ML20054L990

Procedure to Evaluate Structural Adequacy of Piping Sys in Creep Range

ML20054L990
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Site:	Clinch River
Issue date:	07/06/1982
From:	Ohall A WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP.
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References
PROC-820706, NUDOCS 8207090130
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A PROCEDURE TO EVALUATE STRUCTURAL ADEQUACY OF A PIPING SYSTEM IN CREEP RANGE A. K. Dhalla*

t PUBLISHED AS:

Bench.mrk Problen Studies and Piping System at Elevated Temperature,

ASE Publication PVP-63, American Society of Mechanical Engineers, Neu fork, 1982.

~

• Fellow Engineer, Westinghouse Advanced Reactors Division, Madison, PA 15663 i

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l 8207090130 820706 PDR ADOCK 05000537 l

A PDR

ABSTRACT An inelastic analysis procedure to establish structural adequacy of an elevated temperature piping system is presented in this paper. The analytical method is incidental to the procedure used to comply with Code Case N-47 inelastic strain accumulation and creep-fatigue damage criteria.

INTRODUCTION A typical hot leg of the primary beat transport systes sodium loop in a I

Liquid Metal Fast Breeder Reactor (LMFBR), illustrated in Figure 1, consists of a 24-inch 316 stainless steel piping system with six elbows. The operating temperature of 1015'F (546*C) requires evaluation of plastic as well as creep strain accumulation and creep-fatigue interaction in the piping system.

Initial piping configurations as well as hanger and snubber locations are established by the elevated temperature piping screening rules developed over l

the years (1-3].*

The screening rules in (3) are set such that the use of the ASME Code flexibility factor and stress indices (4) permits negative margins at the most highly loaded locations relative to elastic limits and simplified l

inelastic Code Case N-47 (4) limits. These negative margins are set because the inelastic analyses results show that the elastic and simplified inelastic

(

rules of the ASME Code are very conservative (2]. The noncompliance with the elastic and/or simplified inelastic Code rules necessitates a detailed l

i inelastic analysis. The detailed inelastic analyst = results presented in this l

paper are based upon the pipe-bend finite elements of the MARC computer program (5).

The purpose of this paper is to illustrate an inelastic analf:*.4 procedure that may be used to establish structural adequacy of an elevated temperature piping system. The analytical method is incidental to the procedure used to comply with Code Case N-47 inelastic strain accumulation and creep-fatigue damage criteria. Specifically, the following four areas required careful interpretation of the inelastic analysis results:

1.

Evaluation of deformation behavior in the creep regime.

' Numerals in brackets designate references at the end of this paper.

2.

Extrapolation of analytical predictions computed from two load cycles to the full design life of the plant.

3 Evaluation of fabrication and girth butt welds at the elbow ends.

4.

Evaluation of environmental effects on the creep-fatigue damage predictions.

The paper also provides simple guidelines to select only a few piping systems in a heat transport system for detailed inelastic analysis, instead of analyzing all piping systems which do not comply with the " elastic" Code criteria.

GE,NERAL REQUIRD4ENTS AND ASSIMPTIONS FOR AN INELASTIC ANALYSIS The methud recommended for the time independent elastic-plastic and time dependent creep analysis of the elevated temperature structural components is described in (6). These recommendations for the elastic-plastic-creep analysis are incorporated in the MARC general purpose finite element computer program (5]. which was used in the present analysis.

Material Properties For stress analysis, both time-independent elastic-plastic and time-dependent creep anterial data age required for the piping system. The Young's Modulus E, Poisson's ratio, v, and instantaneous thermal expansion ccefficient, e, all vary with temperature, T.

The bilinearized (6]

cyclically hardened yield stress, oy, lysis.

and the plastic work-bardening slope E

are also needed for inelastic ana These time independent material p

properties used in the analysis are as follows:

(28.90 x 10 - 6850.0 (T-70)) poi E

=

(23103 0 - 4 9925 (T-70)) pai o

n y

(0.2654 + 4.2688 x 10-5 (T-70))

v s

(9.062 x 10~0 + 2.518 x 10~9 (T-70)) in/in/*F a

6 E

1 365 x 10 p,1 p

where T is in degrees Fahrenheit.

