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CHAPTER

38

38.1 INTRODUCTION

Piping systems tend to be rather complex structures thatinclude straight pipe and a variety of complex components, suchas elbows and tees. A typical piping system might include 50 orso components along with many intervening lengths of straightpipe. Each of the components is subjected to a complex set ofloadings. The evaluation of any component by the detailed analy-sis methods prescribed in NB-3200 would be an onerous task.

As indicated by Tables NB/NC/ND-3132-1, many piping com-ponents are standardized. For example, elbows and tees areincluded in ANSI B16.9, Factory Made Wrought Steel Butt-Welding Fittings.

The complexity of analyses of piping components and thestandard aspect of piping components has led to use of stressintensification factors (also called i-factors) in addition to stressindices and flexibility factors for evaluations of piping systems.The intent of i-factors and stress indices is to provide for a simpleyet reasonably accurate and conservative evaluation of compli-ance with Code stress l imits. Piping components (e.g., elbows andbranch connections) may have directional dependent responses.The concept (except as discussed in Section 38.11) is to use themaximum directional dependent i-factor or stress index as a mul-tiplier of resultant moments.

Flexibility factors are involved in piping system analyses.Inaccurate flexibility factors may lead to grossly incorrect calcula-tions of stresses. In general, a conservative flexibility factorcannot be defined; the goal is to establish and use reasonablyaccurate flexibility factors.

In this chapter, the general concepts behind the development of

i-factors, stress indices, and flexibility factors are briefly dis-cussed with references to details of developments. In Section38.8, an example of a relatively simple piping system with loadsis given; the piping system output analysis is used to illustratehow i-factors and stress indices are used to check Code compli-ance andfor a branch connectionto illustrate the quantitativesignificance of flexibility factors. The ASME Piping Codes arediscussed in Sections 38.9, 38.10, and 38.11.

38.2 TERMINOLOGY AND SYMBOLS

As used herein, the word Code is ref. [1]. Portions of the Codeare identified as they appear in the Code; for example, TableNC-3611.2(e)-1 and NB-3228.5. Equations from the Code areidentified by a B (for Class 1 piping) and a C (for Class 2 or 3piping); the number that follows the letter is the specific equationnumber from the Code. The elements of the Code equations aredefined as follows:

B1,B2 primary stress indices:B1 for pressure and B2for moment

C1, C2, C3, C3 primary-plus-secondary stress indices: C1 forpressure, C2 for moment, and C3 and C3 forthermal gradients

Do outside diameter of pipe (for branch connec-tions, the run pipe)

do outside diameter of branch pipeE modulus of elasticityf number of cycles dependent factor, ranging

from 1.0 for 7,000 or fewer cycles to 0.5 for100,000 or more cycles (see Table NC-3611.2(e)-1)

h tRb r2; elbow characteristic

i stress intensification factorI moment of inertia of pipe or elbow (Ir, Ib for

run, branch-of-branch connections)K1, K2, K3 peak stress indices: K1 for pressure, K2 for

moment, and K3 for thermal gradientsKe factor used for Sn 3Sm (see NB-3228.5)

k flexibility factorNf test cycles to failure; see equation (38.1)

Nd1 design cycles for Class 1 pipingNd2,3 design cycles for Classes 2 or 3 piping

Mj resultant moment:j A,B, or C forMA,MB, andMC. The sub-scriptsx,y, andz denote an orthogonal set ofthree moments.

[M2xj + M2

yj + M2

zj](1/2) =

7

>

STRESS INTENSIFICATION

FACTORS, STRESS INDICES,AND FLEXIBILITY FACTORS

Everett C. Rodabaugh

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2 Chapter 38

MA resultant moment from weight and other sus-tained loads

MB resultant moment from nonreversing dynamicloads

MC range of resultant moment from thermal

expansionMi resultant moment as defined in NB-3650Nf test cycles to failure, through-wall crack; see

equation (38.1)P internal pressurer mean radius of pipe or elbow

r2 radius at outside juncture between run pipeand branch pipe or nozzle

Rb bend radius of elbowSta test elasticequivalent stress amplitude (half-

range); see equation (38.1) and Fig. 38.1SOL calculated stress by equation (C8)STE calculated stress by equation (C11)

SA allowable stress range f(1.25Sc 0.25Sh);see equation (C1) in NC-3611.2

Sc basic material allowable stress at minimumtemperature

Sh basic material allowable stress at temperature

consistent with loading under considerationSm basic material allowable stress intensitySn calculated stress by equation (B10)Sp calculated stress by equation (B11)

Salt calculated stress by equation (B14)T wall-thickness of run-pipe of branch connec-

tionst wall-thickness of pipe or elbow

Z section modulus of pipe or elbow (Zr and Zbfor run and branch-of-branch connections)

Symbols not included in the preceding list are defined whereused in the text.

FIG. 38.1 MARKL-TYPE FATIGUE TESTS AND ILLUSTRATION OF LIMIT LOAD CRITERION


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COMPANION GUIDE TO THE ASME BOILER & PRESSURE VESSEL CODE 3

38.3 STRESS INTENSIFICATION FACTORS

Stress intensification factors (i-factors) were introduced into ASAB31.11955, Code for Pressure Piping. The i-factors are based oncyclic moment (displacement-controlled) fatigue tests by Markl (seerefs. [2] and [4]) and also by Markl and George (see ref. [3]) and are

used for Code Classes 2 and 3 piping. For the discussion in thischapter, NC-3650 (for Class 2) and ND-3650 (for Class 3) areidentical.

Markl [2][4] tests were run on components made of A106Grade B material and included the following:

(1) elbows and miters;(2) straight pipe with a girth Fillet weld;(3) straight pipe;(4) straight pipe with a girth butt weld;(5) ANSI B16.9 tees, with outlet size equal to the run size; and(6) unreinforced branch connections, with outlet size equal to

the run size.

Markl [2] introduced the following equation:

(38.1)

The force, F, was obtained from a preliminary force versus thedisplacement test as indicated in Fig. 38.1. As noted, the displace-ment used in some of the subsequent fatigue tests was in the plastic-response region. This application is consistent with the use ofelastic pipingsystem analyses; in effect, it may be viewed as astrain control rather than a stress controlthat is, fatigue is afunction of the strain amplitude or range.

The constant of 245,000 (psi for Sta in psi) was used by Marklfor his tests on carbon steel components. Later tests on austeniticstainless steel components by Heald [5] indicate that this constantis about right for such materials. The constant is not necessarilyappropriate for materials with a significantly different modulus ofelasticity, as for aluminum components with E 1e7 psi, forexample. Available test data indicates that the constant of 245,000

in equation (38.1) is about 245,000 times the modulus of elasticratiothat is, the constant is about 82,000, which emphasizes thestrain control rather than stress control of equation (38.1). Designmargins for materials with E significantly less than 3e7 psi arediscussed in Section 38.3.2.

38.3.1 Girth Butt Welds

Markl, on the premise that a girth butt weld may exist any-where in piping systems, opted to make i 1.000 for a girth buttweld using Fleetweld No. 5 stick electrodes. (They weresmooth on neither the inside nor the outside surface.) Marklalso tested plain straight pipe by using a forged transition piece;he obtained i 0.64. In principle, if a girth butt weld is flushinside and out-side and there is no metallurgical notch, i could beas small as 0.5.

Scavuzzo [6] presents the results of Markl-type tests on girthbutt welds by using four-point bending instead of the cantileverbending used by Markl [2][4] and Heald [5]. Scavuzzo, for verylow cycles to failure, obtained i-factors significantly less than1.00for example, i 0.3 for Nf 249, but for Nf 144,000,Scavuzzo obtained I 1.02. Rodabaugh [7], using elasticplastictheory, showed that for tests at lowNf (significant amount of plas-tic response), four-point bending will result in lower i-factors forgirth butt welds. Rodabaugh [7] suggested that for use with elasticpipingsystem analyses, i-factors derived from cantilever testing

'

i = 245,000/(StaN0.2

f )

are more appropriate than those derived from four-point bendingtests.

38.3.2 Design Margins

The nominal design margin can be deduced from equation

(C11) withMA P 0.

