Sam Kannappan, P.E.
Engineer
Tennessee Valley Authority
Knoxville. Tennessee
A WILEY-INTERSCIENCE PUBLICATION
New York
.
JOHN W LEY & SONS
Chichester
Brisbane
Toronto
Singapore
PE STRESS
Sam Kannappan, P.E.
Enginear
Tennessee b l l e p Authoris),
KnoxviBIeo Tennessee
A VVrLEV-INTERSCIENCE PUBLlCATlObV
JOHN WELEV dtlr SONS
Mew Vork
e
Chichesler
rn
Brlsbane
a
Toronto
.
Singapore
PREFACE
Copyright @ 1986 by John Wiley dt Sons. Inc
All rights rexrved. Publiskd simultaneously in Canada,
Reprduction or translation of any part of this work
k y o n d that permitted by Section 107 or 108 of 8he
1976 United States Copright Act witbut the pemission
of the copright owner is unlsvvful. Requests lor
pmission or further information skould be x:ddrcssed to
the Pemissions Department, John Wiley 61 Sons, Inc.
Llbnrr). of Coegnss C ~ ~ ~ l q lInr rPPbgielrrrlcn
g
hca:
Kannappen, Sam.
Iniroduclion to pipf stress analysis.
"A Wiley-intenciente publicaiio~."
Until 1967 piping design was p d o r m e d primarily using ruie-of-thumb
layout design procedures and p r e a n a l ~ e dpiping 1ayr.ut data in tabular
form. The publication of ANSI E131.1-1667 Power Piibing Code and the
availability of analysis computer programs have intrduced cost-eflective
piping design.
The objective of this book is to present a practical appmacl" to analylica!
piping design. It is intended to be used by engineers in the industry and
students interested in piping design. Knowledge of applied mechanics and
strength of materials is a must for understanding this b k .
The text contains many illustrations, code equations, tables, and examples. Work$d out example problems are included to assist the reader in
undersfanding the principles discussed in each chapter. Exercises and
references are given at the end of each chapter.
Piping analysis lopics, such as support stilifness, overrapping, decoupiing
of branch lines, wind loads, arsd other advanced topics, are covered in
another book entitled Advanced Pip S~ressAnalysis by the same author
and publisher.
il am indebted to many organizations, including the Amellican Ssiery of
Mechanical Engineers and the Expansion Joint ManufacturesqAssmiation,
lor granting permission to reproduce design, tables, and graphs. 1 thank all
my friends and the members of my own family, my wife Meena, sons
Rsmesh, Narayanan, Ram, daughter Abirami, and my brother S. Narayanan, lor their support lor me in writing this h k .
fncludes index.
I . Pip lines--&sign and construction
2. Strains and stresses. I. Title.
Knoxville, Tennessee
Decembcr B Y8.B
Pdntrd In the United States of h e r i c r
I098165432 1
CONTENTS
Farces and Moments on a Piping System 1
Static and Dynamic Loads 4
Piping Specification 7
Explenation of Terms Welaled to Pipa S u p p s ~ s11
The Guided Cantilever Method 12
Comparison of Simplified Analysis Methods 14
2 DESIGN OF PRESSURE CQIVlPQNEWS
Calculation of Minimum Wall Thickness of a Pipe 22
~eihforcementsfor Welded Branch Connections 29
3 PIPE SPAN CALCUUTION
Span Limitations 34
Neturel Frequency 35
Drainage 37
Guide, Spacing far Wind Loading 46
Design Rules for Pipa Sarpporls 47
4 ANSI PIPING CODES ARD ASME CODES
intarnel Pressure and Longitudinal Stresses W
Petroleum Rslinsy Piping Code Requirements
for Formal Ansbsis 53
lnplane and Butplans Bending Moments 55
Stress Inben~iCif~ t i n nC ~ r * v - " 6
am
"
ENecl of Pressure o n Stress Intensification
and Flexibilihl Factors 66
Stresses in a Piping System 72
Cold Spring 76
5 EXPANSION LQOPS AND EXPAlUSlON JOlNTS
(..>
Design Loads and Sewice Limits 171
Flexibiliv and Stress Intensification Factors 171
Analysis l o r Class 2 Piping Stress Evaluation 882
Naturat Frequency 183
Piping Systems t o Be Ansiyzed 183
Useful Mints In Piping Design 185
82
Expansion Loops 82
Stresses and Loads in Loops 85
Expamion Joints 92
Types of Expansion Joints 95
Pressure Thrust Force 96
Computer Modeling 186
lnitial Anchor and Supporl Movements 187
Modeling of Piping Ebmenrs 190
BVomenelature 102
EMarnsl Moments I82
Comparison of Allowable and Actual Moments 103
7 PlPlNG CONNECTED TO NONROTATlNG EQUIPMEM
10S
Local Stress Calculation Using WRC 107 Bulletin 109
Rotational Spring Rate for Cylindrical Vessel 118
8 PlPlNG CONNECTED TO ROTATlNG EQUIPMENT
E
Br
t
Piping Gsnnected t o
Piping Connected t o
Piping Connected t o
Piping Yield Method
Stetem Turbines 123
Centrifugal Compressors 128
Centrifugal Pumps 128
130
VsSves 132
Analysis lor Reaction Forces Due
ta V a k e Discharge 136
Aluminum Pipine) 139
Copper Alloy Pipe 141
Underground Piping 1@
EHernal Pressure Design 155
Vessels Under External Pressure 158
Jacketed Prsssurs Piping System 160
Metric Units 165
Malsrlel Behavior at Elevated Temperature 165
Refrecloy Lining 167
123
Al.
A2.
A3.
A4.
A5.
Total Thermal Expansion for Metals 202
Modulus of Elasticin/ l o r Metals 218
Allswablet Stresses in Tansion far Materials 212
Propefiies and W e i g h of Pipe 226
Sample Calculations for Branch Reinforcement 236
CHAPTER O N E
PIPE STRESS ANALYSIS
k i p stress analysis provides the necessaay technique lor engineers to design
piping systems without overstressing and oversoading the piping compnents
and connected equipment. The Following terms from applied mechanics are:
hrlcf(y tliscussed (not defined) here to familiarize tdle engineer with them.
FORGES AND MQMEIVBS QFd A POPING SYSTEM
FORCE: The force is a vector quantity with the direction and magnitude of
the push (compression), pull (tension), or shear eFTects.
M C D M F NMonlenl
~:
is a vector quantity with the direction and magnitude at
twisting and bending eflecls.
I
I
Forces and moments acting on the piping system due lo diWerent t y v s of
loadings, such as thermal expansion and dead weight, will Re discussed taler
in detail.
Stress is the farce ger unit area. This change in length divided by the
original length is called strain.
Stress-%GrainCurve for Ductile and Nsn&ctlla Material
For a ductile material, suck as ASTM A53 Grade B, the stress-strain curve is
given in Figure 1. I . Until the proportions! limit is reached, variation al stress
in the material with respect lo strain follows a straight line, Hmke" law
slope as Young's modulus of elasticity E. Ulrimire tensile s
-qc
i
I
tb
p
1s
'q'
.-
*
1.
-
A list of common piping meterials under severe cyclic conditions is given
next (reference I):
JrC
Pipe for Severe C y c l k CorodNons
Only the following pipe* shall be used under severe cyclic conditions:
(a) Carbon Steel Pipe
Allotvable (temperature < 105°F)
Allowable ltemperalure at 800°F)
FIGURE 1.1 Twical siress-strain curve for ductile material (ASTM A53 Graie B).
the curve at which any further strain will cause permanent deformations to
stressed elernenas. Allowable stress is the yield strength divided by factor of
safety.
A typica! stress-strain curve for a nonductile material like cast irtln is
g S e n in Figure l . 2 The stress-strain diagram lor a given piping material
shows the limitations on stress to avoid permanent deformation or rupture.
,
API 5L, Seamless
API 51,, SAW, Factor ( E ) 0.95 or greater
AP1 5LX 42, Seamless
APl 5LX 46, Seamless
APl 5LX 52, Seamless
ASTM A53, Seamless
ASTM A 106
ASTM A333, Seamless
ASTM A369
ASTM A38 1, Factor ( E ) 0.90 or greater
ASTM A524
ASTM A67 1, Facror ( E ) 0.90 or greater
ASTM A672, Factor ( E l 0.91) or greater
ASTM A69 1 , Facror ( E ) O.Yi) or greater
(h) Low and Infermediare Alloy Sfeel P i p
A333, Seamless
A335
A369
A426, Facror ( E ) 0.W or
ASTM A67 1, Faclor (E) 0.90 or
ASTM A672, Factor ( E ) 0.90 or
ASTM A69 1, Factor (E) 0.90 or
ASTM
ASTM
ASTM
ASTM
(c)
greater
greater
greater
greater
Sfainless Sfeel Alloy Pipe
ASTM A248, Seamless
ASTM A3 12, Seamless
RGURE B*2 Tplcrl strewtrain curve lor noductile matedal (csst iron).
* From ANSllASMB B31 t .J, Section 305.23, 1980 edition
i
~ ~ S A358,
T M Factor (El 0.90 or greater
AS'kM A376
I
ASTM A430
ASTM A451, Factor ( E l 0.90 or greater
Coppr and Copper Alloy P i p
(64)
ASTM 842
1
,
ASTM
ASTM
AS'TM
ASTM
Bldl
58 165
8167
B4Q7
ASTM B2 10, Tempers O and Mi 1 12
ASTM 8 2 14, Tempers O and H 112
FOB
I
meckanica! properties and chemical composition ol each one of the
a b v e materials, see ASTM standards (reference 2).
Special piping materials include inconel, hastclloy, zirconium, and aluminum alloys. Selection of a specific material depends upon the process
temperature and its corrosion properties. Sizing of the piping depends upon
volume flow with minimum Bow friction (reference 8).
STATIC AND DYNAMIC LOADS
Lpadings aResting the piping system can be classified as primary and
secondary. Primary loading occurs from sustained loads like dead weight.
Primary loads are called non-self limiting loads. An example of a secondary
loading (sell limiting) is a thermal expansion load. Because dillerent piping
codes define the piping qualification criteria in slightly di6Verent way, each
code will be addressed separately later.
Static Loadings include:
I.
2.
3.
4.
Vibration.
Discharge loads.
Nickel Alloy P i p
AIurningtm Allay P i p
tf)
I , impact forces.
2. Wind.
3. Seismic loads (earthquake).
4.
5.
ASTM B466
(el M c k e l and
Live loads under weigh! ePlecl include weigh8 of content, snow, and ice: loads
Dead loads consist ot weight of piping valves, flanges, Insulation, and oihe~
superimpsed permanent loads.
Dynamic loadings include:
Weight eBect (live loads and dead laad%).
Thermal expansion and cnnrrereth cRcccs.
Effects of s u p p r l , I M ~ a, d terminal mvcflrcnts
Internal or external premure hading.
'I'hemrul eflacts include thermal loads that arise when free thermal expansion
or eonrracrion is prevented by supports or anchors, loads due to temperature
gradients in thick pipe walls, and loads due Ica diaerence iao thermal
coefficients of materials as in jacketed piping. The coefiienr of linear
expansion of a solid is defined as the increment of length in ;a unit length for a
change in temperature of one degree. The unit is microinches pe"i"eh per "F.
'I'he unit for the mean coefficient of thermal expansion between 7(3"F
(installation temperature) and the given temprature is given as inches of
expansion per 100 Ft of pipe length in Table A % of Appendix (va9raes are Bar~ns
ASME 83 1.3 Piping Code]. To convert from incklinchFF to inch1100 It, thc
lr~llowingrelation may be used:
Expansion coeficient (in./ l OHD lt)
= (coeficient) x
L 2 x LOO (design temp. - installation temp.] (1.11
Young's modulus or modulus a! elasriciry E is unit stress divided by unit
strain. For most structural materials the modulus of elasticity for compression
is the same as for tension. Value of E decreases with an increase in
temperature. Table A2 of Appendix gives E values for piping materials for
the normal temperature range. The ratio of unit lateral contraction to unit
axial elongalion Is called Poisson's rado. Codes allow a value of 0.3 Is be
used at all temperatures lor all metals.
S P E C I ~ IGRAVITY:
C
The specific gravity of a solid or liquid is the ratio of
the mass of an equal volume of water s t some standard remprature
(physicists use 39°F and engineers use 60°F). The specific gravity of
gases is usually expressed in terms of hydrogen and air; i t Is a raurnkr
without a unit.
DENS!
TY: The density p Is the mass
I
8:
LdleLe1.1
4
p a b e * , ilatio sod D e d t y
Density ($b/ih.')
Material T m
hot modulus E;k is prmifted in eaBculating forces and moments at the
equipment nozzles. However, the higher value (at 70°F or at installation
temperature) should be used in stress calculations.
Piping Msterlalr
Poisson's Ratio
0.283
Cashn steel with
0 ~ 3 %carh~onor Dess
Austeniaie steels (SS)
Inttrmediimte alloy steel
5% Cr Mcp--9%Cr Ma
Bra= 166% Cw344"o Zn)
Aluminum alloys
PIPING SPEGIFBGATIQN
0.288
0.283
Piping svcification is written for each service such as steam, sir, oxygen, and caustic. The specification contains information a b u t piping
material, thickness, recommended valves, Ranges, branch connection, and
instrument connection. Figure 1.3 shows a spcificalion far caustic service.
0.316
0.100
S ~ e c ~ ~WEIG~OT:
iic
The specific weight (LI is the weight per unit volume.
' n ~ einterrelation of density and specific weight is w = gp, where g is
a~celerariondue to gravity.
Tablc I . I gives values of Poissonvs ratio and density lor common piping
material.
Example
1, Fi sd tEIe linear thermal expansion (in./ 100 It) between 7 0 and 392°F for
c'airboo steel. CwRcient for 375°F = 2.48 in./lO(lft (values from Apwndix Table At).
CwRcient lor 4W5F 2.70 in./100 I r
Differcoke p r degree in expansion = (2.7 - 2.48)/25 = 0.0088
By lit~earinterplation, expansion lor
-
;
An 8 in, pipe needs a pipe with thickness of 80 schedule (which allows for
allowance and maximum internal pressure of 2W psig up to
150°F) with a kvel-edged AS3 Grade B seamless. The g i o k vaive used is
crane 35 1 d (reference 1 in Chapter 3).
The flanges are oF 150 psi pressure
rating with raised face and weld neck slip on t y v . The marerial of the fiange
is A-1[)5 ( p r standard ANSI B16.5). The requirement for the branch
connection (here weldolet or tee) is given on the branch connection table.
For an 8 in. header and a 3 in. branch, the weldoler is required for given
internal pressure. The pressure and temperature conditions in the pipeline
should always be within (inside the hatched line) the pressure-tem~ralcaee
curve given in the specificalion.
4 in. corrosion
Piping systems should have suacient Bexibiliry so that thermal expansion or
contraction or movements of supports and terminal points will not cause:
2. Find the modulus of elasticity lor austenilic steel at (a) -2fHPF. (b) 70F,
and (c) 625'F,
E at 2 W F Z 29.9 X 106psi (read From Appendix Table A2)
E at 7VF: = 28.3 .X 10""psi
E for 625°F shouid be interpolated &tween values of 600°F and
"I05F
E for 625°F i s
25.4
- 25((25,4 - 24.8)f 1001 = 25.4 - 0. i 5 = 25.25 x
10' psi
Note the8 the E value decreases with increase in temperature. Lower
values of Young's modulus means that the Rexibility is higher. Use of
Failure of piping or support from overstress or fatigue.
2. Leakage at joints.
3. Detrimental stresses or distortion in piping or in connected equipment
(pumps, vessels, or valves, For example) resulting from excessive
thrusts or moments in the piping.
1.
Flexibility denotes the measurement of the presence ol necessary piping
length in the proper direction. The p u r p s e of piping flexibility analysis is to
pmdduce a piping layout that causes neither excessive stresses nor excessive
end reactions. To achieve this, layout should not be stifle lr is also not
desirable lo make the system unnecessarily flexible because this requires
excess materials, thus increasing initial cost. More length with many bends
increase$ nrecqrlrc. dron t ~ ~ h i r h -. ;**#
-
i~ncs3 In. and larger
3 4 rn
4CRD rap
lnstr.
)DO pu mrrrd lace weld rcfck oPilice
bdu wrh
ZA-194 GR2 -t( heavy
k x . nun. Noce I
C.rlceu: iL,m. l P b e O I ~ l
steel stud
full face
b2 in. ud l u g e .
ws:
. . Wr kmgtleo a d e n g n per ANSI 816.5 rt8.
7 . Ulc: reAon upc lor s n d con**
k n g e w11h r r e w d tap
L ~ n n2 in. a& k ~ g c r
Pkrr aarsrr ~ n e i y ~ ~ a
Flexible pfping
Expsnsicn joint
lFfGURE 1.6 Piping with expansion joint.
RGURE 1.4
FIexible and sliB piping
Figtjre 1.4 shljwr examples of stiR and Rexihle piping When a piping is
subjected lo change in Iemprature and if the pipe is not restrained from
expansion, no stresses are developed and the pipe just expands or contracts.
When the pipe is restrained, stresses and forces of cotlsiderahle magnitude
are: created. For example, at a refinery near Houston, Texas, when two axial
restraiitts were present in a straight steam line (see Fig. I . I)), the hending of
a largt: support frame and the faiture of a pipe at the shcs-pipe weld area
w@u~c$~.
The thermal force that is developd when tr3lh ends of a hot piping are
reslraivcd is enormous and is also independent ol the length of piping.
'ThermB Fc~rce= E(strain due to expansion)(nletal area)
( 1.2)
Exay d c
vJ
Calculate the force developed in a 10 in. sch 40 carbon steel pipe A53 Grade
B subjected to ZWaF from an installation temperature of 7fPF.
The metal area of a 10 in. sch 40 pipe is 11.9 sq i n (Appendix Table Ad).
'I'llc expailsion coeficienl at 200°F is 0.99 in./l0O (I (Appendix Table A I ) .
E = 29.9x
Iflnpsi (Appendix Table A2)
The layout a l s piping system provides inherent Rexibility through
changes in direction. The stiff piping system shown in Rgure 1.4 can be made
Rexiblc in different ways. Figure i .5 shows the inclusion of an expansion loop
if space permits. An expansion join1 (Fig. i .h) may he added (see Eq. 5.4 for
FICIPLIRE 1.3 Piplnr
with
F
I
O
*
~
bw-~
61GURE 8.7
Leg pravided by turning equipment.
pressure thrust calculation) or the equipment may be turned by 98degrees
anti thus provides the leg lo absorb the expansion, as shown in Figure 1.7.
When a piping system lacks built-in changes in direction, the engineer
should consider adding flexibility by one or more of the following means:
b n d s , Imps or offsets, swivel joints, corrugated pipe, expansion joints of the
he,ellows or slip joint type, or other devices permitting angular, rotational, or
axial movements. Expansion joints and expansion loops w i l l be discussed in
derail in Chapter 5.
EXPUNATION OF TERMS REUTED TO PIPE SUPPORTS
ANCHOR: A rigid restraint providing substantially full Fsxiry for three
translations and rotations a b u t the three reference axes. A large
slumber in the order of 10" 2blin. is assumed lor translational stiffness in
the digital computer programs to simulate the fixity. The details of a
structural anchor n a y he obtained from each company" p i p ssupprt
standard.
BRACE: A device primarily intended lo resist displacement of the piping
due lo rhe action of any forces other than those due to thermal expansion
or to gravity. Note that with this definition. a damping device is classified
as a kind of brace.
CONSTANT-EFFORT
SUPPORT: A support capable: of applying ei relatively
constant force at Any displacement within its useful operating range
(e.g., countenweight or compensating spring device).
DAMPING
DEVICE: A dashlpot or other frictional device that increases the
damping of s system, oRering high resistance against rapid displaccments caused by dynamic loads while permining essentially free movement under very gradually applied displacements (e.gavsnubkr).
from a structure, and so
I l n ~ c e n : A s u p p r l by which piping is surpnded
,
I
" I
*
.
?
1
.
L a ~ r i paw: A device that restricts translatory movement Lo a limited ,)
arkrtounb in one direction along any single axis. Paralleling the various
stops ahere may also be double-aciihg limit stops, two-axis limit stops,
8 ~ $8
d on.
Rasa~~sm
SUPPORT: A s u p p r t that includes one or more largely elastic
m e m k r s (e.g., spring).
R a s r r ~ oOR SLIDING SUPPORT: A device providing support from heneath
the piping bur orifering no resislance other than friclional to horizontal
motion.
R ~ s a w ~ a mAny
: device that prevents, resists, or limits the free movement
of the piping,
RIGID cso~ta_r,SUPPORT: A s u p p r ? providing stillness in at least one ,
direction, which Is comparable to that of the pipe.
STOP: A device that permits rogation bur prevents translatory movement in
at least one direction along any desired axis. If translation is prevented in
h l h direclions along the same axis, the term double-acting stop is
preferably applied. Stop is a!so known as ""Bumper."
S U P ~ R TA
: device used speciAcaliy to sustain a portion of weigh! of \he
piping system plus any suprimposed vertical loadings.
'$iwto-nxrs STCPP: A device which prevents translalory movement in one
direction along each of two axes.
.
,
lFlGURE 1.8 Guided csntilevec apptoxirnation.
pl;tne system under the guided cantilever approximation, as shown in Figure
I .M, The deflection capacily of a canlilever under this assumption can be
given Ry Eq. 1.3 (reference 3):
where h = permissible deflection, inches
SA = allowable stress range, psi (given by Eq. 4. I D
& = length of leg needed lo absorb the expansion, feet
g)o = outside diameter of pipe. inches.
The limitations of the guided cantilever method are:
Lnce a compiete (weight, thermal plus pressure, and thermal plus pressure
weight) analysis of the piping system has been conducted, support
msa8ificarions can be: made very easily.
Wlsan a p i p line moves as a result of thermal expansion, i t is necessary
!ha%flexible hangcrs Re provided that support the piping system throughout
its thermal cycle. Three types of hangers are generally employed:
s;pl
I.
Rigid s u p p r t or rod hangers that suppsedly prevent any movement
along the axis of the hanger. Rod hangers are used when the free
thermal deflections are small enough so ghat their restraint of movement does not produce excessive reactions in the pipinn
. . - system.
.
2, ,Variable support or spring hangers provide a supporting force equal
to hot load (reference 6 ) while allowing deflection.
3. Csnsranr s u p p r l or eonstant effort hangers that provide an essential!~canslant supwrting force throughout the thermal cycle. Ideally,
constant s u p p r t hangers do not restrain the free movement of the
system and therefore do not increase the piping stresses.
.
I . The system has only two terminal points and it is composed of straight
legs of a pipe with uniform size and thickness and square corner
intersections.
2. All legs are parallel to the coordinate axes.
3. Thermal expansion is absoskd only by legs in a perpendicu8ar
direction.
4. The amount of thermal expansion that a given leg can absorb is
inversely proprtional to Its stiflness. Because the legs arc of identical
cross section, their stiRness will vary according to alre inverse value ol
the cube of their lengths.
5. In accommodating thermal expansion, the legs act as guided cantilevers, that is, they are subjected to &@ding under end displace:
meats; however, no end rotation is permitted, as shown in Figure 1.8.
THE GUIDED GAWILEVER METHOD
One of the simplified methods used in piping dysign is known as the guided
canrilever mcthd, Ixcsuse deflections are assumed in occur in a single-
As a further refinement of this method, a correction I ~ ~ o ~ sllws
t l s ~fort
reducing the bending moment, due to the rotation of the leg adjacent lo the
one c o n ~ i d ~ r eCdR O he 11";er" ( r ~ f e r ~ .lb
nr~
I . Talk turns (reference 5 )
2. BTT Grinnell (reference 6)
3. M.W. Kellogg (reference 3)
HGORE 1.9
Anchor with initial movement
Calculate leg & required lor the two anchor problem and force P given in
FIguse 1.9.
Pipe outside diameter = 45 in.; thickness = 0.237 in
Expansion coefficient = 4 in.1100 la
Stress range = S, = 15,0(10 psi
Cnid modulus = 27.9 x 10"si
Deflection B = I + 20(4/100) =. 2,3 in.
Rearranging Eq. 1.3 (guided cantilever method):
4
moment PL
Bending stress = Sb= -= -
Z
22
4.5 + 4.5 - 2(0.237)
= 2.13 in.
2
Z = section modulus = m2(lhickness)= n ( 2 . 13)2(0.237)= 3.38 in.'
4 . Digital computer solution including bend Rexibiliry factors (reference 7 )
5. Digital computer solution using square corner approach (not including the k n d flexibility)
'Table 9.2 includes the range of diameters (&24 in.), wall thickness, and
nomenl of inertia I used in the calcplations. Table l .J shows the configuration of a U loop (expansion loop) an E s h a v , and a Z shape. The maximum
bending stress is also given for each method.
Figure I . I 0 shows the variation of k n d i n g stress with area moment of
inertia I for the loop. Were I was selected instead of diameter because I also
includes the e6lecl of wall rhickrress. As can Ine seen the Grinnell method
gives
very highly conservallve results. Expansion loops are further discussed
in Chapter 5.
1.1 1 shows the variation of k n d i n a stress lor the L shape. The
-Fivure
c7
Kellogg method gives higher stress vaIues. Figure 1.12 demonstrates the
variation of bending stress with moment of inertia for the Z s h a p . The
digital computer solution using EZFLEX computer progma" gives lower
n u n k r s , which is understandable because the other methods are meant to he
conservative. The Kellog method is discussed in derail in Chapter 5 (Eqs. 5.2
and 5.31
-
Mean radius r = -
as,z 2(1 5,000)(3.38)
Force P = -=
L
20.(13(12)
-
42 1 .R Ib
Results obtained from other simplified methods and the digital computer
aided piping analysis are compared here. However, each method is not fully
explained because the references give a detailed explanation and they also
need charts and graphs for their soiurion.
To understand the diliferences ljetween each of the methods, results for
three problems (Table 1.3)for range a f diameters 6 2 4 in. are presented here
(reference 4).
TABLE 1.2
B"IwShes Used 1m Compr~trhorrol Sirniptilied Methods
PIP 0D
(rn 1
Sch
6.625
8.625
40
40
Moment of
MduOus
of
Wall
Thickness
inertia I
Section Z,
(in.4)
(in.')
6.025
7.98 1
10.250
I2.W)
13.376
15.250
17.376
0.280
0.332
0.250
0.375
0.3 16
8.375
0.3 12
28.14
72.50
L 13.70
279.30
314.30
562.10
678.d.M
0.375
n 175
11 14.W
ton? n
lnside
Diameter
10.75
12.75
20
Std.
14.00
16.30
L 8.W
20
Std.
20
20 00
Srd.
i9.250
91 (W)
"i(l
3'19$;
8.58
86.81
21.16
43.130
44.901
70.30
75.51
111.4
1 6 1 $4
Legend
Comp sqriare corner
a Camp using e l h w
@
0
Tube turns
d Kellug~
x Grinneli
7
Area moment of inertia I in
"
FJGURE 1.10 Bending stress in symmetrical Imp
10' psi
64
turns
4f
b/
Anchor
/I
7
200 400 600 800 1000 I200 1400 1600 1800 2000 2200
Area moment of tncrt~a.In
FnGURE #.I2 Bending stre= in Z-shepd piping.
EXERCISES
Area momenl of rnerl~a,1 In 4
RGURE 1.II. Bending slres in L - s h e p d piping
(a) Find lola! expansion for intermediate alloy steel (5Cr Mo through
9 Cr Mo) pipe at temperatures of ( I ) -55OF, (2) 43 i0F, (3) 1572°F. lf the
temperature given is out of range for the material, suggest suitable
material lor that temperature. Consider length of 120 TI.
(h) Find lor auslenitic steel the following at installalion temperature:
Young's modulus
(2) Poisson's ratio
(3) Density.
( c ) Calculate total elongation in 132 1t of p i p made of c a r k n steel
subjected to 645°F.
(I)
(a)
(Ip)
Find E values for low chrome steel at -1 15*F, 7WF, and 800°F.
Explain the eflect of temwraturc an E value,
Find cold and hot stresses for ASTM A53 Grade B p i v at 7WF and
625°F.
Calculate the thermal force developed in the piping that is fixed at b t h
ends as shown in Figure 1.13. It consists of an 8 in. sch 40, c e r b n steel
pipe with operating temperature 300°F. Use Eq. 1.2.
a = coeficient of thermal expansion st 3280F = 1.R2 in./100 I t
s
epe
-*.**a
Anatva#a
0
Referensaw
FlGURE 1.13 Thermal force
B"
FlGURE 1.17 Calculation of force and rnornent at amhor.
IilGURE 1.14 Unequal legs piping w ~ t hL-shape
4. Ca&cmlatethe stress of the rayout in Figure 1.14. 11 consists of a 10 in. s c t
40,c a r h n sreei p i p of A53 Grade B mareria! at 5f100F.
S, = %O,OC)(lpsi
5.
*
Sh = 17,250 psi
A I0 in. sch 40 c a r h n steel pipe with A53 Grade R material has a
temperature of 200°F. The allowable stress S, .= Sk= 20,000psi. Cala
cerlale leg L needed in Figure i .15.
a 5 in
RGURE l.lB Piptng connected In a vessc
6. Two equipment nozzles have thermal movement and layout as shown in
Figure l.!6. What will be the length L?
The carbon sreei p i p has a nominal diameter o f N in. and a =
9.82 in./l(N) TI.
SA = l18,000 psi
For a 6 in. sch 4 0 c a r h n steel pipe A53 Grade B, the linear expansion
i s 3 in. Allowable stress range SA = 28,CBOO psi.
8,
E = 27.9 x I On psi
7, Two vessels are connected by piping as shown in Figure 1.17. What is the
length required for lhe leg? What is the force and moment?
A vessel has an average operating temperature: of 500°F"'.
With a line from
the vessel nozzle going to an equipment as shown in Figure 8,18, what
should be the length L?
Ir is a \ 2 in. sch 4 0 pipe with a temperature of 400°F. The pipe is of
A53 Grade B material. S, = 20,00(1 psi and &, = 16,350 psi. (Ira practical
cases, L is limited by tower height.)
0 5 in
REFERENCES
i
I
0 6 in
I
Z
ANSIIASME 83 1 3- 19RO Ckcmical P k n t and k"c@oleurn Refinery Rplng
ASTM Annuel Book ol ASTM S~anderds,D~flerenr
/or Di&rcnr Mfmab.
ACURE 1.15 A Z-shaped piping with initial anchor movements
3
4
M. W Kellagg, Design oj Piping System. New York:
Estrems, Fernando and S. Kennappan, "Comparimn ol re~ulrsfrom diflerenl simplified
methods with digital computer calculations "
9. T u k Turns Division of Ckmctron C o v . ""Piping Enginecsin~,Line Expamion a d
Rexibility."
6 1TT Gdnncll industrial Piping. "Riping Design s d Engineering.'"
7. EZFLEX Piping Flexibility Analpis Program.
8. Crane Company. ""Fiow of Fluids.'"
L
i
CHAPTER
where d =. inside diameter = D, - 2r
Eq =quality factor that is the product of casting quality factor &,
joint quality factor 4, and srructural grade quality factor E,
when applies. Values of i$ range from 0.85 to 1.0 and devnds
upon the method used lo examine the casting quality (see Table
2.2a). Value of EI ranges from 0.6 to 1.0 (given in Table 2.2b)
and depends upon type of weld joint. Values of & may be
assumed as 0.92.
TWO
DESIGN OF PRESSURE
COMPONENTS
GALCUMTIOM C)F MINIMUM WALL
THICKNESS 09":A PIPE
TABLE 2.1
Vetoes eol V CoeRRclcnt I s k Uwd In Gq. 2-1"
a
Piping codes require that the minimum thickness fm, inclttding the allowance for mechanicai strength, shall not be less Ihan the thickness
calculated using Eq. 2.1.
I
1
*
I
Ferritic steels
Austenitic steel
Cast iron
Nonferrous metals
04
11 5
(1 7
04
04
0.7
04
0.7
04
04
-
-
-
-
04
-
-
09
"Reference ANSIIASME 8.71 3, Tablc 304 1 I
where
-
lm
minimum
-
=%d
J
required wall thickness, inches
r = pressure design thickness, inches
6" =: internal pressure, psig
DD= outside diameter of pipe, Inches
S aOBowabIe stress at design temwrature (known as hog stress), psi
(see Appndix Table A3)
A = allowance, additional thickness lo provide Tor material removed
in threading, corrosion, or erosion allowance; manufacturing
tolerance (MT) should also be considered.
Y = cwRcient that takes material properties and design temperature
into account. b r I < d / 6 , values of V are given in Table 2.1.
For temperature below 900°F. 0.4 may be assumed.