For time dependent creep properties, the following analytical expression for creep strain, e, as a function of time, t, is used:

e "DD

+ e,t (1) e pg The parameters e, p and e, are as follows:

In c = 1 350 - 5620.0/R - 0.05060s + 1 9180 Ino 2

in p = 31.0 - 67310/R + 0 33060s - 0.001885o in e, a 43 69 - 106400/R + 0.294o + 2 5961no where, R is temperature in degrees Rankine, and o is stress in kai. For the above anterial properties SI conversion units are: 1 kai : 6.894757 MPs,

'C s ('F - 32)/1.8, and 'E a ' Rankine /1.8.

The effects of environment on the material properties of the piping system are not included in the ASME Code (4]. According to Sections NB-3120 NCA-1130, NCA-3252 of the ASME Code (4) it is the responsibility of the nner/ designer to include these environmental effects in the material property data. Consequently, these effects have to be evaluated separately (7].

Briefly, the thermal aging, corrosion, and irradiation effects have minimal

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influence on the 316 ss piping material. Fatigue strength of the 316 ss in flowing sodium is increased under some conditions and reduced in some others; and these effects in the sodium environment are also considered minimal.

However, the inert sodium environment does not allow surface oxidation which reduces creep-rupture strength of the material by 4.75 at an operating temperature of 1015'F (546*C). In addition, the flowing sodium may transfer carbon and nitrogen in 316 stainless steel from the hotter to the cooler regions. But for this specific piping system, these interstitial mass transfer effects are insignificant for both short and long term material properties.

I Lead Histogram During its 30-year operating life at 855 availability, the piping system experiences deadweight and pressure loadings, thermal transient events, differential movement of the IHX and the Primary Pump with respect to flexible piping system during temperature flucttAtions, and creep deformations and relaxation of thermal expansion loads during full pcwer creep-hold time.

The specified thermal transient events vary in intensity and frequency of occurrence. The sequence of transient events (load path) affects the final response of the piping system. However, due to the high costs associated with inelastic analysio, it is not practical to analyze all transient events.

Therefore, it is necessary to select only two or three most severe thermal transients and lump milder transients into one of the selected transients to evaluate upper bound creep-fatigue damage and the strain accumulation to comply with the ASME Code Case N-47 criteria. An examination of the temperature changes occurring during these transient events shows that the postulated 863 thermal transient events can be conservatively placed into three groups. Figure 2 shows a synthesized load histogram. This load histogram envelops all normal, upset and emergency events experienced by the 1120 l

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O 40 80 120 160 200 240 INCREMENTAL LOAD STEP NUMBER Figure 2. Load Histogram for MARC Pipe Bend inelastic Analyses l

piping system. The first tran21ent ev;nt, d:cignated ca 3E, cnv31 spen 36 moat severe thermal downshock transient events, radial AT = 129'F (717'C); the second event, designated 4U, envelopes 36 moderately severe up and down thermal transient events, radial + AT = 39'F (217'C) and -aT = 45'F (25'C); and the third event, designated 2U, envelopes the rest of the 791 less severe events, radial AT = 39'F (21.7'C).

A conservative sequence of transient events was established by the simplified thick cylinder computer program developed by Chern (8). Three simplified thick cylinder inelastic analyses were performed to evaluate the sequences 3E-4U-2U, 20-4U-3E, 4U-3E-2U. The maximum strain, and consequently, the cyclic range is about the same in all three cases. However, the assumed sequence in histogram 3E-4U-2U introduces an additional minor cycle within the overall strain cycle. The difference in ratchetting strains predicted by the three sequences is also very small. Consequently, the sequence 3E-4U-2U, as shown in Figure 2, is utilized to predict inelastic response of the piping syatom.

Assumptions and Limitations of System Analysis 1.

The simplified pipe-bend model (Elements 17 and 14 of the HARC program) neglects the stiffening effects of the straight pipes welded to the elbow (9]. Therefore, in this paper the end of the elbow welded to the pipe is eval;;ated by a semi-empirical approaco presented in (10), to overcome this limitation.

2.

The axial stresses within the curved elbow are neglected in the MARC pipe-bend analysis. This may not be a very serious limitation, because the predominant loading in an LMFBR piping is due to thermal expansion loading, and pressure loading is of secondary importance.

Furthermore, the effective stress (based upon Von Mises yield criterion) with zero axial and radial stress would be 155 higher than if axial stress equal to half the hoop stress is included in the analysis. From the design qualification point of view this assumption is conservative.

3 The pressure loading, as well as thermal loading due to radial gradients, are not applied to the straight pipes of the simplified system model, because the straight pipes are not as highly loaded as the elbows.