(38.2)

Figure 38.2 is a plot of stress range versus cycles. In equation(38.1), Sta is an amplitude; in equation (38.2),MC is a range. This2:1 ratio of range to amplitude is a key aspect of basic designmargins. Figure 38.2 is for A106 Grade B materialthe materialused in Markl tests. It is apparent in Fig. 38.2 that the design mar-gin varies as a function of cycles: at N 10, the basic designmargin on stress is 8.24, whereas fromN 7,000 to 100,000, thedesign margin on stress is about 2 and then decreases to about1.2. For other materials with about the same modulus of elasticity,the basic design margins would be different: for example, forA106 Grade A material, Sc Sh 12 ksi, and the margins would

be 15/12 times those indicated in Fig. 38.2. For A106 Grade Cmaterial, on the other hand, the margins would be 15/17.5 timesthose indicated in Fig. 38.2.

To further discuss margins, we look at the complete equation(C11):

(C11)

In equation (C11), 0.75i shall not be taken to be less than 1.00.Markls tests were run with essentially zero internal pressure.

Heald [5] ran tests with a constant PDo (4t) 5100 psi, with noapparent effect on the results. However, if the pressure cycles inphase with the moments, the PDo/(4t) term provides a reasonableallowance for the combined pressure and moment cycles. Itshould be noted that equation (C11) is not an evaluation of the

adequacy of pressure design; it is covered by NC-3640.Markls tests involved a minor amount of weight loadingthat

is, 0.75i MA/Z was not zero. Healds tests involved a bit moreweight loading. These minor values of 0.75 i MA/Z had no effecton the results. Indeed, available data suggest that values of 0.75i

MA/Z (noncyclic) up to approximately 10 ksi would have no effecton the fatigue life. Thus the inclusion of the 0.75i MA/Z term pro-vides conservatism relative to equation (38.1).

Some nonferrous materials are permitted by the Code for Class3 piping. For 6061-T6 aluminum material, with E ~1e7 psi,available data indicate that the constant in equation (38.1) is about(1/3)245,000. For 6061-T6, as welded, Sc 6.0 ksi; Sh (400F) 3.5 ksi; Sh SA 11.875 ksi as compared to 37.5 ksi for A106Grade B material. Because the allowable stress for 6061-T6, aswelded, is less than (1/3) of that for A106 Grade B, the designmargins for 6061-T6, as welded, would be expected to be not lessthen indicated in Fig. 38.2.

Other nonferrous materials have not been reviewed from thisstandpoint. However, to the extent that allowable stresses arereduced in proportion to the reduction in E, margins indicated inFig. 38.2 would be expected.

38.3.3 Code Guidance for i-FactorsFigure NC-3673.2(b)-1 gives i-factors for 15 types of compo-

nents. These i-factors are applicable forDo/t up to 100.

STE = PDo>(4t) + 0.75iMA>Z + iMC>Z 6 (Sh + SA)

STE = iMC>Z (Sh + SA)


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4 Chapter 38

Many of the i-factors are identical to those suggested by Markl[4]. However, in the 55 yr. since, additions and changes have beenmade; the description of branch connection has been added, forexample. These additions and changes are part of an ongoingprocess by the Code Working Group on Piping Design.

Minichielo [8] details a procedure for experimental determina-tion of i-factors for components not covered by the Code (e.g., abranch connection in an elbow).

NC-3673.2 includes the following relationship:

but not less than 1.00 (38.3)

Equation (38.3), for moment loading, ties NC-3650 (Class 2 piping)with NB-3650 (Class 1 piping).

i = C2K2>2

FIG. 38.2 DESIGN MARGINS FOR SA106 GRADE B: Sc = Sh = 15 KSI


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The most relevant basis for equation (38.3) is a combination ofelbow tests and elbow theory, along with the definition that i 1.00 for a typical girth butt weld. Fatigue tests of elbows within-plane moments resulted in failures at the location and directionindicated by elbow theory. The failures were remote from thewelds; thus K2 1.00. By elbow theory for an in-plane moment

(38.4)

From equations (38.3) and (38.4),

(38.5)

Equation (38.5) agrees with that shown in Figure NC-3673.2(b)-1for welding elbow or pipe bend.

For Markls typical girth butt welds, it is reasonable toassume that K2 2. Then equation (38.3) gives i 1.0; in agree-ment with Figure NC-3673.2(b)-1 for girth butt weld.

38.3.4 EPRI ReportsOne of the reviews mentioned in the foregoing paragraph led toa series of reports under the sponsorship of a group of electricutility owners through the Electric Power Research Institute(EPRI). At the present, these reports are proprietary; however, thearticles prepared by Wais (see refs. [9][19]) are open-literaturepublications, abstracting eleven of the EPRI reports, and analo-gous open-literature publications may be available in the future.These articles include data on stress indices, flexibility factors,and i-factors.

38.4 C ANDK STRESS INDICES

C and K indices are used for Class 1 piping in equations (B10)and (B11). They are analogous to i-factors in that they provide thebasis for fatigue evaluations and are (as for i-factors) subject toongoing reviews. Table NB-3681(a)-1 provides C and K stressindices for commonly used piping system components; these areapplicable forDo/t up to 100.

38.4.1 C1 andK1 Stress Indices for Internal

Pressure LoadingThe term stress indices was introduced in the first (1963) edi-

tion of ASME Section III. Although it took several editions andaddenda to get the definition complete, the definition now in NB-3338.2 is essentially:

The term stress index is defined as the ratio of the stress com-ponents st, sn, and sr to the computed membrane stress inthe vessel, s.

for nozzles in spherical vessels or heads

for nozzles in cylindrical vessels

where

P service pressureDi inside diameter of vessel

T wall-thickness of vessel

The stress indices shown in Table NB-3338.2(c)-1 an extensiveseries of internal pressure tests of nozzle in vessels. This data issummarized and discussed by Mershon in refs. [20] and [21].

s = P(Di + T)>(2T)

s = P(Di + T)>(4T)

i = 1.8>h(2/3)>2 = 0.9>h(2>3)

C2 ' 1.8>h(2>3) for h 6 '0.5

In the early editions of ASME Section III, piping was not cov-ered. Stress indices for pressure, moment, and thermal gradientloads were introduced in ANSI B31.7-1969. (ANSI B31.7 wastransferred to ASME Section III in 1971.)

C1 and K1 are used in equations (B10) and (B11):

(B10)

(B11)

For branch connections, Do is the outside diameter of the runpipe and t is the wall-thickness of the run pipe.

As a simple alternative to the 16 stress indices in Table NB-3338.2(c)-1, the following equation was developed for branchconnections in piping systems:

(38.6)

in which C1 is not to be less than 1.2thus, because K1 2, C1K1will not be less than 2.4;D is the mean diameter; T is for the runpipe; d is the mean diameter; and t is for the branch pipe or noz-zle. (The basis for this equation is given by Rodabaugh [22].)

Equation (38.6) is limited to d/D 0.5; and the general limita-tion, D/T 100. Also, to use equation (38.6) as it is applied tothe configuration shown in sketch (d) of Fig. NB-3338.2(a)-2, theexternal Fillet radius, r2, must not be less than the larger of 0.5 tand 0.5T.

We now discuss comparisons between equation (38.6) andTable NB-3338.2(c)-1. Table NB-3338.2(c)-1 is limited to D/Tfrom 10 to 100, d/D 0.5. The third limit can be written in thefollowing form:

NB-3338.2 generally requires that r2 must not be less than thelarger of 0.5t and 0.5Tthat is, the same minimums that areincluded in the basis for equation (38.6). With these minimumvalues of r2, Table NB-3338.2(c)-1 is more restricted in coveragethan equation (38.6).

Within the range of mutual coverage, C1K1 ranges from about2.4 to 3.9 versus the S 3.3 in Table NB-3338.2(c)-1. In theextended coverage of equation (38.6), C1K1 can be quite a bithigher than 3.3; for example, for D/T 100, d/D t/T 0.5,t/r2 1.00, and C1K1 6.54.

In early editions of ASME Section III, the range of primary-plus-secondary stress was limited to 3Sm. When piping was intro-duced into ASME Section III, the recognition that the range ofprimary-plus-secondary stress could exceed 3Sm and still have ade-

quate fatigue life led to NB-3228.5, Simplified ElasticPlasticAnalysis. To implement NB-3228.5, it is necessary to divide thetotal stress in to primary-plus-secondary stress and the peak stressportion of the total stress. Table NB-3681(a)-1 does that by C1primary-plus-secondary stress index and C1K1 total stress index.

