New Piping Flexibility Rules in ASME B31.3 AppendixP - Becht & Diehl - ASME - 2006

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Charles Becht IVBecht Engineering Co., Inc.,

22 Church Street,P.O. Box 300,

Liberty Corner, NJ 07938e-mail: [email protected]

David W. DiehlCOADE Inc.,

12777 Jones Road, Suite 480,Houston, TX 77070-4674

e-mail: [email protected]

New Piping Flexibility Rulesin ASME B31.3, Appendix PAlternative rules for performing flexibility analysis were added, as Appendix P, in ASMEB31.3, the Process Piping Code, 2004 edition. These rules are considered to be morecomprehensive than before; they were designed around computer flexibility analysis. Todetermine stress range, the difference in stress states, considering all loads, is computed.This paper describes the new rules, their intent, and provides several example pipingstress analyses, comparing the results of an analysis using the Appendix P rules with thatusing the rules in the base Code. �DOI: 10.1115/1.2140289�

Keywords: ASME B31.3, Appendix P, piping flexibility, piping stress analysis

BackgroundThe overall intent of the Appendix is to provide alternative

flexibility analysis evaluation procedures, that are technically con-sistent in terms of criteria with the rules in the base ASME B31.3,Process Piping Code �1�, �hereafter referred to as the Code�, butprovide for evaluating operating conditions with all loads ratherthan thermal stress in isolation of other loads. The reason for thisapproach is that there can be an interaction between the variousloads �e.g. weight, pressure, thermal expansion� that can be lostwhen considering one load separate from the others. This is par-ticularly true when there are nonlinear effects, such as the liftoffof supports, and restraints with gaps that permit some movement.The desirability of providing these new, alternative rules comesfrom two issues:

• Current computer analysis programs can easily evaluate thecombined loads accurately. When the flexibility analysisrules were originally written for the Code, these calculationswere done by hand and the rules had to be simple.

• Current computer analysis programs permit consideration ofnonlinear effects, which create substantial difficulties in in-terpretation and evaluation of results, using rules in the baseCode.

The new rules are not anticipated to provide significantly dif-ferent results, from the standpoint of passing or failing pipingsystems, than the existing rules. The intent is to provide a morecomprehensive, general approach.

Stress LimitThe displacement stress limits in the Code limit the range of

stresses, that is, the difference in stress between two conditions.This is done in Appendix P by taking the difference between op-erating stress states. In addition, the maximum operating stressstate is also limited in Appendix P to limit the combination ofstress range and sustained stress.

The intent of the Code rules is to limit the stress range to twicethe yield strength �or yield plus hot relaxation strength in thecreep regime� �both reduced by a further safety factor�. This stresslimit is set so that the piping system will shake down to elasticaction after the initial cycles of operation. Furthermore, the stressrange is limited to protect against fatigue damage. There is also alimit on the maximum combined stress, sustained plus displace-

Contributed by the Pressure Vessels and Piping Division of ASME for publicationin the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 19, 2005;final manuscript received October 13, 2005. Review conducted by G. E. Otto Widera.Paper presented at the 2005 ASME Pressure Vessels and Piping Conference
�PVP2005�, July 17, 2005–July 21, 2005, Denver, Colorado, USA.
84 / Vol. 128, FEBRUARY 2006 Copyright ©

aded 01 Nov 2007 to 67.108.135.98. Redistribution subject to ASM

ment, to limit ratchet. Appendix P accomplishes these samechecks using operating load cases. Note that sustained stress limitsare not addressed in Appendix P and are in addition to the rules inthe appendix.

The stress range is calculated as the difference in stress betweenvarious operating conditions. Thus, if a support is lifted off in onecondition and not another, that effect contributes to the stressrange. Calculating the stress range based on combined loads is amore precise and comprehensive method of evaluating stressrange. The stress range is limited to SoA, the maximum permis-sible operating stress range. This is the same as the presentlypermitted displacement stress range SA, except that SL is not sub-tracted. In addition, the maximum operating stress is limited toSoA, to preserve the aforementioned ratchet check.

