ML13324A659

Summary Rept on Evaluation of Interaction of Piping & Structures,Return to Svc

ML13324A659
Person / Time
Site:	San Onofre
Issue date:	06/30/1985
From:	Southern California Edison Co
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ML13324A657	List: ML13324A656 ML13324A659
References
TASK-03-06, TASK-3-6, TASK-RR NUDOCS 8507010258
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Text

SUMMARY

REPORT ON THE EVALUATION OF INTERACTION OF PIPING AND STRUCTURES SAN ONOFRE UNIT 1 RETURN-TO-SERVICE JUNE 1985 8507010258 850626 PDR ADOCK 05000206 p

PDR

TABLE OF CONTENTS

1. PURPOSE

2. BACKGROUND

3. SCOPE

4. PROCEDURE 4.1 General 4.2 Confirmatory Interaction Evaluation 4.3 Conservatisms in Evaluation Methodology

5. EVALUATIONS AND

SUMMARY

OF RESULTS

6.

CONCLUSIONS APPENDICES I. Secant Stiffness Method as applied to the evaluation of pipe-structure interaction 1

1. PURPOSE On February 11, 1985, the NRC staff requested that a summary report be prepared on the confirmatory evaluation of piping and structures submitted on October 25, 1984. This report is in response to that request and is derived from the NRC submittal dated October 25, 1984.

2. BACKGROUND In December 1983 SCE proposed a plan for returning San Onofre Unit No. 1 (SONGS 1) to operation. The basis of the plan was to assure that structures, systems and components necessary to achieve and maintain a hot standby condition have sufficient design margins to resist the 0.67g modified Housner earthquake.

At the same time, SCE proposed the Return-To-Service (RTS) evaluation criteria to be applied to piping systems and to supporting elements of structures in order to demonstrate the plant hot standby capability.

The staff requested that the following confirmatory evaluation be performed prior to plant restart:

1. Screen all of the systems for which the inelastic criteria have been applied and identify the relative location of structural elements for which inelastic behavior has been calculated.

2. If adjacent supporting elements are involved, perform one or two representative simple coupled system analyses to examine the global system effects on the local behavior of piping and structural supporting system.

3. Perform an engineering evaluation which judges the integrity of the piping, support elements and connections on a system-wide basis, identify any additional analyses or corrective actions that result from that evaluation.

In response to that request, a report was submitted to the NRC by letter dated October 25, 1984. This report provides a summary of the information included in our October 25, 1984 submittal.

3.

SCOPE The scope of the return to service seismic evaluation of large bore (greater than 2") piping systems required for hot standby involved 29 lines. The total number of pipe supports required to maintain functionality of these piping systems was about 500. Table 1 gives the line numbers and the number of pipe supports required per line to maintain functionality of the piping systems.

The total number of steel beams that are directly or indirectly affected by pipe support reaction loads from the above 29 piping systems was about 180. Of these 180 beams, about 150 of them remain elastic. The remaining 30 beams are shown by analysis to act inelastically.

Of the 500 pipe supports about 30 are either directly attached to structural beams that are inelastic or are supported by elastic beams that connect to inelastic beams.

4. PROCEDURE The procedure for the basic evaluations of piping, pipe supports and the structural elements and the confirmatory evaluations on a system basis is shown in Table 2.

4.1 General The development of basic analysis and design information in SONGS 1 for plant restart utilized current industry practices, that is

a. Elastic seismic analysis of structures were performed to develop instructure response spectra. Explicit representation of piping was not included in the mathematical models. The tributary masses of systems and components were lumped to structural masses. This is a conservative procedure as described in Section 4.3.

b. Seismic thermal and gravity analysis of piping and supports were performed to determine the subsystem responses. These analyses used the instructure response spectra from 'a' above as seismic input.

c. The piping, pipe supports, structures and structural elements were then evaluated combining the seismic pipe reaction loads thus obtained with the other design basis loads to assure their design margins.