Table NB-3681(a)-1 gives 15 sets of C1 and K1 for variouscomponents. One of these sets, for branch connection, was dis-cussed previously. The basis for indices for welds and wall-thick-ness transitions is given by Rodabaugh in ref. [23], and the basisfor the rather complex set of C1 and K1 for reducers is given by

(d>D)3(D>T)(T>r2)>(t>T)40.5 6 1.5

6

66

C1K1 = 2.8(D>T)0.182(d>D)0.367(T>t)0.382(t>r2)

0.148

Sp = C1K1(PDo>2t) + momentterm + thermalgradientterms

Sn = C1(PDo>2t) + momentterm + thermalgradientterm


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6 Chapter 38

Rodabaugh as well in ref. [24]. The following paragraphs providea brief discussion of two components covered by neither ref. [23]nor ref. [24].

38.4.1.1 Elbows The following equation for C1 is from shell the-ory for maximum stress caused by internal pressure (ignoring theend effects of whatever might be welded to the ends of the elbows).

The origin of the preceding equation lies with a paper pub-lished by Lorenz in 1910. Because of end effects, the maximumstress tends to occur about midway between the ends. The surfaceof an elbow is considered to be smooth enough so that K1 1.0 isappropriate.

38.4.1.2 Butt-Welding Tees

Butt-welding tees made to the requirements of ANSI B16.9 areavailable for d/D ranging from about 0.5 to 1.00. Unfortunately,ANSI B16.9 controls only center-to-end dimensions, end diame-ters, and minimum wall-thickness not less than the nominal thick-ness of the designated run pipe. The requirement in ANSI B16.9that the pressure capacity of the tee must not be less than the pres-sure capacity of the designated run pipe can be met by a rathernominal increase in wall-thickness over the nominal thickness ofthe run pipe.

In forged tees, the transition between branch and run portionsconsists of a fairly large radius, with wall-thickness changingsmoothly between branch and run portions. B16.9 tees, however,may be machined from a forged block of material, for which apotential then exists for sharp corners at the run to branch inter-section. This uncertainty regarding what constitutes a B16.9 tee,

along with sparse data on the stresses in B16.9 tees from internalpressure, has led to the selection of C1 1.5 and K1 4.0, whichis probably very conservative for most B16.9 tees, particularlythose with d/D 1.00.

ASNI B16.9 reducers pose a similar problem that has beenaddressed by specifying C1 and C2 in terms of the reducersdimensional parametersthe cone angle, for instance. Althoughit is possible, no attempt has yet been made to do something simi-lar for B16.9 tees.

38.4.2 C2 and K2 Stress Indices for Moment LoadingC2 and K2 are used in equations (B10) and (B11) as follows:

Sn pressure term C2Mi/Z thermal gradient term (B10)Sp pressure term K2C2Mi/Z thermal gradient term (B11)

As indicated in Section 38.3.3 (and worth repeating here), NC-3673.2 includes the relationship expressed in equation (38.3) asfollows:

but not less than 1.00

This equation, for moment loading, serves to correlate NC-3650(Class 2 piping) with NB-3650 (Class 1 piping). Thus, because ofMarkl [2][4] tests and, later, Markl-type tests conducted by oth-ers, a relatively good basis exists for the 15 sets of C2 and K2

i = C2K2>2

6

C1 = 1.5: K1 = 4.0

C1 = (2Rb - r)>32(Rb - r)4: K1 = 1.0

shown in Table NB-3681(a)-1 for various components. At pre-sent, equation (38.3) does not always hold. However, its applica-bility is the subject of continuing work by the ASME WorkingGroup on Piping Design.

38.4.3 Stress Indices for Thermal Gradient

LoadingsAlthough piping system analyses quantify the moments used in

the Code equations, heat-transfer analyses or some approximationthereof is needed to quantify the thermal gradients. Such analysesstart with assumed fluid-flow rates, fluid properties, and pipingmaterial properties.

C3 and K3 are used in equations (B10) and (B11) as follows:

Sn pressure term moment term C3Eab|aaTa abTb|(B10)

pressure term moment term (B11)

is used in equation (B13) as follows:

(B13)

The symbols used in equations (B10), (B11), and (B13) aredefined in NB-3653.1 and NB-3653.2. The temperatures Ta, Tb,T1, and T2 are quantified by a heat-transfer analysis. Withrespect to T1 and T2, see Fig. NB-3653.2(b)-1.

The basis for several of the thermal gradient stress indices isgiven by Rodabaugh [23]. For example:

Component C3 C'3

Girth butt weld 0.60 0.50NB-4250 transition 1.0

1:3 slope transition 0.60

Reference [23] gives the results of elastic stress analyses of theforegoing components, all of which are axisymmetric. The resultswere then bounded by the simple equations or values tabulatedabove. C3 represents the primary plus secondary stresses; C'3 rep-resents membrane stresses.

Conceptually, the NB-4250 transition is between pipe and acomponent such as a valve or pump nozzle, and the 1:3 transitionis between two pipes of different wall-thicknesses ( tmax is thethicker of the two pipes). K3 indices are largely the same as the K2indices discussed in Section 38.4.2.

The major problem in evaluating thermal stresses lies in esti-mating at the design stage what will happen to the piping systemin service. Class 2 and 3 piping do not include explicit rules for

evaluating stresses caused by thermal gradients. However, NC-3111(g) (General Design, Loading Criteria, Loading Conditions)indicates that temperature effects shall be considered. If at thedesign stage a designer of Class 2 or 3 piping anticipates that sig-nificant stresses caused by thermal gradients might occur, he orshe might use the Class 1 piping procedure for considering theeffect of those stresses.

38.4.3.1 Basis for C3 and C3 Branch Connections One compo-nent not covered by ref. [23] is the branch connection. To illustrate

0.35(tmax>t) + 0.25

1.0 + 0.03(Do>t)

pressureterm + momentterm + C3Eab aaTa - abTb

C3

+ K2C3Eab aaTa - abTb + Ea T2 >(1 - v)K3Ea T1 >(2(1 - v))Sn =

indicatesabsolutevalues


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the simple bounding basis of the C3 and C'3 indices, the following

explains the basis for the C3 1.8 and C'3 1.0.

For the branch pipe considered as a thin-wall cylindrical shellrigidly restrained at one end (the run pipe is assumed to be therigid restraint) and for a differential thermal expansion, R|aTa

abTb/, between the branch pipe and the run pipe at their juncture,the following two equations must be satisfied:

(38.7)

(38.8)

where

V shear force per unit length at branch piperun pipe junc-ture

Mmoment per unit length at branch piperun pipe juncturebEt3[12(1 y2)]:l [3(1 y2)]0.25/(Rt)0.5, E modulus

of elasticity of branch pipe materialv Poissons ratio

R

radius of branch pipe,t wall thickness of branch pipeaa(b) coefficient of thermal expansion of branchrun pipe

materialTa(b) temperature of branchrun pipe

Solution of equations (38.7) and (38.8) leads to the followingequation:

(38.9)

The axial bending stress, Sab, is . For(Et2/R) 0.1513, Sab 1.816E|aaTa abTb|. The 1.816, roundedto 1.8, is C3 for branch connections.

The hoop membrane stress, Shm, is given by

Thus

38.5 FATIGUE EVALUATIONS: CLASS 2OR 3 PIPING AND CLASS 1 PIPING

Equation (C11) is for fatigue evaluation of Class 2 or 3 piping.The limit, Sh + SA, is a function of the number of anticipatedcycles through thef-factor. Nominal design margins are discussedin Section 38.3.2. Code compliance is either a yes or no answer: ifthe calculated stress by equation (C11) is less than Sh SA, then theanswer is yes; otherwise it is no.

Equations (B10), (B11), and (B14) are for fatigue evaluation ofClass 1 piping. For Code compliance, the allowable number ofcycles, per Appendix I of ref. [1], must be less than the postulatednumber of cycles.

The basis for Class 1 piping fatigue evaluations consists ofstrain-controlled fatigue tests on polished bars, the results ofwhich are included in the ASME Criteria Document [25]. Thedesign curves in Figs. I-9.1, I-9.2, and I-9.3 were derived from thecycles-to-failure data by incorporating a nominal margin of 2 onstress or 20 on cycleswhichever is more conservative. The

C3 = 1.0.

