Attachment 1 - Asme b31.8 - 2007

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ASME B31.8-2007

Table 832.2 Thermal Expansion of Carbon andLow Alloy Steel

Temperature, Total Expansion, in./100 ft,F Above 32F

32 0.060 0.2

100 0.5125 0.7150 0.9175 1.1200 1.3225 1.5250 1.7300 2.2350 2.6400 3.0450 3.5

of all parts of the line and all restraints, such as rigidsupports or guides, shall be considered.

(d) Calculations shall take into account stress intensi-fication factors found to exist in components other thanplain straight pipe. Credit may be taken for the extraflexibility of such components. The flexibility factors andstress intensification factors shown in Table E-1 maybe used.

(e) Properties of pipe and fittings for these calcula-tions shall be based on nominal dimensions, and thejoint factor E shall be taken as 1.00.

(f) The total range in temperature shall be consideredin all expansion calculations, whether piping is cold-sprung or not. In addition to the expansion of the lineitself, the linear and angular movements of the equip-ment to which it is attached shall be considered.

(g) Flexibility calculations shall be based on the mod-ulus of elasticity corresponding to the lowest tempera-ture of the operational cycle.

(h) In order to modify the effect of expansion andcontraction, runs of pipe may be cold-sprung. Cold-spring may be taken into account in the calculations ofthe reactions, provided an effective method of obtainingthe designed cold-spring is specified and used.

832.4 Reactions

(a) Reaction forces and moments to be used in thedesign of restraints and supports for a piping system,and in evaluating the effects of piping displacements onconnected equipment, shall consider the full range ofthermal displacement conditions plus weight and exter-nal loads. Cold-spring may be useful for maintainingreactions within acceptable limits.

(b) The reactions for thermal displacements shall becalculated using the elastic modulus corresponding tothe lowest temperature of an operational cycle.

23

Table 832.5 Modulus of Elasticity forCarbon and Low Alloy Steel

Temperature, Modulus of Elasticity,F psi 106

100 30.270 29.5

200 28.8300 28.3400 27.7500 27.3

(c) Consideration shall be given to the load carryingcapacity of attached rotating and pressure-containingequipment and the supporting structure.

832.5 Modulus of Elasticity

The modulus of elasticity for carbon and low alloysteel at various temperatures is given in Table 832.5.Values between listed temperatures may be linearlyinterpolated.

833 DESIGN FOR LONGITUDINAL STRESS

833.1 Restraint

(a) The restraint condition is a factor in the structuralbehavior of the pipeline. The degree of restraint maybe affected by aspects of pipeline construction, supportdesign, soil properties, and terrain. Part 833 is applicableto all steel pipingwithin the scope of B31.8. For purposesof design, this Code recognizes two axial restraint condi-tions, restrained and unrestrained. Guidance in cat-egorizing the restraint condition is given below.

(b) Piping in which soil or supports prevent axial dis-placement of flexure at bends is restrained. Restrainedpiping may include the following:

(1) straight sections of buried piping(2) bends and adjacent piping buried in stiff or con-

solidate soil(3) sections of aboveground piping on rigid sup-

ports(c) Piping that is freed to displace axially or flex at

bends is unrestrained. Unrestrained piping mayinclude the following:

(1) aboveground piping that is configured toaccommodate thermal expansion or anchor movementsthrough flexibility

(2) bends and adjacent piping buried in soft orunconsolidated soil

(3) an unbackfilled section of otherwise buriedpipeline that is sufficiently flexible to displace laterallyor which contains a bend

(4) pipe subject to an end cap pressure force



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fittings for these calcula-hese caminal dimensions, and thensions, an

en as 1.00.n temperature shall be considerede shall be consid

culations, whether piping is cold-hether piping is caddition to the expansion of the lineexpansion of the

and angular movements of the equip-he equip-h it is attached shall be considered.ed shall be considered.

bility calculations shall be based on the mod-bility calculations shall be based on the mod-lasticity corresponding to the lowest tempera-sticity corresponding to the lowest tempera

f the operational cycle.perational cy) In order to modify the effect of expansiono modify the effect of expan

ontraction, runs of pipe may be cold-sprung.f pipe may be cold-sprunspring may be taken into account in the calcunto account in the calcuthe reactions, provided an effective method oeffective method othe designed cold-spring is specified andpecified and