&-
Type of Supplementary Examination
Sudace examination (1)
Magnetic particle method (2)
Ultrasonic examination (3)
Type I and 2
Type I and 3
0.85
0.85
0.95
T y ~ e2 and 3
1.W
*Reference ANSIIASMF R11 1 Tahle 302
0.90
B .CICB
3 7r
0.7
0.7
-
m
w
1PS
eslculallon s(
h
(1
Minkurn Wen Thlcknrro oil P@co
28
I
From the manufacturer and p i p section p m p r l i e s information, (see
Appendix A4) a l o i n . p i p with sck 20 is selected with nominal wall
rhickness
0.25 in. T;or p i p s under external pressure see Eqs. 9.10
EIecrrie resistance weld
Electric fusion weid
(single butt weld]
As required hy specification
As required by specificaiiorp
tl R S
O Kt1
Electric fusion weld
(single butt weld)
Electric fusion weid
(single butt weid)
Electric fusion weld
(double butt weld)
Electric fusion welcf
(double butt weld]
S p ? t radiograph
(1 YO
If%Ooh radlogrnph
As
required hy ~pectlicatton
Spot ratl~ogr;~ph
E2ectric fusion weld
(tloerble butt weld)
BY ASTM A2 I 1 specification
Double submerged arc..
welded p i p (wr APB 5L or ~ L X )
ItN)O/n
r;$cPtogr;iph
AS required hy sprlfication
Radiograph
-
I
~ , ~ ~ o k at
i n ~g q 2.1
. again, we see that:
r,=ocA
(w)
--
0 85
0 00
I
TCIIcknesr
Ail@mal@E q u a t i ~ n to
s Galculatcr
PI;q,
+A
;?~sE,+ PY)
12.11
where r is the pressure deqign thickness in inches.
Equafionq 2.3 and 2.4 (I-am6 equation) may aiso Re used lo calculate
cn)
l=-2-
0 75
0 '15
Pr),
il:
(2.3)
2 SEq
(2.41
"Reference
831.3 ANS:/ASME 302 3 4
I
pJ
Exa mpba
.
the' minimum permissible wall lhickrlcrs frlr a
in n6~nlit12,~
diameter pipe under 351) psi and hSII°F. Material is ASTM p, 106 Grade R
cormsion all0wance is 0 0 5 in., and mgl{ tolerance ( ~ , ris
)
124%.
--
Thickness r, =
350~sig
=
=
De = 10.75 in.
PDe
+ A
2(SEq + PV)
8,
=
Nominal thickness =.
1
The allowable working pressure of a pipe can be determined by Eq. 2.5:
stress (tensile) for A I Oh Grade B = 17,000 psi (see
A p p n d i x A3)
3SO( 10.75)
- + (1.05 = 0.144 in.
24 17,0(M1x I + 350 x 0.4)
0.144
0.144
- = 0. I64K in.
( 1 -MT)-61 -0.125)
Allowrrbte Working Prrrsauro
(2.1)
E, = 1.O for seamless pipe
-65.4 ( h c a u s e the lemperature is less than 9fNrF)
Equaticlns 2. l, 2.3, and 2.4 are valid lor r < C),16 (thin p i p ) .
The pipe with 1 2 D/h (thick-waliled pipe) or PISE* r 0.385 requires
consideration taking design and material facrors inlo accOunl suck
theory of failure, fatigue, and thermal stress (reference 1).
a(SE9)8
P = Da-2Yf
(2.5)
where r = specified wall thickness or actual wall thickness in inches.
the minimum wall thickness after k n d i n g should not be less
For
than the minimum required for straight pipe.
Blanks
'9r0
I
- c@rn~"*~~,@a
8
I
wh
.,)
4 zinsae
dhme!er of gasket o raised face or 11. iplrilllface
flanges Or gasket
diamefer forbringjoint and fuliy refaioedgaske,ed
flanges in inches.
lest Fr@ssur@
hydroitalic g s f ~ressurea[ any p a i s in the system sl.,uld
'8
minimum
iesy
design prtssure. For kmperagures above o s ( l o ~,he
,
pressure P, i s given by:
(Design pressure)
6
=
Stress
(
42.7)
(see n p p n d j r Table
5
&sign temperature (& at design fempemgurel
Allowable Pressure in Miter Ben&
M a ~ l)cm&*
r
An angular
of 3 degrees or less (angle o in Figure 2.2) dries
"quire
as a miter bend. Acrepfahle methflds (,,,
/'ressurc design of mutliple and single miter bends are given in (a) i,sd (h)
-iPext.
Mec''i~'e
Itlifer
The maximum allnwble internalpressur, shr,,
lesser
value calculated from E ~ s2.Ra
. and b T b w equafil,ns arc not
applicable when 8 exceeds 22.5 degrees
T-c
.643 tan B
Pm =
aD,,==
J
(2.Ha)
~
(2.Hb)
( b ) Si@gk
m r Bends (or Widely Spaced Miler Bends)
( I ) The
sllnwabfe imemal p.crsure for a single milcr bend
@ not greater than 22.5 depries shali
.alrubkd by g q
The maximum aliovabte internal prwure for a sing,c mi[sr
&d
,
with
@ greafer than 22.5 darers shall
calculafd by E~ 2 ~ ~
T-c
Pm =
( T - 1 ) + 1.25 [an B*Ftom ASMUANSI BJt 3. Letinn 18( 2 3
(2.8~)
:
I
i
dam*
-i b.4
.8(r
t')
\<
($,\)The following nomenclature is used in Eqs. 2.Ra. 2.Hh. and 2 . 8 ~for
the pressure design of miter h o d s :
RslnforcemsnS lor W d M IBnnch Cconncbct
.d
For rwo-weld miter (see Fig. 2.2):
,
c = corrosio~allowance
Pm = maximum allowable inlernal pressure for mirer bends
r2 = mean radius of pipe using nominal wall T
RI = e@eclive radius of miter bend, defined as the shortest distance from
the pipe centerline lo the intersection of the planes of adjacent miter
joints
Eq = quality factor (see Eq. 2.26)
S =: allowable stress at design temperaiure, psi
T = pipe wall thickness (measured or minimum per purchase specificalion) ,
6 = angle of miter cut, degrees
a =: angle of change in direction at miter joint = 2 8
For compliance with this code, the value of R , shall not hc less than that
giqrere by Eq. 2.9:
r"6,
The mean radius of the pipe = 35.5/2 == 17.75 in.
?'he material consists of A312 TP 304 H saainress steel. Temprelure k
I3I(PF.
Allowable hot stress is Sk = SEq = 3060 psi (From A p p n d i x Table A3).
Interpolate &tween Sk = 37fHl psi for 130(PF and Sk = 29W psi for
1350aF.Bend radius, R , = 54 In. (see Table 4.4).
Using Eq. 2.Xa. allowable pressure is
.
D,,
R1 =+tan f3 2
whcre At has the following empirical values (not valid in SI units):
Value of
(7. - c h in.
Using Eq. ?.Xb, file allowable presstire is:
Value of
AI
-
67.86 psig
The maximum allowable pressure lor the miter is the smalier of the values
calculared a h ~ v eThus
.
Pm= 58 psig.
REIIIVFORGEMEWS FOR WELDED BRANCH CONNECTIONS'
See Chapter 4 lor Burrher discussion on miter bends.
C~IcuJatemaximum allowable internal pressure for the multiple miter hend.
Plate thickness is f i n . Corrosion allowance is zero. Manufacturing allowance is 0.01 in. Miter OD is 36 in.
When a hole is cut in a pipe subjected to internal pressure, the disc of the
material that would nc~rmally be carrying tensile stresses in the hoop
direction is removed and sn alternate path must be provided. To achieve
this, a simplified ""area replacement" or 4'compensation'~approacl?i
is used.
This method provides for additional reinforcement maleria!, which is within
a specified distance from the edge of the Role, equal to the area of the
material removed. Reinforcement st branch inlersectlans are also
occasionally needed to dislribute stresses ~trlslng from p i p loads, See
discussian of stress Intensification lactors (Sin In Chapter 4 lor the reduc-
,,I rclnf~r~emenl
calculation only. When the branch does intersect the
r,,,\grirgdinalweld of the run, the allowable stress S$ s l the run p i p
,1,.,11 1~ t~sedin the calculation. The allowable stress S& of the branch
.~,.,ll used in calculating a*.
. , , , , , l ~ ~angle
r
ktween axes of branch and run
I , , gerql"ircd Reinforcement Area. The reinforcement area A, required
11r.c)nnection~
under internal pressure shall k:
I,,
A , = (rhd,)(2- sin
I t c r ~ t l ~cxlcrnal
r
FEGURE 2.2
$2.163)
pressure shall be:
Nomenclature lor miter k n d s
tion 0%the calculated vatue of SIF when reinforcement was provideti I
reinforcement requirement for internal pressrlre is usually defined , I ,
piping specification of the project. Additionat reinforcement may he nl.6 ,I,
lor piping loads.
Figure 2. ! shows pipe run-branch connection (reproduced from 11 :I
code). Requirements of the orher codes are similar. A numkr of \ r r l r 6 ,
out problems are given in Appendix H 01 8.11.3 code (Reproduced I l c . r i
Appendix Table A5).
6
I
*,J
+
\ , c A, defined below, and shall equal or exceed the required rein-
,r
I
'r
11)
~ ~ iifea
~ t ~ t
\re;r A*. The area lying within the reinforcement zone resulting
.t,j\
cxcess thickness available in the run wall:
I
,1,
The requirements are not applicable lo branch connections in whit 11 1 1
smaller angle between branch and run is less than 45 degrees, or ill uiii,
the axis of the branch does not intersect the axis of the run.
( 8 ) Nomenclature. The nomenclarure k l o w is used in the ptt-.\ii
design of welded branch connections. 1t is illustrated in Fig. 2.1, i r l ~ i
does Blot indicate details for construction or welding.
Definirions
b =. subscript referring lo branch
dl .= eFCeclive length removed from p i p at branch
d2 = nLRallwidthi' of reinforcement zone
" d l or ( TB- C) + ( T h - c) 3- dr/2, whichever is greater, but in i t i t \ 6 I
not more than Oh
h -- subscript referring to run or header
L4 = Reiglrt of reinforcement zone outside of run p i p
= 2.5QTh - el or 2.5(Tb- e) T,, whichever i s less
Tr = minimum thickness of reinforcing ring or saddle made Irom pip^* 1 1
nominal thickness i f made From plate.)
= 0,If there is no reinforcement pad or saddle
1 -pmessure design thickness of pipe, according to the appropriillc tr
thickness Eq. 2.1. For welded pipe, when the branch does not inll*jbl
the longitudinal weld of the run, the basic allowable stresq f t t r I '
N~*r,t{orcorneniArea. The reinforcement area is the sum of areas
,I
. .
\re;! A,. The area lying within the reinforcement zone resuHting
, t r n excess thickness available in the branch pipe wall:
A3 =
\
2&4(Tb
- 8..
Ib
C)
-
sin @
\re;$ Ad. The area of all other metal within the reinforcemenl zone
~ t l c t lhy weld metal and other reinforcement metal proprly attached lo
r 1111 on branch.
\I.~rt.rl;rlq
used For reinforcement may difler Irom those at the run p i p .
~rl\,rl!)ley are compatible with the run and branch pips witla resvcl lo
*~.~I~IIIIv.
heat treating requirements, galvanic corrosion, thermal expan-
o\
on. If the allowable stress for such materials is less than that for
corresponding calculated area must be reduced in the ratio
'lrc- l~llowahlestress vaiues &fore being counted toward the reinforce*Ircih No additional credit shall be taken far mate~alshaving higher
c\t.\ltlc. \tress values than the run pipe.
* ~ ~ ~ r f n f o r r e r nB
e n fc . The reinforcement zone is a paraltlciogram
' ' \ c lcrlgrh extends 8 distance 06 dl on each side o
f the centerline of the
11 p r p and whose width starts at the inside sur(ace of ahc run piw fin
illrratrled condition) and extendc In R d i q f a n r ~ I f-om * R m m*'0"''8*
. ~ c t c iko
rltci
+
'
IF, the
,,
R....
irlulllple i l p e t t i ~ t g When
~.
iiny two or more adl
L i n i n g s are so closely spaced that their reinllrrcement 28,nes clverlap, the
two or more owning$ sl~allhe reinforcedc with a combined reinforcemerlt
that has an area equal to that required for the reparille openings. (See
ASME/ANSI. Section 304.3.4 of B31.J code for reinforcement requirements of extruded outlet headers lor further reading ) N o portion of the
cross sectiosn shall be considered as applying t o more fhan one c~pening.nr
be eevaluaaed more than once in a combined zrrea Wllcn cwct or mt)re
awnings are to be provided with a combined reinforcement, rhc minimum
distance &tween centers of any two of these openings shjuld preferably he
at least 14 times their average diameter, and the arcn of reinlt~rcement
between them shall be at leas! equal to 50% of the tot;~lrequired for the\e
two openings. (Pipe Fabrication lnslitule Sti~ndardES-7 m;iy he ctmsul!ed
for detailed recommendations on spacing hetween welded no77les )
(I)
Rings and S@dd!es. Additional reinforcemenl providcrl in the form of
rings or saddles shall he of reasonably constant width
0ce
L.I
-.rtt&.,...~nllul
*
A l O i n nominal diameter pipe has design conditions of hO°F and 400 prig.
It is made from seamless material ro specification ASTM A53 Grade I$sch
26). The corrosion allowance is 0.03 in. I t has a 4 in. nomin;il dii~mecer
branch, sch 40 of the same malerial. Whar are suitable dimensions lor the
reinforcemen! if i t is lo be made from a plate c ~ equal
f
quality to that of the
piw malerial?
We start olii by calculating the minimum thicknesses rcqt~iredlor both
the I n i n . header and the 4 in. branch fmm the basic equation:
Aliowakle stress for ASTM AS3 Grade B a! 650°F = 15,000 lh/in.'
From T~ahle2.1, factor 'V
= 0.4 (helow Y(NI°F)
For header, tprsnlureFor branch, a ,,,,,,, -
4 0 0 x 10.75
2( 15,000 x % .(I + 400 X 0.4)
= f l . i 4 i 8 in.
400 x 4.5
2( 15,000 x t .O 40f1 x 0.4)
= 0.0593 in
+
Then:
Minimum thickness of I O in, sch 20 = 0.2 1Xn.i
Excess = 0.2 I LO - 0.14 1 R - 11.03
= 0.0472 in.
Minimum rhickngss of 4 in. sch 40 = 0.207 in.;
Excess --- (1.207 - 0,0593 - 8.03
=0.1 177 in.
l'he minimum thicknesses a b v e are the nominal schedule dimension.
less 821% mil! tolerance (MT) allowed by the standards.
Egeclive length, d l = 4.5 - 2(11.1,177) = 4.2646 in.
d2 = dl = 4.2646 in.
The L4is the minimum of 2.54T1, - c ) or 2 . 5 ( f b - cc) 4-?r,, that is, i t is the
minimum of 2.5 x 0.22 or 2.5 x 0.207 + 0.25. (Assume d in. reinforcement.)
Clearly, the first condition governs so that L4 = 0.55 in.
Required area = I,,, x dl = 0.14 I R Y. 4.2646 = 0.6047 ine2
Compensation area available born header,
A, = (2d2- d,)(excess thickness)
=. 4.2646 x 0.0472= 61.2012 in.2
Compensation area available from branch,
A t s- 12k4)(exeess thickness)
=.
9.1 x<3.1177=0.1294ina
-. 0.33W in.2
= 0.1370 ins2
Total compensation available withour reinforcing pad
Cross-section area of pad reqtjired = (0.6047 - 61.33016)12
This results in a ring with B !i in. outside diameter, &in, wide, and $ i n .
thick. Our neglect of the area of the weld fillets makes no di8erence in
practice. Ir must be pointed out, however, tllal for a service of this severity
a weldoler would be preferred. For more example pmblems, see Appendix
*Table A5.
1, Calculate internal pressure design thickness for 8 in. c a r b n steel AlOh
Grade It) pipe under 420 psig at 80(FF. !Imill tolerance (NFT$= 12.5%)
and corrosion ailowance is 0.05 in. select commercially available
thickness.
2, Calcuiare maximum allowable pressure which can IPe held in a 12 in.
standard weight A53 Grade B pipe at 72S°F. Assume usual MT and
0.1 in. For corrosion allowance.
3. Select the commercially available thickness to hold 500psig at 7WF.
Pipe is 12 in. A106 Grade A material, MT is 12.5%, and corrosion
allowance is 0.06 in.
REFERENCE
*Multiple opaening reinforcement L931.3, Section 304.3.3(b).
I . Rosrke. R. 4. "'Fomulss for Stress and Strain."
a
/'
m-
1
J
CHAPTER THREE
PIPE SPAN CALCULATION
r
eL
%
feet
Z = ncwlulus of section of p i p , in3
LJ
.!& = allowable tensile slress For the p i p material at design temwrature
psi (known as ailowable hot stress)
w = total weight of pipe, 16/11
-. metal weight +content weight 4- insulation weight
b = allowable degeetican or sag, inches
I = area moment of inertia of p i p , in."
E = modulus of elasticity of the pipe material at design tempralure, psi
(known as hot modulus of elasticity)
The exceptions are:
,,lower,., +ipe L ,-..,
8,
L. The piping is in a sreric stale, except for movement induced by
The maximum allowable spans for horizontal piping systems are limited by
three main factors: bending stress, vertical deflection, and natural frequency.
By relating natural Frequency and deflection limitation, the allowable span can
be determined as the lower of the calculated support spacings based on
k n d i n g stress and deflection.
,
temperature changes. EEects sf pulsation, vibration, sway, or earthquake are not taken into account.
2. Concentrated loads similar lo valves are not considered in Eqs. 3.1
through 3.4.
4
NAVCIWL FREQUENCY
I
*4
I
The formulation and equation obtained d e p n d rrpon the end conditions
assumed. By assuming a straight pipe beam, simply supprted at both ends,
Eqs. 3.1 and 3.2 are obtained (reference I ) .This end condition gives higher
stress and sag and therefore results in a conservative span.
For most refinery piping a natural frequency of about 4 cps is suficienr toavoid
resonance in nonpulsaling pipe lines. However, the natural frequency in
cycles per second is related lo the maximum deflection b in inches by:
R!
based on limitation of stress
k=
based on limitation of deflection
(3.2)
The end conditions can be also assumed as a mean between a uniformly
loaded h a m simpiy supported at b l h ends and a uniformly loaded beam with
b r h ends fixed. With this assumption (reference 2) Eqs. 3.3 and 3.4 are
obtained:
L=
based on limitation of stress
L=~S
based on limitation of deflection
where g = acceleration due to gravity, 386 in.lsec2 (32.12 ft/sec2).
Therefore tihe natural Frequency for a simple h a m correspnding lo
1.00 in. sag is 3.12 cps. One of the reasons lor limiting the deflection is to make
the p i p stifl enough with high enough natural frequency to avoid large
amplitude under any small disturbing force. Although this may seem tso low,
in practice the natural frequency will be higher k c a u s ( l ) end moments.
neglected here, will raise the frequency by more than 15%; (2) the critical span
is usually limited by stress and is rarely reached; and (3) the piping weight
assumed is often larger than the actual load.
By relating natural frequency and degecriian limitations, the maximum span
is thus detemined by the smaller valves obtained by Eqs. 3.3 and 3.4.
The calculated span is then multiplied by the span reduction factor. Figure
3.1 shows diflerent piping arrangemen& and span reduction factor /'
(reference 3). As can Ix: seen, span reduction lector is less then 1.0.
Assuming that the piping is simply supgorled st h l k ends and the valve i?
bsc
f =086
i
Case 2
$=096
Case 4
ncuRe 3.1
B
For f see E q 3 8
and Table 3 1
Case 6
f = 0 6 4
Case 5
Piping span reduction factor caw I through
q b
'i"ca'edagmids~an (incase 6 of Fig. 3~1, a =
derived:
Bending stress =
Deflection =
where
=
6,
Eqs.3.6 and 3.7 can be
I.SWL~+~M/,L
Z
22.5 wL4+ 36
a=
'I'rhle 3.1 gives valves of
w(a + 6
)
"
a
=L
I' lor dilferenl valves of
n and B.
wc~3
EI
=cQnce""aied weight similar to the valve in pounds.
be
seen. Eqs. 3 6 and 3.7 may h. u r d lo c a i d a l e actue[ .
h n d i n e stress and defiecl.~ when t,, span i s ei8hr.r known or assumed.
To
spaas for piping with concentrakd weight similar lo
va'vesanpherea j ~ n g span (case 6 , Fig. 3. l), span reduction factors may
u*d TOr a
filed ends the span reduction factor is obtain&
h ~ c a m ~ a r i the
n s moment acting at the s u p m l with #hemQmm@
0 ~ ~ 8 n . dfrom only uniformly distributed wekht and is given by:
"
where
DRAINAGE
!I i s often necessary to install pipe systems so they will drain by gravity.
preferably in the direc~ionof normal Row. To achieve drainage each span must
he pi$kedfsp that the outlet will hc lower than the maximum sag of the pipe.
The plleh (d pipe spans is the ratio between the drop in elevation and the length
o i span. i t i s called "average gradient" and is expressed in inches per fwl.
""fey"'"
Gradisat Check foe Drainage
'It'
content weight = 4 (~~)~(lenglh)(densi~yl
P i p Insulation T y p
Density (IWft ')
Calcium silicate
Foam glass
Polyurethane
Fiberr glass
?T
insulation weight = -(OD
4
of insulation - ~~~)'(length)(density)
P~Iystyrene
71
= -4( 1 4 . 7 5 ~-
1(~.75~)(12)
= 6.12 tb/ft
The condition for good drainage is:
,
Total weight of r he pipe w = 40.44 4-34.17 + 6. D 2 Ib/lt
.I(maximum deBection)
65
span
= 80.73 lb/fl
Using Eq. 3.3 based on limitation of stress:
In calc\a!aling modulus of section and area moment inerria of piping,
corrosion allowance may be included, which will resull in a slightly higher
span.
+
Table 3.2 gives the common piping mass-type insutafion materials. The
other type is known as reRecaive and is used inside reactor buildings of nuclear
plants (reference 7).
To illustrate the use of the preceding equations the following Example
Prcsbiems a r t worked out.
Span L =
Z = section modulus = 29.9 in.'
& = allowable stress of pipe material for design temperature
= 22.")
psi lar c a r b n steel A 106 Grade B at 400°F p
r B31.3
code (Appendix Table A 1)
Span L
Calculate the ailowable span for a 10 in. pipe with standard wall operating at
400°F. The material of the piping is carbon steel A 106 Grade 8.The pipe i!
filicd with crude oil whose specific gravity is 1.2; it has a 2 in. thick calcium
silicate insulation of density I I !b/ll3. Metal weight, content weight, and
insuiation weighr may also be obtained from any standard table. Assume t h a ~
the maximum deflection allowed is 8 in.
= 58.2 lt
=.
a
Using Eq. 3.4 based on limitation of allowable deflection of in.:
Span L =
4s
=
= 3g.4
fr
E = Young" modulus (psi) at 40VF for cerban steel with serban content
A
Seil weighr of pipe =-(OD'
4
- densit^ it^ of steel)(length)
0,3O/0 or less
= 27.08 IiO'psi
I = area moment of inertia ol pipe = 160.7 in.'
I
D$rrarery@
[%se ( d l : If the piping material was red brass seamless 843 (cornmescisr9
brass 66 CU-343):
Example CIBmblrm 2
I
C;r$cuOate also the maximum altowable span in the following case (using basic
information from Example I).
(a) iIB I in. static deflection was allowed.
(R) %E the material of the piije was stainless steel A3 12 TP 3 14.
(c) I f the piping material was aluminum seamless B24 I Grade 6061 7'6.
(dl Bf the piping material was red brass, seamless 843 (commercial brass
L=
e=
66CU-34381).
( e ) If nickel piping was used (Ni Cu, specification El t6.5, P No. 42, C;rade 400,
Required span, L = 27 2 I t
hot annealed).
Case (a):
b,
Case (el: If the material was Ni-Cu, specification B165, P No.42 Grade
4 0 0 , hot snncaled:
I f I in. static deflection is allowed:
L=
L=
Case bb): RI the marcrial of the pipe was stainless srcel A312 1.P 304
("r Cr-8 Ni pipe):
1
Kequtred span, L = 37 1 It
Table o l span: To provide the reader with a quick reference values of span,
'[able 3.3a and Table J.3h are presented.
Thc following assumptions were made:
I. Pipe material is car&>n steel AS3 Grade A. Table 3.33 applies
conservatively to all other steels.
2. Temprature ranges from zero to 650°F. At 650°F, Sh= 12,000 psi,
Mtdulus of elasticity Eh = 25.22 lDOnpsifrom the piping code.
3. Specific gravity of fluid is 1.0 (water).
4. Density of insulation i s I I lb/ftl.
Thickness of insulation i s i f in. lor pipe sizes I-4 in.
2 in. for pipe sizes 6- 14 in.
24 in. For pipe sizes 1 6 2 4 in.
Required spare, L = 39.56 f r
Case (c$: Of the piping material was aluminum seamfcss B24 1 Grade 6061
T6 at 400°F:
l.
r
$----rtntia ir
4
kt8 7
II
ltr"ll6,B 7
- a
5. The p i p was treated as a horizontal beam, supprted at b l h ends,
carrying a uniform load equal to the combined weight of metal weight,
water, and insulation.
6 The maximum static deflection was 1 in. and natural frequency was
3.12 cps.
7. .The maximum bending stress was equated to allowable weight slres
-a@
tP
7b'- 4 ~
.
Ill l t i t
4~
m
-
m,
45
hrr other values of allowahh stress, deflection. and nat r I frequency, the
.. 1
i
*
rrnss
id
LM
\pan values given in Table 3.3a need to he multiplied by span calculation
factors (given in Table 3.3b) C,, CZI
and 63;'
Values in Table 3.3b were arrived at as follows:
For any other allowable stress S h . the maximunl span is C,L. where
C,= (&/ 12,000)"~.
2. For deflections other than I in.. the maximum pipc span is C2L'where
C2 ( B / L ' ) " ~ .
3. For natural frequency fofher than 3.12 cps*the maximum span is C3Lp.
where C, = (3. 12/fi't2+
I.
1
l'hese calculation factors are given in Tahle 1.3b for some values of $ and
l'his calculation factor should not &-confused with span reduction factors
given earlier in Figure 3.1.
I.
Using Table 3.3a. calculate the maximum span allowed for a 14 i n rch 411
S h = 12.000 psi. d = I in., and f = 3.12 cpr.)
Span L considering the stress from Table 3.3a = 43 ft.
Span Lkonsidering the deflection
= 4qfr.
Sclect the smaller of the two spans, namely 43 fr"
pipe. (Assume
2. Calculate the span if & was 10.000 psi.
Prom Table 3.3b. the calculation factor is C,= 0.913, span =
0.9 13(43) = 39.2 I t .
3. Calculate the span if A = 4 in.
From Table 3.3b the calculation factor is C2= 0.841, span =
0.84 1(44) = 3'7 It.
4. Calculate tile span if the pipe is connected to a compressor with speed of
R cps.
From Table 3.3b. calculation factor C = 0.625. span = 0.625(44) =
27.5.
Calculation of the allowable span under dynamic loading is complicated.
The conservative formula for calculating the restraint spacing (reference 5 )
based on stress criterion is given by:
(3,li)
where K = seismic coeAcient depending on the peak of R w r response spectra
(mullipte of acceleration, 6).
I'
~ $ . . ~ k ideflection
c
crilerion (reference 4) can be used lo calculate tg
allowable span under dynamic loading.
For a simply supported single span bean, the maximum deflection by taking
one mode is given as:
TABLE 3.5 Suggesled Pi@ S u p p r l Sp@clnl:
Suggested Maximum Span (IQ
4m L4
Maximum b = $El A,,
Srean, Gas, or
P i p Size
(in.)
Water Service
Air Service
= pipe mass/fmr
E = modulus of elasticity, psi
B =. moment of inertia, in.'
A,, = seismic acceleration of pipe- ft/sec2
where
pn
GUlOE SPACING FOR WND LOADING
Table 3.4 gives maximum spacing of guides lor vertical piping.
rahle 3.5 gives suggested pipe support spacing (span) as per ASME
Nuclear CodeBe,
Sectim Btl, Division I , Subsection NF-3 133. t - l .
TABLE 3.4 Maximum Spacing ol Guides
-
Nominal Pipe Size (in.)
I
Guide Spacing (:\I
22
1;
23
2
3
24
27
4
29
6
8
14
16
33
37
41
45
47
50
18
53
20
56
60
10
12
24
1. Guidesshould be kept a b u t 40pipc disrneters clear of
corncn or loop
2. &I= o l p i p guidcc m hImn
kr
ruure rhrl m M g h l w r n m
WP
3. Calculrliond rhrd M nn
6
k given k rrlrrcwc
Notes:
i. Suggested maximum spacing between pipe suprports for horizontal
straight runs al standard and heavier p i p st maximum opraling
tempramres of 750°F.
2. Dtxs not apply where span calculations are made or where thete are
concentrated loads between supprts such as Ranges, valves, a d
specialities.
3.
The spacing is based on s maximum combined k n d i n g and sheer stress
of 15(W psi and insulated pipe filled with water or the equivalent weight
o l steel pipe lor steam, gas, or sir service and the pitch of the line is such
that a sag o l 0 . 1 in. between supparts is prmissible.
DESIGN RULES FOR PIPE SUPPORTS
Supports lor piping with longitudinal axis in approximately a horizonla!
position shall be spaced to prevent excessive shear stresses resulting from sag
and bending in the piping with special consideration given when carnpnents
such as pumps and valves that impose concentrated loads. The suggested
maximum spans lor spacing of weight supports for standard weight and
heavier p i p are given in Table 3.5.
48
P b e Span Calculation
(
i
1
E x 4
thick calcium silicate with density 12.25 Ib/l13.The material crl \he @ping
is c a r b n steel A106 Grade li: and the temperature of the oil is ~ ( ) ( P E
Assume tl~esnaxirnurn deflection allowed is 1 in.
C H A P T E R FOUR
-
2, Calculate the span if a valve weighing 1050 lh was located at tile midspan
of
Exercise 1.
< ,1lru8;eicthe span if a valve weighing 1050 ib was located at one-third
span distance lrorn one support of Exercise I .
3,
4 CalculaQe the span if the pipe considered in Excrcr\e I has a
e l b w between ihe supports.
?I()
ANSI PIPING CODES
AND ASME CODES
degree
5, Calfulate the static deflection in a I 0 in, sch NO slainie$s ~ r c c lpipe filled
with water and with 3 in. of fiber giacs insulation
1
P
I
2
3
REFERENCES
1 7 1 Sumrrs
~
for IndustrroI P ~ p t n~ ~y s r c m Pttrtln
~.
lnc ,
a
rluor Dcrlpn (iutdcs and O Truong Serntnar on P ~ p ~ n~gy \ t c m \ A
, ~GM
Unlvcrslry. I exes
DM!, Onc Drstgn Standards
Bart, W.
Ng~ogl,B K. '"~lmpl~edSeismic Analysts Mclhtds for Small pap5 " ASME 7 ~ . p v p . 4 3
Stevenson eo , "'Seismic Destgn of Small Dtamc8cr Ptpc and Tuhlng for Nuclear power
Plants," 'BP~
6314. Frllh World Conference of Eer~hquakcEngenecrrng, ~ o m c ,197%
6.rJANSI Standard A5R. I "Wind Loads lor Buildings and Other Structures
7. Wilkes, Gordon 8. "Heat Insulerion," Wbley, NY
,
t
-
I hc A N S ~Plplng ~ o d cand
s ASME Pressure Vessel codes give guidelines for
ptping
design In general, the latest revision of the code should be used. In the
dc\ign of Nuclear Power Plants Piping, the cod@of record, which is not
ncceszariiy the latest revision, lor a specific plant Can be used.
~ o t l related
c~
to piping design include:
I. Power Piping (rclerence 1)
ANSI B31.3, Chemical Plant and Petroleum Refillcry piping
(rclcrence 2)
3. ANSI ~3 1.4, Liquid Transportation Piping brcference 3)
4. ANSI ~3 s. .x, Gas Transportation Piping (reference 4)
5 , ASME Section I l l , Nuclear Components Design (rcfercncc 5)"
I
ANSI 8 3 1.
2
Suhseclion NA
Subsection NB
Subsection NC
SuRsection ND
Subsection NF
General Appendix, Material F"roperlies
Ciass I piping (high energy piping)
Class 2 piping
Class 3 piping
Support design
Nuelcar components design is treated in Chapter 10.
I
I
.
A k .
~ e a- .
! m E R M L PRESSURE AND
LQNGTTUDINAC STRESSES
i
1
.(DL
Code allowable stresses are designed to prevent failure of #hepiping
Two types of failure that the piping should be protected against are:
1.
Direct averstress or failure due to pressure, weight, wind, earlllqualre
and other primary loads.
2 . Fatigue or distortion due to displacement strains (generally thermal
eflecls) which are secondary loads.