Shm = E * hoopstrain = 1.000EaaTa - abTb

y = 0.3, bl2 =6M/t2

M = -2R aaTa - abTb bl2

V>(2bl3) + M(2bl2) = R aaTa - abTb

V>(2bl2) + M>(bl) = 0

margin of 20 (on cycles) controls for low values of Nd1, whereasthe margin of 2 (on stress) controls for high values of Nd1. Ineither case,Nd1 is the number of allowable design cycles.

The low values of Nd1 generally cannot be used directlybecause Sn/3Sm 1.00. Consider, for example, the as-weldedgirth butt weld in a SA106 Grade B (Sm 20 ksi) pipe for whichC2 1.00, K2 1.8. ForNd1 1,000, Salt 83 ksi from the sec-ond line of Table I.9-1. From equation (B14) with Ke 1.00,

But Sn/3Sm 92.2/60 1.537; thus Ke 1 2[(Sn/3Sm) 1] 2.074.

Appropriate values of Ke have been under investigation for sev-eral years. In the future, it is possible that different values of Kewill be in the Code.

Recalculating Salt gives the following:

From the second line of Table I.9-1, for Salt 172 ksi; Nd1(adjusted for Ke) about 150 design cycles.

A comparable number of design cycles for Class 2 or 3 pipingcan be obtained from equation (38.1). We assume that the cycle iscaused by moment loads. With that assumption, and also becausei 1.00, STE Sn 92.2 ksi range. With a margin of 2 on stress,

For this particular example, Class 1 150 design cycles, Class 2or 3 132 design cycles.

Rodabaugh [26] gives broad-scope comparisons between thefatigue analyses of Class 1 and Class 2 or 3 piping. Comparisonsare given for both carbon steel and austenitic steel materials. Asin the preceding example, there are parameters in which Nd1 and

Nd2,3 are close to each other, but there are other parameters inwhich the differences are appreciable.

For Class 1 piping, it is not necessary to use the values of Kegiven in the Code. If these values are not used, a plastic analysismust be made. For Class 2 or 3 piping, the equivalent of Ke isinherent in the fatigue tests results that are characterized by equa-tion (38.1).

Conditions under which Ke is used involve low estimates of thenumber of cycles that will be applied to the piping system duringits postulated life. At the high end of the cycles spectrum, it maybe noted that equation (38.1) has no endurance strengththatis, a stress level below which the number of cycles is infinite. InTable I-9-1 (line 2), the implicit design-basis endurancestrength is 12.5 ksi. (Work is underway to extend Fig. I-9-1 to

higher than 106 cycles.)All three classes of piping use a linear cumulative-damage

hypothesis to sum up the fatigue damage from cycles of differentstress ranges.

The major problem consists of anticipating at the design stagewhat will happen to the piping system in service. Fatigue damagehas occurred in nuclear power plant piping because of vibrationand thermal striping. These types of cycle loadings have not beenroutinely evaluated in the design stage. However, even if all sig-nificant cycle loadings were anticipated in the design stage, the

Nd2,3 = (245>92.2)5 = 132designcycles

Salt = KeSp>2 = 2.074 * 92.2 * 1.8>2 = 172ksi (amplitude)

Sn = 2Salt>K2 = 2 * 83>1.8 = 92.2ksi (range)

7


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8 Chapter 38

problem of environmental effects may still exist. Markls tests(and Markl-type tests by others) all have been run over short timeperiods with air or tap water inside the specimens. Analogously,the polished bar tests that form the basis of Class 1 piping systemfatigue analyses have also been run over short time periods in anair environment. Thus the Code fatigue analysis procedure shouldbe considered a check of as-built adequacy and may need to besupplemented by in-service inspections.

38.6 B-STRESS INDICES

B-stress indices are used for both Class 1 and Class 2 or 3 pip-ing. Table NB-3681(a)-1 (Class 1 piping) and Fig. NC-3673.2(b)-1 (Class 2 or 3 piping) provide B-stress indices forDo/t up to 50.The components covered by Table NB-3681(a)-1 and Fig. NC-3673.2(b)-1 are not all the same; but to the extent that the compo-nents are the same, the B-stress indices are essentially the same.

For components with two ends of the same nominal size (See38.8.6 for branch connections), B-stress indices are used in equa-tion (B9) and equations (C8) and (C9) as follows:

(B9)

(C8)

(C9)

where

Sy material yield strength

The limits shown for equations (B9) and (C8) are for designconditions; the limit shown for equation (C9) is for Levels A andB Service. The resultant momentsMi,MA, andMB are nonrevers-ing; examples are weight, steady-state relief-valve thrust, andany load that the Code characterizes as nonreversing.

The foregoing equations are intended to prevent gross plasticdeformation caused by such nonreversing loads as weight. A con-ceptual example is shown in Fig. 38.1. As the load F increases,the displacement first increases elastically, then it is in the plasticregion. The goal is to limit the plastic response sufficiently so thatelastic analyses of piping systems remains reasonably valid.

The criterion adopted for this purpose is from II-1430. The titleof II-1430 (Criterion of Collapse Load) is a bit misleading; asindicated in Fig. 38.1, a piping component usually does not col-lapse at the load FL. A more appropriate termat least for pip-ing to use in the title is Limit Load.

The basis for most of the B-stress indices is given byRodabaugh in ref. [27]. All of the B-stress indices are based onthe concept and criterion discussed in the preceding paragraphs.The following sections discuss three aspects of B-stress indices.

38.6.1 Straight Pipe

Test data indicate that forDo/t > 50, the mode of plastic failuremay be buckling rather than a limit load as noted in Fig. 38.1;thus B-stress indices are limited in application to pipe with

Do/t 50. Also for Do/ t 50, test data indicate the limitmoments agree reasonably well with the theoretical equation,

66

B1 = 0.5 and B2 = 1.0

B1PDo>(2t)+ B2(MA+ MB)>Z6 lesserof1.8Shand1.5Sy

B1PDo>(2t) + B2MA>Z 6 1.5Sh

B1PDo>(2t) + B2Mi>Z 6 1.5Sm

which follows, given by Larson [28] based on shell theory andvon Mises yield criteria.

(38.10)

where

P internal pressureD pipe mean diameter

t pipe wall-thicknessSy pipe material yield strength

Mb bending momentMt torsional moment

Equation (B9) gives limits in terms of Sm; Sm/Sy varies withmaterial and temperature. Thus the margins between Code-allowablemoments and equation (38.10) vary with material and tempera-ture. The lowest margin occurs forMt, with P Mb 0. For (C8)Sm 1.35Sy (austenitic material at around 6501F). The margin is

M(limit)/M(allowable) 0.86. About the highest margin is forMb, with PDo/(2t) Sm Mt 0; (SA106 Grade B material at100F); Sm 20 ksi, Sy 35 ksi: the margin isM(limit)M(allow-able) 1.94.

These margins of about 0.861.94 are for the equation (B9)limit of 1.5Sm. Margins for straight pipe tend to be the lowest forany of the components covered by the Code. Because elbows withhigh h behave like straight pipe. The margins are also low forsuch elbows. If margins for the design conditions are not to beless than, say, 1.5, a possible Code change would be to place alower bound onB2 of 2.0.

38.6.2 Elbows

There is a significant amount of test data on limit loads ofelbows that is abstracted and discussed in ref. [27]. The controllingcondition is for an in-plane, closing moment. For an elbow withsmall h to undergo significant plastic deformation, the maximumelastic stress, Smax/Z 1.95/h

(2/3) (which is mainly a through-wallbending stress), can be exceeded by a through-wall plastic factorof 1.5. ThusB2 (1.95/1.5)/h

(2/3) 1.3/h(2/3). The statement butnot 1.0 arises from the nature of the equation for Smax. Theequation is valid for h ~0.5. For larger h, the underlying theoryindicates that Smax 1.00/Zthat is, the same as for straight pipe.

For an elbow,B1 0.1 0.4h but not and 0.5. Test data for

elbows with small h show that internal pressure increases the limitmoment. Thus B1 could in principle be negative for such elbows.Reference [27] and the Code did not go quite that far:B1 where is notto be taken as less than zero. The upper bound onB1 of 0.5 returns tothe aspect that, for large h, elbows behave like straight pipe.

