ML13311A395
| ML13311A395 | |
| Person / Time | |
|---|---|
| Site: | San Onofre, Quad Cities, 05000000 |
| Issue date: | 12/31/1980 |
| From: | EDS NUCLEAR, INC. |
| To: | |
| Shared Package | |
| ML13311A392 | List: |
| References | |
| 01-0590-1135, 01-0590-1135-R00, 1-590-1135, 1-590-1135-R, NUDOCS 8505310261 | |
| Download: ML13311A395 (60) | |
Text
QUAD CITIES UNIT 1 FUNCTIONALITY STUDY OF PIPING SYSTEMS IN RESPONSE TO THE SSE EVENT Prepared for:
COMMONWEALTH EDISON COMPANY Prepared by:
EDS Nuclear Inc.
December 1980 EDS Report No. 01-0590-1135 Revision 0 85053261 PDRA5005206 PDR
EDS NUCLEAR INC.
REPORT APPROVAL COVER SHEET Client:
Commonwealth Edison Company Project:
79-14 Bulletin Response Job Number: 0590-013 Report
Title:
Functionality Study of Piping Systems in Response to the SSE Event Report Number:
01-0590-1135 Rev.
0 The work described in this report was performed in accordance with the EDS Nuclear Quality Assurance Program. The-signatures below verify the accuracy of this Report and its compliance with applicable quality assurance requirements.
_* Prepared By:
Date:
3 1D Reviewed By:
Date:
Approved By:
gl 6
Date:
2.
REVISION RECORD Rev.
Approval No.
Prepared Reviewed Approval Date Revision
_________ ~ ~
~
~
~
~
~
~
~
~
~
~
~
~ ----
01-0590-1135 Revision 0 Page i TABLE OF CONTENTS Page Table of Contents List of Tables ii List of Figures
1.0 INTRODUCTION
1 2.0 SELECTION OF PIPING SYSTEM FOR DETAILED EVALUATION 3
3.0 ELASTIC ANALYSIS 5
3.1 SUPERPIPE Math Model 6
3.2 Stress Results 7
3.3 Elastic Analysis Discussion 8
4.0 PIPE ELBOW CAPACITY 11 4.1 Experimental Data 11 4.2 ANSYS Analytical Correlation 12 5.0 NONLINEAR ANALYSIS 14 5.1 Time History Motions 14 5.2 ANSYS Math Model 15 5.3 PWHIP Math Model 16 5.4-Response Results 17 6.0 DISCUSSION 19
7.0 CONCLUSION
21
8.0 REFERENCES
22 APPENDIX A:
Computer Program Descriptions A-1
01-0590-1135 Revision 0 Page ii LIST OF TABLES Table Title Page 2.1 Identified Piping Systems 24 3.1 RHR Flexible System Frequencies 25 3.2 RHR Stiff System Frequencies 26 3.3a Preliminary Calculation of Stresses in 27 RHR Seismic Piping -
Run 1 3.3b Preliminary Calculation of Stresses in 28 RHR Seismic Piping -
Run 2 3.3c Preliminary Calculations of Stresses in 29 RHR Seismic Piping -
Run 4 3.3d Stresses in RHR Seismic Piping - Flexible System 30 3.3e Stresses in RHR Seismic Piping - Stiff System 31 3.4 Estimated Class Break Piping System Stresses 32 5.1 Material Stress - Strain Law 33 5.2 Detailed ANSYS and Simple PWHIP System Frequencies 34 5.3 Pipe Moments Comparison 35 6.1 Summary Stresses 36
01-0590-1135 Revision 0 Page iii LIST OF FIGURES Figure Title Page 3.1 RHR Piping System -
Flexible 37 3.2 RHR Piping System -
Stiff 38 4.1 ANSYS Correlation Study with a 6" Elbow 39 4.2 Moment Deflection Curve for a 3" Schedule 40 40 Long Radius Elbow 5.1 Required Input Spectrum for the RHR System 41 5.2 Acceleration Time History Based on the El Centro 42 Record 5.3 Displacement Time History Based on the El Centro 43 Record 5.4 Acceleration Time History Based on the Pacoima 44 Dam Record 5.5 Displacement Time History Based on the Pacoima 45 Dam Record 5.6 Response Spectra Based on El Centro Record 46 5.7 Response Spectra Based on Pacoima Dam Record 47 5.8 Comparison of Damping Levels in Response Spectra 48 5.9 Math Model for ANSYS Analysis 49 5.10 Math Model for PWHIP Analysis 50 5.11 PWHIP Nonlinear Analysis - Displacement Relative 51 to Ground 5.12 PWHIP Analysis -
End Moment 52 5.13 ANSYS Analysis - Moment in Elbow Element at Nodes 53 39-40 5.14 Moment at Anchor Node 51 54