4.2 Confirmatory Interaction Evaluation As described in Section 4.1 the procedures followed in SONGS 1 for evaluation of structural elements and piping systems, were in accordance with the current industry practice, and did not consider explicit interaction models. In order to assess the effect of structural member inelasticity (ductilities greater than one and less than ten) on the functionality of piping and supports on a system basis the following procedure was followed:

Step 1 A pipe isometric was developed for each of the 29 Return-To-Service Safe Shutdown pipe systems. Each isometric shows the pipe routing, the active pipe supports, and a description of the structural members to which the pipe supports are attached. For each structural member, a listing is added to the isometric indicating the exact beam number and ductility value for that beam. The information also indicates if the beam remains elastic. For complex structural support arrangements, whereby a pipe support relies upon several structural beams, each beam's ductility value is given. An example of one such isometric is given in Figure 1. This isometric shows supports on elastic beams at node points 25, 35, 130, 165, 200 and a support on an inelastic beam at node point 162.

Step 2 For the case where no inelastic structural members occur for a pipe system the pipe system was considered to be qualified with no further confirmatory evaluations.

When a structural beam was inelastic, the pipe system was investigated in the vicinity of this inelastic structural member.

This was done for every case of an inelastic structural member.

The criteria utilized in performing the evaluation of the pipe system was as follows:

1. On a chart, sketch all upstream and downstream piping and pipe supports for two supports on either side of the inelastic structural member.

2. Tabulate the peak pipe stress (strain) for each critical region within the two span criteria. Tabulate the margin versus allowable pipe stress (strain).

3. Tabulate the actual pipe support reaction loads for each pipe support, for two spans from the area of inelastic structural support. Tabulate the pipe support margin versus allowable support load.

4. Tabulate additional components which may be affected, including nozzles, penetrations, and anchors.

As an example of the results of Step 2, the sketch and checklist which was used for MS-362 is provided in Figure 1 and Table 3, respectively. The checklist documents the minimum pipe strain and pipe support margins.

Step 3 In performing the confirmatory evaluations one or two of the following methods were used for each evaluation:

Method A:

For the case where a single structural support was inelastic, and no other structural support was inelastic (within the two-span criteria described in Step 2) a check was made to assure that sufficient capacity remains in the pipe stress margin, and pipe support margin, to absorb any extra displacements at the inelastic structural support.

In cases where the margins were high and the structural member ductility was low the pipe system was considered to be qualified with no further computations.

Method B:

For the case where multiple structural supports are inelastic on a pipe system, and these supports are within 2 spans of each other, the following was done:

first the margins in affected piping, pipe supports, structure supports and components (nozzles, etc.) were checked.

Next, support stiffnesses utilized in qualifying piping, supports, and structures were reviewed. If this stiffness approximated the reduced stiffness of the supports due to beam inelasticities, then in effect the original pipe analysis utilized support stiffnesses representing the inelasticities in the beams. This also meant that the pipe stresses and pipe support loads computed in the original analysis included the structural member inelasticities and were representative for use in subsequent evaluations and designs performed.

In this case, the pipe system was considered to be qualified with no further computations.

Method C: If the stiffness used did not approximate the reduced stiffness, an iterative procedure was followed where at each cycle the inelastic support stiffnesses were modified according to the beam ductilities obtained from the results of the previous cycle pipe reaction loads. This procedure was called the secant stiffness method and an explanation of how it is applied is given in Appendix I of this report.

In Appendix B of the October 25, 1984 submittal, the results of the secant stiffness iterative analysis for the FW-04 pipe system were presented.

Method D:

For the case where multiple structural supports were inelastic on a pipe system, and the pipe system has significant margins for pipe stress and pipe supports, then the pipe system is considered to be qualified based on similarity to the results shown in Appendix B of the October 25, 1984 submittal.

Step 4 The conclusions and corrective actions, if deemed necessary, were then documented on a system basis.

4.3 Conservatisms in Evaluation Methodology As was discussed in Section 4.1, the evaluation of piping and structures in SONGS 1 was based on uncoupled analyses. Coupling of the systems with regard to mass and stiffness would tend to reduce the seismic responses. A specific case in point for SONGS 1 is the piping/structure interaction model developed for the evaluation of the north turbine building mezzanine.

The mezzanine steel framing is at elevation 30'-0" in the north extension of the turbine building and supports portions of the line FW-04 which is required for plant hot standby. Additionally, portions of the mezzanine steel framing support a number of electrical raceways required for plant return-to service. In the structural evaluation of the mezzanine, pipe reaction loads of the safety injection line, SI-51, although not required for plant hot standby, were also included since they share common supports with FW-04.