The limits
of cllcuialed SfreseS caused by sugajned loadi and disljscemrnl
slrcios are:
' a
:
'.
,,-
'ncr@al~ W U W S~~~..SS@I: Stresses due to internal pressure is
sidered safe when the pipe wall thickness and any reinfclrcenlent are
adequate. (See thickness calculation .
i Chapter 2.1
LoflgifudinalSfresses($1:
The rum of lonpiludinaI ~ f r ~ryil,lling
s s ~ ~
from pressure*weight, and ofher sustained loadings shall n4,g exceed (he
allowable stress for material a t maximum metal lcmperalure S ,
P 8 ~ thickness
e
used in the ca!culation of $ must be reduced by
such as corrosion. erosion, manufacturing ff,lcrancc,
and
grove depth*
hasic
,fi
nllowabk Stress Range for Displacement Sfresses: 'The a,,l,wahle
stress range SA k given by:
SA =f(J.25.r(
+ 0.25Sk)
14.1)
where Sc =basic allowable stress lor the material at minimum (cold) metal
temperature, psi
psi
fZsfress reduction factor lor cyclic conditions (0,
of full lemprafure cycles over expected [ i f e ~
Table 4-1 gives values of slress range reduction factors,
.% = hot stress,
7 , W Do 14,OC)O
14,mlo2 2 , ~
2 2 . m to 45,000
4S,oOn lo IOQ,fXXI
Over 1m,CK)O
0.9
0.8
0.7
0.6
05
total
. ..
I
/'
W~.J Sh is greater than the calculated value of Si . the dillerence between
i
them may be added t o !he t e r m 0.25Sh in Eq. 4.1. I n this case the
stress range &comes:
. ,,
,.
a 0
~
Q' 8
,_I((,.a. en., 1.
&. .m
h..*$-*#~
k.J+
bbd a
valve lilts. ' l ' l ~ crnalcrial i s srainless steel pipe A3 12 TP 304 ( 18 Ge-18 Ni
pipe). Whac is thc allowahlc expansion stress range?
allowable
'l'wo things to note are:
I
Appendix Table A3 gives values of cold stress S,and hot stress ,Th l o r piping
materials f r o m B3 L .3 piping code.
Representative values of S,and Shfor cartxfn steel, alloy steel A 3 3 5 5 Cr-i
Mn, and f o r stainless steel A3 12 TP 304 are given i n Table 4.2 f r o m B3 1 . I
(reference I), B31.3 (reference 21, and Section I I I (Class 2 materials
subsection Pic, reference 5). A s can be seen, 831.3 code gives higher
sllowable stress, whereas Section I I I , Class 2 materials are allowed higher yield
strc.is. AppendixTable A 3 gives 8 3 1.3 values for the most c o m m o n materials.
For other codes, appropriate references should he uscd i n the actual design.
Calculation o f allowable stress range Sn using Eq. 4.1 is Frequently
encountered. Three examples are given here t o show the calculation of S,.
",
Because relief valves d o not operate very frequently, we w i l l be justified
in assuming that the pipe w i l l experience less than 7000 cycles 0%stress.
.
2.
Therefore ( = 1 .O.
T h e fact that the range From ambient to operaling temperatures is
negative makes n o diflerence. II is the temperature change that
mallcrs.
I:or ASTM A? 8 2 T P 304 seamless pipe, the allowable stress i s (minimum to
100°F)
S, = SI, = 20,tNIO
SA = /( 1.25.5'
+ +0.2.S,YhIpsi
SA = 1 .O( 1 .2S x 20,000 4- 0.25 x 20,000) -- 30,1)00 psi.
1, A pipe is fabricated of seamless carbon steel rt, rperificarion A S I ' M A I f 1 0
Grade Bid. %he design temperature is 700°F. What is the allowahle
bd
expmsion stress range? Refer t o ANSI B3i .3 (latest edition) t o find the
value nl Sc and Sh s t r ~ s sat m i n i m u m temperature lo IOO0F (i.e.,
$1 = 20,ml(d lb/in.' Stress at 700°F (i.e., Sh) = 16,WOOlb/in.2 (Appendix
Tahle A?). In the absence nf any reason For taking a lower value assume
/ = 1.0; then S, = l.0(1.25 x 20,000 + 0.25 x 16,XIN1) = 29,000 Ib/in.*
PETROLEUM REFINERY PIPING CODE
REQUIREMEWS FOR FORMAL AMALVSBS*
N o formal analysis (II adequate flexibility is rctluircd in systems which:
I. A r e dupiicatcs of succcssful!y operating installaliot~so r replacements
without significant cliange o f systems w i t h a satisfactory service record
2 . C a n be readily adjudged adcqtlate by compa"son with previously
analyzed systcms.
3. A r e of u n i f o r m size, have n o more than two points o f Axation and no
intermediate restraints, and sarisly Eq. 4.3:
2, A pipe suppiies steam l o a jacketed process vessel that is operated o n a
batch process with a 4 hour cycle. 'The steam temperature is 2110°F and the
marcrial sf the pipe is a seamless l o w and intermediate alloy steel pipe,
ASTM A335 5 0 - 4 M o . If the installation is operated continuously and
the design life is t o be 12 years, what is the allowable stress range for
thermal stresses i n the pipe?
Allowable stress (cold) = &
-
20,000 Iblin.2 (Appendix Table A3)
Allowable stress (325°F) = Sh = I W, 1 (K) lb/in.2
Number of cycles =
x 365 x 12 = 26,280
J = 0.7 (for 22,fN)M5,000 cycles) (see Table 4. If
S'A
i
,
f6( i .assc.(- 0.%5Sh)
3, A Dine in
ia relief system attains
a temperature o f -90°F when the relief
where D = nominal pipe size, inches
y =. resultant o f total displacement strains t o be absorbed b y the piping
system, inches
bl = Anchor distance, straight line distance ketween anchors, feet
L =developed length o f p i p i n g between anchors, feel
SA= allowable stress range, psi (include stress range reduction factor f
*
From ASMEIANSI 113 1.3, suhseclion 3 19.4.1, Requirements, for Analysis.
:
dJ
1
ANSl Plplng Codsr and ASME Plplng Co&r
where more than 7900 cycles of movement are anticipated during
life of installation).
Ee -- modulus of elasticity of the piping material.in the cold c o n d i ~ i o ~ ,
psi
Becatlse no general proof can be oflercd that Eq. 4.3 will always
conservative, caution should be exercised in applying i t to abnormal
configurations (unequal leg U-bends), lo large diameter thin-wall pipe (srres\
intensification factors of the order of five or more), or to conditions where
extraneous notions, other than in the direction connecting the anchor points,
constitute a large proportion of the expansion duty.
User must he aware char compliance with Eq.'4.3 does not ensure that the
terminal reactions will he satisfactory. A value 01 0.03 may be assumed for the
right-hand side in Eq. 4.3 if enough information was not available. (Eg. 4.3
does not incrtlde weight effect.)
4.
s
d
Check if formal analysis is necessary in the piping arrangement given in
Figure 4.I using Eq. 4.3.
The diameter is I0 in., temperature is ?(iO°F, coell?cieni is 0.023 in./![
ofpipe lor carbon steel A 106 Grade B (see Appendix Table A I).
The expansion in each direction and terminal movement is:
lnplanr rnd Q W s n r Bendng Mllomrn(ll
E., = cold modulus for c a r b n steel = 27.9 x lo6psi (Appndix
Table A2)
L =developed length= 15-4-10-4- 1 5 + 5 Q + 2 5 = 115fl
U
= anchor
distance = 58.5 1t (straight line distance between anchors)
S, = 14 1 .2SSc + 0.25Sh) = 1.25(20,000)+ 8.25(20,00(3)
= 30,000 psi
Equaricln 4.3 states that formal analysis is not necessary it:
Because Dyl(L - u12C; 30SA/&, no formal analysis is necessary from the
thermal flexibility point c ~ view.
l
bx = 4040.023) = 0.92 in.
A y = 450 - 10)(0.023)+ (2 - I ) = I .9Z in
h r -. 15(0.023)= 0.345 in.
Y=
= 2.13.
Ed = nominal pipe size = IO in.
The B3 1.3 code defines inplane and outplane k n d i n g moments, which are
shown in Figures 4.2 and 4.3. Alter application of the inplane bending moment
LEG 3
I
MI
LEG 2
q0
RGURE 4.3
s
lnplsne and outplana moments in hranch connection (ANSllASME AJI 3 )
kg.the hcnd or branch conneoion s t i l l remains in %heoriginal plill~c.Hut whcn
""!plane hcmfing moment M. was applied. the bend or hranch tt,nncciion
goes out of the original plane. The torsional moment ahot~lihe axis of the pipe
i s denoted hy M,. Power Piping Code (811. i ) and Nucleibr C,t,dc [ASME
See. I I I ) dcr not diflerentiate herween inplane itnd oulplonc hending
moments. See Table 1 0 . I for Nuclear Ctjde equations.
STRESS lNTENSlRCATlON FACTORS
Piping auxiliaries like hends (e.p.. elhowr. miter knds) and brianch ccln"eciionr (e.g~*
welding lee. fabricated tees) have Rexihilily chari~eteristich ,
flexibility factor k , and Stress intensification factors (Sin.In this erea most
codes including British standard 893351 use the work dc,ne
Mart[
(reference 6). Table 4.3a (reproduced from Appendix D.ANSl 83 1.3, IYH()
revision) gives equations for calculating values for h, 1,inplane S f F i,,
outplane SIF B- Note that other coder do nor allow the use of lower value for
outplane SIF (0.751h"') compared with higher value of I I . u ~ for
~ ~inplane
/ ~
SIR".
with pad or
saddle
a
0.9
/
fabricated tm
I
0.9
,--
ne~bility
Factor k
Intensification
Factor i
or weld neck &nge
Double-vveldcd s l i ~ n
1
h g e
1
I .2
1
1.3
1
1
l .B
2.3
5
7.5
F"rllet-wid& joint or
=ken weld Range
I_ap ~ o i n rRIange ( ~ t h
16.9 lap joint stub)
pipe joint,
or screwed Ilange
Corngated sh%ight pip. or
corngat& or crashed bend4
1.0
Scvcr: A N S U a M E 831.3. 1980 Edrton. Append~xD
Norcs: ( A p p l ~ to
s Table 4.3a and 4 3b)
I 7-he Bexrbrlrcy factor k ISI the table app11es to bgnd~ngtn anv plane The Itexlbrl~rv
factors k and stress ~ntcnstficattonfacton I shall not he l e u t M u r a t a
factors lor torston equal uncty. b r h facton applv over the e(fecnvc arc leneth (shown bv heavv ccnterltncs 10 the sketches) for cumed and miter kru21 a&
to r
k !ntersecr8on p l n r for tees.
?fie values of k and 8 ran be read direcrl? from Char! A bv enterrng with the characterrsrrc h computed from the fomuias gtven a b v e Norrrrmb~wn
i?:
lor elbonrs and mrter k n d s the norn~nalwall thickness of the fitring
tees, the nocninal wall thicknw of the matching prpc
T,-. r k erotch thicknws of t=
Tp= @ or orsaddle rhickrrrrss
8 = one-hall angle bemeen adjacent miter axes
d i m of mrching pi^
R , =be& d r % s of welding e l b w or p i p bed
r,
cmteb radius
= &ter spasing at centerline
J
Dha OD of branch.
w e h g a rn atraehed to one or both ends. the values of k a& I in the table shall be camected by the factors C,.
which can be read directly (porn
g ~ t h rt
k ~ o m p c l l ~kd.
awsply to Is;.ndin_g. Rexibiticy factor for tomion equals 0.9.
n"
a, a >r!f,
h-4Tlr.
~ l r c*gmr
:
is c a u 6 o d that cast burr welded fittings may have considemQL~/
heavier walk than that of the pipe with which they are
brge emrs
w y k i n d r ; l c & unless the elIecr of these greater thicknesses is comidered.
b i g w r m a r be 4adsW that this Iahxrcation has a pressure rating equivalent to stmight prpe,
A sirrgag hrem%6cationfactor e q w l to 0.91h3' may be used for b t h r, and 1, if desired.
,*" In Qrge d i m r e e thpe-wail e l b - and beds. p r s w e can s~gnificanrlyaffect the magnitudes of k and i.To comeca values Imm 8878: table
.
I
-lot
-
a
>\
B
5. Calcutate SlFsnd Rexibility factor lot I2 in. standard schedule long radius
elbow.
(a) For welding elbow,
bend radius = R , = I .5(nominal diameter) = 15(12) = t R in.
-
7 = nominal wall thickness = 0.375 i n (see Appendix Table A4,
properties of pipe) and assume thal elbow arld pipe have same ihictness,
PZ
f i2.75 - 0.375
2
2
= mean radius of pipe = O D -
-,
h = flexibility cllaracteristic = TR
=
- = 6.1175 in.
(equation from .Table 4.3a)
I
I
wb
By modeling Ranges at the elbows, the lower Sib JaDues can be
sdvanrageously used. However, the flexibility factor. also has k e n
reduced which is not desirable.
MUER BENDS
Miter k n d s shall be used, when more economical, for changes in direcfioo on
in which
space limitations prohibit the use of e i b w s . Miter bends in horizontal suction
lincs to centrifugal pumps should be a minimum of six pipe diameters from rke
strcrion flange. The equations to calculate stress intensification factors foe
miters are given in Tahle 4.38. The miter bend can bg: either closely spaced or
widely spaced as determined by using the following equations.
The miter is closely spaced if the mi<er space S is:
(4.48)
S < r2( l -C- fan 8 )
stccl w.ater piping, drain lines, and internal piping in pressure vessels
( ~ 2 ) ~
Scot B
R , = Bend radius = -
2
The miter is widely spaced if rhe miter space S is:
S 2 r,( l + tan 8)
0.9 =
id= inplane stress intensification factor = ---
h2"
0.9
(0.176)""
R, =
= 2.86
I'he lower value i, = 0.75/hZ' is allowed for 82 1.3 and 81 1.4. 11
desired, a higher value i = O.WhU' may be used lor bolh i, and i.. Chart A
in Table 4.3b may be used to read i6 and i.. For B3 I . I , Power Piping and
Nuclear Piping. Section !!I. Classes 2 and 3 piping. use the higher value
only.
If one end is Ranged. the correction factor = C, = hlf3 =
(0.17638"" 0.5604.
(4.4~)
r2( 1 4- cot @)
2
where 8 = rnifer angle, degrees
r2 = mean radius of the matching pipe, inches
(For maximum allowable internal pressure calculations, see Equations 2.8a,
2.8b, and 2.Xc.)
The miter angle 8 is equal to 1 i f lor a five-piece (or lour-weld) miter, sketch
(d) in Table 4.4. B i s equal to 15 for a lour-piece (or three-weld) miter, sketch
(c), Table 4.4 and 8 is eqttal to 224 for a three-piece (or two-weld) mitrer,
sketch fh) Table 4.4. Table 4.4 shows these miters and also gives miter
space S.
Flexibility factor = 6,
6. Calculate the SIF and flexibility Factor k lor an 8 in. four-piece miter. The
plate thickness is 0.322 in.
For an 8 in. nominal pipe, r2 = mean radius = 4.152 in, For a lour-piece
(three-weld) miter, 8 = miter angle =. 15".
From Table 4.4, S = miter space = 6& in. Check for closely or widely
spaced miter: r2(1i-tan 15) E 5.26 ill.,which is less than the miter space
from the fable, Thus the given miter is a widely spaced miser.
"
I
)
..
I
**@n.drBefnI
.I
35
Using the c q ~ l a l i o nf r o m the code. Tahle 4.3a.
= flexibility charactcrislic =
I
-Icot
- (3
2
k = flexibility factor
=
8.52
(0. I 835)s'6
-F -- 1 + cot 15 69.32% 0.1835
G"
2
r2
= 6.24
I'ahlc 4.3a gives equations l o calculate the Rexihilily factor and SIF for the
ftrllowlng branch inlersccfion types:
I. Welding lee
2. Reinforced fabricated tee with pad o r saddle.
3. Unreinforced fabricated lee o r stub-in
4. Exrrtrtlcd welding tee
5. W e l d in contour insert (wcldoler)
6. Branch welded o n fitting
[)ranch inlerseclions are sometimes identified hy trade names or names given
hy ;I specific manufacturer. I! is i m p r t a n l l o rcmemher that SlF value should
not be less than I (Nore I of Table 4.3Ftil,.
When pild thickness T. is greater than if times the pipe thickness f . the
equation 10 calculate h hccornes
It = 4
T-
-
(see Note 5, Table 4.3h)
44.49)
f-2
When this condition is reached h is n o longer the function o f pad thickness*
'I.hat means credit cannot be obtained l o r a pad thickness p r t i o n that is
greater than
times the pipe thickness.
SII: v;tlues for most branch intersection types are a function o f r u n pipe
dirncnsions and no1 branch p i p .
7.
Calculalc SIF and ir factor for an R in. diameter standard r c h pipe with
4 in. branch if:
i f intersection is a n unreinlorced fabricated lee
i f pad thickness used is equal to pilpe thickness
(c) i f pad thickness used is 0.57 in.
(a)
(R)
T h e header wall thickness is F = Q.372
n
u
'*.
mrl,
T ~ P
"*,T
m
\ *7
r-7-
-a@:els~f
7-
-ip- is
ma
is
AS^
4abs
,.ng C,-,
E n s c ~uc P r t r s ~ udn
l ~ S b w r r .aalbn~L.lrl.rr~nan,
(Lk h e unrcinforced fabricated tee:
.,-8b:
.
(37 .r.
--.or8
TABLE 4.5 FPcdblllly and Stmss h f e d l c r l l o n Fartor Oer %&
k = flexibility characteristic -- %!r2 = 0.322/4.15p = 0.0776
Stress Intensificalion Factor
k = flexibility factor = 1
4 = outplane S1F = 0.9/lr2I3= (3.9j(0.0776)211= 4.95
4
= inplane SlF = 3i,
+f
= 244.95)
-+ 4 = 3.96
~)cscription
Flexibility
Factor
k
Outplane:
4,
Inplane
i,
FIexibility
Characteristic
h
Sketch
T
(h) The seinft~rcedfabricated tee:
-
T,= pad thickness = 0.322 in., k
fr
= I .O
(c) The pad ihickness=0.57 in. See Note 5 of Table 4 . 1 b he;
I 4 7,use h = 4(.P'.lr2).
1 ..5(0.375) = 0.5625
Given pad thickness
F, = 0.57 in. > 8.5(0.375).
Flexibility factors and SIF are very important constants in pipe stress
calcuiarions.
'Table 4.5 gives equations for calculating Wexibiliay characteristic h,
flcxihility laclor k , oulplane and inplane stress inrensigcation factors (i, and 4)
For ellww and bend.
.The Rcxibility lactor k in the table applies to bending in any plans. The
flexibility lacror k and stress intensification lacror i should not be less than
unity; factors lor torsion equal unity. Both Factors apply over !he eRective arc
Icngth (shown by heavy center lines in the sketch) for curved bends.
A single intensification Factor equal ro 0.9hw3may be used for h t h il and ie
if desired.
The correction factor CFK lor flexibility factor due ro pressure o n e l b w or
bend is given as Eq. 4.Sa:
The correction factor CFI for SiF is given as Eq. 4.5b:
EFFECT OF PRESSURE ON STRESS lNTENSlFtCATlON
AND FLEXIC?IILnTV FACTORS
Some piping codes (references 2 and 3) give formula. for correcting flexibility
factor and stress intensification factor (SIF) for e l h w s nr bends. The elfect of
pressure on streis. farces, and moments by u.ing corrected stress inknsification factors and flexibility fectors is disru3xd n a t
When pressure eRecl is ronqidrrcd. SIF walre. are kwcr. thm reducing the
actual thermal slresr. Hoverer. 8 h . a w h n Lnce i r r r c a u s hccaurc the
flexibility at the bcnd has reduced Pir.%ute rsn aflcrt stgnikantly the
magsliavdgt of the flexibility lector r& S I F in large drrmrcr thin w.881 r I r - c - .
where
T = nominal wall thickness of
the fittings lor e l h w s and miter bends,
inches
r2 = mean radius of matching pipe, inches
R 8= k n d radius of welding elbaw or p i p bend, inches
P = gauge pressure, psi
iE, -cold rndulus of elasticity, psi
Equations 4.53 and b lor correction factors are given in Chemical Plant and
-.- (83 1.3- 1980) and Liquid Petrdrmm "TransPelroleurn Refinery
- Piping
-
~
,,,E(.,
@ Bend
on S. -. lotan
o n
,
9xi
Dlarneter = 8 6 2 5
Thickness = 0 322
I'llc flexibility Fitctor is:
1"
I"
T l i + PR + WT effect
Temp = 450 F
Expanilon c w l l l c ~ e n t= 3 16 rg 1100 It
Pressure = 250 pstg
E = 2 7 9 x IObpsl
'l'hc correction laclor CFK for the flexibility laclor (Eq. 4.5i-s)
FrGURE 4-4 Syrnmctrica?expansicln ~txtp.
To illustrate the effect of pressure o n flexibility factcbr iind strcrs inlensilicalion factclrr, an example prohlcln using welding e l h ~ w s(Nodc SO) is
used as shown i n Figure 4.4.
'l'hc corrcctcd flexibility factor is:
8,
The a~trtsidcdiameter o f a pipe is 8.625 in
8.625 +[n.62.s - 2(t).322)1
2
--
- = 4.15 l 5 in.
'r = t0.322 in.
RI= I .S(nonninal
<'trrrcclirjn factor CFI For SIF (Eq. 4.5h)
diameter) = 1.5(8)= 12 in.
P = 250 psig
iE, = 27.")
10' psi
The flexibility characteristic is:
Corrected outplane SIF
--
etors
i...
.i
I'hc outplane SIF:
Anchor
9
a! Pr&--".,
2.44
1.03527 - 2'34
1
Note that the flexibility factor and the stress inlensification factor reduce when
pressure e l l c c l o n e l b w s Is considered. Four different diameters were used
rarrging From 6 l o 12 in. l o r result comparison.
'I'ahle 4.6 gives the results obtained. For example, w i t h a n 8.625 in. OD
pipe, SIF factors are t = 2.44 and 6 = 2.03 when no pressure eFTecr was;
considered, resulting i n expansion stress of 18,396 psi at bend 58. When
presnlre effect was considered, for the same R in. nominal diameter pipe.
1, = 2 36, if, = l.%,
and expansion stress o f LR,009 psi at k n d 50 were
ohrained.
f h e percent cllange i n results drre to the pressure eFTect l o r the 8 i i . line is:
percent change (lower) i n expansion stress =
18,396
- 18,009
B 8,396
x 180
pcrcerrr change (larger) i n axial force at anchor = 1125-1113 x 100
8113
For the same expansion l o o p with 8.625 in. OD pipe. the pressure range was
changed. As l'ahle 4.7 shows, the pressure effect hecomer more significant
w i t h increase i n pressure.
I t is possible that including pressure eflect o n SIF and o n flexibility factor
could make the diflerence between the expansion stress valves obtained with
and withou! pressure effect. fhis enect will be significant in the case of large
rliarneler thin-wall elhows.
TABLE 4.7 ERecl of Pressure rl Elbows (Node 50)
OD = 8.625 In., thickness = 0.322 In., tcmpemfurc = 450°F
-
Stress
Inlensifteation
Factor
Pressure
(pig)
No pressure
2511
350
450
550
650
18
fa
Axial
Expansion
Stress
Force
Change
al
O/o Change
(psi)
(lower)
Anchor (Ib)
(larger)
1113
-
o
/'
2.44
2.03
18,396
-
2.36
2.32
2.29
1.96
1.94
18,0(r)
2.1
2.2
2.5
2.6
6'125
1
1137
1148
2
2.8
1170
2.26
2.23
1.91
1.89
1.86
17,975
17,942
17,910
17,878
ll59
3
4
5
LJ
rlprn,
sr a n - - AE Pi,
,lo&%
As stated k f o r e only 83 1.3 and B3 1.4 piping codes have allowed the use of
using Eq. 4.5b to include the effect of prewure on S1F. Basic work on this area
and the formulation For the equations i s found in reference 7 and this
information was used to reduce rhe stress in piping in real case analysis. Two
large diameter (65.74 in.) long (6500 11) steam lines were built to supply
saturated steam at 400°F lo heavy water plants at Ontario klydro's Bruce
Nuciear Power Development (reference 8). i n preliminary analysis, the
eqoations Ior Flexibility and stress intensificariorl factors given in power code
R3 I I were t~sed(reference 0. I n fttrther analysis Eqs. 4.53 and b were used
and the piping was qualified.
STRf SSES O
N A PIPING SYSTEM
The eqrralion for expansion stress Sf; i s given hy Eq. 4.6. 'The cqu;irion for
resulranl bending stress S, i s given by Eq. 4.7. For branch connections, the
I resu!lant
Rending strcss equation requires attentit?n becatrsc !he scction
modulus vaiue Z used For header and branch i s slightly dillcrcnt. E(luitrions
4.8 i~wd4.9 show this diflerence. The calculated value of expansion slress SI.
needs to he lower than expansion stress range &, earlier defrnctl hy Eq. 4.1.
The s!resscs in a piping system i s generally low for smaller tcmpcrat~rrc
variation, smaller diameter, smaller expansion coefficient, lower modultrs of
e l ~ ~ l i c i tand
y , !he longcr the length of the pipe in a direction pcrpcndicular r c l
1
dihcction of expansion.
The pipc wall thickness has no significant eRect on bcnding stress due to
thermal expansion hut i t aflecls the end forces and rnonlcnts in direct raticl. So
overstress cannot kc remedied by adding thickness; on the contrary, this tcnds
lo make matters worse by increasing fqrces and mclments.
I. !%endingand torsional stresses shall be computed using the as-insrailed
modulus a d clariticity Ee and then combined in accordance with Eq. 4.6 l o
deterwrit~ethe computed displacen~entstress range S,:, which shall not cxcecd
the allowable stress range S
:,
where
S = resultanl bending stress, psi
'\ J
he thermal expansion stress (Eq. 4.6) is based on the maximum shear theory.
2. 'The resultant bending stresses Sb Lo be used in Eq. 4.6 for e l k w s and
nliter k n d s shall be calculated in accordance with Eq. 4.7, with moments as
sl~ownin Figure 4.2.
[
,fk = resullant bending stress, psi
where i, = inplane strcss intensification laclclr from Table 4.3a
i, = outplane stress intensification laclor from Table 4.3a
n/l, inprane hending moment, irr. ib
Mg,= outplane bending moment, in. IR
Z sectic~nalmodulus of pipe, in.'
3. The resultant bending stresses Sb 10 be used in Eq. 4.6 for branch
connections sllall be calculated in accordance with Eqs. 4.10and 4.9 with
moments as shown in Figure 4.3. For header (Icgs I and 2):
-
-
1
7
0
whcre S, = resuItan1 Rending stress, psi
Z, = ellccrive section modulus For branch of lee, in.' = w r i t ,
r, = mean branch cross-sectional radius, inches
r, = effective branch wall thickness, inctrcs (lesser of fb, and ( t ) ( b ) )
gk = thickness of pipe matching run of lee or header exelusivc of
reinforcing elements, inches
fb = thickness of pipe matching branch, inches
i,, = ourplanc stress intensification lacros
i, = inplane stress intensification factor
4. AIIowable stress range SA and permissible additive stresses shall Bn:
computed in accordance with Eq. 4.1 and Eq. 4.2.
St -- M/22 = torsional stress, psi
Aa, = torsional moment, in.-llr
Z = section modulus of pipe, in,'
*
From AMSDEASME 19141.3-IWX(Section 319.4.4.
9. Calculate torsional stress, bending stress, and expansion stress at the
intersection of 4 in. sch 80 header and 3 in, sch 40 branch (Fig. 4.5).
I
L
/
i
Leg t
iorsiona, stress is:
I
4 tn diameter
sch 80
Branch
3 tn d~ameter
sch 40
S
M
Y
242)
- 2322 x 12 = 3262 psi
264.27)
Leg 2
The compnred displacement stress range is:
Sf:=
-
Moments acting at the intersection is given below:
leg 1
leg 2
leg 3
-550
425
-I80
2322
I821
-920
= 13,630 psi
NO0
-8%)
682
-
S~ltcrion: For header, y moment is torsion; x moment is inplane; and z
moment is aulplane moment.
For branch, y moment is outplane; x moment is inplane; and z moment
is torsional moment.
Assume unreinlorced fabricated fee (stub-in), that givcs rhe highcst
number lor SIF.
*
Mi
"22
RGURE 4.5 Stresses at run and branches
)leader
Header
Branch
----
= 0.337 in. (see Appendix Table A4 for 4 in. sch 80)
i0,7 17 psi
S , = J I O1 72
,~
-t4(25581' = 1 1,876 psi
For Branch Leg
3:
J
A
2
rz = - (4.5
- 0.337) = 2.082 in.
7" -= 0.216 in.
Z = 1.724
(Appendix -Kable A4)
Z, cffecrivs section modulus lor branch
-
Z = 4.27 in."
= wrta,
r,
r,
-
-
j(3.5 - 0 . 2 16) = 1.642 in.
ieqrcr of
L = 0 . 3 3 7 in.
I,,( t b ) =
4 = 0.75(3.03)C 0.25 = 2.52
For Header Leg I : The resultant bending stress is:
Itr
OF
(job)
(Tand
mean the sanlc thing)
J.t).1(0.2 16) = 0.654 in.
= 0.337 in.
-
7,
n( 1 .642)2(0.337)= 2.85
in.'
--- 11,892 psi
--- 41,136 - 9638 psi
4.27
=
= 12,804
psi
~ u d dSprhng
I
1
'y ,i
~ r & ~ ' t bsame
e
SIF is ~lscdfor the header ;$nil hrilnch. in hentling s,rc\,
J
37
"
1 Ite foll(~wrngdillicultics havc Iwcn faced with rcspect t o cold spring:
srrlcu9a!inn (83q.4.1 1 ) lor branch, thy seclion mtrdtrlt~svairlc is modifictj.
1.
A pil~ingsystcnl nlay he colrl sprung clr prestressed to rcclt~cc; r ~ ~ c lforce
~ o r itntl
lnomerrts c;r~rscdhy thcrmitl expansion. C'old sprirlg m:ry he ctit short for 1101
pipi~rgor cut Pang lor cold (cryogenic) piping. 'l'hc crtl short is :rcctjmplishcd h\
sllc~rfcningttrc overall length trf pipc hy desired amotrrrt hrtr not exceeding the
calculalcd cxpransic~n.Cut long is done hy inserting it lcngrh (mitking the Icngtl~
c l F pipe Iongcrl. '!'be amount of colt1 spring (C'SI isexprccsctl ;rs it pcrcclltiige o!
fr;lclion of tl~ermalexpansion.
Q'scdir for coid spring is not allowcd lor stress calsuiaiions. I>illercnl codes
saatc the same mearling by slightly clillcrcnt wcbrciiing. I'hc Following is Iron1
Nrrclear C'odc, ('lass 2 piping NC'-3t77.3-3 ASMll Scciiolr III:
NC-3673.3 Cold Springing. No crcilit f o r cold spring is ;rllc)wctlwith rcg?rcl t r ,
tresses. In calc\llitting cntl thrt~slsand nlctrr~cnts;tvting ctn cq~tipn~i*lrl.
~ h ;icltr;~l
c
rcitclicsns a #any one i i n c . rillher thi~nthcir rangc, shtili 1% r~ccc!.('rctlil f o r ccbltl
springir~gi s allatwcd in thc ralrt~l;ltionsof lhrrrsls ;mtl n1ctn1c.111~.
p~c~virlctl
tl~c
mctl~tnlilloh1;tininp the tlcsig~~crl
cold spring is \pccilictl ;rrvtl ri5ctl.
k
iJigrsrc. 4.6chows the position of !Ire pipe hcforc arttl ill tcr ctrltl s p ~ i r ~(cut
g
shoat in rhiscirse). 'I'Re lcnglli of pipe is X S It i l l x rliructior~iiritl grows I .5J in. aE
the tcmpcratatrc of 300°F. l'hc pcrccntitge colt$ spritig tlc~sirctlis 50'XI. ' i ' l ~ c
itnrounr of Icnglh to he ciri short is C(JII~II 10the ~ ~ ~ ~ J of
I I pc cI ~ c ~ n t i tcold
g~'
sp"ing ;and actual expansicln; hcrc ir isf1.17 in. For pritcticitl rerrsorls, t o ircl~icvc
thc. sirrrlc" ;It the conslrtrclion site ctjlcl spring of :in. is ~lsctl.As ca11he S ~ C I illc
I
pipc ici ptlllcci! hack during installation. 'I'his is tlt~ncb y pkysie;~lforce ttsirlg
cqtsipmcnt ?;\rcrl as a tractor. Wltcn flrc pipc gels ! ~ ( l t ,i t crosses tllc rret~trirl
pc~sititrnktnd grc3ws toward the cjrflcr side.
2.
3.
4.
5.