01-0590-1135 Revision 0 Page 1
1.0 INTRODUCTION
In response to NRC bulletin 79-14, Commonwealth Edison Company (CECo) is required to show the operability under seismic excitation of seismic class piping systems in Quad Cities Units 1 and 2, and Dresden Units 2 and 3 Nuclear Power Stations, for those systems shown to exceed FSAR limitations. EDS Nuclear (EDS), at the request of CECo, is performing analysis and design of piping systems to meet the requirements of this bulletin.
In the course of this work, EDS has found that several existing piping systems in these Units exceed FSAR stress limits. The solution to these overstress situations is to provide new supports on the affected systems and to qualify the upgraded piping system to the code of record.
The intent of this report is to study the stress levels, due to SSE excitation, of several piping systems before the addition of new required supports. Various analysis techniques, including both elastic and inelastic methods, are used to show that piping systems previously shown to be significantly overstressed can in fact be shown to remain functional during and after the SSE event.
A total of seven piping systems in the Quad 1 plant have been shown, to date, to exceed the operability stress limit due to the OBE event. Of these systems, six describe "class-break" problems. The last is the Recirculation System (RRCI).
The studies in this report address a "class-break" piping system, the RHR system, and include both elastic and nonlinear analyses. The results are extended to the RRCI and the other class-break piping systems.
Elastic analyses of the RHR system were performed using the response spectra technique.
Results from these analyses indicate that original high stress levels of 102,000 psi (based upon hand calculations) are very conservative. Detailed elastic analysis results gives SSE level stresses of 40,000 psi, which is only moderately above the ASME code allowable stress level of 2.4 Sh or 36,000 psi.
)
As a bounding case, a portion of the PHR system was subsequently analyzed assuming that a seismic support exists in the non seismic portion of the piping. The analysis confirms that, as expected, the presence of this support reduces the stress levels in the HR seismic piping to below code stress limits.
01-0590-1135 Revision 0 Page 2
To show pipe functionality even if elastic analysis predicts stresses in excess of code limits for SSE motions, nonlinear dynamic analyses of the RHR piping were performed. Results show that a reduction of moments in pipe elbows of 30 percent or more can be expected when explicit nonlinear analyses are performed in lieu of elastic analyses. In addition, pipe elbow moments are under ASME Section III Appendix F collapse levels, while resulting ovality results in less than 1 percent flow restriction.
Several conclusions are made in this study concerning the functionality of as-built piping systems in response to an SSE event. The following main points are noted:
Stresses in the RHR piping, as predicted by elastic response spectra analysis, are slightly over code allowables.
Nonlinear analysis techniques show a large decrease in internal pipe moments for systems shown by elastic analysis to be stressed beyond yield; associated yielding causes Less than 1 percent flow restriction at pipe elbows, the most overstressed portions of the analyzed system.
Based upon these conclusions, it is judged that the piping systems identified in this report would remain functional during an SSE event.