SoA = 1.25f�Sc + Sh� �1�

where f is the stress range factor, SoA allowable operating stress,Sc allowable stress at the metal temperature at the cold end of theoperating cycle, and Sh allowable stress at the metal temperatureat the hot end of the operating cycle

Flexibility AnalysisComplex systems involving multiple conditions of operation,

with supports responding in different manners, can be rigorouslyevaluated using the new Appendix P, whereas significant expertiseand judgment in interpretation of the results are required to oth-erwise evaluate such systems. It should be noted that additionalstresses that may be caused by support liftoff are included in thestress range �as it adds to the stress variation and fatigue� and arealso considered in the sustained stress check.

In following Appendix P, more combinations of loads are likelyto be considered. In this manner, the most critical load cases canbe easily identified. However, this work is done by the computer,so that it should not significantly increase the effort required bythe analyst other than making sure that the appropriate load com-binations are included in the assessment.

The rules in Appendix P also include stress due to axial loads inthe flexibility analysis. These stresses are sometimes significant,and there is a warning statement in the Code �paragraph 319.2.3�d�� that they should be included when significant. In Appendix P,they are always included, so their effect is included in case it issignificant. Note that this change also is consistent with the use ofcomputer analysis. Prior to computer analysis, inclusion of theseaxial loads would have been problematic, and really pointless ex-tra work in most cases, since it is generally not a significant effect.With computer analysis, its inclusion is essentially effortless to theanalyst.

One of the problems in including stress due to axial loads is
determination of what stress intensification factor �SIF� to use.
2006 by ASME Transactions of the ASME

E license or copyright, see http://www.asme.org/terms/Terms_Use.cfm

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Based on committee judgment, except for elbows, the user is di-rected to use the out-plane SIF for the component, in the absenceof more applicable information. This is the higher of the two SIFsthat are provided in Appendix D of the Code �1�. It is saying,considering a tee, that the effect of axial load in the branch is thesame as bending, using the higher of in-plane and out-plane SIFs.For elbows, again based on judgment, no SIF is used. This isbecause axial load on one side is bending on the other end of theelbow, so that the effect of axial load on fatigue should already beconsidered. Note also that it is the bending that causes the oval-ization, which causes the increase in stress in elbows.

Together with the change in rules, the definition of severe cyclicservice is addressed so that it is consistent with Appendix P. Fur-thermore, the paragraph on cold spring and support loads is madeinto a verbal description of the procedure. Also, cold spring con-siderations are tuned up. The base Code allows credit for only 2/3of a cold spring in calculating initial installation and operatingloads on equipment as the exact cut—short or long—cannot beassured. Furthermore, the equation indicates that the modulus ofelasticity of the metal at operating temperature may be used incalculating equipment loads. In Appendix P, the uncertainty inachieving specified cold spring is extended to include an overzeal-ous cut. Appendix P requires examination of two-thirds of designcold spring and four-thirds of design cold spring. It also explicitlystates that the modulus of elasticity at the temperature of the op-erating condition may be used in calculating equipment loads.

The equation for calculating stress is revised to the following,to include stress due to axial loads:

S = ��Sa� + Sb�2 + 4St2 �2�

where Sa is the stress due to axial force= iaFa /Ap, Fa axial force,including that due to internal pressure, and ia axial force stressintensification factor. In the absence of more applicable data, ia=1.0 for elbows and ia= io from Appendix D for other compo-

Table 2 Allowable stresses for examples 1 and 2

Base CodeSc Sh SA �1b�a

1� 20,000 18,900 48,625-SL2� 20,000 20,000 50,000-SL3� 20,000 18,900 48,625-SLAppendix P Alternative

Sc Sh SOAb

1� 20,000 18,900 48,6252� 20,000 20,000 50,0003� 20,000 20,000 50,0004� 20,000 18,900 48,6255� 20,000 20,000 50,0006� 20,000 18,900 48,625

aSA= f�1.25�Sc+Sh�−SL�; here, f =1b

Table 1 Load case defin

Base Code Expansion Stress Range Load SetsLoad Componentsa Descr

1� �W+T1+P1�-�W� Strain2� �W+T2�-�W� Strain3� �W+T1+P1�-�W+T2� StrainAppendix P Alternative Operating Stress and Expansi

Load Components Descr1� W+T1+P1 Opera2� W+T2 Cold3� W Instal4� �W+T1+P1�-�W� Strain5� �W+T2�-�W� Strain6� �W+T1+P1�-�W+T2� Strain

aW=weight, T=thermal expansion, P=pressure. For systemsloads could be replaced with: �1� T1, �2� T2, �3� T1-T2.