I
!Oy ntist;ikc sonlc eitlculirtc Ihc' strcss also with cold spring, which is
wrong. I;irst the system shtjuld pass for strcsr; calculations wifhoua
cctl~sirloringcolt! spring. Only in thc next calculation can cold spring bc
crrlrkitlcrctl For redt~cingIoilds at cc(uipmcnts.
C'onslrt~ctioncrews s o n ~ e I i n ~ ovcr!r,ok
cs
lire tlccd for cold spring and
rllths t l t ~t r o t r~scthe ccjld spr inp. .!'he ;~n~c,rlnt
of force needed tn pull a
Iinrge line itr [lie iiiili:tl position !r>r welding is hugc.
'!'lie colt! rc;rclion :rt lr~llcoid sprirrg nccds lo hc calcarlatcd and matlc
srrrc that file ecluipn~cn!is ;rB>lclo wiihstirnd rl~isirdtliticlnal load dtte 10
t o r ; h t cold spring i t t ccllc! condition.
'l'hc tlcflcctio~isi ~ irt cold springjocirtion still remain the same, hecause
tllc colt1 sprit~gonly rciocirtcs tire pipe wc9d point and does not reduce
titc ibcitbirl ex[t:t~isiolr.This actrribl rleflcctinn is important in the spring
rlc.;ig~l. I F i~llcntionis ntrt pitic!, the splippp: m;ny he 1lntlersi7.ed for
tlcllcctic?rl.
('clltl spliitlr, rlcctls to I>c specifctl it1 weld poirrts lo save cost of
; ~ t l t l i i i c j r ~ ; rwc.lrling.
l
Meximum Reactions far Simple Systems'
Itr)
P
I
i
f I
. 1
: l ' h e tcmpcrattorc for this
c.~~niprll;tliot~
is t l ~ cnr;rui~llrrnlt?r nlinintrtm n~clolbcmpcritlurc, whichcvcr
~wotl~~c,c.s
6I1c I;lr gcr K C ~ I C ~ ~ O I I :
coltl-sprirlg F;~ctorvaryittg I r o ~ n
zero lrrs no cold spring to I .Ofor I(1O0h,
cold spring. ('!'he f;tclor 2/3 is hitscrl o n cxpcricncc. Illat slrows that
spcrilicd colt! spring cannot he fully assrrrccl, cvcn wit11 clahori~lc
prceaulions.) Usually C' of (1.5 is rccornmentlcd.
E,, = nlotlrtlus of elasticity at installation tcmperattrre
I:',, = modttlus of cli~sticilyaf maximum or rninimunr metal lernpcratrirc
K range of rei~clionlorccs or nromcnts (dcrivcd from Rcxibiliry analysis)
corresponding to thc fall! displacement ?;tress range add hesed o n Ea
K,, = cslimalecl instantanetrus maximum reaction lorcc o r moment art maxilntlnl or minimum metal tcmpcralurc
('=
Anchor
-
Norrle
&!(;(IRE 4.6 i'ip~np in itti!i;tl (carlt!) ant!
final fhclcl p b \ t ! t o f ~ 1111dvrCIIIC! \riririg
Y P o r i g i ~ a C'nndition
r
R,: T h e temperitltlre for this c o m p ~ ~ t i ~ lisi ott,,
n
10)
e x p k f e d lemperaturc at which the piping is to hc assembled.
R, = C R or C",R , w!~ichcver is grcatcr
I'ipitlg nlalerial is slainlcs%slecl A 3 i 2 TP 304. T h e lempcrarure is
9OI)"F.
I ' t r r;rlcul;tte ltor reaction, usc Eq. 4.12:
(4.t 3 a )
where norncnclattarc is as &fore and:
where K = nrornent helore cc~fdsprnng = 2500 It-lb
t ' = 0.55
Em = hot modulus = 23.4 x !Oh psii. at 900°F for stainless sfeel
( A l ~ e n d i xTable A2)
I,, = cold modult~\= 28.3 x 10" ~ $ 1
Cl = eslinrrted sell-spring or relaxation factor; use zero if v;~ltico l C', is
ncgativc.
R, = eslirnatcd instantaneous reaction force or nlr>mcni at insla1l;ttictn (en)pcralnrc
SE = cornpuled disftlaccnient stress range (from Eq. 4.6)
:dk hot S ~ ~ Q I Spsi
S,
-
= 2SoO(tt.37)(0.82ttV)
= 758 It-lh.
'l r ) ci~lcul;tlec.trf(l reacrion usc Eq. 4.13;1:
For nlultianchnr systems and for. two-anchclr systems with internlcdiir~c
restraints. Eqs. 4.12.4.1.7a and h are no[ applicable. Each case mils! he st~ttlictl
to cslimalc location, nature, and extcrrl of !oral overstrain anil i t s ctfcc.t o n
s'ress dfstribu~ionand reactions.
.' If a piping systcrn is designed with different pcrccntagcs of cc~ldspricig in
mrious directions, these equations are not icpplicahlc. In [his c;isc. the piping
system shall bc: aniriyzcd h y a comprehensive mcthocl. The ~ i ~ l ~ t ~ lhot
i~tcd
reacrionsshall hc based on theoretical cold springs in all dirccticlns not grcilicr
than two thirds of the cctld springs as specified or mcnsured.
10, Calculate colti and hot reaction moncnls at nolzlc (Fig. 4.7) ;rltcr 55'%,
cold spring if moment wirhr~u!colrl spring was 2500 fl-lh from piping
. analysis.
wltcrc
"
or
C'# I(, whichever is prcatcr
(', = rcliixaiion Factor
Bccausc t l l c r ~was riot enotlgh inlormittion t o calcula~ccornptrtcd
cxpi~n\io~l
stress range S, , factor C , could no! bc caBI~.IIIated.
C'cbitl rcircliorl. R, = ('W
= 0.55(2500)
= 1.775 18-lh
la is in~portancthat the equipnrcnt nt,i.;.lc should withstand not or~ly
7 5 8 fl-Ib in an operating condil;ion, hrrr alsc~ 137.5 11-lb in a cold
condition.
EXERCISES
Cul short
lbow
RGklllE 4.7
N, = C'R
Momen8 cslcularion under cold spring
I:ind cold stress and hot stress for a carbon steel scamless pipe at -36PF,
h75"F, 1 125°F:
( a ) material is A93 Grade A; (6)material is API 5 L Grade B.
A mraring, equipment norzle can only allow a force of XOOlb during
operalion (Fig. 4.10. 7'hc carlwjn steel pipe will have an clpcrating
"
lcn~pesattirc"i0bol: arli! :ic;~lcrrl:~cc-ci
I n r c r * r r f ~~*~~
1%
lslerc
--_
i
\ J'
8%
0. (';llculatc the rhcrmal expansion stress for the branch and the header
according lo ANSl BJ 1.3 code Itor the loacting (given in Example: 9 and
in rzig. 4.5) at the branch intcrsecrion: rhc branch and the header are
12 in. standard wall and 8 in. sch 40 well.
IT
FIGURE 4.8 ('old spring cxanrple.
REFERENCES
I
4,
At what condirion can cold spril~ghe t~sctl'" .is# t l i l l i c t ~ i ~~iIiI~C~O I I I I I C F ~ ~ I
with co!d sprir~gin theory
;silt$ pr;lciicC.
d h ) B';bler~lirlc.Itrngiltttlittill stress iri it 1-7 I! sEitttclit~t!\$t*ig!~!~ c i t l i t ~cll>o~v
g
wherr:
Inp9;rrrlc I?eslr!ing nlonlcilt = 47.3 1.1-11)
CDtttplitnc bentling Inrrnlcrll = 32.5 .T11-1I>
Axial force
= 0 2 8 ill
M;~tct-iitlis Ft5.1 iirarlc A ilnd ~cnttlcritlr~c-c
i\ OS2"1'.
v8
6 , C"alctr8;ale SII; a i ~ dflexibility f i ~ c i t ~ r :
( a ) h in. lttng rarlirrs sfit,ttl;trtl 111ickrt~ss
( R l b"1l9cul;rrc cctrrc:ctctl ?.ill: ;~ntlti if tl\c cll~crwis twtr C K ) ~ ll;tr~gctl.
\
fcb M i ~ c rb c i ~ dwiih = i 5 O i111tI ! 2 in. ( l i : ~ n t ~ ~
w ci lr! ~t l ~ i c k t ~
0.25
e~~
ill,
7*
( i t ! c ' ~ t ! ~ t l i l iilCr!nitI
l#~
~ x p i i t ? ~ i (f \ tt lb f ~ ~ the
p i p i ~ ~S !gI ~ ) ~ V Iilb
I !'igittc 4.0.
pip^ is i f ) i l l . S C ~ I8 0 ,453 l i r ; ~ ~1%!pil~c
~ i ~ ttOtB"!:.
t
(RI 11 t l ~ ctIislil8tcc ~ C I W C C I;I ~ r ~ c h $is~i~tcrci~sctl
rs
to 300 I t , W I I ~ I I will IIC 10c
.!'he
force'!
8
-
!"or it s~ilmlcsspipe, A 5 3 Ciririlc 13, the i~llowithlcxlrcsscs ;I[ 74Y'i.' ;trirl
h0OnO.' itre Zl),OllO psi i+ntl 17..30(lpsi, rcspcctivcly ;iccorclitlg lo ANSl
8 8 1 1.3 e'rrilc. B'trr it12 acttrill pipir~g\yslcrrl ;rt (iOfFl:. (Btc ctr~l~l~ttlctl
pilli~rg
strcwcs at ceslirin Ig~cirlionsarc: as follows:
(a1 I.ol~giOrdin;llstrcss tlt~ettl; pt-csstrrcwcigl" l ; r r ~ t botllcr s~rslitictctlIcii~tling
is VXBIO psi.
(RE C'ompktlcd displ;tccmcnt slrcss ribngc is 3 3 . 4 7 psi.
( c ) Slrcsscs clue Itr wind I t r i ~ t lis 5K22 psi.
Iloc.; h i s piping systcnl mect the slrcss cri!cri;b lor ANSI 113 i . 3 cc~lc'?
FIGURE 4.9
Axial ftjrre in restrained piping
ANSI 853 l . I - 18b,N(B. Power Piping C'tdc.
ANSI 113 1 3- l O U 0 . C'l~emicalPlant and Pe~rokumRclinery Piping C'twlc.
I , ANSI l)l 1.4- I V7.4. Liqrtid 'l'ranrp>rlalitrnPiping Ctdc.
4. ANSI H? I .X. I)()1'. (ias 'l'ransmissitrn 'l'ranspctrtation Piping. C'c~le.
5 . ASMI:. Scctron 141. Nuclear Comptrncnl.; ('tnlc.
kfi~rkl.Arc "I'rliguc 'I'esls trl Piping ( ' c ~ ~ ~ n c n l7ians.
s , " ASME, Val. ?4(3), pp. 217-3113
ir
!April 1V)52!.
7 KtKT;ih~,,ph. I:. ('. "l3ltect of lntcrnal Pressure o n I..lexibility and SlF on C'urwcd Pip,'"
lolrnrul crf Appltc.d Mt.c.hanirt.Val!. 24; 'l'rans ASME, Vt.rl. 70 ( M a y 1957).
K . R(;rchacck,S."llcsign and Operation trl a 1-argc Diameter Steam Linc at Onlario Hydro's
Ortrcc N~~rlcar
Powcr I~evclopmen#,"
ASME. 78-PVP-86.
CHAPTER FIVE
FIGURE 5.1
Symnelrical Imp
EXPANSION LOOPS AND
EXPANSION JOINTS
:
A s c1;scsibcal earlier i n Chapter t Jwo ticviccs uscd t o i c t ~ p r c i vthe
~ llcxihilityrrf
pipiujg are cxpitnsion loops and expansion joints. '!.his ehijptcr will rlcirl with
the?;#: t w o topies in more derail.
EXPANSfON LOOPS
L-qjps provide lhc ncccssary k g t j f piping in a perpcrltlic~I;~r<lircctioit 80
absotb the thcrnral cxpi~tlsion.'8'hey
sitfcr when c o n i p i ~ r u dwith cxp;rr~sion
j ~ ~ i n abur
? , lakc mctre .;paw. Expansion loops miry hc symn~ctrical(Fig. 5. l ) o r
nonsymrncrrical (Fig. 5.2). Symmelrical loops arc advi~nt;~gcousto tlse
hecausc Bcg B-I (Fig. 5.11 is used cfliciently lo iihsorh :rrr cclui~litntottrjt of
cxpnr\sion Brunt b o t h directions. I ' h e bend lerrglh L1 is given by:
Sometimes nonsymmetrical Inops are used to utilize lhc cxisfing support
steel ilg to iocatc Ihc loclp at road crossings. Vertical direction supports are
provided to support the gravity weight at the ceiculi~tedspan as discussed i n
Chapter 3. Horizontal l w p s (bend length either Flat o r horizontal) would need
a few more supprrts when compared w i t h vertical loops i n the hend length
portion, as shown by supports S,Sl i n Figure 5.7. 'The optimum ratio of height
per width can be estimated and used.
When several piping loops are laid side h y side o n a pipe rack, the size of the
loop including the ratio height per width may be modified it) lay the loops one
inside the orher as shown in Figure 3.3. B ~ Jthe
I final size of each l o o p (bend
length) must k larger than the calculated k n d length.
Holler and earper lincs are placed o u ~ s i d cas o u l w Ioops hcc;~usctlic I6)nger
height H is needed, Smallcr lines with lower tcmpcrnlures are pl:tr.ctl ac irl.;itIr
Itrctps, lI)c.c;tusc !hi.; loop ;~rr;lngcment m;ry change the entire pipe rack layout,
i s arlvisithlc 10 cstimatc the loop's sizes w i t h simplified caDculations or
rbontog~;"plas
(Fig. 5 . I?)
itt early stages of the project. Guides o n h ~ t sides
h
of
lltc loop, s l ~ o w nits (it and (i,i n Figure 5.3, arc in~portm"lor proper
fl~nciic)ningOF $oops hcc;ktrse guicles direct the expansion into the hend El
;tlong ~ h ;&xis
c of the pipe. wliich avoids sirifring the lines sidewitys. A practical
p ~ ~ " l i conl t~c n cncounfcrcd is interference when suffrcicnl gap was not
provitlctl Ft?rill the design. T l i c gap, alter considering insulation o n h l h Oines,
sht~rtldhe Iitrger litan the tliflereritial expansion at elhows El and E2 as shown
i n Figure 5.4. To avoid interference, gap > f a x 2 - Ax I),
where A x 2 and Ax I
itrc expansions occurring i n the same direction at the same time.
Scc Izigurc 5.4 showing gap requirement and ;\!so thc considering of
ittsrrlirtion.
C'atltic~nshotlld hc exercised i n calculating the dilferenlial expansion if the
inner loop is no! opcr;tlittg and is at 70°F. I n this case, the actual gap is less as
shown i n Figure 5.5. Figure 5.ha shows that without guides the l o o p expansion
is not directed properly. Figure 3.6b shows that the pipe occupies (known as
snakes) space needed for future piping layour. T h i s figure demonstrates the
neccssity for guides.
FIGIIRE 5.3
ayour in plan of many hc~rironta!Impc
it
Insulatton
FlGUWE 5.8 Verlical Imp%a8 road crossings
I
FIGURE 5.4 Ciap rcquircmcnr with hotR lines h o ~ .
Gap
'I'I~rcc-dirncnsioni11
loops (Fig. 5.7) are widely used hecause this arrangshfoek the routing of low temperature line?;under !he Imp. The
~r\tritlritincr I~eighris irhoul 3 F l . 'l'he loilp bend length L? is illso taken here as
1. = W + 211 wilhout giving credit for the two raisers.
Vcrticitl ittops itre placed at road crossings and somerimes are nonsym~ ~ \ c r r i c . i ~ loc;lled
lly
due lo the Itjcarion of the road. Vertical guides may he
rtcsen?;;try 8%) keep Ihc lit?evertical as shown in Figure 5.8.
I ~ ~ Ctlocs
I I ~ t10t
FlGURE 5.S
Stresses and Lo@* in Loops
~"equiremcnr.rllner t r r rrn;~lleritwtp is
no1 operaring
(';ilcol;tlion of stress and ltrads in loops by the M, W. Kellngg method
(reference 3 in Chapter I ) follows.
( n l S~ngleloop
( h ) Pipe rack plan
FaGURE 5.6 ( a l Need lor guides lo ctrntrol the direction of dcncction (h) Pipe rack with and
without ew3ugh ~uides.
( i i v c n ;a Ioop trl 7(1 111. O i l X in. tilick AS'B'M A- 135, Grade A pipe. K , L is
5 0 ft. ('s~~itlcs
:Ire loc:~tccl10 I t 0 1 1 either sitlc of the loop, so !hut t = 4(11t. Thc
tliscitnrr I3clwcerr ;~rrchorsA' and D' is I00 I s (Fig. 5~9).
The line temperalure in
475°F ;art<! is t~scdFor oil piping. Firlcl
lit)
'!'he rcciuirecl height r ~ Kl 2 L itntJ
'l'hc lorccs ilctiti~it1 points A' irnd B'and IRe mcPmencs acring at point?;
A ;\nd 13.
$vmmrfrlctr( e~ponriont*
(e
l h r r m d LapcJcrr
kwd
FIGURE 5.9 Stress and loads in s svm1~
r
\
.,-I
'rhe unit linear thermal expansion for c a r h o steel ;,g JZ.,,
n.1130 in.!fl;
= 1f)f) 0 . 0 = 3 in. .$A = !'),8Y() psi (ignf,ringc<,depcr,nir\,,,
lo exclude longiludinal joint eficiency):
Enter in Figure 5. I0 with 0.0571
-.
Read over lo the curve representing K , = (I ilnd ~
which is 0 . 3 2 KzL is fherclore 40 x 11..32 = I 2.80
(h)
monlcnt
Of
O W I(,
Q
[he v;,l,,e
inerlir for 2 0 in. 01) x 1 i,, thick pipe =. , 4 5 7
,I,
K,
;,,,.I
The nf?mf?yraphpresented as Figure 5 . I 2 may he ,led f<jcstimnge,he size
the e ~ ~ a n loop.
~ i ~Out
~ nof the hjur arrangements of single-plase expansiclo
loopr
type A is popular due the ease in bhricalicrn using standard
andrtraighg pipe iengths. Other arrangements require pipe hending (I,
a specific configuration.
In arriving a @the nomograph, the following were assumed:
The formula used is the guided cantilever formula given by Eq. 1 . 3 .
Leg required:
FlGURE 3.10 Design of loops using M.VV. K e l l o g ~chart.
&I
ion 4k.
I..
-
I Moment of inertia of p i p , in,#.
BI, -. Elcl)nneion from AQlo B', in.
Vllue lo!
used 29 X 106 p i ,
-
F = F~rrre,Ib.
= R l f ~ t ~ ~ aIt-lb.
ir,
First ntillst.ril+trlcnotcu direction.
Seclttd R I I I ! I ( ' F ~ J I ~ r!t!l~O~~x
tw,tli~n.
Sigtw are Illlt~euf ft~rccstrr iltrttnerrts nrling
dl
,
K.
2
I
FlGURE 5.12
where
Nomograph to determine Imp size.
& = 20,000 psi
E = 2%
1 Ioh psi
d = expansion to be absorbgd by the loop, inches
D = nominal diameter, inches (Note that Eq. 8.3 uses outside
diamcrer)
& = Distance between guides, f t
L,= Distance between anchors, f r
L2 = Bend length required lo absorb expansion, I r
Kit
R C U I E 3.18
Moments and lotre. in a loop using M. W I(e!lngg chart.
1- Find the size of the Imp to absorbexpansionin 2W tr of B 2 in. c e r h n slccl
pipe at 4 0 ° F . Assume height to width ratio.
Total expansion = 2(30(0.027)= 5.4 in.
'
X,
,.t,r
FlGURE 5.13 Eslimaled loop size using nomograph,
3 lma
"dL,
i
'5.
'v
KI = 0.5 and K 2 = 0.5. from Figure S.IU, read L'S~IIO DA as 0.03
Deflection h = 200(0.0316) = 6.32 in.
OD = 6.625 in.
11.03( 10') 0 A
SIFCSS= S = -
Using the nomograph and assuming a siraight line starling from a 12 in
diameter and through a 5.4 in. expansion, read hcnd letlgrh L2 as 5 0 11
Assume N W ,then L2 = 2 ) 1 + I%/ = 5 0 f f . Thu'i I I = W = 17 I!, making k 2 = 51 ft.
By calculation
-
= 785t) psi
Motnenrs and fircos
"The estimated Isop size Is given in Figure 5. i3.
2. Crsing the Kellogg method, calculate stress, force, and moment in the
,J
I
expansion lotjpslrown in Figure 5.14. Thc pipe diameter is (3 in. sch 40, the
tempcralure i s 450°F and has carbon steel piping. Use Figures 5. I0 and
5.1 1 to arrive a t thc solution. This problem is the same lor which results
wcre presenred in Chapter I , Table 1.3. Were thc prohlcm is solved step by
step.
'The expansion coelficienl lor carbon steel at 450°F = 0.0316 in./ft
(Appendix A l )
W
conslant K , = - =
widrh
20
= 0.5
I- guide distance = 40
K ~ =H- =
height
- -2=0
L guide distance 4 0 u.5
n G U R E 5-14 Stres and loads cslculetion using Kellogg metltcla
Using Figuw 5.1 1 , read:
'
A , = 0.2 1
where K = i1.5
A, = 0.5
K z = 0.5
I = 28.14 in.'
b
SINGLE EXPANSION JOINT
UNIVERSAL PRESSURE BAMNCEO
p.
FlGUEPE 5.15 Coordinate used.
EXPANSION JOINT
WITH INTERMEDIATE ANCHOR
PRESSURE BALANCED
HINGED EXPANSION JOINT
EXPANSION JOINT
Nore: First subscript denotes direction; second subscript denc~tes
location. Signs are those of forces and momeclls acting on anchors (see
Fig. 5. 5 ) .
SINGLE EXPANSION JQiNT
WITH TiE RODS
1.1 1984expansion joints were itllrjwed is nuclear piirit~gdcsigo except it)r ih$
PbSMESection I I I , Nuclear Class I Code. Suhsectiotl NIi-.lh7 I . Z 51;1(cstIii11
erpansion joints are nt9t allowed in Clils~1 NI% tl~clcilrct~rnponcntrP ~ I ~ I
at:cidentr with expansion join! inst;~ll;~titbns
are of conccra fnjm ;I s;~letypoint
01 view. Expansion joints are used r t l i~hsorhirxial c c ~ n ~ p r c s s or
i o ~cxtcnsion
~
Iillerill nlfsel a f ~ angular
d
roliltirhn. As per st;tnd;&rds01 the L:xpitn~i{,n J8,inf
M;~nulactures(reference I ) , forsior~;tlrtrti~tit)nsllottld hc avoided otl 1l1e
bellows kcause torque produces high stress levels it1 hciiows.
! Expansion joints can be broadly classified as sliding and flexihle. 'l.l~ercis ;r
relative motion of adjacent parts in the case 01 stipping jrlints. Slip jalints.
)r;vel joints, and hall pjintr arc grouped tinder sliding joints. Dresser coupling
and Yictaulic couplings are a few twde nanlcs of ylinls of this type. Slidil~g
joints are BISO known as packed joints hcciruse packing to ccjntain internill
pmessure without Beakage is necessary. Flexible expansitrn joinrs may he furthcr
divided inlo bellows joints, metal hose. and cornlgafed pipe (rr.fcrcnccs 2
and 3).
The h~llowiagare terms i15ed in the design and specification of expilnsi(~n
joints (see Fig. 4.16 lor symlx,ls used for some nl the lerms):
Again Arrclrrrr: A main anchor must k designed to withstand the lorees and
mtanients imposed upon it by each of the pipe sections I(?which the anchor is
attached. In the care of a pipe section containing an expansion join^, kyrces and
mon~enlswill consist of the thrust due 80 pressure IEq. 5.4). the k ~ r c erequired
to deflect the expansion joint (Eq. 5.5). and the Riclional forces due lo pipe
alignment guides and supports. When a main anchor is installed at the change
ofdirectinn o l ROW, the eRecl at the elbow of the cenirilugttl thrust due 60 flow
(Eq. 5.61must also Re considered.
lntcrmrdiafr Anchor: An intermediate anchc~rdivider a pipe line intt)
individual expanding pipe sections, each of which i s made flexible through the
use of one or more expansion joints.
UNIVERSAL f XPANS1ON JOINT
WITH OVERALL TIE RODS
DIRECTIONAL INTERMEDIATE
ANCHOR WITH GUlOE
UNIVERSAL EXPANSION JOINT
WITH SNORT TIE RODS
MAIN ANCHOR
SIDE VIEW
END VIEW
PLANAR PlPE ALIGNMENT GUIDE
OIRECTIONAL
MAlN ANCHOR
SPRlNG SUPPORT
INTERMEDIATE
ANCHOR
5s
PlPE ALIGNMENT
F
FrGURE 5.15
GUIDE
Tygxa of expansion joints (standards of she Expansion Joint MsnoBacaures
Association).
Dirnfisnol A ~ c h n r : A directional anchor or sliding anchor is one designed
lo absarh loading in one direction while permilling motion in another
direction.
Bellnw.r: Tile flexible element of an expansion joint consists of one or more
eorrugationc and the tangents, if any.
t
o e # l h ; , ~ a @ r i a l :A list o f metal
Bellows material
304 stainless steel
3 16 stainless sieel
32 8 s!ainless steel
34"ir~tainless steel
N i c k e l 200
Wlonel 4 t h )
bellows materials is given below:
\
Temperartire Range "F
(specified b y ASME Section VI!!)
~ : ~ u a l i z i norgReinlnrcing Rings: These help t o reinforce the elbows against
,ntemal pressure and help t o maintain the desired s h a p of i h c elbows.
(itride$: Guider; are i m p r t a n l parts o f expansion joint p r f o r m a n c e ,
-300 l o 740
-3l)tl to -750
- 304)
i5OI)
--300 to I 4 0 0
-300 14) t?OO
-300 t o YIIO
TYPES OF EXPANSION JBINlfS (BBB Fig. 5.l@)
EXI*ANSION
JOINT: 'rhe sin~plestf o r m of expansion joint, o f single
I?eIIt)wr;constructicln, designed to absorb all of the movement of the p i v
section in which i t is installed.
\ ) o r i ~ i lF. EXI*ANSION
JOINT: A double expansion joint consists o f t w o klBowa
joined h y a c o m m o n connector which ii anchored tosome r i g i d part o f the
irrstaIlaticln by means of an anchor Rase. T h e anchor base m a y be attached
tllc c o m m o m connector eilher at installation o r ar time n
E manufacture.
Each hellowsacts as a single expansion joint and absorbs the movement o l
the pipe section i n which it is installed independet~tlyof the other beliowr.
Dotllrle cxp:lnsion joints should n o t be confused w i t h universal expansion
joints.
INII.WNI\I.I.V
C i t ~ t l > l : ~EXPANSION
)
JOIN^: A n internally guided expansion joint
is d e s b n c d in provide axial guiding within the expansion joint by
incorporating a heavy telescoping internal guide sleeve, w i t h or without
the use of heitring rings. (Flore: T h e use o l a n internally guided expansion
joint doer not eliminate the necessity 01 using adequate external pipe
guidut;.)
U ~ t v r : ~ c nEXI~ANSION
l
Jclf~r.: A universai expansion joint contains two
beltr~wsb y a c o m m o n connector f o r the p u r p s e o f absorbing any
cornhit~;ttion of the three hasic movements, that is, axial movement,
Iirtcrir! deflection, and angular rotation, Universal expansion joints are
ttsuiilly furnished w i t h l i m i t rods to distribute the m o v e m e l t between the
IWO ~CII~IWS
of the expansion joint and stabilize the c o m m o n connector.
'I-his definition docs not imply that only a double bellows expansion joint
can absnrh universal movement.
SIIJ(;II
I#,
Squlrn~in a B e l b w s Explnricrn Joini: A tern, e m p l l ~ y c di t , clcal,lr i h c
t9ccurreflce of inslability due In internal pressuru ;III~
is predt,nlinittcly
assa~ciatcdwith joints OF 2 0 in. dianleter or sm;rllcr.
F
~
~fl a~n t pha t l si i o n~lvinf:
~ ~This can he igtcreasud try ilgjnarr ~lclll,ws
(ma\:t still he
wilhsl;~nd the pressire). i~xcrci~se
i n tjumt~erg j f hellljws,
ane%y multiple k l l o w s .
Erlerllnl Cover: A cover used t o protect the exterior c ~ fthc hcllt,ws fntm
foreign objects, especially when the joim is buried undergnnind,
Infcm;bi liner o r slecve is used for the h)lltrwinp:
2
where f l o ~
~elfbciliesare high (for stc;lnj lines whe~,v e l ~ l c i t yC I ~ L . C ~ S
- fiMMffiminlill. o f diameter i n lines upto 6 - i n sixe)
3. when abrasive materials are presenr
4. !hen rhere is reverse o r turhulcrt! flow
5, for all hifi temperacure applications
6. for 318 copper elbows
W h e n lateral dellecth>no r rotalion ir present. the liner must he sulficicnlly
smaller in diameter 80 provide the necessary clearance.
Tie Rods: These are mdr o r bar devices l o r the purpose o f restraining the
expansion joint f r o m the thrust due to internal pressure. T h e numher and sire
o f the rods depend u p o n the magnitude o f thrust force. Tie rods may also act as
deflection limit rods.
EXI'ANSION
JOIN.I : A hinged expansion joint containsone k l l o w s and
is designed 1 0 permit angular rotation i n one plane o n l y b y the use of a pair
111 pins i h m u g h hinge plates attached t o the expansion joint ends. T h e
hinges and hinge pins must h e designed t o restrain the thrust o f the
expansion join8 due t o internal pressure and extraneous forcer. where
applicable. H i n g e d expansion joints should k used in sets ol two or three
t o luncric~nproperly.
SWIN('I EXPANSION
Jcfl~r: Pb swing expansion joint is designed t o a h o r b !atera!
!il~(il.f)
deflection and/or angular rotation in one plane. Pressure t h r u d and
extranectus forces are restrained b y the use o f a pair o f swing bars. each of
wlticti i s pinnetl to the expatlsictn joint ends.
.
-,clees
1
(1%
E x a h ~ s l oJOIW:
~
A gimbal expansion joint is designed Lo permit
angular rotation in any plane by the use of two pairs of hinges affxed to a
common floating gimbal ring. ~ h gimbail
d
ring, hinges, and pins must be
designed Is restrain the thrust of the expansion joint due to internal
pressure and extraneous forces, where applicable.
PRHSUREBALANCED
EXPANSION
JOIKI: A pressure balanced expansion joint
is designed to absorb axial movement and/or lateral deflection while
restraining the pressure thrust by means of lie devices interconnecting the
Bow hilows with an opposed kllows also subjected lo line pressure. This
I y p of expansion joint is normally used where a change of direction
wcrrrs in a run of piping. The Row end of a pressure balanced expansion
joint sometimes contains two bellows separated by a common connector,
in which care i t is called a universal pressure balanced expansion join^.
GlMb. ,L
.I
4 ,
'
7
anchor force should include pressure thrust, centrifugal thrust, friction at
supprts and guides, and force to compress the bllovvs.
using the EJMA [relerence I ) equarion, calculate hydrostatic examination
t e a pressure if the design pressure is 125 psig and design temperature is 5WF.
The bellows material is c a r b n steel ASTM A53 Grade
?'he test pressure is: (using Eq. 2.7)
EZ.
where Pd = design pRssure = 125 psig *
$ = allowable stress of bellows material at test pressure (70"R =
20,000 psi ( S , from Appndix A3)
Sd = allowable stress of bellows material at design :ernprmlure of
Sl)(FF
= 18,"J)fIpsi (Sk from Appendix A3)
PRESSURE THRUST FORCE
Tile static thrust Fsdue to internal pressure is given by Eq. 5.4:
8,
i
'
where a = eflective area corresponding lo #he mean diameter of the corrugations, sq in.
p =design line pressure based on most severe condition, psi
~ ' h force
e
required lo campress the expansion joint in the axial direction F.. is:
Fm = (axial spring consranr)(amounr of compression)
(5.5)
The centrifugal thrust l$ at the elbow due to flow is given by:
2ApV2 @
Ffl = -sin
8
wilere A = internal area of pipe, sq in.
p = density of fluid, Ib/lt3
V = velocity of Flow, ftlsec
g = acceleration due to gravity = 32.2 Fr/sec2
8 =. angfe of k n d
Figure 5.17 shows the elbow where a main anchor is located. The design
i
R G U R E 5.17 Anchor lorce
anchor
st
eibnw.
I, (a) Size the expansion loop for the lollowing conditions:
Diameter = 16 in. standard weight
Material = A53 Grade A
= 220 I t
Distance between anchors
80Ib
Vlltllt of pipe length
Span
=
25 ft
Temperature = 750°F
(b) Calculate the force at anchcars lor shoes with Tenon slide plate.