01-0590-1135 Revision 0 Page 3
2.0 SELECTION OF PIPING SYSTEM FOR DETAILED EVALUATION To date, EDS has performed analysis of existing as-built piping configurations in the Quad 1, 2 and Dresden 2, 3 Nuclear Power Plants in accordance with project specific instructions1.
These instructions state that a piping system meets operability requirements if the combined stress from OBE plus gravity plus pressure does not exceed one-half the ultimate strength of the piping material.
Operability criteria require that only seismic class piping need be evaluated.
The seismic class piping must remain functional during and after the SSE event in order to bring the plant to a safe shutdown condition.
In the course of the analysis work, two types of piping systems have been identified:
"closed-loop" systems and "class-break" systems. A closed loop system is comprised of seismic class piping from pipe anchor to pipe anchor. A class-break system is comprised of seismic class piping beginning at one pipe anchor, followed by an amount of non-seismic class piping; the class "break" occurs at the end of the second of two safety valves in the seismic portion of the piping.
To perform the analysis of all piping systems in-a timely manner, and to conform to code of record requirements, several assumptions were made in the original analyses. In general, closed loop systems were analyzed using finite element response spectra method with the SUPERPIPE code. Class-break systems, owing to their extreme length, were analyzed using simplified conservative hand calculations.
When compared to the CECo operability criteria, seven piping systems were identified to be overstressed. These systems are noted in Table 2.1.
Of these, the RRCI (Recirculation) system is a closed loop system, while the remaining six are class-break systems.
In the as-built configuration, the RRCI system was analyzed using the response spectra technique. Stresses were found to be slightly over operability stress criteria. The six class-break systems were analyzed by hand calculations, and all systems were shown to have stresses greatly in excess of the operability stress limit. Hence, it was decided that a more representative piping system on which to perform further analyses would be one of the class-break systems.
01-0590-1135 Revision 0
___Page 4
Of the six class-break piping systems, the RHR system was chosen for analysis for several. reasons:
Hand calculation predicted stresses of 102,000 psi, which was significantly over the operability allowable of 30,000 psi.
The RHR system has unsupported (non-seismic) piping in excess of 200 foot spans.
Complete fabrication isometrics were available for the RHR system.
One detailed model of the RHR system could include three different branches of seismic class piping.
The specific Quad 1 plant identifier for the portion of the RHR system discussed in this report is 1-1067-3".
The EDS specific identifier used for this portion of the RHR system, as used in other EDS analysis packages, is Ql-RHRS-03B.
Sections 3.0, 4.0 and 5.0 discuss the analyses performed on the RHR system. The RHR system was modeled both in a flexible configuration ("as-engineered") and in a stiff configuration (by adding a fictitious support in non-seismic piping close to the class-break).
The stiff configuration of the RHR system has dynamic characteristics similar to those of the RRCI system; the stiff configuration is then used to perform nonlinear analyses.
Section 6.0 discusses the conclusions of these analyses, and shows that the piping systems remain functional during the SSE event.
01-0590-1135 Revision 0 Page 5 3.0 ELASTIC ANALYSIS Based upon stress levels, availability of information,*and configuration, the RHR system described in Section 2.0 was chosen as the representative piping system for further study by elastic and non-linear methods. Previous simplified operability calculations assumed a cantilever model with an equivalent static seismic loading of 1.5 times the peak acceleration of the appropriate response spectrum. This simplified analysis technique was used as it is both conservative and easy to apply. The combined stress for OBE, gravity load and pressure, including appropriate stress intensification factors, was found to be 102,000 psi.
This exceeded the original operability allowable of 1/2 Sult (30,000 psi) for this load combination.
In response to this apparent severe overstress condition, further elastic and nonlinear analyses of the RHR system were performed to:
confirm conservatism in the simplified operability calculations determine behavior of "class-break" piping determine actual piping stresses confirm functionality of piping system after initial yield.
This Section describes the elastic analyses performed. The following Sections 4.0 and 5.0 describe the nonlinear analyses performed.