4.

Seismic loading is not explicitly treated in the inelastic system analysis. This loading can be treated as an equivalent static loading, whieb is a topic of another paper (11).

PIPING SYSTEM ANALYSIS Ceneral Procedure The following sequence of steps is followed to evaluate structural integrity of the piping systes:

1.

Select an economical mesh to reduce overall inelastic analysis computer costs.

2.

Perform heat transfer analysis to obtain a nonuniform temperature distribution due to thermal transient events.

3 Store temperature distribution on a permanent file, and select thermal load steps for subsequent (MARC) inelastic stress analysis.

1 4.

Establish load histogram, and investigste sequence of thermal loading.

5 Select appropriate time-independent and time-dependent material properties for stress analysis.

6.

Complete required subroutines for thermal and creep analysis to interface with the (MARC) stress program.

7.

Perform inelastic analysis for at least two load cycles to establish ratchetting strain increments per cycle.

l 8.

Extrapolate, appropriately, the accumulated strain values and the i

creep-fatigue damage to satisfy the ASME Code criteria. If the extrapolated values do not satisfy the Code requirements, then either i

analyze one more load cycle using the same load histogram, or reduce conservatise used in establishing the original load histogram.

I Evaluation of Structural Response Basically, two groups of plots are required to study the inelastic response of the piping system. The first group, designated as profile plots (Figure 3), displays the distribution of stresses (or strains) around various

' elbow cross-sections. From these plots, it is possible to observe circuaterential stress and strain redistributions that occur during transient l

events and during steady state creep-hold time. The second group of plots, designated es history plots (Figures 4 and 5), provide a complete stress (or strain) variation during the entire loading history. To facilitate evaluation of piping system response, a computer program POST MARC was developed to post-process analysis results generated on the POST file by the MARC program.

An examination of profile plots indicated that elbow-1, closest to the IhX, and elbow-6 closest to the Primary Pump are the most highly loaded elbows in the piping system. The most highly strained locations can be selected from effective stress profile plots such as those presented in Figure 3 The effective stress redistribution at varjous creep hold times shows relaxation of thermal expansion stresses during creep hold time. Based upon stress (and strain) distributions observed in profile plots, specific elements are selected for the ASME Code evaluation. These critical locations within the 8

elbow can then be examined further by ccncentrating upon stress or strain yariations during the entire loading history. For example, the following two response variables are shown in Figure 4 (a) inelastic (plastic + creep) hoop strain, (b) effective stress. Total strain accumulation of a principal component can be obtained from history plots shown in Figure 4a.

The effective stress history plots, in Figure Ab, provide a sensure of creep-rupture damage accumulation. Interestingly, when the effective stress is relaxing on the inside surface, the load is transferred to the outside surface, where the effective stress increases. Thus, the purpose of displaying both the history and the profile plots is to select for detailed evaluation elements which are highly stressed (or strained). For example, the local response at one highly strained location is illustrated in Figure 5 (117* froe extrados at inside surface of elbow-1). Tne capital letters in this figure designate the loading state displayed in Figure 2.

-Discussion of Restuls Figure 3 indicates that nonuniform stress distribution is smoothed out during creep-hold time. A complex stress redistribution occurs through-the-thickness as well as around the circumference of the elbow; these redistributions can be investigated by extensive displays similar to those presented in Figures 3 to 5 An important observation is that the redistribution during creep hold time and reverse yielding due to thermal transients in thin elbows is different from a thick complex structural component with gross or local discontinuities (12). In a complex structural component the local plastic zones are generally constrained by surrounding elastic material. Consequently, during creep, the effective stresses in the plastic zone relax and redistribute into the surrounding lower stressed material. Rarely, the effective stress increases during subsequent thermal cycles, because the bulk of the surrounding material is at a lower stress into which the redistributed stresses are easily absorbed. This is not the case in thin piping elbows. Even if the peak surface effective stress were to relax during the first creep hold time, it may increase during a subsequent creep hold period, because'in thin elbows there is little room for stress redistribution. If the effective stress at a lower stressed location s

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those induced during initial heat up.