The purpose of the evaluation performed was twofold:

a) Demonstrate that an uncoupled analysis of the piping/structure systems is more conservative than interacting systems and that a lumped mass representation of a piping system is more conservative than mathematical models where explicit models of piping and structural systems are considered.

b) Perform the overall evaluation of the mezzanine including all the structural modifications implemented to establish its adequacy to support the feedwater line such that the functionality of FW-04 is maintained during 0.67g modified Housner earthquake. Computer analyses of the steel framing, with explicit representation of SI-51 and lumped mass representation of FW-04, were used in the evaluation.

The details of the analysis and the results were given in Appendix A of the submittal dated October 25, 1984. Comparison of member forces, displacements and ductility demands demonstrated that uncoupled piping/structure systems are more conservative than interacting systems. Further, the comparisons showed that a lumped mass representations of piping systems are more conservative than mathematical models wherein explicit modeling of piping and structural systems is considered.

The relative conservatism of the evaluation methodology described in Sections 4.1 and 4.2 herein (which is based on uncoupled analyses of piping/structure systems) has therefore been demonstrated.

5. EVALUATIONS AND

SUMMARY

OF RESULTS Review of the isometric information identified that of the 29 lines, 22 have no supports interfacing with inelastic beams. Therefore, for these 22 lines no further confirmatory interaction analysis was necessary. The remaining 7 lines were classified into 3 categories:

a. Lines with one support on inelastic beam: MS-362, RC-102

b. Lines with two supports on inelastic beam:

AC-108, MS-01, RC-103.

c. Lines with more than two supports on inelastic beam: FW-04, MS-02.

A summary description of the review of the isometrics is given in Table

4. The specific system evaluations performed for the 7 lines are described below:

MS-362:

Evaluation: - This evaluation was by Method A. This system has one support attached to an inelastic beam with a ductility ratio of 1.16.

The review of pipe stresses/strains and pipe support margins for adjacent piping spans and pipe supports indicated a minimum margin of 15% for the piping and a minimum load margin of 22% for the pipe supports.

Conclusion - The level of ductility of the subject inelastic beam is miTnimal.

Based on sufficient safety margins observed in the piping and pipe supports, it is concluded that slight inelasticity of the subject beam will not impair the integrity of this system.

RC-102:

Evaluation - This evaluation was by Method B. This system has one support attached to an inelastic beam with a ductility ratio of 2.19. In this case a revised stiffness was calculated to account for the beam inelasticity. The support's resultant revised stiffness including the stiffnesses of the inelastic beam was 77 k/in. The stiffness value used in the original piping analysis at this support location was 25 k/in.

Conclusion - The stiffness at the location of the inelastic beam is greater than the stiffness value used in the original piping analysis. Therefore, the piping integrity originally demonstrated for this system is not affected by inelasticity of the subject beam.

AC-108:

Evaluation - This evaluation was by Method B. This system has two supports attached to inelastic beams. One of the supports is a spring hanger which is not considered as an active support during a seismic event. Hence, the beam inelasticity is not of any consequence. As for the other support (an XZ guide), the resultant revised stiffnesses including the stiffness of the inelastic beam are 36 k/in and 286 k/in in the X (NS) and Z (EW) directions, respectively. The stiffness values used in the original piping analysis at this location were 36 k/in in both X and Z directions.

Conclusion - The revised stiffnesses at the location of inelastic beam are greater than or equal to the values used in the original piping analysis. Therefore, the piping integrity originally demonstrated for this system is not affected by the inelasticity of the subject beam.

RC-103:

Evaluation - This evaluation was by Method B. This system has two supports on an inelastic beam. One of the supports is a spring hanger which is not considered as an active support during a seismic event. Hence, the beam inelasticity is not of any consequence. For the other support (an XY guide) the resultant revised stiffnesses including the stiffness of the inelastic beam are 270 k/in in the X (NS) and 223 k/in in the Y (vertical) directions. These values are lower than the stiffnesses used in the original piping analysis. The corresponding stiffness of the piping at the location of this support is only 20 k/in in both directions.

Conclusion - The revised support stiffnesses at the location of the inelastic beam (270 and 223 k/in) are greater than the equivalent stiffnesses of the piping span (20 k/in in both directions) by an order of magnitude. Since the piping span is still much more flexible than the revised support stiffnesses, the support will still act as a rigid restraint with respect to the piping. Therefore, the original assumption and the response computed are still valid. It is concluded that the inelasticity of the subject beam will not impair the integrity of this system.