The elastic analyses were performed with EDS computer program SUPERPIPE. The analyses considered two bounding models of the RHR system. First, a flexible model was developed, which included all 3" and 4" lines connected to line 1-1067-3".
In this model, much of the piping is seismically unsupported, with one span of 215 feet. In addition, a total of three branch runs of this model include seismic class piping. These are runs 1, 2 and 4. Second, a stiff model considered all piping included in the standard "class-break" walkdown. The second model assumes an anchor at the non-seismic end of the walkdown piping. These two models are shown in Figures 3.1 and 3.2.
01-0590-1135 Revision 0 Page 6
The elastic-analyses performed with SUPERPIPE include response spectrum analyses with simultaneous excitation in the vertical and in two perpendicular horizontal directions. OBE and gravity load case analyses were performed on the flexible system, and SSE stresses were extrapolated from the OBE stresses. OBE and SSE load case analyses were performed on the stiff system. Pressure stress was calculated by hand.
Seismic, gravity and pressure stresses were combined and compared to code stress allowables. ASME Code Subsection NC stress intensification and flexibility factors were incorporated in the analyses.
3.1 SUPERPIPE Math Model Two mathematical models were developed to define the system geometry used for elastic analyses. Model 1, illustrated in Figure 3.1, defines the flexible system and consists of 3" and 4" lines anchored at large piping.
Model 2, illustrated in Figure 3.2, defines the stiff system and consists of line 1-1067-3" anchored at large piping and the branch point with line 1-1065-4".
Certain assumptions were made in developing the math models. The non-seismic piping was modeled using "as-engineered" configurations, since walkdown information was not available in these areas.
Individual rod hanger locations were not always uniquely indicated on the fabrication drawings; these hangers were equally spaced on the math models.
Rod hangers were allowed to participate in the restraint of piping under seismic loading, although a few indicated uplifting loads during the excitation.
Detailed review of the pipe system behavior showed that the exclusion of these few uplifting hangers would not significantly affect pipe stresses.
The mathematical models developed were not exact, detailed reproductions of the existing system, nor were they replete with conservative assumptions.
Rather, since this study investigates actual piping behavior, the models represent the pipe system such that analysis results are accurate predictions of the expected behavior of the piping system.
01-0590-1135 Revision 0
.Page 7
Frequency analyses of the two RHR models showed that the first model has several modes with frequencies below 1 Hz. The stiffer RHR model has higher first mode frequencies, with first mode of 2.36 Hz, and other significant modes occurring near the peak of the input response spectrum. The frequencies of these models are given in Tables 3.1 and 3.2, while the input spectrum is shown in Figure 5.1.
3.2 Stress Results Results of the elastic analyses are reported in Tables 3.3a through 3.3e. Tables 3.3a through 3.3d cover the seismic piping in the flexible system. Table 3.3e covers the seismic piping of the stiff system.
Seismic analysis of the flexible system was performed using the response spectra technique. The horizontal spectrum for 0.5 percent damping was developed by Keitn, Feibush Associates, Engineers for the-Quad I Reactor Building at an elevation of 595 feet 2.
A 2 percent damping spectrum 3 used for SSE analyses was developed from a time history motion compatible with the 0.5 percent OBE spectrum, as.discussed in Section 5.1, and is shown in Figure 5.8.
The vertical spectrum used was a constant 0.08 for all frequencies, in accordance with the Quad I FSAR.
Seismic loading of the flexible system consisted of two perpendicular horizontal excitations and a vertical excitation applied simultaneously. Three directional stresses are added by the SRSS method, with closely spaced modes combined by absolute sum, as per USNRC Regulatory Guide 1.92. Gravity stress computation was also performed on the flexible system. A constant pressure stress of 700 psi, calculated for RHRS line 1-1067-3", was used for all seismic piping. This stress corresponds to the piping pressure of 210 psig.
Preliminary stress combinations of OBE, gravity, and pressure stress for all seismic areas in the flexible system are tabulated in Tables 3.3a through 3.3c.