( e ) Calculate the force st guides.
-
(a) Design ths expansion imp, by equation, with i m p height lo width
ratio as I .
Distance between anchors = 225 ft
Ternpralure = 800°F Span = 20 Et
Diameter -. 12 in. standard weight
Material =; A53 Grade B
(h) Calculate the force st anchors for shcres with steel on steel.
(c) Calculate the force at guides.
3. (a) CalmDale the thermal expansion at A and B in the piping system
given in Fieure 5 18. Material 4106 CIr~deR p t 75F".
L
f
.
t
hi
r
- Ex,
I,
Joe,
\
10 f t
js
mGURE J.ZZ
FIGURE 5.18
bop.
7. Size an expansion loop based on the following conditions: a 12 in, A53
Grade B sch 40 pipe; temperature is 350°F. Imp width is 8 It; and length
of p i p is 1 80 ft
8.
Number of loops
FIGURE 3.19 N u m k r a l Imps
(b) Which of the following is advantageous to use: ( I ) symmrlrical
expansion Imp? (2) unsymmetrical expansion loop?
4. The dimension of an expansion loop is limited as shown in Figt~re5. I 9 If
a pipe has a temperature of 6S0°F, how many expansion lnops are
required lor 500 11 long pipe?
5.
11a line is anchored at both ends, but anchors have thermal movement as
shown in Figure 5.20, what is the sire of the loop? It is 4 in. sch 80. A53
Grade L) carbon steel pipe at 350°F.
6. A 6 in. diameter loop has standard sch A53 Grade B pipe with operating
temprelure 375°F.
For loop sbown in Figure 5.2 I: (a) find resultant b r c e F at anchors;
(b) find moment M at anchors.
lilGURE 5.20 Loop size.
FIGURE J.ZI
Laop
Expansion joint.
From manufacturer's catalog find overall length of Reriblt hose needed
for klrf in. oflset deRection for a 6 in. internal diameter hose. Assume type
of end connection.
9. A 12 in. diameter carbon steel standard weight p i p is at 525°F. Design
pressure is 180 psig. Wit11 a single bellows expansion joint in Lke piping
system in Figure 5.22, calculate forces at nozzle and anchor.
The mean area of convolution is 151 sq in.; the axial spring rate is
882 Ih/in.
LO. A 4 0 in. diameter turbine exhaust duct system is fabricated of in. well
c a r h n steel and operates at Full vacuum at 320°F. The movement at the
turbine exhaust flange and the condenser inlet are determined as shown
in Figure 5.23. A universal pressure-balanced expansion joint is located
between two piecesol equipment with the dimensions as shown in Figure
5.23. Determine the forces and moments due to the bellows sliFTness at
the condenser and turbine connections. The data provided by the
expansion joint manufacturer are as follows:
Mean diameter ol bellows d, = 42 in.
Working spring rate f,, = 32,000 Iblin.lconvolulinn
Number of convolutions Row bellows Nf = 6 + 5
Number of convolutions balancing &!lows Nb = 6
ExpansIan Loops and Expansion Jalnbr
--
CHAPTER S I X
FLANGED JOINTS
CiliGURE 5.24 Single bellows expansion join!.
11, A single &!low expansion joint is placed in a 2 0 in. diameier c a r h n steel
pipe: tlral runs between anchors A, El, C. Anchor point B is actually a
directional guide that restricts only the axial movement. The lirle is
operating at 150 psig and 550°F. Pipe lengths are shown in Figure 5.24.
What are the forces and moments acting a# A, B, C? The data provided
by the expansion joint manufacturer are:
Eflccrive area corresponding lo kllows mean diameter = 480 in.'
Mean diameter d, = 2 1.5 in.
Working spring rate 1, = 24,8tN) Ib/in./convolution
Beliows tree rengrh = 12 in.
,
Number of convolutions N = 12
ti
B
REFERENCES
1. Expansion Joint Manufacturers Association 1973 Addenda lo Sgandards of EJMA. 3rd ed.,
1969.
2. R a k t t IL. Benson, Chemetron Corp. "A Basic to Analyzing Piping nexibili~y,"(Xcmiral
Engineering (&l. 23, 1973).
3. Engineeringdare on expansion joints are available from (company or lrade name): Pathway,
~ e x a o i c sAdxo,
,
Solar, Anaconda,Temp. Fex. Tube lurns, &Ilea Brtls.. and Metal Bellows.
f:langes are used to join sections of pipe Pcngrhs and to connect piping to
eciuipmcnts. Two main types of flanges are flat face and raised face. in pipe
\tress analysis, the capability of a flange to carry external moment is given
impclrtance. The actual design of flanged joints can be obtained from other
sources (references 1 and 2).
The eflecls of bolt preload, pressure, temperature, and external moments
are cliscussed below.
I30lr Preload: The initial tightening of the Rolr is a prestressing operation.
-The amount of initial h i t stress developed should bc enough to provide
against a!\ conditions that rend to produce a leaking joint and at the same time
not so cxcessive that the yielding of the b l l s or nanges can produce relaxation
that can also result in leakage. For the joint to be light under hydrostatic (one
and hall times the design pressure) pressure, an initial Roil stress higher than
the design stress value may be allowed.
K
7
S
I
Internal Pressure: When internal pressure is applied, further yielding of b
rnay cause reakage if the margin between initial bolt stress and yield strength Is
less.
External Pressure: The combined force of external bending moment and I-loll
loading rnay plastically deform certain gaskeb that result in loss of gasket
pressure when the connection is depressurized.
I'ernprature:
lncrease in temperature reduces the pressure to which the
flange can be subjected. At elevated temperatures, the design stress values are
governed by creep rate. If the coeRclent of thermal expansion Is digerent
(diflerent material) for Wange and b i t s , leakage rnay occur due to increme in
boll load. Then retightening of the bolt may be necessary, but it must not bc
forgotten that the eflects of rewsred retightening can be curnuiarlve and may
,,,ccssitate the removal of the cornpnent from service For inspection or repair
(,I
damage to the component or support.
f
S, yield stress of flange malerial, psi
@ $oil circle diameter of flange, inches
Ab total cross-sectional area of bolts at root of thread, sq in.
Do outside diameter of flange raised lace
PW pressure concrlrrent with bending moment under dynamic loading
hi: diameter of location of gasket load reaction, inches (can be
approximated by inside diameter of flange raised face)
S allowable bolt stress, psi
Units: moments It-lb
stress
psi
ODE opraling basis earthquake
SSE safety shutdown earthquake
SAM sesimic anchor rnovernent
Faulted condition is associated with SSE or pipe break. I t i s an extremely
low probability event.
LOCA b s s of coolant accident. The result would be an irledvertent
o p n i n g of the pressurized safety or relief valve because of the loss of coolant
in excess of the capacity of the reactor coolant make up system.
GOMPARlSOlBI OF ALLOWABLE ANT) ACTUAL MOMEMS
Method 1: (high strength bolting option) the design limits and sewice level
(irnits A and B are:
S,i36,000 should nor be greater than unity.
As can be seen, the results of Eq. 6.2 wili be t w o limes that of Eq. 6.1.
The design limits and service level limits C and D (faulted) are:
EXTERNAL MOMEWS
The eRecr of external moments wil! be discussed in detail. The allowable
moments can k calirdlaieci by :he three methods outlined hy ASME Section
111, NucDear Power Plants Components Code NC-3658.
ilgerhod I: This refers lo ANSI 816.5 Ranged joints with high strength
bolting (bolt material with allowabie stress at 100°1; not less than 20,000psi).
In method 2: (For flanges at moderate pressures and temperatures)
(a) For service ievels A and B under slatic loads give.n by Eq. 6.1
(b) B"or service levels A and B under slatic and dynamic loads in Eq. 6.2
(c) For service levels C and D under static and dynamic loads in Eq. 6.3
Merhad 2: This method concerns standard flanged joints at moderate
pressures and temperafures in ANSI 13 16.5, MSS SP-44, API 605 standards
(pmssue less than 100psi and temprature less than 200°F).
In method 3: (equivalent pressure method)
Method 3: This is the equivalent pressure method.
Levels A and 113 service limits must be satisfied for all loadings identified in
the design specification in the pedormance of its specified service function.
The eornpnenl or support must withstand these loadings withour damage
requiring repair.
b v e l s C and D service limits permit large deformations in areas of
.
slructura! discantinuitv Ttlc.
-It - *
.
where A.l is the largest moment (actual) from Ergs, 6.7,6.8, and 6.9.
s
~ r c l r r r n - r -
a*
&)cijuallfy
the flange under this nrelhod,
P,,plus design pressure should be less lhan the rated pressure
.._,
I
6101
[~
./
750°F. However, compressed sheet askstos-confined gaskets ere
limited as to pressure provided the gasket material is suitable foe rht
temperature.
(h.6h)
Actual Mormerrls
M(normal)= M..,..,.,.,ic = higher of torsional or resullant of two bending
momenls lor gravity plus thermal normal loading, sustained
anchor movement plus relief valve thrust force and orher
mechanical sustained Ioads.
(6.7)
Mfupret) =
I
,
99793.
P i ~ ediameter = 30 in.
The OD of the flange raised face = 33.75 in.
N u m k r of bolls = 28
Total bolt area = 28(0.8898) = 24-94 sq in.
Diameter of boll circle C =: 36 im*
= higher ol torsional or resullant of two bending moments plus thermal upset plus OBE plus SAM ONE
plus LOCA
(6.8)
Mlfaulled) = M.,,..,d,,,,8c
, , u , , ~ ~ , = higher of torsirri~al crr two resultant
bending moments plus thermal upsel plus SSE plus SAM SSE
plus LOCA
(6.9)
M = greater of the a h v e three actual moments
(6.
10)
This moment will be used to pet equivalent pressure.
AS can be expected, lor approving the use of the Range a! certain locations
- 2 the actual or calculated bcnding moments must be lower than [he allowable
momenb. Table 6.1 gives the equation numbers L>r the aclual and the
calculate the allowable and acrua! k n d i n g moments and check if the
given
Range is qualified according to ASME Secrioo 111, NC-3658 (summer
"
I
I
I he flange material is c a r b n steel SAIOS
The bolt material is SA1Y3 Grade B 7
Bolt allowable stress = 25,000 psi
Flange material yield stress S, = 32,8(M)psi
Pressure raring = 150 psi
Design
" temperalure = 200°C:
Design pressure = 175 psi
Actual moments (It-lb) From piping analysis is given in Table 6.2,
The higher of the torsional moment ar resultant bending moment is
a81owsrble moments for comparison.
Garkru: Section NC-3647.5 allows only metallic or asbestos gaskets if the
expected normal service pressure exceeds 720psi or the temperature
TABLE 6.2 ~ e a u d~ o m r s l slsam Piplag A ~ Y(fa-!b)s ~
Dead weight
Thermal
OBE
OBE SAM
SSE
SSE SAM
LBCA
M ,,, ,,,,,
M ,,,
M w,u.
1,939
6,350
7,979
0
8 1,520
2,825
9,817
0
18,354
0
16,638
61
10,448
0
0
0
0
1 1,682
6,950
12,650
0
lYv646
0
0
(normal) = 1 1,682 + 6950 = 18,632 It-lb (Iron Eq. 6.7)
,,,
td
1,084
i,90 1
8,s I8
0
-
(upset) = 1 1,682 + 6950 + 12,650 = 31,282 [from Eq 6.81
(laulled) = 11,682 + 6950+ 19,646 38,278 (from E q 6.9)
1 1,682
6*950
% 2,650
0
89,646
0
0
Jt..
'.
#'
'4.
,
.bted in Table 6 . 2 Equalionr 6.7, 6.8, and 6.9 are
to calrulac total
actual moment for normal, upset, and faulted conditions.
t
ALLOWABLE MOMENTS
The ball material is S A l V Grade 0 7 alloy steel with allowable strcsi
25,OW psi.
Method I , known as high strength b l t i n g option. is used because the bolt
allowable stress is greater than 20,MH) psi at IVO°F. Thus Eqs. 6.1.6.2, and 6.3
we used to calculate allowable moments.
&farlow dynamic
(faulted) = ( l 1,250)(24,92) - 2 (11~702(1
16
"
1
Table 6.3 gives the comparison of moments of the Example Problem.
.
The effect of Range maleria!. Range rating, and Range diameter on
allowable moment shorn in Table 6.4. internal pressure at flange is 175 psi,
As can ~ x ~ c l the
e dallowable moments are higher lor larger flanges and
higher ratings. The allowable momenu for carbun steel Ranges are higher than
for stainless steel flanges because yield stress (used in high strength bolting
option) for c a r b n sfeel is higher. The yield sfrength (or carbon steel is
3 2 8 W ~ s as
i compared with 2I,1W psi for stainless steel at 200°F.
I. ASME !kc. ill. Div. I code "N~iclearPow9 Plant Components." Article XI-JO(tO.
CHAPTER SEVEN
2. ASME Scc. VIE!, Div. I code. "Design of Ranged Joints," Apgendix 11.
1. ASME S I C I!!. Diu. I code. "Nuclear Power Plant Components." sulnec~ionNC-3M8
(summer 9 979).
""Range Qualification Program," Tsnncssce Valley Aurhoriry.
5. ANSI B 16.5. "'Steel P i p flanges and Ranged Filiings" ( 1 977).
6 API 605. ReaArmed in 1973. "Large Diameter Carh,n Steel Ranger *'
4.
PIPING CONNECTED TO
NONROTATING EQUIPMENT
The external loads imposed on nonrotaling equipment by piping should be
h l o w the allowable loads supplied by equipment manufacturers. Examples
of nonfired equiprnents are hear exchangers, tanks, pressure vessels, drums,
air coolers, and condensers. Examples of fired vessels are b i l e r s and fires
healers.
The actual forces and moments from piping stress analysis may $a: sent to
manufacturers to gel these loads approved.
.The methods lo calculate local stresses on the vessel and nozzle intersect iota arc:
I. Finite clement analysis that is more accurate but could be expnsive
lor ctrrnpuler resources.
Local stress calculation outlined hy Welding Research Council
(WRC) bulletin 107 (reference I).
3. Local stress calculations using Fliigge-Conrad solu!ions (relerence 2).
4. W R C bulletin 297, (reference 8) Local Stress in Cylindrical Shells,
supplement lo W R C bulletin 107.
2.
For each piece of eqt.ipmenl, applicable code and standard requirements
should be satisfied, Instead of reprinting text information available from
other sources, a discussion with specific examples lor cylindrical and spherical vcssels is presented here. .
LQGAL STRESS GALGULCaTIOM USiCIIO W G "107 BULLWIN
Based on work done by Bijlaard, W R C IOWwas prepared. Sign conventions
used are exactly as given in the bulletin.
8.
Vessel (cylindrical) diameter to vessel thickness tatio range is
80%DIT 600.
I
2. Nozzle diameter to vessel diameter ratio range is 0.02 5 d/D s 0.57.
3. Ncaazle thickness is nor considered For cylindrical vessel.
4. Nondirnensional constants read From curve From W R C 109 bulletin
are for acceptable ranges only. Extensions of curves can he used only
if aliiowed. Values outside the range may give unconservative resulls.
5. March 1979 revision of the bulletin gives important revisions.
Earlier versions should Re carefully used.
6. Signs lor stress were obtained by considering the deflection of shell
resulting from the various modes of loadings. Tensile stress is
masked as + and compressive stress is marked as -.
7 . Maximum shear theory has k e n used to delcrmine stress intensity,
8. Welding Research Council 107 omits rhe internal pressure stress.
The sflecl of pressure may be included if desired.
9. The stresses calculated are in the vessel wall (shell) an&nof in the
nozzle. Stresses may be higher in the nozzle wall in case the nozzle
r~peningis not reinforced.
1 0 , Welding Research Corbncil 107 method may be used for ellipsoidal
Reads as well as cylindrical and spherical shells.
I I. Stresses due to radial load in cylindrical shells are not applicable if
the length of the cylinder is less than its radius. The curves are for
length radius ratio of 8.
82. Stresses due to external moment are not applicable if the attachment
is located within rhe distance of hail the shell radius from the .near
end of the wali.
Table 7.1 gives stress concentration factors K, and K b . The equations for
calculaling the stress concentration factors K. and K , are given in Eqs. 7.1
and 7.2. Table 7.1 was generated using Eqs. 7.1 and 7.2.
The actual stress calculated is compared will1 the allowable stress. i f the
actual stress is higher, a pad thickness is assumed and the calculation is rerun
with the total thickness (sum ol vessel and pad thickness) as vessel thickness.
In practice, the assumed pad thickness is equal to the vesse! thickness. If
double the thickness is not enough, efiorrs may k made to reduce the
loadings a n the vessel.
w(,cre r = radius used for nozzle-to-shell interlace (in.) and
~\c..;s
T = shell thick-
(in.).
TABLE 7.1 Conrenlmallon Fsrlom
(Besed on :-in. rrrdius at skit-lo-mzzle inler(rce9
T tin.)
>
I4
I
lh
;
K,
Ko
1.5121
1.5661
1.6574
1.2899
9.3280
6.3650
1. Calculate the local stress lor the cylindrical vrrsrl given as. follows
(reference 1):
Vessel radius = R, = 72 in.
Vessel thickness T = 0.4375 in.
Attachment radius r, = 3.125 in.
Geometric parameters are:
' s.rP.--nCerh..-.~dn fa~autrare l o r the membrane load K
the knding load & = IJJ.
The applied loads are:
I
Radial load F = -97.8 16
-.
crrcrllar moment Rb, = -968 in.-[b
Longitudinal moment M, = - 10,152
Torsional moment M, = 3 1.368
Shear road V, = -4
Shear load V , = -45 1
2. Calculate local stress lor the spherical vessel given akAllowr:
Vessel rnean radius = 16'7.43in.
The nondimensional constants read fmm graphs of WRC 107
are:
WRC 107
Graph
Vessei thickness
=: 1.125
Nozzlethickness
=0.5
Nozzle rnean radius = 11.75
Nozzle outside radius = 12
The applied roads are:
= p = 1377 ib
Radial load
= V ,-- 97
Shear load
Shear load
= 0/, -36
Overturning moment = M I= - 0 58,808 in.-lb
Overturning moment = M2= -47,996
Torsional moment = MT =. - 10,344
The concentralion factors are: K, 2.0 and Kg = 2.0,
The geometric parameters are:,
-
-;
Nondirnensional constants Iron; W R C 107 graphs are as follows:
In an eFTorr lo extend WRC: 107 results lo larger DIT and smaller dlD
valves and lo include the effect of the nozzle thickness, calculation using
FlGgge-Conrad solutions is presented (reference 21.
WRC Bulletin 297 (reference 8) broadens the coverage of WRC Bulletin
107 and is based on Steele" theory (relerence 2). WRC 297 includes the
L
<
"8
--.w
T
MI = 158.1308 in. lb
A9, r -49,976 in. Ib
1.125
'~~"-%3-
2.
5
ve~sclma
e tfic
e
-
0.875
1
T = 1.125 In.
& -* 167.43 111.
-P
M u s
e ouui& d i m
r
"
(
0.5 in.
11.75 in.
re = 12 in.
r,,
a
n l g e m d l y for sunrmrrlon d o,
A
T.
-a
JKrClU
Comenuar~onI=actos4due to:
i
memer;line load, K, = 2.0
knrxling load, K, = 2.0
-9406
8440
8083
-7714
-11.084
9931 4
9760
-8713
-
I
d
.
A
at,
b
.i
mb
'
onsl
I
As a conservative approach, vessel no~2lesare considered rigid in pipe sfre$,
calculations. However. the vessel or drum has inherent flexibility that can
advantageously used to obtain tower and more realistic external momen,,
Out of three primary forces and three primary momenls thal may he applied
lo the shell at a noule, only radial force and two moments are considered
significant in carrsing shell deflection. Rotations of elastic ends are usualit
more significant than translations. Therefore elastic translations of noules and
thus radial Flexibility is ignored.
Inplane and outplane spring rates are imporlant. in a cylindrical vessel, !he
inplane spring rate corresponds to the longitudinal moment, and the ouIplaoc
spring rate corresponds to the circumferenlial moment. As shown in Figlla
7.1, by application of the longitudinal k n d i n g moment, che plane formed h\
vessel and nozzle centerlines remains inplane. The circumfe&ntial moment
will be the nutplane moment hecause this moment will hring nozzle axis inloor
out sf the original plane.
PlpIng Loa&
t
The point of view that using rotational spring constants result in unconservative values for bending moments should be looked into. It is known
thal the primary piping loads (weight, pressure) and its effects remain the
same in magnitude, whereas secondary loading (thermal) and its ef8ec1,
rerease: itself when the resistance reduces. An example is that, under thermal
Isading, the k n d i n g moments acting on the nozzle drops when the rotation i\
allowed. All structural systems have inherent Rexihility that is expressed a\
rotational spring rates for vessel and nozzle connections. These spring rate\
should not be used lor pump, lurbine, or compressor nozzles.
Equation "7.3 can be used to calculate rotational stiffness at the nozzle
connecticn. Equation 7.4 expresses the formula for calculating Reribilily
'
Vf-
\._/"
f,clor K . values for constant C is 0.W for the inplane and
8,u,planek n d i n g (reference 3).
M - El
----
FOR CYLlNDRlCAL VESSEL
PIGURE "I.) Vessel and male srrangernent
:yllnc
p~ e t
I
'eflect of nolzle thickness and data on nozzle Rexihility. Nozlle md vPsse,
treated as thin-walled cylindrical shells.
ROTATlONAL SPRlNG RATE
a
8
"Q
L
e is 0-27 for the
n-
DNK180
(7.3)
\vhere M = sprlng constant in.-lb/degree
(I
r\.n = hending moment, in.-ib
0 = angle of rotation, radians
of elasticity in cold condition, psi
E=
= area moment al inertia of nozzle, i n 4
DN = diameter of nozzle, inches
K = flexibility factor
[ he
f i ~ x r b t l i ffactor
~
K:
where
C = 0.09 constant for inplane bending
c = 0.27 for outplane bending
63 = diarneler of vessel, inches
7'= wall thickness of veqsel, inches
DN = diameter of nozzle, inches
TN = wall thickness of nozzle, inches
These spring rates should not Re used ifnol2le or pad diameter is greater Ihan
one third of the vessel or header diameter.
Example Problem
The following four cases are considered for calculating the spring rate:
1. Vessel nozzle (Fig. 7.2) treated as rigid
2. Using rotational stiffness lor a 48 in. diameter vessel
C ltndrtcal vessel
~iel=
l 132 In , 0 6 2 5 tn thick
n G U R E 7-2 Piping errangemen( fog spring
rate cornnericon
\
_ I
3. Using rotational stiffness for a 60 in. diameter vessel
4. Using rotational sriRness lor a,96 in. diameter vessel
II AR1.E 7.5
~ozaP
/
Moment (ft-lb)
Force (Ib)
The spring constant cafculation lor the 48 in. vessel, I in. {hick with 12.75 in
F,
~'nse
OD nozzle of thickness 0.375 in. follows:
Forces a& N60111~1111I
I V-8
;F,
E
Mx
MF
Ma
1,866
1,725
-466
9,994
9,321
7 980
2,M14
1,SsR~l
1,918
-485
The flexibility factor is:
jn
rn. dia.
in dia.
-476
-475
c)h i
a
50
-469
-476
-476
-451
The example Problem given as Figure 7.2 was selected to compare the
values of spring rates calculated here with already published results using a
slightly dinierent approach.
In the cylindrical vessel:
Shell 132 in., 0.625 in. thick
Pip@36 in,, 0.5 in. thick
E 27.9 x 10" psi
I = 8785 in."
The outplane flexibility factor is:
The spring eor~slanlis:
-
,J
I
The inplane spring constant with K , as 2.98= 3.58 x I O J in.-lhlilcg. 'The
r.juaplane spring constant with K, as 8.94 = I I W lIo4 in.-lhtdeg.
Table: "1.4 gives calculated vaiues of spring constants lor the cases
considered,
The piping stress analysis that was done For the four cases (three diNierent
vessel diameters) and the forces and moments ar the nozzle are given in 7';thle
7.5. As can be easily seen, the bending ntclmeni values in x- and y-axes have
d r o p p d when the flexibility of the vessel noale is included, say, for the 48 in.
diameter as compared lo when the flexibility is not included.
TABLE 7.4
Vessel Diameter
Longitudinal Spring Rare
(inplane)
(in.)
(in.-lbldeg.)
48
60
96
1
I
C ~ l c u l a l c dValues o l Spring Constants
358 x 1 0 '
320 x 10'
253 x 104
Circumferential Spring
Rate
(cxutplane)
(in.-lhldeg.)
119 x 1(P
107 x lo4
844 x 10"
The outptiinc spring rate is:
Tahle 7.4,gives calculated values of spring rates. The values given are for
1.72 in. x 0.625 in. thick vessel with 36 in, x 0.5 in. thick pipe. As can be seen
the values are close, knowing the values used lor rigidity for a system
141" in.-lb/degree.
TABLE 7.6 Cornpndscrn ol Calculated Spring Rates
Source
Stevens, P. 6.
(reference 5)
Simplex (reference 6)
Bijlaard, P. P. (reference 7)
Eq. 7.3
Spring Constant
(in.-lbjdeg.1(outplane)
727,2(Kl
659,7 11 2
588,252
776,569
41s
TI\ ,bring rate values when used give reduced bending moments, thus
avoidkg more piping, noule pads, or consideration of alternate arrange-
ments of piping.
I
Stress range in the vessei shell, which comes under pressure vessel code, i i
of impraance but not discussed here. The equations given here is of
assistance when the knding moments are slightly higher than allowed and
these slightly higher values can be reduced by using spring rate constants in
the analysis.
C H A P T E R EIGHT
PIP~NGCONNECTED TO
ROTATING EQUIPMENT
I . WicAman, K. R. ""Local Strews in SpkTicaI and Cylindrical Shells due to Exlerhal
bsdings," Welding Research Council Bulletin 107 (revised March 1979).
2. Steel, @. R. ""Sress Analysis of Noules in Cylindrical Vessrls with External Load." Journalof
fiemum VcswI Tcclmology, Vol. 105 (August 3983).
3. KannappenS.""Eecl of lnclusionol Rotational Spring Rate of Vessel Noules i n Pipe Stress
Calculations," "Socei ty
of Piping Engineen Conference, Houston in Octoher 1982.
4.
bsktddee National Laborstory (ORNIL). Phase Report 1 15-3.
5.
Paevens, P. G. e l al. ""Vessel Novle and Piping Rexibility Anslyis," Journal of EnginceGng
Jar Indusny, May 1962, p. 225.
6 . Strnplex &bmpurer &gram User's Manual, Pcng Engincrring.
7. Bijlaerd P. P. "'Slresxs from Radial Laads and External Moments in Cylindrical Vessel, The
welding Journal, Vol. 34 (1955).
8. g ,Menbon, J. L. WWC Bulletin 299, August 1984. Supplement to WRC Bulletin 107.
uJ
External loads Imposed by piping on the rotating equipment nozzles should
Re less than allowable loads. Examples of rotating equipment are centrifugal
pumps, steam turbines, and centrifugal compressors.
II excessive loads are i m p s e d , misalignment may result that aflecls
mechanical owration and could cause objectionable vibration. A close:
alignment k t w e e n rotating and stationary parts must be maintained. The
provision lor expansion of the casing and maintaining close clearispaces
requires that the forces and moments doe to the piping are limited.
instead of duplicating what is available in other sources, examples are
given here with references ro diRerenr standards.
PIPING CONNECTED "TO STWM TURBINES
The NEMA standards SM 23 (reference I ) outlines guidelines foe calcularing
allowable loads.
This standard has two parts:
1.
Local allowables at each nozzle
2. Combined allowables for comparing loads transferred to centerline of
the exhaust nozzle
m,
8.8. The
The moth& to transfer forces and moments is given in
foilowing equation is given for wa nozzles, but the: same equation can k
Lktea~dcdfurther (reference 2):
M, = M,(inlet)
+ M,(exhaust) - R(inlet)(Z,I + F,(inlet)( Y , )
(8.1)
Stde view
EIevslian
FIGURE 8.2 Typical single-stage vertically split steam turbine.
*/
Cheek if the given actual loads at the inlet and exhaust ntlzzle of a
single-stage vertically split steam turbine is below NEMA allo~ables.The
inlet diameter is 3 in, and oorler diameter Is 8 in. The NEMA coordinate
system (X-axis parellel to the turbine shaft) is given in Figure 8.1. Two views
of the turbine are given in Figures 8.2 and 8.3 (reference 3).
Tile orientation of X-, Y-,and Z-axes and the distances X,, Y , , Z , for
the Example Problem are shown in Figures 8.2 and 8.3. The distances are
meastrred from the centerline of the exhaust nozzle. The minus sign shown
with XI and Z,distances correspnds with moment summations from Eq.
8.1. The sign for these distances depends upon the locarion of the inlet nozzle
with respect lo rhe exhaust nozzle in the NEMA system. Local forces and
Vcrl~cal
Y
Right angle to
turbine shaft
/
FlGURE S.3 The
X,I/, and Z distances used in
Example Problem lor
J
TABLE 8.1 Fwew and lMlomnl8 h m AnaOysb
-
Forces and Moments
I ((1
turbtnc shaft
FIGURE @,I Cmrdinste ~vstcmuccd in NEMA standaid
w.8.8.
larum
P.
;at the inlet and exhaust nozzles obtained from pipe stress analysi\s-J
Cenn
10 81
t.;
r d l
ask: iisted in Table 8.1.
to
The compnents of resulranr forces and moments afier k i n g transferred
the exhaust can be obtained by using Eq. 8.1.
Tht combined resolrant force and moment after being transferred to the
exfiausa is rr follows:
Combined resultant force at exhaust-I%2BIb
-
Combined resultant moment at exhaust =
647rt-ae,
I
Allowable Loeal Foreso and lVIomenls
I
Local moment MR.!I-fb
-..a-
FilGURE 11.4 Corce moment relationship using SM 23 NEMA standard.
~ b NEMA
s
rule I applies for calculating allowable resultant local force:
fhr exhaust
M
Fatlow
839
3
This is k l o w the 3 in. limit lor the diameter given in the NEMA code.
Therefore D, = equivalent diameter = 8.544.
-
= 166.6D-- = D66.6(8)- A 1053 Ib
3
(Rule I )
A graph (Figure 8.4) can be used lo determine the allowable resultant force.
The caDsularion is shown by dotted lines.
For the iniee,
-
-
F, = SO(8.544) = 427 16
ME 250(8.544)
Fy = 1125(8.544)- 1068 Ib
My --- 125(8.544) = 1848 lr-lb (Rule 2b)
r;;
Ma= B25(8.544]
= lOO(8.544) = 854.4 Ib
2136 ft,-lk,
1068 Ir-8b
The allowable combined resultant force and moment at exhaust is, using
NEMA Eq. 2a,
The alDowaable esmpnerats of resultant forces and moments alter being
NEMA rule 2b,
Bransfemed LO the exhaust is, using
-
Equivalent diamrer
.
.
i
(total
area cd oycnings)
-
744.5Ib
(Rule 2aB
!xlten the actual load Is higher than the allowable, the turbine vendon
may be contacted lo get the higher loads ~pproved.It is the exprience of
the stress engineers that the allowable values are consewalive. It would
v e r y helpful if W.MA prrhlishes the h a ~ i sand criteria of the equations ~ i v e n .
I
\
TABLE 8.2
Nonle
Actual
Bnlet
Exhaust
F, = 213 1b
a=, = 1119
Exceeds
Compwents
F, = - I 8 5
F, = 1040
r;; = 374
M,= 495
OK
OK
OK
OK
OK
OK
M y= 2
Combined resultant
v8
/
Gomprrlsan al ArlusL l o Allarrables
Ma = -4 16
E = 1i21
@
AIIowable
Remarks
OK
Exceeds
American Petroleum lnsritule Standard 617 refers to N E M A SM 23 as the
basis lor allowable loads. The I979 and 1W73 editions have slightly diReren8
wordings in their texts.
API 617, 197% Section 2.5.1, page 7, "Compressors shall Iw designed rc,
withstand external forces and moments at least equal lo 1.85 times the value\
calculated in accordance with NEMA SM 23.'"
API 6 17, 1973, Section 2.4.1, page 5, ""Compressors shall he designed $ 0 .
*~irhsaandexternal forces and moments at least equal to a value calculaled
From the NEMA 23 formulas. For these calculations cctnstants in the
formulas shall be increased by a Facror of I .85."
The ereample presented earlier for steam turbines can be used the same
way for centrifugal compressors except lor the Factor oh I .R5. References 4 to
!a apply to centrifugal compressors. Spcial consideration lor dynamic
vibration is needed in the case of reciprocating compressors, which is outside
the scow oh the discussion here.