832.4 Reactions4 Rea

(a) Reaction forces and momenReaction forces and momdesign of restraints and suppodesign of restraints and suppoand in evaluating the effects oand in evaluatingconnected equipment, shaconnected equipmethermal displacement conthermal displacemennal loads. Cold-springnal loads. Cold-sprinreactions within acceactions within ac

(b)(b) The reactionThecalculated usincalculated uthe lowest tehe lowest te

Elasticity fororlloy Steel cModulus of Elasticity,y,psi 106 c30.229.528.828.30 27.700 27.3w.) Consideration shall be given to the load carrshall be given to the loapacity of attached rotating and pressure-conotating and pressure-cequipment and the supporting structure.and the supporting structure.832.5 Modulus oModulus of Elasticityf ElasticityThe modulus of elasticity for carbomodulus of elasticity for carsteel at various temperatures is givarious temperatures is gValues between listed temperatValues betweinterpolated.interpolated.

833 DESIGN FOR LONIGN F

833.18 Restrraintaint

(a)(a) The restraintraibehavior of thebehavior of thbe affected baffecteddesign, soin, soto all steto allof desof destiontioe

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ASME B31.8-2007

833.2 Calculation of Longitudinal StressComponents

(a) The longitudinal stress due to internal pressure inrestrained pipelines is

Sp p 0.3SH

where SH is the hoop stress, psi(b) The longitudinal stress due to internal pressure in

unrestrained pipeline is

Sp p 0.5SH

where SH is the hoop stress, psi(c) The longitudinal stress due to thermal expansion

in restrained pipe is

ST p E(T1 T2)

whereE p the elastic modulus, psi, at the ambient temper-

atureT1 p the pipe temperature at the time of installation,

tie-in, or burial, FT2 p thewarmest or coldest pipe operating tempera-

ture, F p the coefficient of thermal expansion, 1/F

If a section of pipe can operate eitherwarmer or colderthan the installed temperature, both conditions for T2may need to be examined.

(d) The nominal bending stress in straight pipe orlarge-radius bends due to weight or other externalloads is

SB p M/Z

whereM p the bending moment across the pipe cross sec-

tion, lb-in.Z p the pipe section modulus, in.3

(e) The nominal bending stress in fittings and compo-nents due to weight or other external loads is

SB p MR/Z

where MR is the resultant intensified moment acrossthe fitting or component. The resultant moment shall becalculated as

MR p [(0.75ii Mi)2 + (0.75io Mo)2 + Mt2]1/2, lb-in.

whereMi p in-plane bending moment, lb-in.Mt p torsional moment, lb-in.M0 p out-of-plane bending moment, lb-in.

ii p in-plane stress intensification factor fromAppendix E

24

io p out-of-plane stress intensification factor fromAppendix E

The product 0.75i 1.0(f) The stress due to axial loading other than thermal

expansion and pressure is

SX p R/A

whereA p pipe metal cross-sectional area, in.2

R p external force axial component, lb

833.3 Summation of Longitudinal Stress inRestrained Pipe

(a) The net longitudinal stresses in restrained pipe are

SL p SP + ST + SX + SB

Note that SL, ST, SX, or SB can have negative values.(b) The maximum permitted value of |SL| is 0.9ST,

where S is the specified minimum yield strength, psi,per para. 841.11(a), and T is the temperature deratingfactor per para. 841.116.

(c) Residual stresses from construction are often pres-ent; for example, bending in buried pipelines wherespanning or differential settlement occurs. These stressesare often difficult to evaluate accurately, but can be disre-garded in most cases. It is the engineers responsibilityto determine whether such stresses should be evaluated.

833.4 Combined Stress for Restrained Pipe

(a) The combined biaxial stress state of the pipelinein the operating mode is evaluated using the calculationin either (1) or (2) below:

(1) |SH SL| or(2) [SL2 SL SH + SH2]1/2

Themaximumpermitted value for the combined biax-ial stress is kST where S is the specified minimum yieldstrength, psi, per para. 841.11(a), T is the temperaturederating factor per para. 841.116, and k is defined inparas. 833.4 (b) and (c).