The resulting stress was derived by adding the three stresses (seismic, gravity and pressure) at each point, and conservatively ignores the direct vector addition of the
01-0590-1135 Revision 0 Page 8
individual moments and torques. For these stresses, there were nine locations where stresses exceeded the stress criterion of 1.2 Sh (or 18,000 psi).
However, all stresses were below the 1/2 Sult (or 30,000 psi) allowable used in the original operability assessment.
Exact combination of moments to derive stresses showed that 6 of the 9 points still exceeded the 1.2 Sh B31.1 OBE allowable with a maximum stress of 26,800 psi.
SSE level stresses for these 6 points are tabulated along with the OBE stresses in Table 3.3d.
The conservative assumptions in the original operability analysis yielded an OBE level stress of 102,000 psi.
In the elastic dynamic analysis of the flexible system, the maximum OBE level stress in the seismic piping was 26,800 psi. Modeling assumptions in the SUPERPIPE analysis were not overly conservative; further detailed elastic analyses would not significantly reduce this stress intensity.
However, the simultaneous seismic excitation in three directions was more conservative than the combination of one horizontal and one vertical directional excitation in the original analysis.
The model of the stiff RHR system was computer analyzed for seismic excitation only. The gravity analysis for the flexible system, and a pressure stress of 700 psi, were used to calculate total stresses. OBE and SSE stresses were computed using response spectra at 0.5 and 2.0
-percent damping respectively, with these spectra developed by the procedures discussed in Section 5.1.
The OBE and SSE stresses listed in Table 3.3e are well below code stress criteria.
3.3 Elastic Analysis Discussion RHRS line 1-1067-3" was chosen as representative of those piping systems previously shown to exceed operability stress limits. SUPERPIPE response spectra analyses showed that stress levels significantly decreased compared to hand calculation values when detailed dynamic analyses of
01-0590-1135 Revision 0 Page 9 the RHR system were performed. Inspection of the properties of the RER piping system reveals that similar stress decreases would occur for all class-break piping systems identified in Section 2.0 of this report.. The basis for this statement is as follows:
All class-break problems were originally analyzed by static hand calculation methods.
All original class-break operability stresses were calculated using equivalent static lateral load, at 1.5 times peak spectral acceleration. Actual equivalent static lateral accelerations on flexible systems are much lower than 1.5 times peak spectral acceleration.
The piping systems are flexible, with first mode periods at low values of spectral acceleration.
For the RHR piping system analyzed, a stress reduction of 74 percent was observed (102,000 psi to 26,800 psi).
For the other class break piping systems identified in Section 2.0, similiar reductions in original operability stress levels are expected.
In lieu of performing complete dynamic analyses of these systems, a simplified approach is taken to estimate the stress reductions:
Identify spectral acceleration level used in original operability calculation Identify likely first mode spectral accelerations of flexible system Reduce original stress level by ratio of above acceleration values.
The results of this analysis are shown in Table 3.4.
As much of the nonseismic portions of the RHR and the other class-break piping systems have not been walked down, there exists the possibility that these systems are in fact not "flexible" -
in effect some seismic supports may exist near the class break. To study this possibility, the stiff model of the RHR system was also analyzed, assuming an anchor at the point where the
01-0590-1135 Revision 0 Page.10 --
standard "class-break" walkdown ended. Results from this case show much reduced stress levels in the piping, below code allowables.
It is thus concluded that the six class-break systems originally identified to be highly overstressed by hand calculation in fact have stresses close to code allowables. Further nonlinear analyses discussed in the next sections confirm that at SSE levels, a system shown to be overstressed by elastic methods can be shown to remain functional.
01-0590-1135 Revision 0 Page
.11 4.0 PIPE ELBOW CAPACITY The piping model used to perform nonlinear analyses with Computer Program ANSYS was composed of elastic and plastic straight pipe elements and plastic elbow elements. To maintain functionality, the critical elbow components of the piping system must not distort excessively during the SSE event. This Section 4.0 discusses the modeling assumptions used in the ANSYS analysis, and the verification of the ANSYS theoretical elbow behavior versus experimental test results.
