculation method.
The force 0,5 Fp is transferred to the plate by tie bars or lugs.
For lugs additional check in connecting section shall be performed according to procedure described in
K.8.1.1.3 and K.8.1.1.4.
a) Stresses in section 1:
— The bending stress due to 0,5 Fp is given by:
σ b1 =
254
0,5 ⋅ Fp ⋅ b1
WLF2
(K.115)
BS EN 14917:2021
EN 14917:2021 (E)
And the modulus of resistance by:
WLF2 =
C F1 2 ⋅ LF2
6
— The shear stress due to 0,5 Fp is given by:
τ1 =
0,5 ⋅ Fp
C F1 ⋅ LF2
and shall comply with:
(K.116)
(K.117)
τ 3 ≤ 0, 6 ⋅ f
— The combined bending and shear stress:
σ = 1,73 ⋅ τ 1 + σ b1
shall comply with:
(K.118)
σ ≤ 1,5 ⋅ f
b) Welds between plate and flange:
— The shear stress with 0,5·Fp only considered 2 welds and depending of weld detail is given by:
τ
a6
=
0,5 ⋅ Fp
2 ⋅ a6 ⋅ LF2
shall comply with:
(K.119)
τ a6 ≤ z ⋅ 0, 6 ⋅ f
— The tension stress due to the bending moment considered only 1 weld:
σ a6 =
0,5 ⋅ Fp ⋅ b1
C F1 ⋅ LF2 ⋅ a6
shall comply with:
(K.120)
σ a6 ≤ z ⋅ f
— The combined shear and tension stress:
σ 6 = σ a6 2 + 3 ⋅ τ a6 2
shall comply with:
(K.121)
255
BS EN 14917:2021
EN 14917:2021 (E)
σ6 ≤ z ⋅ f
c) Verification of the flange bolt with maximum load:
The proof is according to the procedure described in K.10.1.1 b).
K.11 Gusset
For (single) gussets (see Table 18 Ref. 6) no easy conservative calculation method is available. The
stresses in the gusset and in the pipe should be checked either by test results of the manufacturer or by
appropriate numerical methods, e.g. FEM. Special consideration has to be given to the ovalisation of the
pipe that causes harmful deformation of the bellows.
K.12 Gusset with reinforcing rings
K.12.1 General
The shape and size of gussets with reinforcing rings is given in Figure K.16.
256
BS EN 14917:2021
EN 14917:2021 (E)
Figure K.16 — Gussets with reinforcing rings
257
BS EN 14917:2021
EN 14917:2021 (E)
K.12.2 Basic definitions
The following definitions are required for the calculations in this subclause:
(
r = 0, 5 ⋅ Dp - s
)
 L + SG 

γ = arcsin  S
 2⋅r 

 [rad]
γ deg =
ka =
(K.123)
180 ⋅ γ
π
[deg]
b = b0 - r ⋅ cosγ
(K.124)
sinγ
1
, if γdeg < 20,71°
cosγ + γ ⋅ sinγ π
2
(
k a = 0,5 -
1
π
)
(cosγ + γ ⋅ sinγ ) , if γdeg ≥ 20,71°
c = 0,78 ⋅ r ⋅ s
(K.131)
 S ⋅ h 2 + 2 ⋅ c ⋅ s2 

E 1 = 0,5 ⋅  R 1
 S ⋅h +2⋅c ⋅ s 
 R 1

(K.132)
E 2 = h1 - E 1
(K.133)
g = E1 - s
Fe =
258
(
1
E ⋅ E 1 3 - 2 ⋅ c ⋅ g 3 + S R ⋅ E 23
3
(
max E 1 ; E 2
F1 ⋅ b
LG + S R
(K.127)
(K.130)
h1 = H G + s
Jr
(K.126)
(K.129)
E = 2 ⋅ c + SR
Wr =
(K.125)
(K.128)
where LG ≥ 2 c
Jr =
(K.122)
)
)
(K.134)
(K.135)
(K.136)
(K.137)
BS EN 14917:2021
EN 14917:2021 (E)
M b = k a ⋅ r ⋅ Fe
K.12.3 Stresses in the gussets
(K.138)
a) The shear stress in the gussets is given by:
τg =
F1
2 ⋅ S G ⋅ LG
and shall comply with:
(K.139)
τ g ≤ 0, 6 ⋅ f
b) The bending stress is given by:
σ bg =
6 ⋅ F1 ⋅ b
2 ⋅ S G ⋅ LG 2
and shall comply with:
(K.140)
σ bg ≤ f
c) The combined shear and bending stress is given by:
σ = 1,73 ⋅ τ g + σ bg
and shall comply with:
(K.141)
σ ≤ 1,5 ⋅ f
K.12.4 Stresses in the ring and pipe
a) The bending stress in the ring is given by:
σ SG =
Mb
Wr
b) The stress in the pipe is:
σp =
(
P ⋅r ⋅E
) (
E ⋅ s + HG ⋅ S R
)
c) The total stress in the resistant section is given by:
σ = σ SG + σ p
and shall comply with:
(K.142)
(K.143)
(K.144)
σ ≤ f
259
BS EN 14917:2021
EN 14917:2021 (E)
d) The longitudinal stress in the pipe caused by F1 with γ in rad:
σl =
F1
s ⋅r ⋅γ ⋅2
shall comply with:
(K.145)
σl ≤ f
K.12.5 Stresses in welds a7, a8 and a9
The positions of the welds are shown in Figure K.12
a) Stresses in weld a7
— The shear stress is given by:
τ a7 =
F1
4 ⋅ a7 ⋅ LG
and shall comply with:
(K.146)
τ a7 ≤ z ⋅ 0, 6 ⋅ f
— The bending stress is given by:
σ ba7 =
6 ⋅ F1 ⋅ b
4 ⋅ a7 ⋅ LG 2
— The combined stress is given by:
σ a7 = 1,73 ⋅ τ a7 + σ ba7
and shall comply with:
(K.147)
(K.148)
σ a7 ≤ z ⋅ 1,5 ⋅ f
b) The shear stress in weld a8 is given by:
τ a8 =
2 ⋅ F1
4 ⋅ a8 ⋅ π ⋅ Dp
and shall comply with:
τ a8 ≤ z ⋅ 0, 6 ⋅ f
c) The tension stress in weld a9 (considering only one side) is given by:
260
(K.149)
BS EN 14917:2021
EN 14917:2021 (E)
σ a9 =
F1
4 ⋅ a9 ⋅ H G
and shall comply with:
(K.150)
σ a9 ≤ z ⋅ f
261
BS EN 14917:2021
EN 14917:2021 (E)
Annex ZA
(informative)
Relationship between this European Standard and the Essential
Requirements of EU Directive 2014/68/EU
This European Standard has been prepared under a mandate given to CEN by the European Commission
to provide a means of conforming to Essential Requirements of the New Approach Directive 2014/68/EU.
Once this standard is cited in the Official Journal of the European Union under that Directive and has been
implemented as a national standard in at least one Member State, compliance with the clauses of this
standard given in Table ZA.1 confers, within the limits of the scope of this standard, a presumption of
conformity with the corresponding Essential Requirements of that Directive and associated EFTA
regulations.
Table ZA.1 — Correspondence between this European Standard and Annex I of Directive
2014/68/EU
Essential
Requirements of
Directive 2014/68/EU
Annex I
Clause(s) / subclause(s) of this
EN
Qualifying
remarks/Notes
2.2.1
6.1.4, 6.2.2.2, 6.3.4.2, 6.4.1 Relevant factors and loadings
2.2.3 a) and b)
6.1.2.3, 6.1.2.4, 6.2, 6.3,
6.4
2.2.1
3.1.1
3.1.5
3.2.1
3.2.2
3.3
3.4
4.1 (a), 7.5
4.1 (a)
4.1 (d)
4.1 (b)
4.3
6(a)
7.1
7.2
262
6.2.3.5, 6.2.4.4, 6.2.5.5,
6.2.6
Fatigue factors for the bellows calculation
7.4
Forming process for bellows
7.2.2
8.3, 8.4, 8.5 (8.5.3
excluded), 8.6, 8.7
8.6.2.2
Clause 9
10
5.2.4
5
5.1.1
5.2.1.2
5.3
10.4, 10.5
6.1.3.1 and 6.1.3.2
6.4.4, 8.4.4
Design and calculation method
Traceability of materials
Manufacturing tests and final inspection technical
documentation
Proof test
Marking and labelling
Handling and installation
Prevention of brittle fracture
Appropriate materials properties
Material suitability for processing procedure
Sufficient chemical resistance
Materials documentation
Risk of overstressing
Allowable stress
Joint coefficients
BS EN 14917:2021
EN 14917:2021 (E)
WARNING: Other requirements and other EU Directives may be applicable to the product(s) falling
within the scope of this standard.