FW-04:

Evaluation - This evaluation was by Method C. The effects of multiple inelastic beams on this system were explicitly determined using an iterative stiffness analysis procedure. The results of these evaluations are given in Appendix B of the October 25, 1984 submittal. These evaluations considered variations in support stiffnesses for a range of values corresponding to all beams remaining elastic to all beams yielding with a ductility of 3. For all cases, piping integrity was demonstrated using the Return-To-Service (RTS) integrity criteria. The revised stiffnesses obtained from the reanalysis of the inelastic beams considering the interaction of piping and structures are bounded by the last two iterations in the iterative process. This is given in Appendix A of the October 25, 1984 submittal.

Conclusion - Since the functionality of this system was demonstraed for all iteration cases and since the final stiffness values are bounded by two of these iterations, it is concluded that the pipe integrity will be maintained.

MS-01:

Evaluation - This evaluation was by Methods A and B. This system has two supports attached to inelastic beams. The resultant revised stiffnesses including the stiffnesses of the inelastic beams compare closely with the stiffness values used in the original piping analysis (647 k/in versus 550 k/in and 647 k/in versus 499 k/in in the axial direction).

Conclusion - Since the revised stiffnesses compare closely with the values used in the original piping analysis and also because there are sufficient safety margins in piping stresses and pipe supports of the adjacent spans, it is concluded that the inelasticity of the subject beams will not impair the integrity of this system.

MS-02:

Evaluation - This evaluation was by Methods A and D. This system has multiple supports attached to inelastic beams. The review of pipe stresses and pipe support safety margins for all adjacent spans showed that pipe stress ratios were lower than 0.6 at all spans, and that the highest stressed pipe support had a maximum stress ratio of 0.78. Therefore, this system exhibits sufficient safety margins against the 0.67g modified Housner event.

Conclusion - Upon reviewing the behavior of the FW-04 piping system with multiple supports on inelastic beams, it is observed that with a reduction in support stiffness, generally pipe stresses and reaction loads of adjacent supports increase while reaction loads of those supports with reduced stiffnesses decrease. This conclusion is substantiated by the results of the iterations on line FW-04 using support stiffnesses. Since sufficient safety margins are observed for this MS-02 system, both in terms of pipe stresses/strains and pipe support load to capacity ratios, it is concluded that inelasticities of the subject beams will not impair the integrity of this system.

6. CONCLUSIONS A confirmatory evaluation has been performed to assess the interaction effects of large bore piping systems required for hot standby and the inelastic structural beams. For this purpose:

1. All of the systems for which the inelastic criteria have been applied have been screened and the relative location of structural elements have been identified for which inelastic behavior has been calculated.

2. If adjacent supporting elements are involved, representative coupled system analyses have been performed to examine the global system effects on the local behavior of the piping and structural supporting system.

3. Engineering evaluations have been performed which judge the integrity of the piping, support elements and connections on a system-wide basis.

A total of seven pipe systems have inelastic beams. For these seven systems it is concluded that the inelasticities in structural elements, which could result during a 0.67g modified Housner earthquake, do not impair the piping and support integrity when evaluated on a system basis.

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TABLE 1:

RETURN-TO-SERVICE PIPING SYSTEMS Pipe Supports Required Line No.

To Maintain Functionality AC-108 5

AF-02 (Suction) 28 AF-02 (Discharge) 93 AF-05 1

CV-10 22 CV-11 17 CV-12/MW-01 66 CV-13 20 FW-04 33 FW-07 32 FW-123 8

FW-124 15 FW-125 8

MS-01 26 MS-02 15 MS-03 21 MS-122 37 MS-362 6

MS-363 16 MW-02 7

RC-102/CV-100-CV-101 52 RC-103 2

RC-107 9

SI-150 8

SI-155 6

SI-158 6

TABL 2:

CONFIRMATURY EVALUATION FLOWCHA e

FINiGI UIPOS/STRCTURAL ELEMENTS EVALUATION PIPING AND PIPE SUPPORTS PREPARE INPUT DEVELOP INSTRUCTURE RESPONSE LAYOUT SPECTRA BY LINEAR ANALYSES PIPE SUPPORT CONFIGURATION WITiOUT EXP.Ic.IT PIPING SUPPoRT STIFFNESS STRUCTURE INTiERACTIOIN PERFORM ELASTIC STRESS DEVELOP SE] SMIC ANCHOR ANALYSES MuVEMENTS BY IJNEAR ANALYSES OF STRUCIURES EVALUATE PIPE STRESS, STRUCTURAL ELEMENTS SUPPORTING PIPING SUPPORTS, AFFECTED EQUIPMENT PREPARE INPUT STRUCTURAL CONFIGURATI(N STATIC ILOADIS SEI SMIC INEN11A l.OADS PIPE REACTION LOADS LEA16 NO PIPE SUPPORTS k I 114:61 FINAL PIPE LAYOUT SU IORT:

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TABLE 4:

SUMMARY

OF PIPING/STRUCTURE INTERFACES Line No.