Reverse yielding occurs during the 4U up transient. The response during subsequent thermal transients is elastic.

j Thus, inelastic strain accumulation occurs only during creep hold time, j

A question arises as to what would have happened if the 3E transient were not included in the analysis to produce a favorable residual stress pattern in the most highly-strained elements? Of course, without performing an inelastic i

I analysis it is difficult to present numerical evidence. However, based upon the experience gained from the piping syntes analysis, it can be said that final response would be similar to the response observed during second load cycle of the present analysis. That is, a 2U thermal transient event, instead of a 3E event, would not have produced additional plastic strains than those accumulated during first heat-up. The 2U event may produce a positive residual stress pattern instead of a negative stress pattern observed at the inside surface (Figure 5). Consequently, reverse yielding may not occur during 4U tranatent. Thus, subsequent to first heat up, time-independent response to a Iced cycle without 3E event may be elastic. Furthermore, as discussed earlier, the creep relaxation and redistribution will schieve a uniform stress level similar to those observed with the inclusion of 3E event, because secondary self-equilibrating stresses do not alter the uniform stress levels achieved during creep hold time.

CREEP-FATIGUE INTERACTION AND STRAIN ACCUMULATION The accumulation of creep-rupture and fatigue damage including hold time and strain rate effects for the combination of Normal, Upset and Emergency Cor.ditions are evalaated according to the following Code Case N-47 equation:

p q

(g"D ) + kul (fD)k < D (2)

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1 Z

jal The notation is the same as that used in Eq. (5) of Appendix T in Code Case N-47 Creep-Rupture Damage

)

The creep-rupture damage is based upon the effective stress during creep hold time at steady state full power operation. The full power operation at 1015'F (546*C) for 30 years at 0.855 availability gives a total of 223533 hours of creep hold time. A typical effective stress variation during creep hold time is illustrated in Figure 4b.

The reduction in creep-rupture life as a result of exposure to sodium at 1015'F (546*C) is also considered. The creep-rupture strength of the pipe surface in contact with sodium is reduced by 4 75. This reduction is in f

addition to the factor K' s 0 9 specified in Code Case N-47 Consequently, l

T values are obtained by entering the stress-to-rupture curve (Figure I-14.6B of Co'de Case N-47) at a stress value equal to the calculated stress divided by a reduction factor K' s 0 9 for the outside surface and a factor K" (0.953)(K') = 0.858 for the inside surface of the elbow.

a The creep-rupture damage, I fr-varies from 0.09 to 0.41.

Althodgh D

the stress level after two load cycles say relax during subsequent creep-hold time, it is conservatively assumed that the stress level at the end of two load cycles is constant for plant design life.

In the simplified piping system analysis, the stiffening effects of the straight pipes welded to the elbow were neglected. Furthermore, the material and fabrication effects due to the radial weld shrinkage, pipe mismatch, and weld condition were excluded from this system analysis. Therefore, a semi-empirical procedure presented in (10] was used to evaluate the welded elbow cross-section. This interim procedure can be used to satisfy the ASME Code criteria without performing additional analysis of the welded c ross-sectien. The maximum creep-rupture damage computed at the welded end is 0 367, which is less than the maximum creep-rupture damage accumulation of 0.41 within the elbow.

Fatigue Damage The ASME Code Case N-47 presents a procedure to compute the effective strain range at critical locations in a structural component. This effective strain range is then used to compute Ng (Figure T-1420-1A,1B of Code Case N-47) for the corresponding anximum metal temperature. The strain components computed from inelastic analysis were examined for each thermal cycle to determine two points in time which contained the maximum and minimum values of total strain components (excluding uniform thermal strains). The evaluation of experimental data suggests that the fatigue life is not reduced due to sodium exposure. Therefore, the ASME Code curves were not altered to account The maximum fatigue damage, I""-

for the environmental effects.

.0008 8

D is predicted at the ineide surface of Elbow-1.

A semi-empirical procedure outlined in (10] was used to evaluate the welded cross-section. The total anximum fatigue damage summation at the welded end of the elbow is 0.12.

This value is substantially larger than the anximum fatigue damage of 0.008 within the elbow. This is not surprising, because at the elbow end cross-section the peak stress intensity due to as-welded condition is substantially higher than that within the elbow where welds are not present.