Figure 8.5 gives the coordinate system used for APl 680 pumps. The
pump shall is parallel to (he X-axis and the Z-axis is along the centerline of
the pedestal. For purnps with larger diameters, allowable values can k
obtained from vendors or determined by exwrimenlal means (references H
and "P.
The allowable force lor each nozzle is:
Fx r 1.3 W .c: I60 lblnominat diameter
b;; .r 1 .OW s I30 lblnominaii diameter
Fy(comp.)s 200 lblnorninal diameter 5 1.2 W
Fy;,(rensionzs 100 lblnominal diameter 5 0.5 W
where W = weight of the pump.
The shear resultant force is:
The allowable moment is:
PIPING GOCIINECTEC) TO GElPrrRlFUGAL PUMPS
The APii 610 (reference 7) standard gives equations lo calculate allowable
forces and moments in the case of centrifugal purnps lor genera! refinery
service. The criteria apply for pumps with 4 in. discharge nozzles or smaller
(suction nozzles may k larger) and situations where the pump is constructed
of steel or alloy steel. The moduius o l elasticity of the piping nratedal at
oprating ternwralure (known as hot modulus) can be used to calculate
actual loads. Using hot modulus will result in lower loads because the piping
is more flexible at higher temperature.
where the minimum value for W is 1
mBb.
(
Relrrrncrr
(.. ,
.'he actual forces and moments from h t h suction and discharge noales
shall bc trsnsfened to the interseelion of X-. Y-, and Z-axes lo obtain the
summation of moments in each dtection for comparison with allowabler.
The leuer of the values obtained from the considered weight and diameter
I
i 2
rA
'
The kndiing moment about the orthogonal directions (other than torsion) is:
should $c u%d as the allowables.
The torsional moment is expressed by:
EAT = M~
The piping yield method is an extreme case in which the component is given
ruRcicnt strength lo fully yield the connecting piping in bending at the
noule. The coordinate system and equations given in reference 10 are
presented in Figure 8.6.
The rorccs and moments for which equipment needs to he designed are as
r~~io~s:
-
0.1.
s,z,
The coordinate system for the a b v e equations is the same as in Figure 8.6,
S, = yield stress of p i p mderial (maximum of 36,W~)sI)
7,-- section modulus of piqe,
axial force (along novle axis)
Six components fraction rnerhclcl requires that the sum of the ratios of the
actual loads to vendor allowable loads be equal to or less than unity.
$ending moment
torsional moment
1
7 +t
I
Equations that are slightly diAerent from these are also used in the industry
[reference 1 1):
REFERENCES
D. National Electrical Manufacturers Assoriation. Publication No. SM 23, 1979 tftec. SM 23,
h", = Fy = Fa = 0.01 Sy (metal area of pipe)
I
I
I
Metal area of
PIW, tn.2
,
Plane of
2, = Section modulus
of piw, tn.3
aafe end
of component
nozxlr
8.06."'Steam Turbine for Mechanical Drive Service.'"
2. General EIectric Company. "Design Recommendations lor Steam Piping Syslernf,'"
Manual Number GEK-27,060.
3. Kannappsn, S. el al. "How to Delemine Allowable Steam Turbine kads,"%ydmarban
m e s s i n g , Vol. 53, No. 8 (August 19741, p. 75.
4, American Petroleum Institute AP1617,4lh cd. (Novemkr 1979),See. 2.9.I,""Ccntailuga1
Compressow for Refining %mice."
5. Anerican Petroleum Institute API 617, 3rd ed. (Oclobea 19731, &c. 2.4.1, ""Centrifugal
Compresson for Refinery Service."
6 . Ksnnappan, S. "Determining Centrifugal Gomprcssot Piping bads," H y d p o c ~ k ~
h c s s i n g (February 1982), p. 91.
7. Ancrican Petroleum lmtitute API 610. ""Cenbifugal P u m p lor &mre'
vice," see. 14.
8. Sinmon C. A. ""Allowable Pump Piping ba&,"Wydracad
4
98.
L
9. Doolin J. M."'lmtali P u m p lor Minimum Stress," Hydracarbo,
r "*\
96.
IO. Meyer R. A. ""Survy of Noale Piping Reaction Criteria lor
Smerural &sign ol Nuclear PIanr F;aciligc~,Val If, p. 283.
D,
-
RGURE 8.6 Piyx: noale coordinate system.
\
C H A P T ~ RNINE
P
(;ale valves connect three major compnents: h d y , h n n e r , and trim.
(reference I). The h d y is generally connected to the piping by means of
flanged, screwed, or welded connections. The h n n e l , containing the moving
parts, is joined lo the M y generaily with b i t s lo parnit cleaning and
maintenance. The valve trim includes the stem, the gate, the wedge or disc,
and seat rings.
-
SPECIAL TOPICS
Valve b d i e s are made of brass or bronze mainly in the smaller sizes and for
n~oderatepressures and temperatures. Cast iron is used in most semiees,
Cast steels are used for severe services of high pressures and high ternperalures.
The topics that did not fall into the major categories of other chapters are
grouped and discussed as follows:
Valve trim materials include the seat ring, disc or lacing, and stem.
Cclmmon trim materials are mone!, bronze, stellike, and stainless steel.
Among the principal factors that influence the prliormance of trim materials are ( 1 ) tensile properties, chemical sfabiliay, and corrosion resisrance al
the operating temperature; ( 2 ) hardness and roughness; (3) a coeficienl ol
expansion that corresponds closely to that of the valve h d y ; and (4)
digerence in properties of seal and disc to prevent sieeing.
The t y p of valve to be used lor a given service is presented in the piping
specification (Fig. 1.3). In general, preliminary stress analysis is carried out
with approximate weight and actual weight obtained from idre manufacturer
(rclcrcncc i ) should be used in thc final stress analysis in critical systems. In
nuclear piping, valves are further grouped as ( I ) active valves and 62)
nonactive valves that are based on their requirement of performance after
earthquake event (Chapter 10). Modeling of valves in computer analysis is
described in Chaprer 10 (Fig. 10.19).Valves require rigid support close lo the
center of gravity. Ir is advisable lo avoid supports on the valve operators. In
general, maximum acceleration a valve can be subjected to is 3 g. i f actual
acceleration exceeds allowable, valve vedor needs to be contacted.
Valves
Pressure relief valve thrust
Aiuminum, Nickel, and Copper Alloy Piping
Underground and Plastic Piping
External Pressure Design-Jacketed Piping
Metric Units
Elevated Ternprature-Creq EFTecrs
Refractory Lining
VALVES
Valves are used in a piping system to achieve the following:
. I
2.
3.
4.
5.
'$0 slop or
start flow of fluids. Examples are gate, plug (cocks), ball, or
butterfly valves.
To regulate Row. Examples are globe. angle, needle, and bunerfly
valves.
To prevent back R w . Examples are lilt check and swing check
valves.
To regulate pressure. An example is regulators,
To relieve pressure. Examples arc spring-loaded safely or pop valves,
rupture disk reIiel valve.
There are several methods available to the designer for determining the
design pressure and velocity in the discharge e l b w and vent pipe, It Is ahs:
There are numerous valve msndwturcna making v r l v a lor many different
s o w of tire mandrclurcn' inlormetion s h u t valves
@
1
I
imxt
ANSI/ASME 8 3 1 1 Power Piping CoBe
sespnsibility of the designer to assure himself rhat the method used yields
conservative res~lrr.4 v e ! h d Idr determining the design pressures and
velocities in the discharge elbow and vent p i p for open discharge insraliarion is shown below and illustrated in the sample problem.
First, calculate the design pressure and vetocity for the discharge
., e l b-w.. .
I. Determine the pressure P, that exists at the discharge elbow outlet
(Fig. 9.1):
.
-
= stagnation enthalpy at the safety valve inlet, B?u/lbm
J
778.16 It-lbf/Plt~
g, = gravitational constant
.= 32.2 ~bm-ftllbl-sec2
PI = pressure, psia (Ibllin." ag\bsolute)
VI .= frlsec
c'ommon -8alues of a and b are listed in Table 9.1.
(9.1)
Steam Condition
2. Determine the velocity V, that exists at the discharge elbow outlet
(Fig. 9.I):
a, Btullbm
Wet steam,
< 90% qualily
Saturated steam,
L 00% quality,
15 p i a S P, 5 1OOOpia
Sugerheated steam,
r 90% quality,
1000 psia < P, r.; 20011 psia"
where W = actual mass Row rate, lbmlsec
At --- discharge elbow area, in.2
29 1
b
11
823
4.33
83 3
4.33
*This method may be used as an approximation. For pressures
>2000 pi,an alternate m e l m s h o u i d be used for verification.
Rsactlon Farces wkh O p n Discharge Systems
The reaction force F due to steady-state flow following the o p n i n g sf the
safety valve includes both momentum and pressure effects. The reaction
force appiied is shown in.l;igure 9.1, and may be computed by the lollowing
equation:
lac:
*pP*
where
6 = reaction force, Ibf
at
pint 1
W = mass Wow rate, (relieving capacity a t a m p d on the valve X l , l
lbmlsec
g = gravitational constant
= 32.2 ibm-ftllbf-seca
Vl =exit velocity st p i n t I , fvsec
PI = static presswe st point I, pis
Al =. exit Raw area at p i n t 1, in.'
* .
-
Anrlyrk for Rerrc(lon Farcas Dur to Valve I;q p
T o ensure consideration of the eNecls of the suddenly applied load F, a
dynamic load factor DLF should
applied (Fig. 9.2).
The methods for calculating the veiocities and pressures at the exit poin,
of the discharge elbow are the same as those discussed in Eqs. 9.1 and 9.2,
AIVALVSlS FOR RIfACTlOIU FORCES DUE
TO VANE: DISCHARGE
Open Discharge Systems
'The moments due to valve reaction forces may be calculated by simply
multiplying the force, calculated as descrikd in Eq. 9.3, rimes the distance
from the point in the piping system being analyzed, times a suitable dynamic
load factor, In no case shall the reacrion moment at the branch connection
bciovv the valve be laken at less than the product as given in Eqv 9.4
I
B
8'
*
ge
I . Calculate the safeiy valve installation p r i o d T using the following
equation and Figure 9.2:
where 7-= safety valve inslallaPion period, sec
W = weight of safely valve, installation piping, flanges, attachments,
elc., Ib
h = distance from run pige to centerline of ourler piping, in.
E = Young" modulus of inlet p i p . Pblin.', at design temprature
I = moment of inertia of inlet pi*, in.""
2. Calculate ratio of safety valve opening time to insta!Baiion v r i o d
(r,lT) where r, is the rime the safety valve takes to go from fully closed t o
fully open (sec) and T is determined in ( I ) above.
3. Enler Figure 9.2 with the ratio of safety valve opening lime: to
installation p r i o d and read rlre DLF from the ordinate, The DEF sllalD
never be taken less than I . 1.
If a less conservative DLF is used, the DL); shall be determined by
calculation or test.
where Fg=force calculated in Eq. 9.3
D = nominal OD of inlet pipe
DEF = dynamic load factor (Fig. 9.2)
Reaction force and resultant moment eFIects on the header, supports,
and noreles for each valve or combinalior~of valves blowing shall he
considered.
in a piping system acted u p n by time varying loads, the internal forces and
. moments are generally greater than those produced under static application
of the load. This amplification is often expressed as the dynamic load factor
DLF and is defined as the maximum ratio of the dynamic deflection at any
rime to the deflection which would have resulted from the static application
sf the load. For siiusturzs having essentially one degree-of-freedom and a
singDe ioad application, the DLF vaiue will range &tween one and two
depending on the time-history of the applied load and the natural frequency
of the structure. If the run p i p is rigidly supported, the safety valve
ir~slallarioncan be idealized as a one degree-of-freedom system and the
tine-history of the applied loads can often he assumed to be a single ramp
luncrion between Ihs no-load and steady-state condition. In this case the
DLF may be determined in the following manner.
13)
Ratio of ssfcly valve owning time to installalion pcrid (Cg/T)
FIGURE 9.2 IOynsmir load fartor for o p n di.ichsrgc *yslrm.
I?
i
u
r
'r/
~ish~b
. .
*
I 6 o ~
I
a
it
t4
herel lore
(-2
I
W
Rsscllon Forces w&Ct Open Discharge Systems Calculatian
F8 =-
v, -9- (fi.-- Pa)A,
Bc
Calculate reaction force with the following (see Fig. 9.3):
Bpraring temprature = 7 W F
Opraling pressure
= 200 psig
I% = 31374 Btujlbm (Iron steam table)
a 823 Btujlbm
b = 4.33 (Iron Table 9.1)
20 OI)Q
W = --!--- = 55.6 Ibm/sec
3 6063
A1 = 51)in.2
I 778.16 tr-lbf/Btu
g, .= 32.2 Pibm-lt/lbf-sec2
Assume dynamic load factor of 2.0.
Therefore
-
-
-;
SO psig
Vd =
2'7 8
32.3
= -X I899 + (SO - 1147)558
Fdp =
3404.5
F ( D L F ) = 3404.5(2) = 61309 Ib
ALUMINUM PIPING
Dinerent aluminum alloy piping has similar desirable cornmion resistance
hut varies in mechanicat proprries. Aluminum alloys most commonly used
for piping systems are alloy 160, alloy 3003, allay 3052, alloy 6W1, and
alloy 6063. Of these, alloy ASTM B241-6063-Td is the most widely used
because i t bas good mechanical proprlies at reasonable cost.
Aluminum has found various uses in the cryogenic or cold temprature
applications. As temperature decreases aluminum shows increased values of
tensile and yields strength with equal or improved ductility or impact
TABLE 9.2
~ ~ b ~ rt$roprgfcs
dci
of VIulorra A l d n m M s j s
Alloy
(2 x 4.33 - I )
--
Tensile strength, pi
Yield strength, pi
Mdulus ol elasticity,
p i x I@'
T k m e l conductivity,
Btu/lir/sq ftPFlin.
Average cceecient of
- --
= 1899 111sec
themel expansion,
in.l"F/in. x 10-""
-58 to 68'
RGURE 9.3 Example Problem for open di~charge
3W3
5052
6W1
BM3
17,W
8,m
41,QOo
16,000
45,O
40,W
35,W
31,W
18
10
9h10
l ,C)98
10
1,070
68 to 212O
12.0
12.9
68 to 392'
68 to 572'
13.5
13.9
10.2
960
13.2
2.1
13.0
13.5
12.1
13.0
I4,B
14.2
13.6
TABLE 9.3
Supprl Spacing lor Aludnum Aflog 6MJ PIlpc
P i p Schedule Number
Nominal
5S
10s
40 S
Pip& Size
(in.)
labre is based on the p i p k i n g uninsulaled, oprating at a maximi
temperature of 4W°F, and conveying a liquid of spcific gravity 1.35
conservative assumptian). If the line is insulated, reduce the span by 30
allowance has k e n made Bar concentrated Doads such ss valv
~quations3.1 and 3.2 may also be used to cslcuirrte: the span.
Support Spacing (It)
COPPER ALLOY PIPE
-
.-
$.
vJ
I,*
resistance. The specific alloys most frequently used in cold temperature
applications are alloy 3003 and alloy 5052.
AIuminum alloys may be welded. The inert-gas tungsten-arc method,
using argon gas, i s the recommended procedure. Further reference material
a b u t installation techniques, fittings, and so on can be obtained from
manufacturers such as Alcoa and Reynotds metal companies.
Table 9.2 shows the physical properties of various aluminum alloys
(reference 4). As can k seen, units for average thermal expansion i s given
as in.lin.PF. See Chapter 1 (Eq. 1.1) lor conversion to in./linear feet of pipe.
The thermal expansion lor aluminum is high and adequate provision must be
made to compensate for the high amount of expansion, The operating pressure
of an aluminum pipe is calculated in the same way as ferrous pipe, using Eq. 2.4
with y = 0.4 and corrosion allowance of zero.
ABurninum i s subject lo galvanic corrosion in the presence of an electrolyte. When in the presence of carbon steel, copwr, brass, nickel, monel,
tin, and lead, aluminum will be corroded. Thus conventional carbon steel
p i p hangers should be avoided. However, the 300 series of stainless steel
and zinc are usually compatible with aluminum. Therefore galvanized (zinc
coating) steel hangers, aluminum hangers, or padded hangers may be used.
Table 9.3 gives supprt spacing (reference 4) For alloy 6063 piping. This
Many applications of the copper p i p have k e n found in the food indusr
.Table 9.4 shows the physical properties. The coefficiento&thermal expanst
of copper pipes is high. Therefore either loops or expansion joints marst
Car absorbing the -expansion. Copper p i p can be joined
threading, soldering, or brazing, and flanges may be installed by any of tRt
methods. Table 9.5a gives dimensions o l rite copper p i p (suitable
threading), outside diameter, wall thickness, and maximum aHowable press!
at a operating temperature of 3W0F for regular schedule. A copper p
should not be forced into place during installation. Forcing the piw into pli
and keeping it under stress can cause Failure. Table @.Sbgives supprt spas1
for a copper pipe. The spacing is based (reference 4) on uninsulated lil
operating at a maximum temperature of 300eFand carrying a Gluid of spec
gravity 1.35. If the lines are insulated, spacing should k reduced by 30%.
allowance has been made lor concentrated loads like valves. I n order
pmvenr galvanic corrosion, copper or padded hangers should be used w
copper piping. Table 9.6 shows allowable stress for alloys of wickel, copr
and aluminum lor B3 1.3, IS13 I.I,and section Ill codes.
A numkr of nonferrous metals and their alloys are vvindly used
corrosion-resistant piping material. Zirconium and titanium are examples
TABLE 9.4 Plryslcrl h w l m of Coppr M a y
Tensile Strength
Themal conductivity
a!. 68°F
Average coeFficient of
linear themal
expansion
77-572°F
Modulus o l elasticity
in tension
54,000
p
i
2164 BtulliirlsqIapFIin.
TABLE 9-31 Dbncmbrrs of S t a n d 4 G o p p r P
T
p (Suilrble lor Threrdlng) I~
onr Anowable w n l l n g hemure (pf)
Rcguler Schedule
Nominal
Pipe
Outside
Sizc:
Diam.
inside
Diam.
Well
Thickness
-
Allowable
Pressure at
300°F or Lower
TABLE 9 A Suppa Spsclwg lor Coppcr R p
tor Regafar & M a l e (referenre 4)
Nominal Fim
Size (in.)
Spacing, It
4
6.5
8.0
9.5
10.5
12.5
13.5
6
8
15.5
17.0
!i
1
1l
2
3
..
" ,.
,.
01106 !N-nC)
'u! CB J?Ao L9PB
iloriv- rdlddo3
.-
PpmV I* 'ON d
m)O&
'ON 4 0 1 19Ia
~
X o w 119131~
..---.,-*m
I
ASTM
Spc.
Mesel/Allay
Yield Stress
(ksi)
I
Density
(Ihlin.7
Spccific
Gravity
Thetmat
Exp. Coef.
E
~t~uli,,
.
(in./in.PF)
0Csvtng
u
a
L
I
I
.
~
C
~
1
-,
Y~elding!
Surface
P~w
(b)
(a)
Zirconium
GI. 702
unalloyed
Titanium, Gr,
D
Hrastelloy BZ,
ASME code case
l612
B337
R.5 % 7
25
51
0.333
h.2 x 1 0
"
31 4 x
111
(@I
(1) Sh@ar
(8) loml failure
RGURE 9.4 U d e r g ~ o u n dpiping failure modes.
these metals. Incoloy, hastellay, and inconel are alloys that have good
corrosion-resistant properties. These alloys are trade names. Their ASTM
specification numbers and properties are given In Table "1.7. The ASTM
, annual 1877 or 1980, part 8, gives more information.
b4
UNDERGROUND PIPiNG
Routing of piping underground is sometimes necessary In cross a road,
piping between buildings, yard crossing, and so on. The factors that are
imprlant in underground plastic piping design are as follows:
1. Longitudinal bending stress
2. Buckling, arching
3. Bowing
4, Soij stiffness and soil geometry (very important for expansive soils)
5, Dead and live load
6. Wail compression, bending, and shear resistance
7. Hydrostatic upiiff
Modes of failure and collapse are described &low as applied lo plastic piping
(reference 8):
I . Caving due to deflection (see Fig. 9.4a)
2. Wall(ring1 compression due to yielding at A (Fig. 9.4b)
3 . Buckjing: (a) eldstic and (b) plastic. In buckled state a p i p resembles
the one shown in Fig. 9 . 4 ~
4. Beam bending (Fig. 9.4d)
5. Longitudinal tension (along axis) (see Fig. 9.4e)
6. Direct shear (occurring al hard soft interfaces) (see Fig. 9.4B)
7 . Failure at joint (See Fig. 9.4g)
I-rleat transfer loss from a buried piw!ine bas become more imprtant in case
of heated ail pipline or in the case of underground steam p i v s for keeping
ice from sidewalks and driveways, Equations to calculate the heat transfer
from a buried p i p is given in reference 3.
Design the following undergroirnd line. Assume data as necessary. The depth
W = 3 ft; trench width -. 2 It 6 in.; material Is ASTM A53 Grade
B; minimum specified yield stress is 35,000 psi ;at 145°F. See Figure 9.5. The
OD of the pipe including insulation is 12 in.
Assume the coeficient ol friction between p i p and soil is 0.3.
Density of saturated clay soil w = LOO lbfCr3.
Pipe contains #6 fuel oil 13 API with swcific gravity 1.2.
of cover =
Steps
I. Calculate frictional resistance
'6.
2. GalcuIate rhemal force R alter calculating longitudinal stress S,.
3, Find point of no movement in which 5 = 6.
4. Calculate hoop stress, bending stress due lo earth load, radial stress
due ro pressure, and tempralure stress due lo operating temperature
5. Calculate combined stress from stresses in (4)using maximum strain
theory.
6 , Find maximum allowable stress using 8 3 1.4 liquid transportation
piping e d e .
7. For p r o p s design the combined stress should be less than the
maximum allowable stress.
Sirst, calculate the load on the p i p from the backfill Wc.
W C= Boad on p i p , Ib/lt
wc
"v,=
Gdl.B:
where
C,+= load coe@cienr
where k = ratio of lateral unit pressure to vertical unit pressure
@ ' = ceaeRcient of friction bemeen fill material and ditch s p , where p
is the cc~eficientof internal lricrion of fill
H =. height of fill above lop of pipe, Feet
I& = horizontal width 01 ditch, feet
Values of the load coefKicient 6, may be taken from the diagram in Figure
9.6 [reiereracc 4).
Sfep I. Calculadm of Frictional Resistance (units Ib/fr): Let We = load on
pipe from backfill neglecting moving load.
Using Marston" formula:
-
where CQ=. load cmmcient. Read from graph in Figure 9.6:
&b", 1.8 x bW x 2.5 x 2.5 = 625 lWfl
w
density of soil = I 0 IMr"
Bg= trench width = 2 . 5
Weight of content
-
= (weight of water) specific gravity
= (21,69)1.2 26 Ib/la
= 5.38 lbffl
-
insulation weight
28.55 Ib/ft
Pipe metal weight
Total weight of p i p = 625 + 26 + 5.38 + 28.55 685 Ib/fr
Frictional resistance = p(total weight) = 0.3(685) = 205.5 Ib/lt
-
Steps 2 and 3. Painr o! No Mouemnr: Frictional force opgoses
force. At the p i n t o l no movement the frictional force is equal 'to the
expansion force.
-
bngitudinal stress = SL Ea(T2- T,)-
,'
where
"rassi
~s~yw
E = 27.9 x 10"lpsi
v '= Poisson's ratio = 0.3
D = 8.625 in.
g(adral slress bS1):
I
a .= linear coefficient of thermal expansion
T2= 145°F
T, = ROOF
r 0.322 in.
I" = 300 psig
Equation 9.8 is from 831.4 Piping Code (reference 3 in Chapter 4 ,
Section 419.6.4(b) of the Liquid Transportation Piping Code. This equation
is for restrained piping, In this case because of underground piping:
-
sl = 27.9 x r 06(6.5x 10-9)(145- 80) - 0.3(300)
Thermal expansion force
6
;;=
S3 = P
I llerrnal srress
-
i..
3W psi
(S4):
s, = Ea(Tz- Tt) = 27.9 X IOn X 6 ~ x5 10-"(14%- 80)
= 1 1,787.73 psi
5, = circurnferenrial spess
=.
8.625 - 2(0.322)
2(0.322)
Sh,,
-I-
v (thermal stress -t- bending stress due lo earth)
= 3717 N5-I-0 3(11,787.73+4170)
= 1 1,787 - 0.3(37 17) = 10,669 psi
= 8507 psi
step 5 . Combined stress ( S ) : Use maximum strain theory:
SL (me181 area) = 10,669(8.4)= 89,625 lh
8M25
-205.5
= 436 I r
Figure 9.7 shows the distance 436 f t from the point of burial marked.
Distance of point of no movement from point of hurial
.J'
crrlt
I
1
= -L
F=d
=
S 7 3 ? q R- 2 y(S1 S,
W;Z
+
S L S R -I- S c S ~ )
+ 3002 - 2 ( 0 3 n 3 7 0
8507 43m18,6m+m
= 1 1,327 psi
Step 4 . Stresses: Hoop spess (SI):
$rep
P(D - 2 8) - 300(8.625 - 0.644) = 37 17 psi
S, =
26
0.644
For bending srwss
(5.
Maximum aliowabIe S & @ S Use restrained piping according lo
B3 1.4:
Maximum allowable stress = b).9O(minirnum o, of pipe)
(SL).use Spangler's equation:
= 0.90(35,000)
$2
(C~WB:)EIR,
=0.177
El3 + 2.592 PR;
where R,, = mean radius of p i p = ( D - r)f2 = 4. I5 15 in. Other terms are the
same as for Eq. 9.8
S2 = 0.177
-
Step 7: The combined stress of 11,327 psi is k 1 o w allowable stress of
3 1,500 psi. Thus the p i p design is safe,
625(27.Y x 106)(0.322)(4.15 15)
2 7 . W X ((1" x 0.322' + 2.592(300)(4.15 15)'
EXTERNAL PRESSURE DESIGN
4179 psi
The design of cylindrical vessels that is subjected to external pressure is
nutlined in the ASME Section V111, Division I UG28tc).
Nomenclature:
PC=: critical collapsing pressure, pi
P, = allowable pressure, psi
r = wall thickness, inches
E modulus of elasticity, psi
& = length between stiRners, inches
Thermal force
Frrcl~onforce
RGURE 9.7
-
Point ol mro movement in s buried pipe
I
I
= 31,500 psi
(9 9)
-sFrah
I
%
.
c~tica8length, inches
Sy yield stress, psi
I
Sc = tangential stress at collapse pressure, psi
Factor A = ScjE
Factor 8 = S,/2
',=:
8tren@hof Pipe Unclkrr Exlsrnsl Pressure (rsferance 10)
The strength of pipe under external pressure is a function of the physical
proprties of the construction material at the operaling temperature and its
geometrical parameters such as the unsupwrred length t,pipe thickness r.
the outside diameter LZ,, and the pipe out-of-roundness.
The behavior of thin-wall cyiindrical shells under uniform externztl
pressure varies according to cylinder length as foilows:
1.
8 / & Long
~
Cylinders: The critical collapsing pressure is given by:
The critical length I,the minimum unsupported length kynnd
which PC i s independent of L, is given by:
a'
2.
Inremdiare Cylinders wifh L < I: The critical pressure PC is a
complicated function of the collapsed confour and the two characteristic ratios rlB, and LID,. For practical design, IL", can be given by
the following empirical equation:
3. Short Cylinders: The cylinder will fail in rkis case by plastic yielding.
The critical pressure can be given by:
( ~ ~ O MChart:
~ C For L > &, the tangential stress Sc at collapse pressure
(given by Eq. 9.101, can be written as:
-
PC
sc
Strain = - = 1.1
E
i
For L 9 L, the tangential stress S, at collapse pressure
9.131, is:
3,
Strain = --=
E
PC ((given by Eq.
L
Equations 9.14 and 9.16 were plotted to develop the geometric chart in
Figure UG0-28.0 of the ASME Boiler and Pressure: Vessel G d e , Section
VIII, Division I . (See Fig. Y.8a and Fig. 9.8b.1
f i r e r i a l Chan: These charts are actually stress-strain curves for materials
ar design ternpratures (S,IE on tihe abscissa and S,/2 values as variables con
the ordinate). (S,IE is called factor A and S,/2 is called factor B in ASME
notation.)
The allowable pressure can be obtained by using the following relation:
Equation 0.18 is the same as Section VIII subsection UG0-28(c)-1 equation.
Ptactical &sign Using ASME Char&: Delemine the pigs: thickness D
under external p r e s s u ~[D/r z 10).
'
'
S g I. Assume a value for I and determine the ratios LID and;
dl,
Step 2. Determine the value,ol factor A from the geometric char1 (using
values obtained in Step I).
S ~ e p3. Determine the value of laclor B by using the proper material
chart and the value of factor .A obtained in Step 2.
Step 4, Calculate the aIIowable external pressure P, by using Eq. "i18
A falling to the left of the applicable
maferialltemperature line. T h e value o f F", can be determined hv
the following formula:
Step 5. f i r values of
(IVore: For D/r < 10 use the procedure outlined in ASME UG-2W(c)-2,)
Stag B .
Assume a value for r and calculate 13:
Step 2. Find the factor A by using rhe proper material chart arid the
value ol B obtained above. i f the value lor lactor B is less than
the value listed in the chart, factor A is given by:
Step 3. Determine the value of LID by entering the factor A and the
appmpriate Dl# curve in the geometric chart. T h e maximum
unstiffened length is obtained by multiplying the value of LID by
D. (If there is no intersection k l w e e n the vertical projection of
A and the D/r curve, then stiReners are not required for any
length.)
See ASME Section VIII, Division 1, subsection UGO-29 lor design of
stiAening ring design.
r
*
i
U
L
I
t
I
11%"
is common lor all materials. This chart is used onb..dr determining the [actor A when factor A is not obtained by formula in the spcial caw w k n
Dm!r< lo. (See UG-28(c)-2.D
The remaining charts in Appedix V are lor specific m a t e ~ a or
l classes of
materials and represent p u d o stress-strain diagrams containing suitebic
factors of safety relative both to plastic Wow and elastic colPap.
Rdsrence from ASME Sectlen VIII, UA-2113
( a ) Cylindrical Shell Under Exicrnal Prrssura. [An example of the use o l the
rules in UG-28(c)] [Eq. 9.18).
GIVEN: Fractionating tower 14 f t inside diameter by 21 11 long, bend sine to
k n d line, 6tted with fractionating trays, and operating under a vacuum at
7WF. The tower to be constructed of SA-285 Grade C carbon steel. Design
length is 39 in.
R E O I J I R E ~ ) : shell thickness, r
Step I .
Assume a thickness I = 0.4 P 25 in.
Assumed outside diame~erDa = 1611.625in
Steps 2, 3 . Enter Fig. UGO-28.0 in Appndix V (Fig. 9.Ra and Fig. 9.8b)
at the value of LID, = 0.231; move horizontally to the D,lr line of 540 and
read the value A of O . O O 5 .
Steps 4, 5. Enter Fig. UCS-28.2 (Fig. 9.10b) at the value of A = @ . m 5
and move vertically lo the material line lor 7 W F . Move horizont11IByand read
B value of 6100 on ordinate.
Step 6. The maximum allowable external pressure [Ecg. 9.181 lor the
assumed shell thicknesses of 0.3 125 in. is:
Vessels Un&r E ~ c ~ m Pressure
al
Nore: The lines on Figure UG0-28.0 of Appendix V (Fig. 9.Ra and h) express a
geometrical relationship between &/Q and Q , / t for cylindrical shells and t u k s
Since Pa is grea~e;than the design pressure I" d 15 pi, the hjsumed thickness
should be satisfactory.
14-
Spmlial Teplcr
,~,ksts-.
I
\
.lasure
,
J
SVI
/
4616KnEI) PRESSURE PIPING SYSTEM
I
h ,,P
sch I0 S core p i p is:
Method of ~ a l c u l a t i nCore
~ Pipe Thickness
Example 1 : The pipe is 4 in., operating under a full vacuum at 65VF. The
external pressure is 100 psig. The maximum length of spool piece without
stiflening rings is 10 tt 0 in. Pipe material i s stainless steel ASTM A-312,
T y p 3 16 (Fig. 9.11).
CaicuBate the core p i p thickness.
6
4
r rO(67W) - 208 psig
&=-B-=:--------
3
Do
3(42.85)
For values of constant A falling to the !ell of applicable malerialllemperature line. the maximum external pressure can be direcriy evaluated from
the following equaticln:
Step 1. Assume the thickness of pipe is scb 1 0 s (0.120in.).
Tl(min thickness) = 0.120 x 0.895 (assume 12.5'/0 manufacturing
tolerance)
= 0.105 in.
&
--
where E = modulus of elasticity of material at the temprature k i n g
considered.
The external design pressure is 115 psig (the core in full vacuum and
external pressure is 100psig, the pressure acting in the same direction
&comes additive).