Remarks

1. AC-108 Two pipe supports supported jointly by the same two structural beams, one elastic and the other one inelastic 2a. AF-02 No supports on inelastic beams (suction) 2b. AF-02 No supports on inelastic beams (discharge)

3. AF-05 No supports on inelastic beams

4. CV-10 No supports on inelastic beams

5. CV-11 No supports on inelastic beams

6. CV-12 No supports on inelastic beams

7. CV-13 No supports on inelastic beams

8. CV-161 No supports on inelastic beams

9. CV-162 No supports on inelastic beams

10. FW-04 More than one pipe support attached directly to an inelastic structural beam or to an elastic structural beam which in turn is supported by an inelastic structural beam.

TABLE 4:

Continued Line No.

Remarks

11. FW-07 No supports on inelastic beams

12. FW-123 No supports on inelastic beams

13. FW-124 No supports on inelastic beams

14. FW-125 No supports on inelastic beams

15. MS-01 Two pipe support attached directly to an inelastic structural beam.

16. MS-02 More than one pipe support attached directly to an inelastic structural beam or to an elastic structural beam which in turn is supported by an inelastic structural beam.

17. MS-03 No supports on inelastic beams

18. MS-122 No supports on inelastic beams

19. MS-362 One pipe support attached to an elastic structural beam which on one side supported by an inelastic structural beam.

20. MS-363 No supports on inelastic beams TABLE 4:

Continued Line No.

Remarks

21. MS-01 No supports on inelastic beams

22. MS-02 No supports on inelastic beams

23. RC-102 One support directly attached to an inelastic structural beam.

24. RC-103 Two pipe supports attached to elastic structural beams which on one side are supported by an inelastic structural beam.

25. RC-104 No supports on inelastic beams

26. RC-107 No supports on inelastic beams

27. SI-150 No supports on inelastic beams

28. SI-155 No supports on inelastic beams

29. SI-158 No supports on inelastic beams APPENDIX I Secant Stiffness Method as Applied to the Evaluation of Pipe-Structure Interaction SAN ONOFRE NUCLEAR GENERATING STATION UNIT I SECANT STIFFNESS METHOD AS APPLIED TO THE EVALUATION OF PIPE-STRUCTURE INTERACTION Prepared by SOUTHERN CALIFORNIA EDISON COMPANY April 15, 1985

TABLE OF CONTENTS Section Page

1.0 INTRODUCTION

1 2.0 THEORYI 3.0 PROCEDURE 2

4.0 CONCLUSION

S 5

REFERENCES

SECANT STIFFNESS METHODS AS APPLIED TO THE EVALUATION OF PIPE-STRUCTURE INTERACTION

1.0 INTRODUCTION

As a part of the SONGS-1 Return to Service (RTS) effort, a nonlinear approach was used to evaluate secondary steel members.

Ductility limits were used to measure the capability of inelastic structural elements to maintain their design function. Where this inelastic behavior occurs, support deflections may occur which are greater than those which would be predicted by the initial stiffness values used in the linear analysis.

Since the overall effect of these nonlinearities does not warrant the use of a nonlinear analysis technique, the secant stiffness method is used for the evaluation. This technique is used to develop a reduced stiffness at the yielding support structure which conservatively approximates the maximum deflection which will occur at this support.

As described below, the modified stiffness is based on energy equivalence between the elasto-plastic model and its linear representation.

An explicit evaluation was performed using this procedure for Problem FW-04 and the results were transmitted to the NRC (Reference 1).

This report describes the theory and application of the secant stiffness method as may be applied to the evaluation of pipe-structure interaction for the SONGS-1 Long Term Service (LTS) program.

2.0 THEORY A secant stiffness evaluation is an energy-based technique used to approximate the nonlinear (elasto-plastic) behavior with a quasi-linear elastic model.