(b) For loads of long duration, the value of k shall notexceed 0.90.

(c) For occasional non-periodic loads of short dura-tion, the value of k shall not exceed 1.0.

(d) SL in para. 833.1(a) is calculated considering boththe tensile and compressive values of SB.

(e) Stresses induced by loads that do not occur simul-taneously need not be considered to be additive.

(f ) The biaxial stress evaluation described aboveapplies only to straight sections of pipe.

833.5 Design for Stress Greater Than Yield

(a) The limits in paras. 833.3 and 833.4 may beexceeded where due consideration is given to the ductil-ity and strain capacity of seam weld, girth weld, and



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erwarmer or coldercolderoth conditions forns for T2T

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SB p M/Z

ending moment across the pipe cross sec-nding moment across the pipe cross sec-n, lb-in.b-in.

he pipe section modulus, in.ection mod 3

The nominal bending stress in fittings and comng stress in fittings and conts due to weight or other external loads isr external loads is

SB p MR/Z

where MMRR is the resultant intensified mis the resultant intensified mthe fitting or component. The resultant mor component. The resultcalculated ass

MMRR pp [(0.7575iiii MMii))2 + (0.75io M

wherehereMi pp in-plane bending min-plane bendingMMt p torsional momentorsional momeMM00 pp out-of-plane bout-of-

iiii pp in-plane stin-planAppendixAppendi

tion factor fromfrom

oading other than thermalhermal

X p R/A

al cross-sectional area, in.l area, 2

al force axial component, lbnent, lb

mmation of Longitudinal Stress inongitudinal Stress inestrained Pipe

The net longitudinal stresses in restrained pipestresses in restrained pip

SSLL pp SSPP ++ ST + SSXX ++ SB

Note thatat SSLL,, ST,T SX, orr SSBB can have negatcan have n(b) The maximum permitted value ofmaximum permitted value of

where S is the specified minimum yiethe specified minimum yieper para. 841.11(a), andr para. 841.11(a T is the temfactor per para. 841.116.actor per para. 841.116.

(c)) Residual stresses from consResidual stresses from conent; for example, bending inent; for example, bspanning or differential settlspanning or differentare often difficult to evaluaare often difficult to evgarded in most cases. Igarded in most cases.to determine whethero determine whethe

833.4 CombinedCombine

(a) The comThe comin the operahe opein eithern either

(1)(1

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ASME B31.8-2007

pipe body materials; and to the avoidance of buckles,swelling, or coating damage.

(b) The maximum permitted strain is limited to 2%.

833.6 Summation of Longitudinal Stresses inUnrestrained Pipe

(a) The net longitudinal stress in unrestrained pipe is

SL p SP + SX + SB, psi

(b) The maximum permitted longitudinal stress inunrestrained pipe is SL 0.75ST, where S is the specifiedminimum yield strength, psi, per para. 841.11(a), and Tis the temperature derating factor per para. 841.116.

833.7 Flexibility Analysis for Unrestrained Piping

(a) There is no need for formal flexibility analysis foran unrestrained piping system that

(1) duplicates or replaces without significantchange a system operating with a successful record

(2) can be readily judged adequate by comparisonwith previously analyzed systems

(3) is of uniform size, has no more than two pointsof fixation, no intermediate restraints, and falls withinthe limitations of the following empirical equation

DY

(L U)2 K

whereD p nominal outside diameter of pipe, in.K p 0.03, for U.S. customary units listed in the equa-

tion aboveL p developed length of piping between anchors, ftU p straight line separation between anchors, ftY p resultant of total displacement strains, in., to be

absorbed by the system

NOTE: No general proof can be offered that this empirical equa-tion always yields conservative results. It is not applicable to sys-tems used in severe cyclic conditions. It should be used withcaution in configurations such as unequal leg U-bends havingL/U > 2.5; or nearly-straight saw-tooth runs; or where i 5 dueto thin-walled design; or where displacements not in the directionconnecting anchor points constitute a large part of the total dis-placement. There is no assurance that terminal reactions will beacceptably low even if a piping system falls within the limitationsof para. 833.7(a)(3).