SOA= f�1.25�Sc+Sh��; here, f =1

Journal of Pressure Vessel Technology


nents. Ap is the cross sectional area of the pipe, and S=SE or Som.Both the maximum operating stress range SE and the maximum

operating stress Som are limited to SoA. The limitation on maxi-mum operating stress was included to address concerns regardingratchet. The same as in the base Code rules for evaluating dis-placement stresses, the nominal wall thickness is used withoutallowances �i.e., corrosion, erosion, and mechanical� and mill tol-erances in the stress calculation.

ExamplesThree example cases are included. Results from the existing

rules in the base Code, and based on an evaluation per the newAppendix P, are provided. Take particular note of the load casesconsidered in the Appendix P evaluation. Table 1 provides theload case definitions, Table 2 provides the allowable stresses, andTable 3 provides detailed information for the first two examples.

The first is a sample problem included in Appendix S of the2004 edition of the Code. It is a simple problem. Figure 1 showsthe system, and the results of the two assessments are provided inTable 4. To compute the allowable stress for the base Code, thesustained stress SL must be known. The Code does not addresswhat stress intensification factor �or stress index� to use in thiscalculation; 0.75i was used in the calculations provided in thispaper. The results of the calculations for the existing rules andAppendix P are similar. In terms of percent of allowable, the re-sults are within a few percent.

ns for examples 1 and 2

onge between installation and operating positionsge between installation and cold shutdown positionsge between operating and cold shutdown positions

Stress Range Load Setson

positiontdown positionposition �includes fluid weight�ge between installation and operating positionsge between installation and cold shutdown positionsge between operating and cold shutdown positions

th linear boundary conditions �e.g., Example 1�. Base Code

Table 3 General information for examples 1 and 2

OD= 16 in.wall= 0.375 in.

mat’ l= A 106Bcorr.= 0.063 in.

content dens.= 1.0SGinsul. thick.= 5 in.insul. dens.= 11 lbf/cu.ft.

Operating State 1temp�1�= 500°Fpress�1�= 500 psi

Operating State 2temp�2�= 30°F

press= 0 psiInstalled State

temp�ambient�= 70°Fpress= 0 psi

Corroded Section Properties �for sustained & occasional stress�Axs= 15.38 in.2

Z= 59.16 in.3Uncorroded Section Properties �for expansion and operating stress�

Axs= 18.41 in.2

Z= 70.26 in.3

itio

iptiranranran

oniptitingshuled

ranranran

wi

FEBRUARY 2006, Vol. 128 / 85


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The second sample problem is shown in Fig. 2. It is a casewhere the piping lifts off a support when the system heats up. Afirst question with respect to the existing rules is what SL to usewhen determining the allowable displacement stress range. Theexample uses the most severe value of SL at each point, consider-ing both the sustained stresses when the piping system is in thecold condition and the sustained stresses when the piping systemis in the hot condition, without the center-span support. Note thatthe loss of a support is dramatic, but shifts in sustained stressesoccur in systems even without the pipe lifting off of supports.

Fig. 1 Simple code compliant model

Table 4 Sample calculations „force

Midpoint of lower bend �29� Intermediate Values:i=2.620; in-plane stress intensification factorSL=9,914 using ��P*Ain�+Fax� /Axs+ �0.75i�Mb

with fluid weight

Base CodeLoad Set1�2�3�Appendix P AlternativeLoad Set Fa �w/o P� P*Ain Fa total1� −10,405 91,327 80,9232� −3,348 0 −3,3483� −3,866 0 −3,8664� −6,538 91,327 84,7895� 518 0 5186� −7,056 91,327 84,271

Midpoint of upper bend �39� Intermediate Values:i=2.620SL=6.007


86 / Vol. 128, FEBRUARY 2006


The results for the second sample problem are provided inTable 5. In this case, in terms of percent of allowable, the differ-ence is about 12%, with the base Code more conservative. If theanalyst had used the sustained stress in the installed condition, asis commonly done, the results using the base Code approachwould have been less conservative by 14%.