As applied to piping analysis, it provides for the use of a linear support stiffness which allows displacements equal to those experienced by a yielding support structure.

The development of a secant stiffness is shown graphically in Figure 1.

The response of a support with an applied load (R ) and a resultant displacement (d ) is defined by the linear support stiffness (Ka)*

Assuming that the support would actually yield at a load (Ry) and a displacement (dy), the analysis stiffness is defined as, K a = Ra/da = Ry/dy The elastic strain energy (Ee) theoretically expended in loading the support to beyond yield is determined by integrating the linear function, so that, Ee = Ra(da) /2 A more accurate representation of the yielding structure would allow it to deflect beyond yield without an increase in applied loads, as defined by the nonlinear function in Figure 1. The elasto-plastic strain energy expended thorough yielding is determined by integrating the nonlinear function through the plastic deformation (dp), so that, I

E = R (d )/2 + R (d -d ) =R (d -d 12) p y y y p y y p y The plastic deformation is limited by holding constant the strain energy expended. Thus, for analysis purposes, E = Ee An equivalent linear stiffness (i.e., the secant stiffness, Ks) which would allow these yield displacements in a linear analysis is described by the function, Ks = R /d = K a/

, where A= d /d (ductility)

(Note that dp is unknown to the analyst.)

As defined for the SONGS-l secondary steel member evaluation, the definition of ducility A is provided in Reference 2. This ductility is used to estimate the revised (or secant) stiffness for inelastic beams.

The piping model is then reanalyzed with the secant stiffness defined for the yielded support structures. The yielded beams may now experience loads which result in a ductility less than one (in which case the revised stiffness is valid) or may yield again (in which case a new secant stiffness has to be defined). This phenomenon is shown schematically in Figure 2.

The piping analysis will accurately distribute loads to adjacent supports as each iteration with revised secant stiffnesses is performed. Analysis support loads will converge as an accurate pipe-structure interaction model is approached.

3.0 PROCEDURE The procedure is outlined in the flow chart shown in Figure 3. An initial analysis is executed with generic support stiffnesses. The support loads developed with this analysis are then applied (along with other postulated loads) to the pipe supports and secondary steel members supporting the line.

Secondary steel members are evaluated and the members which exhibit inelastic behavior are identified. Secant stiffnesses are developed for members loaded beyond yield. These stiffnesses are then compared to those used in the initial piping analysis. If all stiffnesses are found to be representative of those determined by the structural evaluation, the pipe-structure interaction is considered to be accurately represented.

However, if the analysis stiffnesses are not representative of those determined by support evaluation, another piping analysis is performed using the revised stiffnesses.

I I

The support loads resulting from the second piping analysis are used to reevaluate the supporting structures, and another set of support stiff nesses is determined.

These stiffnesses and support loads are compared to those from the preceding piping analysis. This procedure is iterated until a set of analysis stiffnesses is found to be representative of those determined by the preceding structural evaluation and the support loads converge.

At this point, pipe-structure interaction is accurately represented.

4.0 CONCLUSION

S The effects of pipe-structure interaction will be included as an integral part of the LTS evaluation of piping, pipe supports, and structural steel at SONGS-1.

Where yielding of structural support steel is anticipated, particular attention will be given to the impact of resultant displacements on the functionality of all attached piping and supports.

The secant stiffness method of approximating the elasto-plastic behavior of structural steel may be employed to model the inelastic behavior of supporting structures. An evaluation performed in accordance with the procedures defined herein will be used on a case-by-case basis to address inelastic support structures on a piping system.

REFERENCES 1.

Letter from M. Medford (SCE) to W. Paulson (NRC) dated August 29, 1984, "Docket No. 50-206, SEP Topic 111-6, Seismic Design Considerations, SONGS-1."

2. Bechtel Power Corporation Project Design Criteria, Subjob 430-471, Revision 2, "Impact of Pipe Support Loads on Structures."

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[I for Inelastic Beams

+ Inelastic Beams Determine Secant

,Elastic Stiffnesses Beams Compare Analysis Stiffnesses to Revised Stiffness and Check Loads for Convergence NOT REREPRESENTATIVE REPRESENTATIVE Reiterate Piping Analysis With New Stiffnesses Generate New Loads Pipe-Structure Interaction is Adequately Represented Figure 3