Advances in the power of personal computers have made feasi-ble the use of elastic-plastic, finite-element-analysis for paramet-ric studies. Taboul[29] and Matzen [30,31] have published studiesofB2-Indices for elbows. This work may lead to Code revisions of

B-stress indices for elbows.

60

6

B2 = 1.3>h(2>3) butnot 61.0B1 = - 0.1 + 0.4h butnot 60nor 70.5

#

+ 33.464Mt>(pD2tSy)42 = 1.0

(3>4)3(PD>2tSy)42 + 3Mb>(D

2tSy)42


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38.6.3 Seismic AnalysesBefore 1994, the Code did not define nonreversing loads and

reversing dynamic loads. The limit on equation (B9) for Level Dwas the smaller of 3Sm and 2Sy. These limits were based on thehypothesis that earthquakes give loads on piping that are notequivalent to those caused by such sustained loads as weight.

The long, complex history leading to the Code changes made in1994 is given by Jaquay [32]. This work was later supplementedby a Japanese Joint Research Proprietary Report, Simulation ofTest #37 and Parametric Study, in May 1999.

The crux of the 1994 change for Class 1 piping consisted ofincreasing the stress limits on equation (B9) for Service Level Dfrom the pre-1994 of smaller of 3.0Sm and 2.0Sy to the post-1994of 4.5Sm. Moreover, the pre-1994 limits did not distinguishbetween reversing and nonreversing dynamic loads. The post-1994 limits apply to stress due to weight and inertial loading dueto reversing dynamic loads in combination with the Level D coin-cident pressure.

That the 1994 Code changes are still being reviewed by theCode is an indication of the complexity of the Code evaluationprocedure for earthquake resistance of piping systems.

Underlying this complexity is the estimate of what sort of earth-quake should be considered at the design stage.

38.7 PIPING SYSTEM ANALYSESAND FLEXIBILITY FACTORS

The moments used in Code equations are quantified by use of apiping system analyses. The early history of piping system analy-ses is discussed by Markl [33], including 124 references. Some ofthe early work dates back to 1911: for example, the article by Th.von Karman on stresses and flexibility of curved pipe.

At the present, piping system analyses are usually made withone of the several now-existing proprietary piping system analysiscomputer programs. These analyses use beam-element models.The flexibility (or stiffnessthe reciprocal of flexibility) of ele-ments, such as elbows and curved pipe, are routinely included inthe analyses. For elbows and curved pipe,

for in-plane and out-of-plane moments (38.11a)

for torsional moments (38.11b)

The relationships between the three moments and three forceswith the three rotations and three displacements can be represent-ed by a 6 6 matrix. This rather complex matrix for elbows ispart of the piping system analysis computer programs.

For the very simple case of an in-plane moment (Mi) constant,no other moment or force

(38.11c)where

Ki 1.65/h(2/3)

ui in-plane rotation of one end of the elbow with respect tothe other end of the elbow

Mi in-plane moment; constant through arc angle, aRb bend radius of elbowa arc angle of elbow in radiansfor example, a p/2 for

a 90 deg. elbow

ui = kiMiRba>(EI)

k = 1.00

k = 1.65>h

E modulus of elasticity of elbow materialI moment of inertia of elbow cross section, usually taken to

be the same as for the attached pipes

Equations (38.11ac) are based on theory in which the endeffects are negligible. If, for example, a flange were attached to

either one or both ends of the elbow, a correction should be made.[See Code Fig. NC-3673.2(b)-1, note (1).]

That the correction should be made is significant becauseusing a flexibility factor higher than the actual one is not neces-sarily conservative for all of the piping system analysis results. Aconservative flexibility factor cannot be defined; the goal is toestablish and use best estimate flexibility factors, which is dis-cussed in Section 38.8.7. Other flexibilities, such as that indicatedin NB-3686.5, can be included in piping system analyses by usinga point spring conceptsee Section 38.8.6 for an example.

Before about 1960, the loadings usually considered in pipingsystem analysis consisted of restraint of thermal expansion,weight, and wind loadings. The purpose of the analyses was toquantify moments for Code stress evaluations and to check theadequacy of supports and hangers as well as to check loads on

such equipment as pumps and compressors. Since about 1960,however, dynamic loadings, such as those from earthquake andwaterhammer, are often included in piping system analysis.However, the i-factors, stress indices, and flexibility factors arethe same as those discussed earlier in this chapter.

38.8 EXAMPLES

38.8.1 Example Piping SystemThe example piping system is shown in Fig. 38.3. The system,

although simple, serves to illustrate aspects of the use of flexibili-ty factors in piping system analyses and the use of i-factors andstress indices in the subsequent checks of Code compliance.

The material is assumed to be SA106 Grade B. For this materi-al, at temperatures up to 370F, Sc Sh 17.1 ksi; Sm 20 ksi.Also assumed is that the temperature of the piping system risesfrom 70F to 370F, after which it returns to 70F, and that theinternal pressure rises from 0 to 100 psi and then returns to 0inphase with the temperature change. (This cycle is assumed tooccur 1,000 times during the design life of the piping system.) Inaddition, the temperature change is assumed to be slow enough sothat no significant thermal gradients occur. Finally, it is assumedthat there are no dynamic loads.

The stress range from pressure is given by PDo/(2t) 100Do/(2t): 3,200 psi for the NPS 24, 0.375 in. wall pipe, and1,180 psi for the NPS 6, 0.280 in. wall pipe.

In the piping system analysis for weight, it is assumed that thepipes are filled with water and insulated so that the weight per in.of length is 24 lb./in. for the NPS 24 pipe and 2.7 lb./in. for theNPS 6 pipe.

Elbow factors are listed as follows:

Analyses are made for the following two assumptions concern-ing nozzle flexibility:

(1) no nozzle flexibility, and


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(2) having nozzle flexibility modeled as a point spring (asprescribed in NB-3686.5).

(38.12)

(38.13)

The basis for equations (38.12) and (38.13) is given in ref. [22].For this example,Do 24 in., T 0.375 in., do 6.625 in., andt 0.280 in. With the dimensions in these two equations:

ki = 0.2(Do>T)1.53(T>t)(do>Do)4

(1>2)(t>T)

ko = 0.1(Do>T)1.53(T>t)(do>Do)4

(1>2)(t>T)

For this example, in which do/D 0.276, the torsional flexibili-ty, as a point spring, is close to 0; that flexibility was used in theevaluations of with nozzle flexibility.

38.8.2 Moments

For the example piping system shown in Fig. 38.3 and for theconditions indicated in Section 38.8.1, the moments are shown inTable 38.1. Examples of details of the stress calculations aregiven in Sections 38.8.338.8.6.

ko = 23.2 ki = 5.81FIG. 38.3 EXAMPLE PIPING SYSTEM


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38.8.3 Code EquationsEquations (C8), and (B9) are checks of sustained load capacity;

(C11) is a fatigue check for Class 2 or 3 piping; and (B10), (B11),and (B14)in conjunction with the S-N data in Appendix I ofref. [1]represent the fatigue check for Class 1 piping.

The examples that, for simplicity, do not involveMB

or thermalgradients are considered to be in both design conditions andService Level A; they are evaluated by (except for branch con-nections, see Table 38.2) the following equations:

(C8)

(C11)

(B9)

(B10)

(B11)

(B14)Salt = KeSp>2

Sp = K1C1PDo>(2t) + K2C2Mi>Z

Sn = C1PDo>(2t) + C2Mi>Z 6 3Sm

SB9 = B1PDo>(2t) + B2Mi>Z 6 1.5Sm

STE = PDo>(4t) + 0.75iMA>Z + iMC>Z 6 (Sh + SA)

SOL = B1PDo>(2t) + B2MA>Z 6 1.5Sh

Equation (C8) is used in this example rather than (C9) becauseof its lower limit for design conditions. Values of MA and MCare summarized in Table 38.1. For the example assumptions, M i inequation (B9) is equal to MA, and Mi in equations (B10) and(B11) is equal toMC.For the assumed material (SA106 Grade B) and temperatures,

for Class 2 and 3 piping

for Class 2 and 3 piping,f 1.00 for 1,000 cycles

for up tofor Class 1 piping

38.8.4 Girth Butt WeldsGirth butt welds are at nodes 10, 30, 40, 50, 60, 70, and 80, and

all seven locations should be checked. Table 38.1 summarizes the

370FSm = 29,000psi

Sh + SA = Sc + f(1.25Sc + 0.25h) = 42,750psiSh = Sc = 17,000psi


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38.8.5 ElbowsEnds of elbows are at nodes 30, 40, 60, and 70, and these four

locations should at least be checked. (In unusual piping systems,the maximum stress may be somewhere between the two ends.)Table 38.1 summarizes the results for Class 2 or 3 piping.