Since Pa is greater than the design pressure, 1 LSpsig, the assumed
thickness is thus satisfactory.
D
at 650°F. The e x t e r ~ a lpressure is 100 psig. The maximum length
&(outside dia.) = 4.50 in.
'
O(spol length)
= 120 in.
thus
120 - 26.66
Do 4.50
I
1
11.50 - 42.85
0.105
-c-m*
T
r
*
!i
Saep 2. Enter value of LID, = 26.66 (Fig. 9.86) in Figure UGO-28.0,
Appendix V,ASME Section VIII, Division l , move horizontally to the D,/t
line of 42.85 and read the value A of 0.0006.
For value of LID, r 50, enter the chart at 50 for determining the value of
constant A.
I
-
I
;*#l
Stc"p3. Enter (Fig. "6.9a) in Figure UHA-28.2 at the vaiue of A = 0.0006
and move vertically to the material line for 650°F (interplated k l w e e n the
4 M and 700°F material lines). Move horizontally and read B value of 6700
on the ordinate.
Step 4. The maximum ailowable external pressure (Eq. 9.18) lor the
Example 2: The pipe is 4 in., operating under internal pressure of 125 psig
of spool
piece without stillening rings is 1011 0 in, Pipe material is stainless steel
ASTI'M A-3 12, Type 3 16. (See Fig, 9.12.)
Calculate the core pipe thickness. Steps 1 to 4 are the same as in Example:
I , the results are derived from Figures U 6 0 - 2 8 . 0 (Fig. 9.8b) and UHA-28.2
(Fig. 9.9a) of Appendix V, ASME Section Vllb(, Division 1.
From Step 4 in Example I , the maximum allowable external pressure (Pa",)
lor the assumed sch 1 0 S core piw is 208 pslg.
External design pressure ( P ) =: 1110 psig. Since F", is greater than P, the
assumed thickness is satisfactory.
The external pressure is the governing factor lor safe design of a core pipe
in the jacketed piping system. If there had not been any external pressure, the
pipe carrying 125psig Ruid pressure at 65VF could have thinner \wall
section.
For calculation of jacket thickness, use: Eq. 2.1 (from ASME BJ1.3,
-----
1
1
- - -
mGURE 9.12
PV-CP-
pi-inpl
Jacketed piping (Righer p"es3ure
in
bragah
in.
rn
It
IJd
m
1t2
yd"
in."
m"
rn
Area
m'
Volum
Mm
Fmce
Beding, torque
B
qS
-
m2
m'
ftl
m'
U.S. gallon
Imperial gallon
lit re
m1
n'
m'
lb (avoirdupois)
kg
ton ( m e t ~ c )
tons fshorr 2W l h )
kg
let
N
IbB
N
kgl.m
Ibf.in.
Ibl.in.
Ibl.l8
N,m
N,m
kg
N,m
N.m
Preluwc, stress
kgflm"
Energy, work
Ibtrtlr"
Ibf/in."pi)
Uplin.'
bar
Btu (IT)'
I
Power
ft.lbf
h p (550 Il.lblls)
D
W
C
F
F
K
M
C
K
Tempeature
Tempfalure intewsl
63
F '
Pa
Pa
Pa
Bar
Pa
K or C
2.54*
3.048"
9.144'
E -02
E-01
E-01
The internal pressure design thickness r shall iite not less than that calculated
by Eq. 2.1, when 8 is less than DIB (see Chapter 2):
6.4516' E -04
9.29034* E - 02
8.361274 E -01
1.638706 E - 05
2.831685 E-02
3.785412 E -05
4.546090 E - 03
6.0'
E-03
4.535924 E - 0 l
I . O M ) * E + 03
9.07 1847 E + 0;
9.80665' E + 0
4.448222 E + W
9.80665' E + lK)
1.129848 E - Q I
1.129848E-Ol
i.355818 E + f B
9.80665' E + 00
4.788026 E - 01
6.894757 E + 03
6.894757 E + 06
0
E-05
1.055056 E + 03
1.355818 E + W
7.456999 E + 02
t, =
I, = (1,
+ 273.15
+ 459.67)/1.8
4 = (1, - 32)/1.8
1.0,
'
E+OO
5.555555 E-Ol
* ~ e l a t l a r nthat
~ ~are exact in # e m s of 1 k basc units are followed by r r i n ~ l cn t c r i s l .
tThe frclnn are rvriften rt a numkr greater than one e n d less than ten with sia or less decimal
plwo. W r n m k r k lotlored by the Ictter E (tor erponenr). r plur or minw s p b l , and m o
digits r k h idkclte @)u
p n r e r d t0 Lry rrMch Ik numkr must hc multiplied $0 obtain rhf
capecr v s l w Fm rarmple.
Metric units are used in most countries sf the world and piping design c d e s
and standards start dealing with metric units. ln a future edition equations
given in this b k will p r h a p s be rno$ified to accommodate metric units. Ail
equations given here may be used for piping design in metric units by using
proper conversion factors. (See Table 9.9, which is reproduced from Pressure
Vessel Code, ASME Section VI11, Division I). Afaes calculating pipe
thickness, diameter, and so an, using British units, the next standard values
on the conservative side in metric units may be selected. Caution must be
exercised to refer ro piping codes and standards in force in each country.
MATERIAL, BEHAVIOR AT ELEVATE0 TEMPEWTURE
[reference lob
Elevated temperatures are those at which creep effectsare significant. Figure
9.13 is the result of a uniaxial tensile specimen subjected lo a load-indblced
stress level at a given test (low) ternwrature. Both stress and strain achieve
their maximum value at the same time and remain constant at the maximum
values thereafter (as long as the load is maintained). When the test ternperalure is high enough, the strain will increase with time, and p s s i b l y until
fracture alter load application as shown in Figure $14. In this case creep
ellects are significant. If, o n the other hand, the elevated tenrprature
uniaxial test is one at which the specimen is initially strained a fixed amount
ei
re
Ttme
B"1GhilRE 9-14 Stress and strein versus lime at elevated tcmiperature (creep eflects)
fFICuRE 9,15
Stress and s?rain versus time al elevated lernprsture (stress relaxation).
Ia
96
and then held constant. The stress-strain history would be somewhat similar
' t o Figure 9.f 5. The reduction of stress as shown in this figure is called the
stress relaxation due lo creep elffects.
From these figures it can readily be seen that erevated lemperature
material khavior is a Function of stress, temperature, and rime.
Application sf Creep Data to Piping Design (relsrence 2)
At tempcralures k l o w the creep range, allowable stress values are
esrablisl~edat the towest value of stress obtained from using 25% of the
specified minimum ultimate strength at r m m temperature or 25% of the
minimum expected ultimate strength at temperature, or 62i0/0 of the minimum expcred yield strengrh for 0.2% oflset at temperature. For bolting
material, the stress values were based on 20'A of the minimum tensile
strength, or 25% of the yield strength lor 0.2a/o ollsei, whichever is lower. (It
is recognized that bolts are always expected to function at stresses above the
design vatuc as distinguished from other parts.)
No credit is allowed lor any improvement in tensiie properties by special
heat treatment.
at higher temperatures, where creep governs, the stress values were based
ow 186% of the stress to produce a creep rate of O.Olo/o lor I QOO hour, the
values so chosen k i n g based on a conservative average of many reprred
rests as evaluated by the Sukomrnitree, greater weight k i n g given to
longer-lime tests in evaluating data. In addition to the abve-stated creepstrength requirement, stress values were also limited to IOC)K%olthe
' stress to
produce rupture at the end of IOO,W hour, the values so chosen being based
on a conservative average as evaluated by the Sukommitree. However, in
most cases, the creep strength is far below the mpture strength. Also, in a few
cases, the Sukommittee has provided stress values without any rupture test
data on the spcific composition, such approval k i n g based on tests of
materials of similar corngosition.
En the transition range of temwralures, the stress allowances were limited
to values obtained from a smmrh curve joining the values lor the low- and
hkgh-tempraturn ranges, the curve lying on or h i o w the curve? of 62i0/c of
the minimum expected yield strength a4 temperature.
In the choice of stress values in the range where a percentage of the tensile
strength or yield strength governs, the limitations Indicated a b v e have been
waived in certain cases, identified by a fmtnote,bas i t was felt that higher
slress values might be justified when deformation was not in itsell objectionable, provided all other requirements were met.
In the design of equipment not covered by codes, the design stress veiues
may be decided upon by the manufacturer and purchaser of fhe piping, and
shuuid he based on the best available data plus a knowledge of the expected
life of the equipment as well as the operating conditions and the pssible
hazard to personnel. Rules generally fallowed are:
Up 10 750 or 850"F, 25% of the short-lime tensile strength and not
exceeding 62j0/e yield strength.
b. Above 9W0F, tOOO/oof the stress ro produce a second-stage creep
rate of 0.01% in 1000 h, or 80°/o ol the stress to product rupture in
100,000 21, whichever is lower.
a.
Refractory linings are used in kilns, coke ovens, furnaces, and stacks l o
protect metal parts from direct exposure of very high tempratures (Fig.
9.16). Refractories need to withstand very high temperatures without me[ting, should have necessary mechanical and hear transfer properties, should
not react with the medium inside the furnace, and large quantities need to k
available at low prices (reference 5). Based on the chemical property,
relracrories are classified as acidic (example, silica), basic (magnesia), and
'This lW% value pertains to t k Unlired Pressure Vessel Code.In the Power hilev C d e tBir
8Ire3~limitation is 60% of the average or 80% of the minimum streu ta prduce rupture in
100,Oolr as rcpctrted by test data.
B*
'
Ercarc
t: J
38%
(d) The piping code 831.1 allows use of inpiane and ourplane SIF.
(e) Pad is needed when area required is smaller than ares removed.
f ) lnternal pressure when included decreases the SIF value for an
elhw.
(g) When the egects of flanges are included lor an elbsw, the flexibility
factor reduces.
(h) Expansion loops take less space compared wirh exparadon joints.
RGURE 9.16 Refractory itnirrg
(chrome ore). The standard form lor refractories is brick. In steel
a large diameter, inclined p i p s with refractory lining are used,
Calculation of weight to he supported at support points is of importance ( ~ i ~ .
9-16].
Density of refractory
Density of steel
Density of insulation
Inside diameter of refractory
Outside diamter of pipe
Outside diameter of insulation
= 40 Ib/lr3
= 0.283 Ib/in.J
= 1 1 1b/ft3
= 39 in.
= 48 in.
= 52 in.
Weight Per foot -- weight of (refrmcrory + p i p m d a l + insulation)
(9.20)
(4g2- 472)1z(0.283)
2. True or false?
fa) Cold spring can be applied only to hot piping.
(6) For span calculation hot modulus should b4: used.
(c) Internal pressure increases flexibility factor value for e 9 b w .
(d) Expansion loops are safer than expansion joints.
(e) The vessel nozzle growth is to be included in stress calculations.
(I)Piping (refinery) design is governed by ASME code.
(g) Outside diameter of 6 in. nominal pipe is 61in.
(h) The exit diameter Is larger than the inlet diameter in pressure reliiel
valves.
3. An underground pipeline with ASTM-A53 Grade B malerial and 12 in.
sch 4 0 pipe has the following conditions:
Oprating temperature: 175°F
installed temperature: 70°F
Depth of burial: 3 It 6 in.
Specific gravity of content: 0.73
Operating pressure: 3- ppsig
(a) Where is the location of the natural anchor? (b) The amount of
thermal expansion at the end7 (The friction coeficient = 0.75.)
4,
= 151.55+255.83+26!
=:
428.46 Ib/lt
EXERCISES
1, True or false?
Cold springs cannot k u ~ 80d reduce t k moment on a vessel.
modulus al elssrkiry crn frE w d fw ~ 1 5 cea (~~ u 1 ~ l i o n .
( ~ 1For span calculsficrn, mrlrimum d c & c @ h n allwed imide piant is
1 in.
1
I
Calculate dynamic reaction force wirh open discharge system.
How = 1 6 5 . m lb/hr
Area (21 valve orifice = 55 sq in.
I = 778 Fr-lb/Btu; g = 32.2 Bllsec2
Temperature = 650°F; PR = 155 psig
12, = 1374 Btullb (from steam tables)
a = 823 Lltu/lb; b =. 4.33
Discharge line is 6 in. sch 4 0
5, A double-acting reciprocating gas compressor has a maximum rated
speed at 650 rpm with a pulsation pressure limited to 13 psi, The
discharge p i w is 3 in. scls 40. What wil! be the pulsation force? What is
the maximum span of p i v support? lp= 3.02 in,'
6 , A 20 in. carbon steel p i p bas a wall thickness of 0.25 in. The minimum
specified yield stress is 47,000 psi at a design pressure 600 psig, The
design temperature is 17VF and the winter 8empere8urc Is 25°F. If the
bending stress is 9 2 0 psi, wdal is the rie-in temperature? (The tern- .
p r a t u r e range bemeen summer and winter is 25 lo 100°F.)
7. A crude pipeline of 18 in. diameter is lo be designed with i n operating
pwssure of 1300 psi and an operating temperature of 170°F. It is decided
that API-SLx, Grade X52 electric-resisrance-welded pipe will be used
The joint elificiency of the weld is 85%. The specified minimum yield
stress is 53,000 psi. Construction temperature is expected to be 75°F. I[
the h n d i n g stress is 9750 psi, what will be the pipe wall thickness?
8, If the pipe of Exercise 7 wiPl be fully restrained, what will be the
longitudinal stress at anchor point?
9, For a 2Bin. pipeline the required maximum operating pressure is
67Opsig and the maximum expected operating temperature is 165°F.
The material of pipe will be API-SLx, Grade X52 with a specified
minimum yield stress of 49,000 psi. Based on pressure the calculated wall
thickness is 0.25 in. If the rie-in temperature has to be at ?S°F with a
kndirng stress 7700 psi, calculate stress in the pipe.
REFERENCES
t
-2
I . Information on valves are available from:
Vogt Forged Steel Valves, Fittings, Union, Ranges, Catalog F- 12.
-.--
1 a:
:
;I(
;
?'
2.
4.
4.
5.
6.
7.
8.
9.
10.
Powell Valves, Catalog 75
Welvorrh Valves, Catalog 130
Crane Valve Fittings, Catalog No. 60
King, C . Reno and Ssbin Croker. Piping !#and Book, New York: McGrew-Clill
Amir, S. 9. "Calculating Hear Transfer from a Buried Pipeline." Chemical Engineering
(August 4, 1975).
Schweirzer. Nandbaok o/ Conosion Resistant Piping, industrial Press.
Mord, Melvin. Rxtbook o/ Engineering Maren'als, New York: Wiley,
ANSI Standard A58.1, Wifld Lnads /or Buildings and Other Sfrucrures
keonards, Ci. A. Fourrdarion Engineering, NEW York: McGraw-Hill.
Wens-Corning, Plastic Pipc Program.
l%r Grinnell. ""Pipe Hanger Design and Engineering," in Wcighf o/ Piping Matedals,
revixd in 1979.
Truong, 8.
Piping Conference". at Texas A & M University, Texas,
April, 1983.
NUCLEAR COMPONENTS
CODE ASME SECTION Ill
DESIGN LOADS AND SERVICE LlMmS
Nuclear Components Design G d e , ASME Section III (reference 5 in
Chapter 4) requires ellecrs of earthquake lo be included in the design of
piping, piping suppo"s, and restraints (see Section IZI, subsection NG-3622,
Dynamic ERfects). The loadings, the movements including earthquake
anchor movements, and number of cycles lo be used in rke anaigsis are part
of the design sgecificalions. The stresses resulting from these earthquake
eRecrs must be included with weight, pressure or other applied loads when
making the required analysis. Section 111 also requires design ioadings
(NG-36 1 ).2(b)), and service loadings (NC-361 I .2(c)) be sgecified. Sewice
loadings are grouped as Level A (Eqs. 10.18 and 10.111, Level B (Eq
10.9U), Level C (Eq. 10.9E), and k v e l D (Eq. 10.9@ service limits. See
also Chapter 6 lor a brief explanation of these service limits. Sewice limits
LI, C,and D require inclusion of earthquake loads. Design loading is given
by Eq. 10.8. Equation numbers 10.4 to 10.7 have k e n eliminated so that
equation numbers used in (Table 10.2) will be the same as those used in
Section Ill (reference 5 in Chapter 4)
and Class 3 (PlDi
Nuclear piping is classified as Chss I (NB),Class 2 (NQ?),
piping. The piping connecting the reactor and the steam generator and othe!
critical piping comes under Class I analysis, which is k y o n d the present stop"
of this book. Sample analysis of a Class I Nuclear Piping System prepared b'
ASME Boiler and Vessel Committee would b9: helpful lor further reading
Design of Class 2 is presented here. M a t companies conservatively desigl
Class 3 piping under Class 2 guidelines.
B m c h carnmcfion (6)
1
Butt weld (1)
6
LS&O~->O.I
Figure 10.1
Fig. NC-3673.2tbr-2, &c III
1
1.0 forBush weId
1.(3 for =-welded
1
2.1
'i
C
Fact-wlded joint, socketwelded Bange, or ing1ewelded slip on Range
Fig. 1\1(2-3673.2(b)-3,
sketch= (a). (b), (c),
(6)and (I)
sketch (dl
---
/-
i
.-
30" tapered nransi~on
(ANSI BL6.25) (1)
Corecen~creducer
( m S I B16.9 or
MSS SP48) (7)
--
*e;d$ed
p r p jmnl
or tku@AzcdedRange
--
I
2.3
or corngated or cm-d
&a,
R - W d m o f e l W 0 f p kX
~%
m.
%
<)ne end
bged
6
= ha/""
h t h e& b g e d c = hv3
6. 17ne e q m k n ; ~ p p b nonly il rtne Iollorrkrrg eodrix,m are met:
(a) l"bc reiiolorcemnt area r e q ~ e m e n aof NC-3643are met.
in the l o n g i ~ d h aclirecljon
l
or is mt less brvvo
d corner radiur r, (Eg.
NC-3673.2(bb2) (fig. 10.1) is bemeen 10 and 50% of T,.
r2 is no%less than the larger of T,/Z. iTh4 y)/Z (Fig. NC-3673.2(b1-9 (Fig. 10.1) sketch (c))or T,i9.
(0 % ourelr radiius r, is mr lers thm the Irrger of
(d)
i
( e ) The outer radius
oRscr for the configurarians s b n in Figs. NC-3673.2(b)-Z (Fig. 10.1) skercbc~(a) anrl (b)
5 0.5.
7, llYe qwbw apaiies only if r)K: Iollooving c o d t i o m are mt:
(a) C o w angle a does not exceed 60 &g., and the mducer is concenrric.
(b) 77M: larger of D,lr, arad 4 / r z does not exceed 100.
not l e u than r, t h u g b u r rhc:M y of t k raducer, except in and i m h t e l y adjacent to the c y i ~ c a l
1 e d , where rhe thic
shall
lesz r,.
bending; Rexibility factor for tonion equals 0.9.
9. Tbc dnigncr i~cautiorred that cast bun weldingelbows m y have collsidenbiy hssvier walls than that of rhr pipe ulth wkich they
are ured. Lvge e m n m a y br: inlroduced unleu the ~Becrof rhssc greater lhickncues 8s consrdcred.
t h
(g)
%/l: 5 50 and FJR-
am
4.
dk
1b-
I
,al
A. S ,
I,.
Frsxil
8
mnd S
Inten
-;
8
1' d
__+I
2. Calculate SIF for concentric reducer with a larger diametcr of 6.625 in.
and smaller diameter of 4.5 in. Thickness on the larger side is 0.280 in.
and smaller side is 0.237 in. (Fig. 10.2).
.Cone angle of reducer = a = sin-"
= sin-"0.193 18)
a = 11.138 deg
Check for use of the SIF equation rn Table 10.1, Note 7:
--I bPII. Ti
Branch
= 1.00
Use
2
(dl
RGURE I0.I
Branch dimensions (ASME Section III. NC 3673,2(b)-2).
The above Equations apply only if conditions of Note 6 with Table 10.1
are met. Note that r&/R, = 0.5033, which exceeds the limit of0.5 slightly.
The stress intensification factor should be taken as the higher of the
value calculated above by the equation and the SIF for the branch pipe.
The SIF lor the straight p i p assuming the socket weld will be equal
to
2.3.
FIGURE 10.2 Concentric reducer
""r.
4
--
&.
or
M (DW, CS, PL)
M (Ti, St. or S2)
and
En, = M (BSIq
M A -- M (DW. CS. PL)
Icrovj
rim
calculated as t h e e compnenls M,.M,. M, The terns
M,. MgrMc r e p r e n t
rhc q u a r e m o t of the sum of the sq
d to reduce st-.
Cold spnng loads may be considered in load evaluataon on suppon and q u i p e n c . Irrelloa may
applied at spring supporn to relieve m d e load. Pressurn r h m t (in case of expamion jolnt kllours wthout lie rods) is icl&d evrch r k dm,
weight loads.
3. Evatua(ion of Eqs. 10.9U d 10.9F k not q u i f e d for caregoq PL piping (where only limited svucrural integrity is rquirrtd).
M E C& %tion In, Divkion 1. s u k c r i o n NC-3652. Analysis of Rping.
4.
avaaable at r k a n a l ~ i ps h a and rhw not inclded in the evaluation for fault& c o d t i o n .
5.
g ~ d F ~, $t
C
at
b r nroverrnenu SI and SZ may be inciluded in Eq. 10.9 or 10.10 but mr both.
10.9Upius Eq. 10.10 Or 10.11 m a t k ~ l i ~ k d .
vememt such as budding wctlemna.
MD for enaeisgcncy or faulted (scra&ry) load caw in Eq. I O . 1 k must include b t h contninmna t h e m 8 m v e w a t (CT)& ccrsn~nr.
w e a n t (CP)after a d a i g n basis accident (DBA).
l?g: c a l c u l a d by orsing fomdo PDba,f2(thickws).
s m s CS~F
2. Cold spiping sbuld not bc w
11. Td& 10.1:am k wed c o m w a ~ v e l yBar Class 4 -kg
hm com~mare%)a h .
f*
'-A
ANALYSIS FOR CUSS 2 (NC COMPONENTS) P ~ P ~ N G
STRESS ,EVALOATIOO\I
Table 10.2 gives criteria lor rigorous or comprehensive analysis for Class 2
piping (Reference I). The explanation of the abbreviations used in the
i s as follows:
-
!
DW = deal weight
CS cold spring
PL =. preload
VT valve thrust
WH = water hammer
E l = owrating basis earthquake load (OBE)
E2 =safety shutdown earthquake load (SSE)
JB = jet impingement
S 1 .= seismic anchor movement due lo ODE
S2 =. seismic anchor movement due ro SSE
BS = building settlement
Ti =: thermal iioad
CP = containment movement due to pressure after DBA
CT = containment movement due to temperature after DBA
P= design pressure, psi
Do==
outside diameter of p i p , inches
d, inside diameter of p i p , inches
i==stress in%ensificationlector
(i 2 1 , CD.75i2 1.0)
0.75 i cannot be less than 1.0
Z==andulus of section, in.'
AVC =active valve coeficienr (0.75 to 0.9)
DM = dynamic movement
DBA = design basis accident
& = basic allowable stress at minimum (cold) tempemlure, psi
& =basic slBowable stress at design temperature, psi (see Sec. I t l for
vaDues)
SA = allowable stress range (Eq. 4.1)
Pm, -: geek pressure, pi
Sy= yield stress, psi
PT beD!ow~pressure thrust, Ib
MBF Mm under faulted condition. It, Ib.
-
e
ifrhe natural frequency of a piping system is at or near the frequency cob an
exciting source, lor instance, a compressor, the resulting amplitudes may
bending stresses that read to premature fatigue failure. A necessarg,
design criterion must be therefore that the natural frequencies In a piping
sysiern must be significantly higher than or diflerenr from the frequencies of
ihe exciting source.
Natural Frequency In cycles per second is given by Eq, 10.3.
where L = length of pipe, feet
E = modulus of elasticity, psi
I = moment of inertia, in.'
W = weight of pipe, Ib/lr
a =value depending u p n end conditions and the m d e
consideration. See Table 10.3 lor values of a.
TABLE IO.3
End Condition
Rorh ends
sinply supplrted
Berth ends fixed
N ~ I u mFrequency
l
Calrulrllon ( a Value for
Configuration
I st
Mode
Fundamental( B st)
Second m d e
m. t(D.3)
Vaiuc of a
0.743
2.97
First rnoclc
Second mode
One end fixed;
one end simp'ly
First m d e
suppotted
Second mode
1.16
3.76
*
=L
Stress analysis will normally Lx: p d o r m e d for piping systems in the following categories:
1. Lines 3 in. and larger (a) connected ro rotating equipment, or (b)
subject to diaerential settlement of connected equipment andlor
supports, or (c) with temperatrrras less than 20°F
-
,
Lnites connected lo reciprocarlng equipment
\: Lines 4 in. and lareer connected to air coolers, steam generators:';,'
4.
5.
6.
7.
8.
9.
10.
11.
12.
9 3.
14.
15,
I
t o n g radius elbows will be used. (If short radius .4 i n y other k n d
radius, mark on the isometric.) For short-radius e l h w , radius=
diameter
Any allowable loading from manufacturers on pumps, turbines,
compressors? (From the vendor drawing for equipment.)
Any preference to use expansion imps, expansion joints, and so on,
if needed? (Chapter 5 )
Mark type of intersection (reinforced fabricated tee, elc.)
Mark support locations (available steel crossing, and so on) on the
isometric
1s hydraulic testing load condition 80 be considered to gel structural
support loads? (Eq. 2.7)
Pipe stress isometrics (x-, y-, z-axis) piping plans, and sections are
necessary.
fired heater lube sections
Lines 6 in, and larger wirh fchperatures of 250°F and higher
Lines with tempratures of 600°F and higher
Lines 16 in. and larger
.aloy lines
High pressure Pines
Lines subject lo external pressure
Thin-wailed p i p or duct of 18 in, diameier and over, having an
outside diameter over wall-thickness ratio of more than 90
Lines requiring proprietary expansion devices, such as expansion
joints and victaulic couplings
Underground process lines
internally lined process piping
Lines in critical service
Pressure relief sysierns
Maximum movements at branch location must be iower than
specified limit. The branch line should $e laid with enough flexibility
to absorb the header movement.
2. In nuclear piping analysis, the branch also needs to be included with
the kcader if the area moment of inertia ratio !hlh< 40. In other
words decoupling is not aifowed. Check company criteria foe the
ratio lo use.
3. BF branch pipe is analyzed separately, the movements at the decoupling should Re included as initial (or inrposed) movement in the
branch line calculation.'
4. The modulus of elasticity value at operating temperature may be
used for piping to calculate the loads at equipment as per standard
AP$ 610 (reference 7 in Chapter 7). Using Eh,wilf result in lower
loads because Eho, is lower than Ecold.The piping is more flexible
when E value is lower.
5. The guide should nor be located close to the change in direction. A
minimum leg is required for absorbing: the expansion. Calculate the
minimum leg as per m e t h d outlined in Chapter I .
6 , Credit cannot be obtained for cold spring in stress calculation. Only
loads at the equipment may be reduced by including the edfect of
cold spring.
7. Provide longer p i p s u p v r t shoes when axial deflections care large.
8. Nuclear Regulatory Commission issues regulatory guides to be !lo!lowed in design.
8,
Information Needed for Pipe Stress Analysis
B
pi
Outside diamefer of piping, wall thickness (or nominal diameter,
sch nurnkr) (Appendix A4)
2. Temperature, internal pressure
3. Material of piping. (Expansion coefRcien8. Young" smctdulus, and
material density will be selected for this material.) (Appendix A 2 )
4. insulation thickness and insulation material. ( I f not given, standard
thickness lor calcium silicate will be selected.)
5. Spcific gravity of contents
6. Any wind load lo be considered? If yes, thc direction of application
is imporrant.
7. Any anchor initial translation, bx in inches, B y in inches,
b a in inches. (For towers, exchangers, and so on, nozzle initial
translation is important.)
8. Corrosion allowance lor piping, inches
9. Range rating, psi (ANSI Bl6.S)
10. Standard valve weight and flange weight will be ((Reference 1 in,
Chapter 9 ) used. (For spcicai valves mark I ~ Cweight on pipe stress
isometric.)
1.
-8
ar
r Car
'on III
iSML
I
assumplions of a program logic, coding could kt,..Jesenl.
a h o r the following will assist computer modeling.
The results or commonly knodn as ourpur lrom computer-aided analysis
generally consist of the following:
Fmm Inpug: Coordinates of nodes or data points, length, diameter,
thickness, k n d radius, !oral weight of pipe, temperature, expansin"
coeficienl, modulus of elasticity, pressure, valve weights, lengths,
wind loads, support location, and types.
2. Results: Deflections, rotations, forces, moments, SIF, resultant
bending stress, torsional stress, and expansion stress.
3. Requirements for diflerent codes vary. The ASMEfANSl 831.3
compliance is discussed next.
(a) Wall thickness used should be greater than the minimum thickness required using Eq. 2.1.
(6)Pressure input should be lower than the allowed pressure calculated using Eq. 2.4.
(c) Expansion stress SEcalculated using Eq. 4.7 should .be less than
the expansion stress range lrom Eq. 4.1 or 4.2.
(dl Expansion stress does not include either weight or pressure
loading but only thermal loads.
(el The. additive stress SL should not exceed hot stress Sk.
SL = resultant knding stress from weight loads + longitudinal
pressure stress, SLP:
where
1,
I f the piping system is overstressed or if equipment nozzle loads are
excessive, then flexibility of piping system needs to be impmved as discussed i l l C11apLers I and 5.
ilntormatio%
Initial anchor movements, described later in detail
Type of intersections (see Figures 10.6 through 10.1 1)
Reducing tee
Fabricated lee
Unreinforced lee
Reinforced tee, pad or saddle
Weidolel
Sockoler
Sweeplet
Pipet
Lalrolel
Socket weld tee
Elbows, bends, miter k n d s , eibolet, socket weld eBhw, eldlet,
support on the bend, and flanged e l h w s (see Figures 10.17 through
10.18)
Concentric and eccentric reducers, reducing insert, and hail
coupling (see Figures 10.13 through 10.161
Cold spring, cut short or cot long (Eq. 4.12)
Wind loading (Reference 6 , Chapter 9)
.
Valves, flanges, valve operators, cap, blind flanges (see Figures
10.19 through 10.2 1)
Releasing anchor for a specific direction of the resrrainr, flexible
anchor, spring rate inclusion at nozzle anchors (Eq. 7.3)
Expansion joints (single bellows, gimbal, hinged, universal), presstlre thrust calculation (Eq. 5.4)
One directional supports
Insulation weight, content weight, refractory weight (Eq. 9.20)
L m p closure, coordinates of balance points
Jacketed piping (Figure 9.1 L)
4. Actual deflection (maximum considering dilleren! load cases) should
be lower lfian sleeve clearance.
5- Stress ratio is the ratio of code stress (Table 10.2) to allowable stress
and should be less than 1 .a.
Anchors and supports are moved by a calculated amount in the analysis to
include:
COMPWER MODELING
DiWerenl computer programs suggest the inputing (input coding) of
dih6"erent piping components dillerently. The following description outlines
,
a
4
-
4
-
.*
.
a
.
I
.I
llUlTlAL ANCHOR MOVEMEWS AND SBIPPQRT
MOVEMEWS
-
8
.
I. Movement due lo thermal growth of towen, heal exchangers,
pumps, turbines, and so on
Id0
i
~ r u % ~ oe~*sr~url(lnl;l
@r
~ v v l aSweL
r
,,,tian
*.,
(2
'x.
2. Building sertlemenl, rank settlement (may occur when piping is cald)
3. Seismic anchor and s u p p r t movements known as SAM
Figure H(D.3 shows a vessel with noures with different orientations. Calculated thermal movement is based on the mean temprature and length of
the vessel section. It is not unusual to have many diflererlt temperatures at
different elevations.
Thermal coegcient lor the temperatures is obtained from Appndix A I ,
and shown in Table 80.4.
The vessel material is carbon steel and diameter is 72 in.
Vt:rticaP tilerma1 growth at nozzle A = 12(O.m99)+ 14(0.014)
= 1.OM2 in.
Growth at nozzle B = 0.3 148 C 3(0.027) = 0.3958 in.
Horizontal radial growth at 13 .=
(0.027) = 0.08 1 in.
1
Growth at G
=I
O in.
Vertical growth at support D = 0.53 + 2.5(0.04 1 1 ) = 0.632 in.
Flexibility problems are severe when the vessel is hot and the piping is
cold. Elevation dillerenee between nozzle A and support D should be
mir~imumto avoid large growth diflerential and thus avoid a spring support.
Hf the support is built from structural steel (cold), a spring a! this support
location is necessary. When supported from the vessel, the support design
T
CmIFlrknt
(Iw P;eg. L0,3b
TABLE 10.4
Temp. O F
FIGURE 10.3 Tberrnel growth at the vesxl
in./lWft
load at D is critical and the vessel shell needs checking for local stress.