Strain Accumulation In the parent metal, Code Case N-47 specifies averaged through-the-thickness strain limit of 15, linearized surface strain limit of 25 and the peak local strain limit of 55. These limits are reduced by 505 at the weld. Table 1 presents a summary of total inelastic accumulated strain at the surface of the most highly stressed elements in the piping structure. The maximum surface strain is 1315, which is below the 25 limit specified in the Code.

l l

As discussed earlier (Figure 5) the plastic strains in the piping system occur only during the 3E and 4U thermal transient events. Subsequent 2U transient events do not produce additional plasticity even in the most highly stressed elbows. Therefore, the total accumulated surface strains in Table 1 are computed as follows. The total strains consist of plastic and creep strain accumulation during 36 transient events due to 3E and 4U thermal cycles. In subsequent 2U thermal transient events only creep strains are accumulated, since there er a no additional plastic strain accumulations.

l Therefore, the ratchetting (plastic + creep) strains computed between load cycle 1 and 2 are multiplied by 36 (3E + 4U events) and added to the total inelastic strain at the end of cycle 2.

The creep strains accumulated during subsequent 791 2U thermal events are based upon the highest " uniform" effective stress of 16.0 kai (110 3 MPa) computed for the piping system.

These upper bound creep strains are then added to the total inelastic strains at the end of 36 load cycles, to conservatively obtain the total inelastic strain accumulated at various locations in the piping systen. Table 1 summarizes the evaluation of the inelastic results, which comply with the ASME Code Case N-47 criteria. Buckling criterion of the Code was evaluated separately (10] and will not be discussed further.

COMPARISON WITH PRELIMINARY SCREENING RULE PROPOSED BY SEVERUD [2]

Severud [2] presented screening rules based upon approximate calculations, engineering judgement, and detailed inelastic analyses of the Fast Flux Test Facility (FFTF) pipelines. The shaded line in Figure 6 is the stress intensity 3, a preliminary design limit. This stress intensity is the sua of thermal expansion stress,,oTE, and linear radial gradient stress, ed*

The square points on Figure 6 show elastic 3 values for the FFTF pipelines of different configurations, which were analyzed by detailed inelastic analysis. The circled point on the saae figure is the elastic S value for the piping system analyzed in this paper. Since all these piping systems satisfied the inelastic ASME Code criteria, a dotted line in Figure 6 can be used as a design limit. Accordingly, many other similar piping systems

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N with less severe thermal transients, with S less than the dotted line in Figure 6, ora also be qualified to satisfy the ASME Code criteria.

Interestingly, for these pipelines the very conservative elastic lial.te (such s

as Sq in (2)) are exceeded by a substantial margin. Consequently, in s..

initial piping layout it is economical to set negative elastic desigr margina as illustrated in (2 and 33, and svaluate structural integrity by detailed J

inelastic analysis of only one ce two most highly loaded piping systems.

x-It should be noted that the use of this screening procedure implicity includes a nisaber of persaaters ahoracterizing satorial, geometry and loading. Consequently, the desiggehould proceed by grouping the piping systems according to those persaators. Detailed inelastic analyses need be' performed only fcr representative n. ambers of these groups to verify the applicability of this approach.

N'

' TABLE 1 t

SIM4ARY R D UL"S OF CRITERIA CHECK Location Allowable Total Strain Strain Dist. in Deg.

Creep + Fatigue 'N Dhange AccuaG ation Limit From Extrados

-Damage Summation D

(%)

(5) _

Inside Surface (Parent Metal)

ELB-1, EM -5 0.091 + 0.001 s 0.092 0 9987 0 99 2.0 117' ELB-1 EW-8 0.217 + 0.003 = 0.217 1.0 1 31 2.0 195*

ELB-2 EM -56 0.202 + 0.000 = 0.202 1.0 1.28 2.0 177' ELB-6, EW-213 0.214 + 0.000 = 0.214 1.0 1.29 2.0 Outside Surface (Parent Metal) l ELS-1 EM-4 0.115 + 0.000 = 0.115 1.0' O.55 2.0 87*

ELB-1, EM-8 0 347 + 0.000 s 0 347 1.0 0 50(*)

2.0 195*

ELB-2, E W -56 0 396 + 0.000 = 0 396 1.0 0 50(a) g,o 175*

ELB-2, EW-213 0.414 + 0.000 s 0.414 1.0 0 50(*)

2.0 177*

i NOTE: (a) Upper bound creep strain accumulation l

earlier paper (10) is used to evaluate the welded end cross-section of the most highly loaded elbows.

The analytical predictions are also compared with the simplified screening rule proposed in [2]. The use of this screening procedure implicitly includes a number of parameters characterizing material, geometry, and loading. Consequently, the piping system design abould proceed by grouping the piping systems according to these parameters. Detailed inelastic analyses need be performed only for representative members of these groups to verify the applicability of this approach.