The third case is a vacuum-jacketed pipe. The problem andresults are described in Table 6. Since the existing rules do not-consider stresses due to axial loads in the displacement stresscalculation, there is a dramatic difference between the results fromthose rules and those of Appendix P. This is because, in a double-wall piping system, when one pipe runs hotter than the other, they

lbf., moment in ft-lbf, stress in psi…

based on cold loads

Mb Sb=SE SA41,160 18,420 38,7113,262 1,460 40,08644,421 19,880 38,711

Mb Sb �Sa�+Sb SOA96 −51,513 23,053 27,450 48,62582 −7,092 3,174 3,356 50,00010 −10,354 4,634 4,844 50,00006 41,160 18,420 23,026 48,625

3,262 1,460 1,488 50,00078 44,421 19,880

SOM=24,45827,450

48,625

Mb Sb=SE SA52,427 23,462 42,6184,154 1,859 43,99356,581 25,321 42,618

Mb Sb �Sa�+Sb SOA19 −52,243 23,380 27,899 48,6259 4,339 1,942 2,001 50,0007 184 82 170 50,00006 52,427 23,462 28,068 48,625

4,154 1,859 1,887 50,00078 56,581 25,321

SOM=29,89929,899

48,625

Fig. 2 “Lift off” model

in

/Z,

Sa4,3−1−24,6284,5

Sa4,5−5−84,6284,5

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exert axial forces on each other to force displacement compatibil-ity. Although the existing Code provides a cautionary statement toaddress this, Appendix P directly includes the effect in the calcu-

Table 5 Sample calculations „force

Midpoint of lower bend �19�Intermediate Values:

i=2.620SL=9.914 �installed�SL=14,000 �at T1�SL=9,914 �at T2�

SL�max�=14,000


Midpoint of upper bend �24�Intermediate Values:

i=2.620SL=6,007 �installed�SL=15,251 �at T1�SL=6,007 �at T2�

SL�max�=15,251


Midspan support �35� Intermediate Values:i=1.000SL=11,657 �installed�SL=15,296 �at T1�SL=11,657 �at T2�

SL�max�=15,296

Base CodeLoad Set1�2�3�Appendix P AlternativeLoad Set Fa �w/o P� P*Ain Fa total1� −5,572 91,327 85,7552� −321 0 −3213� −735 0 −7354� −4,836 91,327 86,4915� 414 0 4146� −5,250 91,327 86,077

lations. The case shown has a colder inner pipe made of stainless

Journal of Pressure Vessel Technology


steel combined with a hotter pipe made of carbon steel. Becausestainless steel has a higher coefficient of thermal expansion thancarbon steel, if both pipes were carbon steel the calculated stresses

lbf., moment in ft-lbf, stress in psi…

Mb Sb=SE SA39,142 17,517 34,6253,262 1,460 36,00042,403 18,977 34,625

Mb Sb �Sa�+Sb SOA35 −49,496 22,150 26,586 48,62582 −7,092 3,174 3,356 50,00010 −10,354 4,634 4,844 50,00045 39,142 17,517 22,162 48,625

3,262 1,460 1,488 50,00017 42,403 18,977

SOM=23,59426,586

48,625

Mb Sb=SE SA47,941 21,455 33,3744,154 1,859 34,74952,096 23,314 33,374

Mb Sb �Sa�+Sb SOA58 −47,757 21,372 25,930 48,6259 4,339 1,942 2,001 50,0007 184 82 170 50,00045 47,941 21,455 26,100 48,625

4,154 1,859 1,887 50,00017 52,096 23,314

SOM=27,93127,931

48,625

Mb Sb=SE SA49,108 21,977 33,3294,986 2,231 34,70454,094 24,208 33,329

Mb Sb �Sa�+Sb SOA59 21,171 3,616 8,275 48,6257 −32,923 5,623 5,640 50,0000 −27,937 4,771 4,811 50,00099 49,108 8,387 13,086 48,625

4,986 852 874 50,00076 54,094 9,239

SOM=13,91513,915

48,625

in

Sa4,4−1−24,6284,6

Sa4,5−5−84,6284,6

Sa4,6−1−44,6224,6

would be higher.