Node 30(a) is used as in the following as a specific example:For the NPS 24,0.375 in. wall,Rb 36 in. bend radius elbow.

For this elbow,B1 0.1 + 0.4h 0.00 (its lower bound) andB2 1.3/h

(2/3) 6.17.

(C8)

(C11)

Because 980 psi is less than 1.5Sh 25,650 psi, and 25,500 psiis less than (Sh + SA) 42,750 psi, the elbow end at Node 30(a) isacceptable as Class 2 or 3 piping.

For Class 1 piping:

(B9)

(B10)

(B11)

Because 980 psi is less than 1.5Sm, equation (B9) is met. Thenext step is to see if the fatigue requirement is met.

Because Sn is less than 3Sm ( 60,000 at psi), Ke 1.0,and

(B14)

From Table I-9-1 (line 2) and the interpolation equation inTable I-9.1,Nd1 30,000 cycles. Because Nd1 is greater than thepostulated 1,000 cycles, the elbow end at Node 30(a) is accept-able as Class 1 piping.

For comparison with Class 2 or 3 piping,

design cycles

Thus for this example,Nd1 30,000 cycles does not agree verywell withNd2,3 82,000 cycles. Refer to the discussion presentedin Section 38.5.

38.8.6 Branch Connection

The nozzle is at Node 25, modeled as a point spring in thepiping system analyses. The moments at Node 25 are shown inTable 38.1.

Nd2,3 = (490,000>25,500)5

>32 = 82,000

Salt = 1.0 * 54,700>2 = 27,300psi

370F

*74,000

*12>162

=54,700

psi

Sp = 1.0 * 1.244 * 3,200 + 1.0 * 9.25

Sn= 1.244* 3,200+ 9.25 * 74,000* 12>162= 54,700psi

SB9 = 0.0 * 3,200 + 6.17 * 2,140 * 12>162 = 980

C1 = 9.25 K1 = K2 = 1.00B1 = 0.00 B2 = 6.17 C1 = 1.244

+ 4.27 * 74,000 * 12>162 = 25,500psi

STE = 0.5 * 3,200 + 0.75 * 4.27 * 2,140 * 12>162

SOL = 0.0* 3,200+ 6.17* 2,140* 12>162= 980psi

i = 4.27

h = 0.375 * 36>11.81252 = 0.09675

i = 0.9/h(2>3)

Code evaluation of a branch connection is more complex thanfor girth butt welds or elbows. Among other aspects, the evalua-tions involve two pipes: the run pipe and the branch pipe or nozzle,with different radii and wall-thickness. There are two i-factorsirand iband two sets ofB2, C2, and K2.

The 2001 Edition of Ref. [1], 2002 Addenda, made significantchanges to indices and i-factors for branch connections:

For Class 1 piping, C2b andB2b were reduced by a factor of 2.For Class 2 or 3 piping, ib andB2b were reduced by factor of2 for r/R up to 0.5, and coverage was extended up to r/R 1.00.

These changes are based on refs. [34,35] and constitute anotherexample of the continuing review of the subject of this Chapter bycode committees.

The i-factors and stress indices are summarized in Table 38.2.and will be used for the examples in the paragraphs that follow.

For Class 2 or 3 piping, the branch end and two run ends areevaluated separately. For Class 1 piping, Mb andMr must be cal-culated as indicated in NB-3683.1(d) and Fig. NB-3683.1 (d)-1.

38.8.6.1 Class 2 or 3 Piping: Check of Run Ends (Node 20)

Both run ends should be checked. Node 20(a) will be used in thefollowing as a specific example, in which the moments at both runends are essentially identical. This is because the ratio of themoment of inertia of the NPS 24 run pipe to the NPS 6 branchpipe; 1,943/28.1 69.

From Table 38.1, MA 6,200 ft. lb. and MC 19,700 ft. lb.For factors, see Table 38.2.

(C8)

(C11)

Because 2,300 psi is less than 1.5Sh 25,650 psi, and 5,420 psiis less than (Sh + SA) 42,750 psi, the branch connection check ofrun ends is acceptable as Class 2 or 3 piping.

38.8.6.2 Class 2 or 3 Piping: Check of Branch End (Node 25)

See Tables 38.1 and 38.2.For Node 25(a) (no nozzle flexibility):

(C8)

(C11)

For Node 25(b) (with nozzle flexibility):

(C8)

(C11)

The inclusion of nozzle flexibility in the piping system analysisturns an unacceptable system [STE 107,000 psi (Sh SA)42,750 psi] into an acceptable system (STE 19,900 psi 42,750 psi).

= 19,900psi+ 5.54 * 2,560 * 12>8.85

STE = 0.5 * 1,180 + 0.75 * 5.54 * 6 * 12>8.85

SOL = 0.5 * 1,180 + 2.77 * 6 * 12>8.85 = 610psi

+ 5.54 * 14,200 * 12>8.85 = 107,000psi

STE = 0.5 * 1,180 + 0.75 * 5.54 * 3 * 12>8.85

SOL = 0.5 * 1,180 + 2.77 * 3 * 12>8.85 = 600psi

+ 2.143 * 19,700 * 12>164 = 5,420psi

STE = 0.5* 3,200+ 0.75* 2.143* 6,200* 12>164

SOL= 0.5* 3,200+ 1.65* 6,200* 12>164= 2,350psi


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38.8.6.3 Class 1 Piping For Class 1 piping,Mb andMrare calcu-lated as indicated in NB-3683.1(d) and Fig. NB-3683.1(d)-1. Forthis example, the run moments do not change sign; thusMr 0.

For Node 25(a) (no nozzle flexibility):

(B10)

Because Sn 3Sm 60000 psi at without nozzle flexi-bility, the system is not acceptable. However, we continue theexample to look atNd1 andNd2,3.

design cycles anddesign cycles (B11)

For Node 25(b) (with nozzle flexibility):

(B10)

(B11)

Because Sn is less than 3Sm (60,000 psi), Ke 1.0, and

cycles anddesign cycles

Thus the branch connection, without inclusion of nozzle flexi-bility in the piping system analyses, is unacceptable for Class 1piping. The inclusion of nozzle flexibility turns an unacceptablesystem [Sn 3Sm] into an acceptable system with allowable designcyclesNd1 196000 as compared to the postulated 1,000 cycles.

38.8.7 Best Estimate of Flexibility FactorsTable 38.1 shows that best estimate ko 23.2 and ki 5.81

reduced MC at Node 25 from 14,200 to 2,560 ft. lb. However, forother Nodes, inclusion of the nozzle flexibility sometimes increasedrather than decreased the moments. Although trivial in this examplefor maximum calculated stresses, the example serves to illustrate

that conservative flexibility factors cannot be defined. Thus thegoal should be to use best estimate flexibility factors.

38.8.8 Summary of Examples

(1) The piping system is Code compliant with respect to equa-tion (C8) for Class 2 or 3 piping and with respect to equa-tion (B9) for Class 1 piping [1]. This is not cycle-dependent.

(2) The girth butt welds and elbows are Code-compliant for Class 1(Nd1 1,000) and Class 2 or 3 piping (STE 42,750 psi) [1].

d2,3 = (490,000>19,900)5>32 = 283,000

Nd1 = 196,000

Salt = 1.00 * 33200>2 = 16600psi

* 12>8.85 = 33,200psi

Sp = 2.0 * 2.18 * 3,200 + 1.00 * 5.54 * 2,560

= 26,200psi

Sn = 2.18 * 3,200 + 5.54 * 2,560 * 12>8.85

Nd2,3 = (490,000>107,000)5>32 = 63

Nd1 = 160

Salt = 2.80 * 121,000>2 = 169,000psi

= 121,000psi

Sp= 2.0* 2.18* 3,200+ 1.00* 5.54 * 14,200* 12>8.85

= 2.80 (seeNB - 3228.5)

= 1 + 23(114,000>60,000) - 14

Ke = 1 + 23(Sn>3Sm) - 14

370F

= 114,000psiSn = 2.18 * 3,200 + 5.54 * 14,200 * 12>8.85

(3) The branch connection, with assumed no nozzle flexibility,is not Code-compliant for Class 1 or Class 2 or 3 piping [1].