ACKNOWLEDGEMENTS I

This paper is based upon work performed for the U.S. Department of Energy under contract E4-76-C-15-2395 as a part of the CRBRP Project. The author expresses his appreciation to Dr. R. H. Hallett for his valuable suggestions and comments during the course of this investigation.

REFERENCES 1.

Piping Design Guide for LMFBR Sodium Piping, SAN-781-1, C. F. Braun and Co., February 1971.

2.

L. K. Severud, " Experience with Simplified Inelastic Analysis of Piping Designed for Elevated Tamperature Services," ASME Paper No. 80-C2/NE-15.

American Society of Mechanical Engineers, New York, NY.

3 L. P. Pollono and R. M. Mello, " Design Considerations for CRBRP Heat Transport System Piping Operating at Elevated Temperature," ASME Paper No.

79-NE-5, American Society of Mechanical Engineers, New York, NY.

4.

a) ASME Boiler and Pressure Vessel Code, "Section III, Division 1, Rules for Construction of Nuclear Power Plant Components," American Society of Mechanical Engineers, New York, NY,1977 b) ASME Boiler and Pressure Vessel Code Case N-47 (1592), " Class 1 Components in Elevated Temperature Service,Section III, Division 1," American

. Society of Mechanical Engineers, New York, NY,1977.

5 MARC-CDC, Nonlinear Finite Element Analysis Programs, Vols. I-V, MARC Analysis Corp. and Control Data Corp., Minneapolis, Minn.,1974.

6.

C. E. Pugh and D. N. Robinson, "Some Trends in Constitutive Equation Model Development for High Temperature Behavior of Fast-Reactor Structural Alloys," Nucl. Eng. and Des. 00, pp. 269-276 (1978).

7.

P. T. Falk, and M. Kusanchieb, " Inelastic Analysis of the Upper Internals Structure for the Clinch River Breeder Reactor Plant," ASME Paper 79-PVP-25.

American Society of Mechanical Engineers, New York,1979 8.

4. M. Chern and D. H. Pai, " Inelastic Behavior of Finite Circular Cylindrical Shells," Trans. ASME, J. Pressure Vessel Tech _, 99, pp. 31-38 (1977).

9 A. K. Dhalla, " Plastic Collapse of a Piping Elbow: Effects of Finite Element Convergence and Residual Stresses," Fourth International Conference on Pressure Vessel Technology, Vol. II: Design, Analysis, Components, Fabrication and Inspection, pp. 243-249, the Institute of Mechanical Engineers, London, 1980.

10.

A. K. Dhalla, " Simplified Inelastic Analysis Procedure to Evaluate a Butt-Welded Elbow End," in " Stress Indices and Stress Investigation Factors of Pressure Vessel and Piping Components," Eds. R. W. Schneider and E. C.

Rodabaugh, PVP-50, pp. 109-127, American Society of Mechanical Engineers, New York, 1981.

11.

D. F. Rotoloni and A. K. Dhalla, "A Procedure to Incorporate Effect of Siesmic Events in a Quasi-Static Piping System Inelastic Analysis," (to be presented at the ASME/PVP Conference in Orlando, FL, June 1982).

12.

A. K. Dhalla and R. V. Roche,-" Inelastic Analysis and Satisfaction of Design Criteria of a High Temperature Component," in " Advances in Design for Elevated Temperature Environment," Eds.

S.' Y. Zamrik and R. I. Jetter, ASME Publication, pp. 83-92, American Society of Mechanical Engineers, New York, 1975 l

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Figure 6. Comperison of inelastic Analyses Results with Preliminary Design Limit (21 l

CLOSURE In an IMFBR piping system, complex stress redistributions occur in creep range during elevated temperature operation. To evaluate inelastic response of the piping system subjected to prescribed thersal and sechanical loading it is necessary to study through-the-thickness stress redistributions as well as redistributions around the piping elbows. In addition, the load bistory effects at the most highly loaded locations should be studied to establish structural adequacy of an elevated temperature piping system. A procedure is described in this paper to compute inelastic strain accumulation and For creep-fatigue damage to comply with the ASME Code Case N 47 criteria.

thin piping elbows it is also necessary to evaluate fabrication effects due to

. girth butt welds at the elbow ends. A semi-empirical procedure outlined in an