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tive

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ConclusionNew, alternative rules for evaluating stresses due to displace-

ment conditions �e.g., thermal expansion� are provided in Appen-dix P of the 2004 edition of ASME B31.3. They provide a morecomprehensive assessment than the existing rules and are intendedfor use with computer analysis. As commercial flexibility analysisprograms are updated to apply the new rules, they will generallybecome easier to apply than existing rules, particularly when con-sidering piping systems with complex, nonlinear behavior.

NomenclatureAin � inside cross sectional area of pipe or jacket annulusAp � cross sectional area of the pipeE � modulus of elasticityf � stress range factor

Fa � axial force, including that due to internal pressureia � axial force stress intensification factor. In the absence

of more applicable data, ia=1.0 for elbows and ia= iofrom Appendix D of �1� for other components.

i � out-plane stress intensification factor

Table 6 Hot oil jacket over acid line: 4 in. STSTD carbon steel jacket, temp 500 °F, and pre

Input Data:a

Core:ODcª4.5 in. wtcª0.237 in. T

Sccª20,000 psi ShJacket:

ODjª6.625 in. wtjª0.28 in. TScjª20,000 psi Sh

Pipe Metal Area

Acª�ODc

2 − �ODc − 2 · wtc�2

4

Thermal Thrust Load

Fª�Ac · Ec� · �Aj · Ej��Ac · Fc� + �Aj · Ej�

· ��j · �Tj − �c · �Tc�

�Core is in tension, jaPressure Thrust

Aincª� ·�ODc − 2 · wtc�2

4

ThrustªPc ·Ainc+Pj ·AinjApportioned Pressure Thrust

ThrustcªAc · Ec

Ac · Ec + Aj · Ej· Thrust

Thrustc=2714 lbfStress Calculations

�Using only axial stresSbª0 psi

Expansion StressSEª�Sb2+4·St2

Operating Stress

SacªThrustc + F

Ac

Sac=7267 psi

Somcª��Sac�+Sb�2+4 ·St2

Somcª7267 psiSoAcª1.25�Scc+Shc�

SoAcª49,188 psiSomc�SoAc

aSubscripts c and j are used to denote core and jacket, respec

o

88 / Vol. 128, FEBRUARY 2006


Mb � resultant bending momentP � internal pressureS � calculated combined stress, SE or Som

Sa � stress due to axial force= iaFa /ApSb � stress due to bending momentSc � allowable stress at the metal temperature at the cold

end of the operating cycleSE � maximum operating stress rangeSh � allowable stress at the metal temperature at the hot end

of the operating cycleSL � sum of longitudinal stress due to sustained loads

SoA � allowable operating stressSom � maximum operating stress

St � stress due to torsional momentT � pipe metal temperature

wt � wall thickness of pipeZ � section modulus� � coefficient of thermal expansion of pipe material

References�1� ASME, 2004, ASME B31.3, Process Piping Code, ASME, New York.

SS core, temp 350 °F, pressure 400 psi; 6 in.ure 200 psi

350°F Pcª400 psi �TcªTc−70 °F9,350 psi �cª9.53�10−6 ·1 /F Ecª2.83�107 psi

500 °F Pjª200 psi �TjªTj−70 °F8,900 psi �jª7.02�10−6 ·1 /F Ejª2.95�107 psi

Ajª�ODj

2 − �ODj − 2 · wtj�2

4

F=20,353 lbf

t is in compression�

Ainjª��ODj − 2 · wtj�2 − ODc

2

4

Thrust=7689 lbf

ThrustjªAj · Ej

Ac · Ec + Aj · Ej· Thrust

Thrustj=4975 lbf

gnoring any bending�Stª0 psi

SE=0 psi

SajªThrustj − F

Aj

Saj=−2755 psi

Somjª��Saj�+Sb�2+4 ·St2

Somjª2755 psiSoAjª1.25�Scj+Shj�

SoAjª48,625 psiSomj�SoAj

ly.

Dss

cª

cª1

jª

jª1

cke

s, i

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New Piping Flexibility Rules in ASME B31.3 AppendixP - Becht & Diehl - ASME - 2006