From support location D, the pipe a h v e it grows up and the piping k l o w it
grows downward. The first rigid support, shown as E,should not be located
close to the drop lo absorb the downward growth.
Figure 10.4 s h w s a heat exchanger. The impxlatant thing concerning the
exchangers is finding the base support that i s anchored (An) and the other
s u p p r l that is slotted shown as SI in Figure 105. The base with slots is
't
Y
x
RGDUllE l(l.5 Anchored and slotted supports lor heat exchanger
allowed to slide along the axis of the exchanger i+r direction in Figure
10.4). The selection of which one of the two is anchored could be based on
the growth of the connecting pipe. II is necessary that the exchanger grow
with the piping.
In Figure 10.4 the shell temperature is only 4(PF and the shell contracts
instead of expanding, The coeficient of expansion is 6.07 in./in.l"F.
Member A lo El (Fig. 10.6) is m d e l e d using the same cross section ss the
run p i p but is weightless. Member B to 42 is modeled using the same
internal diameter as the branch p i p but has mice the wall thickness but i s
weightless. A lurnpd weight should be added to point B bar the lalrolet.
The weight of any water or insulation will be included on the p i p
cross-section card.
End Preparation
Stress Intensification Factor Description
SBF
~ u rwelded
t
Poinr A (all connecting members) and
Point C (both connecting members)"
Computed
or general
Vertical growth at P = (+63)(6.07x 10-6)(40- 70) = -0.01 15 in.
r = nominal wall thickness of sun p i p
r = mean radius of run pipe
Point B (both connecting mernkrs)
('8:he negative sign shows that the shell contracts downward, b y =
-3.01 15 in.)
1.O
Horizontal growth at P = Ax = (- 1 1 l(6.07 X 10-')(40 - 70) = 0.002 in.
(The minus sign is used for I I in. because P is on the negative x side
qlchor A l in which horizontal growth starts.)
\
Ax
at Q
-
of
In Figure 10.7 m e m k r A lo B is modeled using the same cross section as
the run pipe but b weightless. Member B to 6: is modeled the same as the
branch p i p including weight per foot of p i p .
( lO8)(6.07 x 10-6)(40- 70) = - 0.0 197 in.
An in movement in x direction.
Sometimes two heat exchangers are stacked one over the other or right
next to each other. The expansion belween the exchangers is critically
inlmrlant.
End Preparation
Stress Intensification Factor Description
Burt welded
or eenera!
Point A (all connecting members)
For F ~ / Y R5 0.5
SIF
Computed
The marileling of piping elements described for Figures 10.6 through 10.21
is from the Tennessee Valley Authority (reference 1).
SIFR 2 1.5
Paint C. (both connecting membrs)"
R G V R E IQ.6 SIF &cling
C"r'JRE
R lul n
N
I aaltrrr n
~ Ii r~Pt
lor 45-degree
Computed
" At tk branch p i e mcrnker side of p i n t C use the larger ofthe SBF calculated Rerc and the
straight pipe S1F. This applks slso to tk lollowing p i n t C references.
Run
I
FIGURE 18.7 SIF modeling lor sweeplea.
R G U R E IF).-SIF
modeling lor 45-degree lateral
In Figuse 80.8 mernkr A to B is modeled using the same cross section as
the nun pipe Rut is weigh0ess.
M e m k r BS: to C (Fig. 10.8) is modeled using rhe same internal diameter
es the branch p i p but has mice the wall thickness but is weightless. A
lumped weight should be added to point B lor the sockolet. The weighl of
any water or insulalion will be included on the pipe cross-section card.
For Socket-welded type laterals mernlrers A to B,14 to C,and B to D me
modeled using the same nominal diameter pipe as the run pipe with rch 80
for 30001b class fittings and sch 160 used lor 60M)lb clars fittings but
weightless (reference 2). A lumped weighl should be added to point B for
the lateral. The weight of any water or insulation will be included on the
pipe cross-section card.
End Preparation
Stress intensification Factor Description
End Preparation
Butt welded
Point A (all connecting n e m k r s )
or general
Point C (both connecting memkrs)"
SlF
Stress intensification Factor Description
SIF
Computed
or general
SIF =
SIF ;2t. I .O
r = nominal wall thickness of the run pipe
r .= mean radius of rhe run pipe
Point B (both connecting members)
0.9
p
I
h s -r 1.97
r = nominal wall thickness of run pipe
r = mean radius of run p i p
8 -45"
Points A, C ,and D (lateral side)
lor r L 0.322'
r < 0.322
30" tapered transition
r = nomina\ wall thickness
1 .(P
h Branch
H *O
1.8
1-9
Weld Boss. Soekst Weld Half Coupling. Thrsadsd Half Coupling. Weld
Couplet
Run
iFIGUElE 10,1 SIF modeling lor sockolel, thredolel, and weidole#.
Member A lo B (Fig. 10.10) is modeled using the same moss section as the
run pipe but is weightless. Member B to C is modeled using the same
nominal diameter p i p as the branch with seh 80 lor 3W0 lb class fillings
and sch 160 lor 60411b class fittings but weighdess. A lumped weight
45" Lateral, 45"Rduclng Lateral, 45"Soeke8 Weld Lateral,
45O TTkrsahd Lateral
Foe butt-welded Isrerals, members A to 13 and El to D (Fig. 10.9) are
modeled the same as the run p i p including weighl per loot of pipe, and
m e m k r li. to C is modeled the same as the branch pipe including weighl
per fmt of pipe,
r side of p i n 8 C use the larger of the SIF cslculaled here and the
txr
?, . *I<. ' nr u, 'C r f i
v
6-
ff
mw#ms
should be added to point B lor the weld b s s . The weight of any water or
insulation will be included on the pipe cross-section card.
End Pr~~)ara!ior~ S:~CS;1n:ensificalion I"ac(or Description
Sib;
H G U R E 10.11 SIF nrodeling lor tee, =kc(
weld tee, and reducing tee.
Point C ( b t h connecting memkrs)"
Mernkr A to li; (Fig. 10.12) has the weight of the p i p and any water or
insulation on the pipe cross-section c a d . See other sheers lor intensification
Factors due to branch attachments on pipe.
R,
= mean radius of run pipe
r & = mean radius of brartch piyx:
T, = nominal wall thickness of run pipe
T b = nominal wall thickness of branch
End Preparation
pipe
=outside radius of coupling or boss
Point B (both connecting memkrs)
rb
2.25
Butt welded
or general
Tee, Socket Weld Tee, Raduclng Tee, Threeda?d Tss
butt-welded tees (Figure 10,1 11, members A to B and B to D are
modeled the same as the run p i p including weight per &lot of pipe. and
mlernkr E3 to C is modeled the same as the branch pipe. For socket-welded
type: tees, members A to B, B lo 6 , and B to D use the same nominal
diameter as the run p i p wilh sch 80 used for 3W111h class fittings and sch
I60 used lor hO(H) lb class fittings but weightless (reference 2). A l u m p d
weight should be added to point B lor the tee. The weight of any water or
insunation will be included an the pipe cross-section card.
,:(;or
I
End Preparation
Stress intensification Factor Description
BMl welded
Socket
Point I3
Points A, C , and D (tee side)
lor r 2 0.322
r < 0.322
30" tawred transition
r = nominal wall thickness
Point 13r
Computed
welded
Points A, C, and D (tee side)
I.0
or general
Rap joint
flange
Socket
welded
Threaded
Slip on
Range
Stress lnstensification Factor Description
Points A and B ( m e m k r side)
for r 2 0 . 3 2 2
r < 0.322
3V tawred transition
r = nominal wall thickness of the pipe
Points A and FO
SIF
1.0
l .S
1.9
1.6
Points A and B
2. 1
Points A and E3
Points A and B
2.3
2. 1
SIP
Computed
1.0
1.8
1.9
RlGURE 10.LZ SIF modeling lor straight p i p
Conccrncirlc R h c s r
Menliber A to
B (Fig. 10.13) is modeled the
same as the largest attached
RGURE 10.13 SIF modeling lor concentric reducer.
End Preparation
Stress Intensification Factor Description
SIF
Burt welded
on general
Point A (reducer side)
Point E (reducer side)
2.0
Member A to B (Fig. 10.15) is modeled using the same nominal diameter
pipe as the p i p connectkd lo point 131 but weightless: sckr 80 for 3 W l b
class fittings and sch 160 lor 6CNK)lb class fittings (reference 2). A iiumwd
weight should be added lo p i n t A For the insert, The weight of any water
or insulation will be included on the piw cross-section card.
SIF = 2.25 (same as socket-welded end).
Computed
Zr = section modulus of the larger pipe
& = section modulus of the smaller pipe
ISIGURE 10.15 S F modeling for reducing insert.
Eceanlrlc Reducer
Coupling, Tkrashd Coupling, Socket Weld Reduces Corrpilng
hlemke A to B (Fig. 10.14) is modeled the same as the largcr pipe
including weight per loot of pipe. The offset between A and B is modeled.
%nd Preparation
Stress lnrensificarion Factor Description
Butt welded
or general
Paint A (reducer side)
SIF
P
I
09
SIF= i;iij
Computed
I
h = 4.4 -
Milernkr A to B (Fig. 10.16) is modeled using the same nominal diameter as
the coupled pipe (largest nominal diameter if ir is a reducing coupling) with
sch 80 lor 30(H) lh class fittings and sch 160 for 6000 1b class fittings but
weightless (reference 2). A lumped weighr should be added to points A and
B lor the coupling. The weight of any water or insulation will be included
on the pipe cross-section card.
SIF = 2.25 (same as socket-welded end).
Is
Point B (reducer side)
Computed
SIF r 2.0
r = nominal wall thickness of the larger
P~P
rl = mean radius of the larger pipe
ZI =section modulus of the farger p i p
Z; =section modulus of the smaller p i p
FlGURE 10.16 SIF &@ring lor coupling.
For butt-welded elbows (Fig. 10.17) member A to C is modeled the same as
the attached pipe including weight per Imt of piw. A IBCP e l b w is
m d e l e d as two 91)0 elbows. If it is a reducing e l b w , m e m k n A to C i s
modeled the same as the largest attached p i p .
For socket-welded r y elbows,
~
members A lo 13 and B to @ are modeled
as straight members using the same nominal diameter as the attached g i v
with sch 80 lor 3000 1b class fittings and sch 160 lor 6
6
m16 class fillings
4 t J q q ! * F ~ @ - ~ ct r ~2 ) A ' t l r - f ~S-tei-ht -h~arlflbe a@Ae8to qoi"rt R fn*
B- t
.
A.
FlGURE 10.17
Valves, Valve whh
SIF mdcling for e l b w s .
No Operator
13, B lo 6 , and LTI lo D (if a p r a t o r exists)
ere modeled using the same internal diameter as the attached p i p but with
twice the wall thickness bur weigktless.,Mernbers A to B and B to C have
the weight of any water or insulation on the p i p cross-section card,
Member B to D is weightless. Lumped weights of the valve and o p r a t o r (if
operator exists) should be added to the points where needed. Two mass
points, one for valve and one for operator C.G, are required.
i n Figure 10.19, members A to
the e8bw. The weight of any water or insulation will be included on the
p i p cross-section card.
EIbolarl (Sockat Wsld, Bun Weld, Thrsackad)
h j e m k r A to C (Fig. 10.18) is modeled using the same cross section as the
pipe but is weightless. Member C to D is modeled using ,he same
internal diameter as the branch p i p but has twice the wall thickness but
weighl9ess. A Dumped weight should be added to point C for the elklet.
The weight of any water or insulation will be included on the pipe
cross-section card.
rrlw
!
'knd Preparation
Stress intensification Factor Description
Burt welded
or general
Point A (member A to E))
Same as the e l h w
Point A (member A to C) and point C
both connecting memkrs)
Point B (both connecting members)"
SIP
IF1GURE: 10.11) SIF modeling lor valves with no o p t a t o r .
All FDsngas
1.0
Computed
Mernkrs A lo B and El to C (Fig. 10.20) are modeled using the same
internal diameter as the attached p i p but with twice and well thickness but
weightless. A l u m p d weight should be added to LI lor the flange(s). The
weight of any water or insulation will be on the pipe cross-section card.
r = nomina! wall thickness of %Rerun
pipe
r = mean rrdim d Ik run p i p
R = kd rdim d e l h
FIGURE IO,Z@ SIF modeling lor Ranges.
I
RGUEIE: IB.21
SIF modeling lor c a p .
for the cap. The weight of a n y water on insulation will be included on the
p i p C ~ ~ S S - S C Ccard.
~ ~ Q ~
REFERENCES
1. Tennessee Valley Aarlbrity, Pli#ng A w ~ ~ hJ e~d Ju p e .
2 . &Rridgc PJQlionaILaliororory Rcgxlfl ORML-TM-4929.
APPENDIXES
WE
Canhn S w l
Temp.
9
Atlsce~hc
CWn-Moly
bw-Chrsm
(b
3Cr Mo)
5 C r Mo
tlvu
9 C r Mo
7.50
7.82
4.52
4.73
4.94
8.15
5.16
695
537
7W
5.63
425
750
5.W
4.92
5.14
5.38
6.16
5.62
Staiurless
Stcek
18 Cr-8 Ni
7.18
I 2 Cr
17 Cr
27 Cr
Moml
25 Cr-20 Ni
6.50
6.77
7.04
7.31
67 Nk30 Cu
3f Nickel
5.22
6.34
6.64
6.94
5.46
5.70
7.25
5.94
-
-
f
'9
I
WY
Allolunm
CastLron
Bronar:
Brass
70Cw30Ni
-4.68
-
-3.98
-3.88
-3.m
-3.40
-3.15
-2.87
-
-3.74
-3.50
-3.26
-4.46
-4.21
-3.97
-
-3.16
-2.70
-2.53
-
-
Dueaile
Temp.
-
-
-
-
-325
-3w
-275
-254)
Matcfiai
Adnm
G ~ Y
C;nstha
Brow
a m&ta ~an far asmuleon and it b not -lied
Brass
70Cu-30Ni
Ni-FcCr
NKr-Fe
that m t e P i d s an suitable lor all the remprames s
Ductile
Iron
Temp.
"F
TABLE 82 M d r a s cr( Elrrstiew,
US. Uariits, Im M e t e
Nlrrtd"
E = M ~ U I UofS El;rshctry, L?rr (mullaply abulated values by
-325
M a t d
unr
-200
-tW
70
206
300
T e m ~ r a mT
,
4W
500
600
700
800
105)
903
lCBOO
11OO
12W
130Q
1-
30.8
30.3
29.8
29.2
28.7
28.3
27.7
27.0
26.0
24 8
23.1
21 1
18 6
15.6
12.2
-
-
-
-
-
13.4
13.2
12.9
12.6
12.2
11.7
11.0
10.2
-
-
-
-
-
-
700
800
9QO
I W
llOQ
1
-
stek
(12Cr, 17 Cr,
27 Cr)
h
y ~t
M
E = Moddm of EIasliciry, hi (mdtigly tabulated values by 1W)
Tew-nm,
-325
a
-200
70
-10Q
rion and it k not implied h
t
marc&
fOO
200
T
300
400
5OO
600
uc slrirable f
a all t k temprarurcs s b m .
12W
m.
PblcM
SF&
M~
&aka
(37)
B m c b b m e Welded
A53
Factor
C&
(E)
CIlss
Temile
Shength
(ki)
%.
Yield
Smngtlt
Notes
(~uii)
M.
Teq.
(26)
Mn.
Tmp.
to 100
I
A
Trprc E
085
48.0
300
1.2
-20
13.6
ia53
1.
B
Type E
0.85
60.0
1.2
ar~o
I
1
0 85
-
34
-20
-20
17.0
-
-
350
0.85
48.0
30.0
1, 2
-20
3.6
0.74
45.0
0.74
0.74
0.74
49.0
52.0
55.0
25.0
30.0
33.0
40.0
5, 34
5, 34
5.34
5,34
-20
-20
-20
11.1
12.1
12.8
-20
13.6
A135
F+n
WcIM
-
A
R p (Shaigbt Seam)
1
M 00
1
3B 8893.1
NO GR c AIM
86"7 OR 10 81%
300
+
-
-
280
P
a
1
-
-
-
10.2
136
17 0
138
19 0
97
l3.B
13 6
10.5
91.4
12.1
12.8
-
10.0
10.9
11.6
122
I
, ,
ca,
-
""g?-I
I
I
I
I
I
I
I
I
4
I
I
I
l
l
1
w
maooco e w m m
I
b i>k;o;D bbobv,
,
_*
e
b
b b b b
r
_
-
C
*
IcN
C
_
)
_
b b '
)3
C r p l M L -
h)
* \ D O 0
p p t x , ~ ,
. . - - w -
";;hi%&
E
-%
0
-
6
TnrPLe
*S
Z
(can?~iaw)
.
Iw Met*
iiaT
P
-
34 Ni
M33
9B
3
-
-
341 M
1 C r 4 Pli-CwdU
21 Ni
A334
M33
9B
3
-
4
4
A333
9A
7
9A
7
-
24 Ni
9 Ni
9 Ni
2 N c ~Cu
2 ~ i - -eu
l
A334
M33
8334
9A
9
oA
9
Cr-f Mo
i C r 4 Mo
3 er+w
5CdMeSI
M35
3
PI
M35
3
Ir2
~335
5
AS35
5
~5
P5b
a 3 5
A334
-35
5
B5c
5
5
P7
A335
4
A335
4
PI 1
81 2
5 Cr-+ %Ti
7 Cr+ Mo
9 61-1
Mo
If C r d Mo
10 - 4 Mo
a 3 3
11A-SG1
8
a34
B1A-%GI
8
P9
-
-
-
-
-
SE,KS?!
Min.
Tensile
Min.
Yield
65.0
65.0
M,0
65.0
35.0
35.0
35.0
35.0
-
65.0
35.0
-
100.0
75.0
75.0
46.0
46.0
69
69
30.0
30.0
30.0
30.0
3
1m.O
63.0
63.0
55.0
55.0
M.O
(iO.0
60.0
-
50.0
60.0
-
50.0
Mt.0
30.0
30.0
30.0
30.0
30 1 )
-
-
-
-
-150
-150
-150
-100
21.7
21.7
20.0
21.7
-100
-320
-320
-100
-100
21.7
31.7
31.7
21.0
21.0
-
-20
-20
-20
18.3
18.3
18.3
18.3
-20
20.0
20.0
18.1
18.1
-20
-20
-20
20.0
20.0
20.0
18.1
18.1
18.1
,
19.6
19.6
19.1
19.6
19.6
31.7
31.7
-20
20.0
18.7
I
0 I
18 7
* , a m . -
4.4y.4
-c$...
- b - . c - . C -
4 m m
b o b
-,-,+-I4
i n o ~ n u lk k k k
raw
Ce--NNcc-.h)=-'h)
I J P I y ? ? J ? J +Pppppp
wln
rD * W c n I n
u , - * 4
PI.
.*
I
I
* , . d e w
-.-
b i 3 b b b b
I
. . C P
C
C
C
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0.065
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0.157
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0.076
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0.161
0.190
0.214
0.358
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0.123
0.167
0.219
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0.88
1.11
0.382
0.334
0.896
1.53
0.242
0.284
0.341
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0.38
0.158
0.104
0.161
0.195
0.321
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0.304
0.284
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0.235
0.291
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0.55
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0.412
1.43
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0.391
0.483
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0.598
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0.226
0.318
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0.278
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0.636
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0.295
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30
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0.375
0.500
0.593
0.219
0.328
0.438
0.519
18.580
19.250
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23.1
30.6
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18.814
16.2
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0.655
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0.625
0.750
0.812
0.711
18.750
18.569
18.376
38.0
45.4
48.9
80
0.875
1.031
0.766
0.902
18.250
17.938
100
120
1.281
1.50
1.121
1.313
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corr;iision allowance = 0.10 in. The design pressure is SO0 psig at 700°1:. is
Ike design adequate for the internal pressure?
I
Solurion:
7 he allowable stress values from Appendix A 'I'able B.3 1.1( A p p c ~ d i x,431
are: for pipe, SE = 14.4 lisi; for ring, SE = 14.4 ksi.
Th= (0.500)(0.875)= 11.438 in.
i
5d
-.
.,. r Gal--.--on%l ~ . 4 n ~ hb.-,
4
I 1'
....art - ,.I*
24,
"
design cojldilions are 350 psig art 4tKPF. I t is assumed that the piping sptcm
is to remain in service until all metal thickness, in h r h branch and Reader, in
excess of that required by Equation 2.1 has corroded away. What reinlorcing is required lor this connection?
Soiution :
The allowable stress value from Appendix A, Table 1 of B31.3 (Appendix
A31 is SE = 16.0 ksi.
T, = (0.281))(0.875)= 0.245 in.
I
r, = 0.500 in.
(350)(8.625)
' -- (2)(16,000) + (2)(0.4)(350)= 0.0W5 in.
L4= 2.5(0.0245 - 0.10) 3- 0.500
= 0.8625. This is greater than 2.5(0.4.3W- 0.lO) = 0.845 in.
h
-
(350)(4.50)[))
= 0.1)4NX in.
( I ) (I6,oOo)+ (2)(0.4)(350)
d , = 4.500 - (2)(0./1488) = 4.402 in.
Reqr~iredreinlorcing area, A , = (1).0W5)(4.402) = 0.4 12 sq. in
Try fillet welds only
- 0, 10) 0.335
6.625 - 2(0.245
---- - - -- - = 7 . 1 15 in
dz = d , =
sin 61)"
0.866
= (2.5)(0.0933)= 11.234 in.
Or
I
,.fl'he required area, A , = (0.274)(7.3 15)(2 0.866) = 2.27 st4 in.
v
(2.111)
'fhe reinforcement area
in run wall, A2
= (1.4tlXscl.
= (7.3 15)(0.438- 0.274 - 0. IO)
in.
(2.12)
in branch wall, A3 = (2) 0.R45
-(0.245 0.866
(2.5)(0.04NH)
= 0.122in. use 0.122 in.
Due rt3 limitation in the height at the reinforcing zone, n o practical fillet weld
s i x will strpply enough reinforcement area; therefore, rile conneclion must
he reinforced hy a ring. T r y a ring of 64 in. 0.D (measured along thc
run). A~.;rrmcthc ling l o be cut from a picce o l NPS W Schedule 40 API L
(iradc A scamless pipe and welded to the connection with minimum size
lillcl welds
Min. pad thickness, 1, = (0.322)(0.875)= 0.282 in.
New I,,
.in ring, A4
or
(2.5)(0.0935)
= 0.281 sq. in.
in fillet welds, A, = (4)(4)($12
Total reinforcement area
+ 0.282 = 0.404 in.
= (2.5)(0.04138)
= 2.986 sqiin.
X, = 0.234(6.25--4.5) = 0.4 10 sq. in.
Leg Dimension of Weid:
An NPS 8 sun (header) in a n (311 piping system has an NPS 4 branch at rlghl
. n r n
f2 U.
1
I
A 0
A D
C
P
I SI
4'
a
n
,,,,!
use 0.234 in.
Reinforcernenl area in the sing (considering only the thickness within 14):
This total is greater than 2.27 sq, in., so that no additional reirrforcement is
required.
i n n l r r (Fin A I \ O a r ~ t RnGonr
= 0.234 in.
I *
Reinforcement area in Gllel welds:
I
X2= (2)(4)(0.228)~= 0.052 sq, in.
Total Reinforcement Area, A4 = %( C X2= 0.462 sq. in.
This total reinforcement area is greater than the required reinlorcirrg area;
therefore a reinforcing ring of (43 in. O.D., cut from a piece of NPS H
Schedule 40 ABI 5L Grade A seamless pipe and welded ao the connectictn
with minimum s i z fillet welds would provide adeqrraae reinforcing lor this
connection.
An MPS 14 3 W Ib forged steel socket welding coupling has been welded at
right angles lo an NPS 8 Schedule 40 header in oil scrvice. The header is
AST'M A53 Grade B seamless p i v . The design pressure is 400 psi and the
design temperature is 450°F. The corrosion aliowance is 0 . l O in. Is additional reinforcement required?
Sod ("ion:
Nkf Since branch is less than NPS 2 (according lo 8 3 1.3 Section 304.3.2(h))
the design is adequate to sustain the internal pressrlre and no ealctrlarions
are ateeessrery. It is presumed, of course, rhar calculations have shown the
run p i v 80 Lo satisfactory for the service conditions acscprding to Equations
2 . l , 2.3 and 2.4.
INDEX
Accelcralion. 35. 133
Active valves. 133. 181
Allowable deflection, 35
Allowable load. 126
AIlowable momrnl, 102, 109
Allowable span. 34
Allowable stres.c, 2. 50, IBO, 212
Allowable %trc.ir,
range, 13, 50
Allowable working pressure, 25
Allowance. 22
Alloy steel pipe, J
Aluminum alloy pipe, 9.40, 132, 139, 2 0 4
Anchor:
dircc~ionalanchor, 93
in~ermedia~c
anchor, 92
main anchor. 9 2
movcmcnl. 4. I87
ANSI coder. 49
ASME code, Scc 111.49. 171
ASTM standard$, 4
Atmospheric pressure, 135
Austenitic s~ccl,6. 202
Average gradient. 37
.
Rack fill. 146
Ball joints. 92
Beam, l8J
Bellows, 10.92. 181
Rending effect, 14
Bending stress, 14, 18. 73, 144
Bends. l I , 95.57, 172, 198
Bevel edged. 8
Bijlard'r curves. 107, 10")
Blank thickness, 25
Bolt circle. 102
Roll preload. 102
Rowing, 144
P 'CP 4 I
Bronze, 204
Bumper, 12
Buried piping. 148
Cap, 199
Carbon steel. 202,210
Carbon steel pipe. 3, ~ 1 , 2 0 2 , 2 1 0 , 2 8 2
Casting quaiity factor, 23
Caqc iron material. 2. 204
Centrifugal compreqsor. (28
Crntrtlugally cast pipe, 217
CenrriCugal pump, I29
Check valve, 8
Chemical composifion. 4
Class 2 (NC) piping, 180
Class 3 (ND)piping, 171
Closed space miter. 57
Codes:
ANSI code, 49
ASME code, 171
B 31.11 code, 72. I33
RJl.3code.53
B 31.4 code, 146
B 3 I .B code, 49
chemical plant code. 53
gas @ransportation
code, 49
liquid transporration code, 146
nuclear code, 171
power piping code, 133
refinery code, 53
Code stress. 72, I80
Cwfficient of expansion, 5,902
Coefficient of friction, 145
Cold moclulus, 19
Cold reaclion, 79
Cold sltring, 76. I B I
C k n rrt ! r I
Cone angle, 176
Conslant efforl supgort, I I
Conrainmenl prasure movement, l 8 l
Content weight, 4,35. 39,226
Conlraclion, 4
Copper alloy piping, 4, 132, 141
Corrosion allowance, 4,7,28
Corrugated piw, 11,@, 92, I75
Couplet. 193
Coupling, 193
Crwpelfect, 132, 165
Critical span, 34
Crotch thickness, 61
Cycles, SO, 52, 171
Cyclic condition, 3
Cylindrical vessel, l i l , 114, 159
ramping device, II
h a d load, 4, 182
h:ad weight, 1, 50
@efleclion,34
Densiiy, 5 , 19
Design basis accident, 181
Design loads, 171
h t i g n pressure, 26
Diameter, 226
Displacement ssrain, 50
()isroriion. 50
Orainage. 37
Dresser coupling, 92
Dynamic load factor, 136
'Dynamic loads, 4, 102, 141
Ductile material, 1 , 204
,
"langed elbow, 60. 176
Flangedjoint, bn. 101
Flexibility, 7, 10
Flexibility characterirlics. 57.68, 172
Flexibility factor, 57.61, 172
Flexibilily stress, 72
Flexible joint, 92
Flow friction, 4
Fluid flow, 2 1
Force, I
Formal analysis, 53
Frictional resistance. 146
I.atrolet, 1%). 192
I.cakage at flange. 7
I.imir slop, 12
l ivc ioad, 4
I.oad coefficienl, 147
I.oadingon pipe. 4
I.OCA. 102
Iocal stress. 109
I.ongiludina1strew, $0, 146
I.ong radiuc elbow, 62
I.oop. 10.68.82, 84, 85, 89
Manufacturingtolerance, 22, 28
Markl equation, 56
Mass type insula~ion.38
Malerials for piping. 3
Maximum strain theory, 144,
Metal area, 10.226
ftl~ralbellows, $4
Metal hose, 92, 9")
Metal weight, 35, 226
Metric units, 132. 167
.
Mill tolerance, 33
Minimum thickness. 22
Mi.rma~cll,I45
Miter bend, 26, 30, 57-63, 172
Miter space, 64
Mode, I83
Modulus of elasticity, l. 5,210
Mod~rlurof <ection, 15, 226
Momcnt I
Momclit of inertia, 15, 226
Monel, 202
M~llriplen~itcrbend, 26
Gap, 83
Casket. 8. 102. 104
Gas piping, 49
Gate valve, 8. 132
Globe valve, 7
Gradient check, 37
Gravity loaditlg, 4, 182
Grinnel method, 15, 21
Guide, 46,83
Guided cantitever method, t L
klanger, I ¶
Ilastelloy, 4, I44
Header, 32, 56
High e18ergypiping, 99
tlooker law. I
Hoop stre%%.
146, IRD
Hose, 92
)lot moduluc, 7, 35
Hol sires, 41, SO
Elydros8atic teri prcrture, 26,97
.
Earthquake, 3, 171
EIMA, 92
E:bolet, 198
EIaow, 57, 172, 197
Emergency condition, 180
End condition, 34
Equipment loads, 109, 121
Expansion, 4,202
Expanqion ccxfflcienr, 10,202
Expansion join!, I t . 81,92,95,99, 181
Expansion loop, 10,82
External moment, 102
External pressure, 4, 101, 149
External pressvre design, 132, 148
Exfraneous motion, 54, 187
Exfruded tee, 59
EZFkEX computer program, I 5
hetor o l mfety, 2
Rilure, 2
Faligue, 7, 50
hutted ~o~ldition,
lw
Ferme, material, 210
Fillet wrltlprl inint 60
impact Force, 5
Incoloy, 144
Inconnel, 4. I44
lnplane bending momcnt, 55
lnplane SlF, 57
Insert, 197
Inside diameter, 226
Installation remperalure. 5
In'iularion, 5. 38
lnrulation weight. 35, 39
Interference, 83
lnrermediatealloy steel. 5 , 6 , 91, 202, 216
Internal pressure, 4, 90, 101
Interpolation, 29
ITF Csinnel merhod, 14.21
Jacketred piping, 3, 032, lBrO
Jet impingement, 18%
joint quality laclor, 23
83
Nailtral frequency, 34, 1.36. 183
NFMA eqclatton, 125
Nickel alloy pipe. 4, 132,202
Nomograph lor loops, 89
Non-ferrousalloys, 141, 21 I
Normal cond~tion,180
Noi.rle load\. I?.)
N O T ~%ttfhes~.
~C
l !B
Nuclear code, 49, 171
Occasional loading, 180
Offrct, II
O p n discharge system, 135
Operating ba.;is aarlhguake, 102, 882
Orifice. 8
Oulplane bending moment, 95
ButplaneSlF, 57
Outride diameaer, 226
Packed joints. 92
Pad, 30,69.65
Pipc T I I ~ I ~ I F1RB
~ ,
Plastic pipins, 132
'
Poisson's ratio, 5, 19
Preloading. 981
Preloadingon bolls, 10%
Pressure components, 22
Pressure design thickness, 22, 30
Pressure drop, 7
Pressure loading, 4, 50
Pressure rating of flanges, 9. 103
Pressure relief valve ihrust, 132,139
Pressure slress, 180
Pressure thrust force, 96. I81
Pressure vessel code, 49, I55
Primary loading, 4
Proportional limit, 1
Pulsation, 35, 169
Pump loading, $28
Rad~alrfrcts. 146
Radirts of gyra~ion,226
Raised race flange, R, 101
Reactor, 171
Rcaztor building, JR
Kcduccr, 175, 179, I95
Rcdircing tee, 194
Rcllective insulalion. 38
Reinforced branch, 58
Reir~forcedtee, $8. 173
Reinforcement, 29, 236
Reinforcement zone, 30
Relief valves, 53, 133
Reqilent support. 12
Resonance, 35
Resting support, I2
Resrraint, 12
Resnlss, 186
Rigid tuppori. I 2
Ring, 32
Rod hanger, 12
Rotatingequipment, P23
Rupture, 181
Saddle, 32.61
Safery shutdown earllrqtlake, 102, B BZ
Sag, 31
Schedule number, 228
Seamless pipe, 3, 8,212
Secondary loading, 4, D7BBI80
Section modulus, 14, 226
Section modulus Tor branch, 73
Seismic anchor movement, 18%
Selsmlc loads, 4,46
Self
*, limiting load, 4
p