In finite element analysis, certain geometric and material property relationships are idealized. In the ANSYS analyses, only a bilinear stress-strain relationship can be used for the non-proportional loading encountered in seismic analysis. This bilinear stress-strain relationship is adjusted so that the behavior of the plastic elbow element closely matches the experimental results.
The experimental results used to verify the ANSYS plastic elbow element were presented in the report ORNL/NUREG-24 by Greenstreet 5.
In this report, load-deflection curves for various elbows were developed. Selected curves were reproduced analytically using ANSYS (Figure 4.1).
Young's modulus and the yield strength of the elbow were modified, and the bilinear stress-strain curve developed to obtain the desired load-deflection relationship. The ANSYS results were also compared with the limit load analysis, which assumes an elastic-perfectly plastic material behavior.
The yield stress (0.2 percent offset stress) is as specified in the code. The collapse load is defined as the load at which the distortion is twice the value at the calculated departure from linearity (ASME Appendix F-1321.1 (d)).
Once the appropriate parameters were determined, they were applied to the analysis of a 3" Schedule 40 long radius elbow used in the analysis of the RHR piping system. The results of the analysis are represented in Figure 4.2.
4.1 Experimental Data The study of ORNL/NUREG-24 experimentally determined-the load-deflection response for sixteen 6 inch (nominal) commercial carbon steel elbows and four 6 inch stainless steel elbows. Each specimen was loaded to produce
01-0590-1135 Revision 0 Page 12 predominately plastic response. The influences of bend radius, wall thickness and material properties were studied.
Specimen PE-8 was chosen for the correlation analysis of the ANSYS elbow element. Specimen PE-8 is a 6-inch Schedule 80 long radius elbow of ASTM A-106 Grade B steel.
The specimen was incrementally loaded with an in-plane point load, from 5,000-12,000 lbs. such that compression stresses were produced on the intrados.
The material properties for the elbow were also given in the report. These were used in the correlation study discussed in the next section. Tests on this and other test specimans showed no significant flow restriction at elbow strains of 1 percent and greater.
At peak strains of 1 percent, elbows carry moments on the order of those predicted using Equation 9 of ASME subsection NC, at level D stress levels.
4.2 ANSYS Analytical Correlation Elastic straight pipe elements and plastic elbow elements were used to model Specimen PE-8 for analysis by ANSYS.
The 900 long radius elbow was discretized into four elements. The bilinear stress-strain curve was developed using the material properties reported in ORNL/NUREG-24.
The elastic portion of the curve was determined from the modulus of elasticity and the 37.8 ksi yield stress 5.
The plastic portion of the curve was determined from the yield strength, yield strain (0.2% offset strain),
ultimate strength5, and the corresponding maximum strain of similar steel 6.
In ANSYS analyses, two options are available to model the flexibility factor of an elbow.
These are the ASME flexibility factor and the Karman flexibility factor.
The Karman flexibility factor was chosen for the analyses.
The first ANSYS analysis showed a much higher yield load than the yield load obtained experimentally. The ANSYS yield load was 11,000 lbs. compared to 7,000 lbs. from the experiment. Also, the ANSYS analysis predicts a higher flexibility factor in the elastic range.
A limit load analysis was done to refine the bilinear stress-strain curve. In this analysis, the ASME
01-0590-1135 Revision 0
_.______Page
- 13.
Subsection NC stress intensification factor i was used to calculate the yield and collapse loads7.
These loads were found to be 8,000 lbs. and 11,000 lbs. respectively.
Using the results of the first analysis, the maximum stress of 27.5 ksi (73% of 37.8 ksi) at a load of 8,000 lbs. was used as the yield stress for the refined bilinear stress-strain curve. The slope of the plastic portion of the new curve was taken to be the same as that of the first curve.