(4) The branch connection, with nozzle flexibility, is Code-compliant for Class 1 (Nd1 1,000) and for Class 2 or 3piping (STEof branch and run checks 42,750 psi.) [1].

38.9 ASME B31.1[36] AND B31.3[37] PIPINGCODES

Stress intensification factors in B31.1 and B31.3 are identicalor similar to those in NC-3600 of ref. [1] for Class 2 or 3 piping.The preceding comments concerning stress intensification factorsfor Class 2 or 3 piping are usually applicable to B31.1 and B31.3.

B31.1 and B31.3 do not use B-stress indices. In B31.1, theequivalent of B2 is 0.75i. See discussion in 38.11 regarding howB31.3 addresses sustained loads. Thus the preceding commentsconcerning Class 2 or 3 piping are usually applicable to refs. [36]-[37]. In particular, comments concerning the ongoing nature ofCode reviews of stress intensification factors and flexibility fac-tors are also applicable to the ASME Piping Codes. The reviews

of ASME Piping Codes start with the B31 Mechanical DesignTechnical Committee.Stress intensification factors are covered in Appendix D of

B31.1 and B31.3. Appendix D is analogous to Fig. NC-3673.2(b)-2of ref. [1]; however, Appendix D of B31.1 is not the same asAppendix D of B31.3.

Analogies between Class 2 or 3 piping and between B31.1 andB31.3 are discussed in Sections 38.10 and 38.11.

38.10 ASME B31.1: POWER PIPING[36]

Allowable stresses in B31.1 are not the same as for Class 2 or 3piping. For example, for A106-Grade B at temperatures up to650F, the allowable stress is 15 ksi for B31.1; 17.1 ksi for Class 2or 3 piping.

Allowable stresses for Class 2 or 3 piping are limited to tem-peratures such that creep is negligible. In B31.1, allowable stressesare given for temperatures in the creep range. For example, forA106-Grade B, the allowable stress in B31.1 at 800F is 10.8 ksi.

Equation (11) of B31.1 is

(B31.111)

The preceding equation is for sustained loads and is concep-tually the equivalent of equation (C8) for Levels A and B.Equation (12) of B31.1 is

(B31.112)

where

MA resultant moment from weight and other sustainedloads

MB resultant moment from occasional loadsDo, tn and Z pipe (run pipe or branch pipe for reducing

branch connections and tees)k 1.15 for occasional loads acting for no more

than 8 hr at any one time and no more than 800hr/year

SOL = PDO>(4tn) + 0.75iMA>Z + 0.75iMB>Z 6 kSh

SL = PDo>(4tn) + 0.75iMA>Z 6 1.0Sh


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k 1.2 for occasional loads acting no more than 1 hrat any one time and no more than 80 hr/year

The preceding equation is also conceptually the equivalent ofequation (C8), but for loads that might be in Level D under ref.[1], e.g., an occasional load caused by an earthquake.

Both equations (B31.111) and (B31.112), as indicated by theuse of resultant moment, are checks of the adequacy to sustainloads without gross plastic distortion.

Equation (13) of B31.1 is

(B31.113)

where

MC range of resultant moment from thermal expansion

Conceptually, equation (B31.1-13) is the equivalent of equation(C11). As indicated by range of resultant moment, this is acheck of fatigue adequacy.

The rules of B31.1 lead to the conclusion that the example pip-

ing system is not acceptable without nozzle flexibility; and isacceptable with nozzle flexibility. In the interest of brevity, therather extensive details are not included herein.

38.11 ASME B31.3: PROCESS PIPING[37]

Allowable stresses in B31.3 are not the same as for Class 2 or 3piping. For example, for A106-Grade B at temperatures up to400F, the allowable stress is 20 ksi for B31.1; 17.1 ksi for Class 2or 3 piping.

Allowable stresses for Class 2 or 3 piping are limited to tem-peratures such that creep is negligible. In B31.3, allowable stressesare given for temperatures in the creep range. For example, forA106-Grade B, the allowable stress in B31.3 at 1000F is 2.5 ksi.

The load capacity check of B31.3 is described in paragraph

302.3.6 as follows:Details of B31.3 checks to determine whether the example pip-

ing system is or is not acceptable are shown in the following para-graphs.

SA 1.2[1.25(Sc Sh) SL]: Sc Sh 20000 psi

SL is calculated by the B31.1 equation, (B31.1-11)

There is no equation for SLthat is, analogous to equation(B31.111). The following question arises: If ii and/or io is greaterthan 1.00, in what way (if any) does the value of ii or io affect thecalculation of SL?

The fatigue check of B31.3 is specified (for other than checkingthe branch end of reducing-branch connections) by equationsB31.317 and 18). These two equations can be combined to give

(B31.3X)

where

ii in-plane stress intensification factorio out-of-plane stress intensification factor

Mi in-plane bending momentMo out-of-plane bending moment

SE = 3(iiMi)2 + (ioMo)

2 + M2t40.5>Z 6 SA

SE = iMC>Z 6 SA + f(Sh - SL)

Mt torsional momentZ section modulus

As indicated by equation (1b) of B31.3, when Sh is greater than SL,

(B31.31b)

For checking the branch end of reducing branch connections,based on equations (B31.319 and20):

(B31.3Y)

For the example UFT branch connection of Fig. 38.3, T0.375 inch, ii t 6.98 0.280 1.95 inch; thus Ts 0.375 inchandZe 11.86 in

3.

Zb section modulus of branch pipe

B31.3 does not cover such a component as a branch connection

in B31.1. Thus the only available comparable component inB31.3 is the unreinforced fabricated tee (UFT). For UFT, h T/R; io 0.9/h

(2/3); and ii 0.75io 0.25. The lower bound onboth io and ii is 1.00.

For B31.3: check of run endsno nozzle flexibility (Node 20):

(see Fig. 38.3 for moment directions)

Both run ends should be checked. In this example, the momentsat both run ends are essentially identical. This is caused by theratio of the moment of inertia of the NPS 24 run pipe to the NPS6 branch pipe: 1,943/28.1 69.

(B31.3-X)

Because SE 8760 psi SA 54000 psi, SEis acceptable.For B31.3: check of branch endno nozzle flexibility (Node 25).


(B31.3-Y)

Because SE 129000 psi SA 58000 psi, SE is not acceptableFor B31.3: check of run endswith nozzle flexibility (Node 20).


Both run ends should be checked. In this example, the momentsat both run ends are essentially identical. This is caused by the

Mz = Mt = 2,719ft.lb.

My = Mo = 913ft.lb.

Mx = Mi = 13,832ft.lb

+ (245>8.50)2}0.5 * 12 = 129,000psi

SE = {3(6.98 * 156)2 + (8.98 * 14,196)24>11.862

Mz = Mo = 14,196ftlb.

My = Mi = 156ft.lb.

Mx = Mt = 245ft.lb.

+ 10,23424}0.5 = 12>162 = 8,760psi

SE = {3(8.98 * 1,310)2 + (6.98 * 16,801)2

Mz = Mt = 10,234ft.lb.

My = Mo = 1,310ft.lb.

Mx = Mi = 16,801ft.lb.

Ze = pr2Ts:Ts = lesserofT,iit

SE = {3(iiMi)2 + (ioMo)

24>Z2e + (Mt>Zb)2}0.5

SA>f31.25(Sc + Sh) - SL4


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16 Chapter 38

ratio of the moment of inertia of the NPS 24 run pipe to the NPS6 branch pipe: 1,943/28.1 69.

(B31.3-X)

Because SE 7180 psi SA 54000 psi, SEis acceptable.For B31.3: check of branch endwith nozzle flexibility (Node

25).