263
BS EN 14917:2021
EN 14917:2021 (E)
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[5]
[6]
Directive 2014/68/EU of the European Parliament and of the Council of 15 May 2014 on the
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SEW 470, 5. Edition: 1976/02 (DE)
VdTÜV-WB 412: 2018/03 (DE)
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MATERIAL DATA SHEET NO. 4107:2018 (Alloy 600) VDM Metals International GmbH, 58791
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MATERIAL DATA SHEET NO. 4118:2018 (Alloy 625) VDM Metals International GmbH, 58791
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STEELS H.T.A.S. Outokumpu Stainless AB. 2004, SE-774 p. 22 [Avesta ] [SE]
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1.4828 Ferrotherm:2007 Deutsche Edelstahlwerke GMBH, 58452 Witten (DE)
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MATERIAL DATA SHEET NO. 4029:2002 (Alloy 800) ThyssenKrupp VDM GmbH, 58791 Werdohl
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PUBLICATION NO. SMC-046: 2004 (Alloy 800) Special Metals Wiggin Ltd., Hereford, England (UK)
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MATERIAL DATA SHEET NO. 4010:2002 (Alloy 400) ThyssenKrupp VDM GmbH, 58791 Werdohl
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PUBLICATION NO. SMC-030:2004 (Alloy 825) Special Metals Wiggin Ltd., Hereford, England (UK)
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BS EN 14917:2021
EN 14917:2021 (E)
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Werdohl (DE)
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EN 764-7:2002, Pressure equipment — Part 7: Safety systems for unfired pressure equipment
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[28]
[29]
EN 764-3:2002, Pressure equipment — Part 3: Definition of parties involved
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ISO 4200:1991, Plain end steel tubes, welded and seamless — General tables of dimensions and
masses per unit length
[30]
ISO 6208:1992, Nickel and nickel alloy plate, sheet and strip
[32]
PE-01-01(Rev 6):2004, Guiding principles for the content of EAM drafts
[34]
VdTÜV-WB 305: 2018/06 (DE)
[31]
[33]
[35]
[36]
[37]
[38]
[39]
CEN ISO/TR 15608:2013, Welding — Guidelines for a metallic materials grouping system
(ISO/TR 15608:2013)
VdTÜV-WB 424: 2017/03 (DE)
VdTÜV-WB 400: 2019/03 (DE)
VdTÜV-WB 499: 2020/01 (DE)
EN 1333:2006, Flanges and their joints — Pipework components — Definition and selection of PN
EN 1593:1999, Non-destructive testing — Leak testing — Bubble emission techniques
EN 1779:1999, Non-destructive testing — Leak testing — Criteria for method and technique
selection
[40]
EN 13480-4:2017, Metallic industrial piping — Part 4: Fabrication and installation
[42]
EN ISO 10675-1:2016, Non-destructive testing of welds — Acceptance levels for radiographic
testing — Part 1: Steel, nickel, titanium and their alloys (ISO 10675-1:2016)
[41]
[43]
EN ISO 3452-1:2013, Non-destructive testing — Penetrant testing — Part 1: General principles
(ISO 3452-1:2013, Corrected version 2014-05-01)
EN ISO 11666:2018, Non-destructive testing of welds — Ultrasonic testing — Acceptance levels
(ISO 11666:2018)
265
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