(b) Any piping system that does not meet one of thecriteria in para. 833.7(a) should undergo a flexibilitystress analysis by a simplified, approximate, or compre-hensive method as deemed appropriate.

25

833.8 Flexibility Stresses and Stresses Due toPeriodic or Cyclic Loading

(a) The stress range in unrestrained piping due tothermal expansion and periodic, vibrational, or cyclicdisplacements or loads shall be computed as

SE p ME/Z

where ME is the resultant intensified moment rangefrom one stress state to another. The resultant intensifiedmoment shall be calculated as

ME p [(iiMi)2 + (ioMo)2 + Mt2]1/2, lb-in.

(b) The cyclic stress range SE SA, where

SA p f [1.25 (Sc + Sh) SL]

f p 6N0.2 1.0

N p equivalent number of cycles during theexpected service life of the piping system

Sc p 0.33 SuT at the minimum installed or operatingtemperature

Sh p 0.33 SuT at the maximum installed or operatingtemperature

SL p longitudinal stress calculated according topara. 833.6(a), psi

Su p specified minimum ultimate tensile strength,psi

T p temperature derating factor per para. 841.116

(c) When the computed stress range varies, SE isdefined as the greatest computed stress range. The valueof N in such cases can be calculated as

N p NE + [ri5Ni] for i p 1, 2, n

whereNE p number of cycles ofmaximumcomputed stress

range, SENi p number of cycles associated with stress

range, SiSi p any computed stress range smaller than SE, psiri p Si/SE

833.9 Local Stresses

(a) High local stresses are usually generated at struc-tural discontinuities and sites of local loadings.Although they may exceed the material yield strength,such stresses may often be disregarded because theyare localized in influence, and may be self-limiting orrelieved by local deformation. Examples include stressesin branch connections caused by pressure or externalloads, or stresses at structural discontinuities. This Codedoes not fully address the maximum allowable valuefor local stresses. It is the engineers responsibility todetermine whether such stresses must be evaluated.



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ore than two pointso pointsints, and falls withins within

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U)2 K

l outside diameter of pipe, in.for U.S. customary units listed in the equa-omary units listed in the equa-

n aboveabdeveloped length of piping between anchors, ftveloped length of piping between anchors, fstraight line separation between anchors, ftght line separation between anchors, ft

p resultant of total displacement strains, in.,of total displacement strainsabsorbed by the systemthe syste

NOTE: No general proof can be offered that this eoffered that this etion always yields conservative results. It is notays yields conservative results. It is notems used in severe cyclic conditions. It shused in severe cyclic conditions. It scaution in configurations such as unequaon in coL/U > 2.5; or nearly-straight saw-tooth2.5; or nearly-straight saw-toto thin-walled design; or where displacalled design; or where displaconnecting anchor points constituteconnecting anchor points constitutplacement. There is no assuranceplacement. There is nacceptably low even if a pipingacceptably low even ifof para. 833.7(a)(3).of para. 833.7(a)(3).

(b)(b) Any piping syAny piping sycriteria in para. 8criteria instress analysis bstress analyhensive methensive met

esses Due toog

nrestrained piping due tong driodic, vibrational, or cyclicl, or c

shall be computed as

SE p ME/Z

he resultant intensified moment rangeintens state to another. The resultant intensifieder. The

all be calculated as

ME p [(iiMi ii))22 + (+ (iiooMMo)2 + MMtt22]]1/21/2, lb-in.,

b) The cyclic stress ranges range SSEE SSAA, where, where

SSAA p f [1.25 (25 (SScc + Sh) SSLL]]

ff pp 66NN0.20.2 1.01.

N pp equivalent number of cyequivalent number of cexpected service life of theexpected service life of th

Scc p 0.330.33 SuT at the minimumtemperaturetemperature

SSh pp 0.330.33 SSuuTT at the maxiat the maxtemperaturemper

SL p longitudinal sngitupara. 833.6(ara. 833

SSu p specified mcifiedpsi

TT pp tempet

(c) WheWhdefineddefinofof NN i

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Attachment 1 - Asme b31.8 - 2007