(B31.3-Y)

Because SE 23100 psi SA 58000 psi, SE is acceptable.The example piping system, without nozzle flexibility, is not

acceptable by Code[1], Class 1: Code[1], Classes 2/3: B31.1[36]:B31.3[37]. The example piping system, with nozzle flexibility, isacceptable by all four of the Codes. Acceptable refers only toconformance with the stress limits of the four Codes.

That B31.1 and B31.3 may not be consistent with one anotheris mainly related to branch connections. As noted on several occa-sions in this chapter, the review of i-factors and their uses is ongo-ing. With respect to B31.1 and B31.3, the reviews start with theB31 Mechanical Design Technical Committee.

38.12 REFERENCES

1. ASME Boiler and Pressure Vessel Code, Section III, Division 1,Rulesfor Construction of Nuclear Power Plant Components, 2007 Edition;The American Society of Mechanical Engineers.

2. Markl, A. R. C., Fatigue Tests of Welding Elbows and ComparableDouble-Mitre Bends, Trans. ASME, Vol. 69, No. 8, 1947.

3. Markl, A. R. C. and George, H. H. Fatigue Tests on FlangedAssemblies, Trans. ASME, Vol. 72, 1950.

4. Markl, A. R. C., Fatigue Tests of Piping Components,Trans. ASME,Vol. 74, No. 3, 1952.

5. Heald, J. D. and Kiss, E., Low Cycle Fatigue of Nuclear PipeComponents, ASME J. of Pressure Vessel Technology, August 1974.

6. Scavuzzo, R. J., Srivatsan, T. S. and Lam, P. C., Fatigue of Butt-welded Pipe, Welding Research Council Bulletin 433, July 1998.

7. Rodabaugh, E. C. and Scavuzzo, R. J., Effect of Testing Methods onStress Intensification Factors, Welding Research Council Bulletin433, July 1998.

8. Minichiello, J. C. and Rodabaugh, E. C., Development of Stress

Intensification Factors, PVP-Vol. 313-2. ASME. 1995.9. Wais, E. A., et al., Stress Intensification Factors and Flexibility

Factors for Unreinforced Branch Connections, PVP-Vol. 383,Pressure Vessel and Piping Codes and Standards, The AmericanSociety of Mechanical Engineers, 1999.

10. Wais, E. A., et al., Evaluation of Stress Intensification Factors forCircumferential Fillet Welded or Socket Welded Joints, PVP-Vol.383, Pressure Vessel and Piping Codes and Standards, The AmericanSociety of Mechanical Engineers, 1999.

+ (248>8.50)2}0.5 * 12 = 23,200psi

SE = {3(6.98 * 117)2 + (8.98 * 2,550)24>11.862

MZ = MO = 2,550ft.lb.

My = Mi = 117ft.lb.

Mx = Mt = 248ft.lb.

* 12>162 = 7,180psi

SE = 3(8.98 * 913)2 + (6.98 * 13,832)2 + 2,719240.5

11. Wais, E. A., et al., Stress Intensification Factors and FlexibilityModeling for Concentric and Eccentric Reducers, PVP-Vol. 383,Pressure Vessel and Piping Codes and Standards, The AmericanSociety of Mechanical Engineers, 1999.

12. Wais, E. A., et al., Stress Indices for Straight Pipe with TrunnionAttachments, PVP-Vol. 399, Design and Analysis of Pressure

Vessels and Piping, The American Society of Mechanical Engineers,2000.

13. Wais, E. A., et al., Stress Indices for Elbows with TrunnionAttachments, PVP-Vol. 399, Design and Analysis of PressureVessels and Piping, The American Society of Mechanical Engineers,2000.

14. Wais, E. A., et al., Investigation of Unreinforced Branch Connectionson Elbows, PVP-Vol. 399, Design and Analysis of Pressure Vesselsand Piping, The American Society of Mechanical Engineers, 2000.

15. Wais, E. A., et al., Stress Intensification Factors and FlexibilityFactors of Pad Reinforced Branch Connections, PVP-Vol. 399,Design and Analysis of Pressure Vessels and Piping, The AmericanSociety of Mechanical Engineers, 2000.

16. Wais, E. A., et al., Directional Stress Intensification Factors for 90Degree Elbows, PVP-Vol. 399, Design and Analysis of Pressure

Vessels and Piping, The American Society of Mechanical Engineers,2000.

17. Wais, E. A., et al., Stress Indices for Circumferential Fillet Weldedand Socket Welded Joints, PVP-Vol. 440, Design and Analysis ofPiping, Vessels and Components, The American Society ofMechanical Engineers, 2002.

18. Wais, E. A., et al., Investigation of Torsional Stress IntensificationFactors and Stress Indices for Girth Butt Welds in Straight Pipe,PVP-Vol. 440, Design and Analysis of Piping, Vessels andComponents, The American Society of Mechanical Engineers, 2002.

19. Wais, E. A., et al., Investigation of Stress Indices and DirectionalLoading of Eccentric Reducers, PVP-Vol. 469, Design and Analysisof Pressure Vessels and Piping,, The American Society of MechanicalEngineers, 2003.

20. Mershon, J. L., PVRC Research on Reinforcement of Openings in

Pressure Vessels, Welding Research Council Bulletin No. 77, May1962.

21. Mershon, J. L., Interpretive Report on Oblique Nozzle Connectionsin Pressure Vessel Heads and Shells Under Internal PressureLoading, Welding Research Council Bulletin 153, August 1970.

22. Rodabaugh, E. C. and Moore, S. E., Stress Indices and FlexibilityFactors for Nozzles in Pressure Vessels and Piping, NUREG / CR-0778, June 1979.

23. Rodabaugh, E. C. and Moore, S. E., Stress Indices for Girth WeldedJoints, Including Radial Weld-Shrinkage, Mismatch and Tapered-wallTransitions, NUREG CR 0371. September 1978.

24. Rodabaugh, E. C. and Moore, S.E., Stress Indices and FlexibilityFactors for Concentric Reducers, Welding Research Council Bulletin285, July 1983.

25. Criteria of the ASME Boiler and Pressure Vessel Code for Design byAnalysis in Sections III and VIII, Division 2, Published by AmericanSociety of Mechanical Engineers, 1969.

26. Rodabaugh, E. C., Comparisons of ASME Code Fatigue EvaluationMethods for Nuclear Class 1 Piping with Class 2 or 3 Piping,NUREGCR/3243, June 1983.

27. Rodabaugh, E. C. and Moore, S. E., Evaluation of the PlasticCharacteristics of Piping Products in Relation to ASME CodeCriteria, NUREG/CR-0261, July 1978.


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28. Larson, L. D., Stokey, W. F. and Panarelli, J. E., Limit Analysis of aThin-Walled Tube Under Internal Pressure, Bending Moment, AxialForce and Torsion, ASME Trans., J of Applied Mechanics, Sept.1974.

29. Touboul, F. and Acker, D., Excessive Deformation and Failure ofStraight parts and Elbows, Proceedings of SMiRT 11, Paper E02/2,

Tokyo, Japan, August 1991.

30. Matzen, V. C. and Tan, Y., Using Finite Element Analysis toDetermine Piping Elbow Bending Moment (B2) Stress Indices,Welding Research Council Bulletin 472, June 2002.

31. Matzen, V. C. and Yuan, X., The B2 Stress Index as a Function ofInternal Pressure, Bend Angle, Loading Type and Material,Proceedings of SMiRT 17, Paper F-02-1, Prague, Czech Republic ,August 2003.

32. Jaquay, K., Seismic Analysis of Piping, NUREG/CR-5361, June 1998.

33. Markl, A. R. C., Piping-Flexibility Analysis, Trans. ASME, Vol. 77,1955.

34. Rodabaugh, E. C., Accuracy of Stress Intensification Factors for BranchConnections, Welding Research Council Bulletin 329, December 1987.

35. Rodabaugh, E. C., Stress Indices, Pressure Design, and StressIntensification Factors for Laterals in Piping, Welding ResearchCouncil Bulletin 360, January 1991.

36. ASME B31.1-2004 with 2006 Addenda, Power Piping, ASMECode for Pressure Piping, B31, The American Society of MechanicalEngineers.

37. ASME B31.3-2004 Process Piping, ASME Code for PressurePiping, B31, The American Society of Mechanical Engineers.


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