ML13330A597
| ML13330A597 | |
| Person / Time | |
|---|---|
| Site: | San Onofre  |
| Issue date: | 04/15/1985 |
| From: | Southern California Edison Co |
| To: | |
| Shared Package | |
| ML13311A380 | List: |
| References | |
| PROC-850415-01, NUDOCS 8504180266 | |
| Download: ML13330A597 (9) | |
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SAN ONOFRE NUCLEAR GENERATING STATION UNIT 1 SECANT STIFFNESS METHOD AS APPLIED TO THE EVALUATION OF PIPE-STRUCTURE INTERACTION Prepared by SOUTHERN CALIFORNIA EDISON COMPANY April 15, 1985 8504180266 850415 PDR ADOCK 05000206 P
TABLE OF CONTENTS Section Pa
1.0 INTRODUCTION
1 2.0 THEORY 1
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 theuse 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 (d y), the analysis stiffness is defined as, K
a = R a/da = R /d The elastic strain energy (Ee) theoretically expended in loading the support to beyond yield is determined by integrating the linear function, so that, Ee = R a(d a) /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,
E = R (d )/2 + R (d -d ) = R (d -d /2) 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 =-E p
e 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 p= 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 11 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.
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-1.1
- 2.
Bechtel Power Corporation Project Design Criteria, Subjob 430-471, Revision 2, "Impact of Pipe Support Loads on Structures."
R a Theoretical Elastic Strain Energy Plastic Strain Energy y
Ka d
d a d
y ap Figure 1 kII XF 2
dy d
d2 d3 Figure 2 Secant Stiffness Method Flowchart Perform Piping Analysis with Generic Support Stiffnesses Generate Support Loads Perform Structural Evaluation of Support/Building Components Determine Ductility Ratio
,for Inelastic Beams Inelastic Beams Determine Secant WElastic Stiffnesses Beams Compare Analysis Stiffnesses to Revised Stiffness and Check Loads for Convergence NOT 1/REPRESENTATIVE REPRESENTATIVE Reiterate Piping Analysis With New Stiffnesses Generate New Loads Pipe-Structure Interaction is Adequately Represented Figure 3 IIIO OF__ DO UM N CO T.
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