The PE-8 elbow was then re-analyzed with the refined stress-strain curve. The correlation of the second ANSYS analysis with the experimental results is presented in Figure 4.1.
As can be seen, with the modified stress-strain curve, the ANSYS elbow element closely models true experimental test results, in a slightly conservative manner.
The results of the correlation study were applied to a 3" Schedule 40 long radius elbow.
The model was made dimensionally proportional to the 6" model to reduce the elastic deflection of the straight pipes. The bilinear stress-strain curve was obtained by increasing Young's modulus by 25% to match the flexibility factor in the elastic range and reducing the yield strength to 73% of code values as prescribed by the above discussed correlation study. The results of the ANSYS analysis match those of.the limit load analysis and are presented in Figure 4.2.
In addition, the analysis was done using both 2 and 4 element discretization with identical
-results.
Hence, further analysis was performed using two element elbows.
01-0590-1135 Revision 0 Page 14 5.0 NONLINEAR ANALYSIS To show that a piping system remains functional during an SSE event, the ASME Subsection NC code allows the use of a stress level of 2.4 Sh.
For both carbon and stainless steels, this level of stress is beyond nominal yield stress values. To satisfy functionality requirements, and to demonstrate the conservatism of elastic analysis methods at this level of*
stress, nonlinear analyses were performed on the RHR piping system. Certain conclusions drawn from the response of the RHR piping can be applied to other piping systems, demonstrating their functionality.
5.1 Time History Motions To perform a dynamic nonlinear analysis of the RHR piping system, it was necessary to input to the direct integration analysis a full time history seismic motion.
The required response spectra for the RER piping system-is the KFAE2 spectrum at elevation 595 feet in the Quad 1 plant. Hence, it was necessary to develop a suitable input motion which would envelope the KFAE spectrum.
The KFAE spectrum is shown in Figure 5.1.
The spectrum is a duplicate of that used for plant design, from a period of 0.0 to 2.0 seconds. No data was supplied in the original spectrum for periods past 2.0 seconds. As some of the RHR piping modes are past 2.0 seconds. the spectrum was extended to 5.0 seconds by using USNRC Regulatory Guide 1.60 values at 0.5 percent damping.
Two time history motions were developed to envelope this spectrum and subsequently used as the two horizontal excitations in the ANSYS analysis.
To assure statistical independence of these motions, two different acceleration time histories were used as a.basis for.developing the final required motions; these were the El Centro N-S 1940 and San Fernando (Pacoima Dam) E-W 1971 motions.
Significant modifications to both the El Centro and Pacoima Dam motions were required in order for the motions to match the desired broadened spectra.
This was -done by adjusting the Fourier series components of each motion, within the approprate frequency bands, so that the, augmented El Centro and Pacoima Dam motions would give the
01-0590-1135 Revision 0
-Page 15 desired response spectrum. This procedure required an iterative process:
first, the input motion is resolved into a response spectrum, using computer code RESPEC; then the spectral energy of the input spectrum is modified to match the required spectrum, using computer code FREAK; this two step process is iterated until the final motion gives a spectrum closely enveloping the required spectrum.
The resulting time history motions are shown in Figures 5.2.through 5.5.
The spectra of these motions are shown in Figures 5.6 and 5.7, and as can be seen, closely envelope the required spectrum. The motions are of 16 second duration, which was shown to be long enough to capture peak responses of the piping systems.
Once the motions were developed to match the required spectrum at 0.5 percent damping, the 1.0 and 2.0 percent spectra were easily calculated. As can be seen in Figure 5.8, the 2.0 percent spectrum is approximately 80% of the 0.5 percent spectrum over the frequency bandwidth of interest.
In the nonlinear ANSYS analysis, the augmented El Centro motion is input in the N-S (x) direction, and the augmented Pacoima Dam motion is input in the E-W (Z) direction.
As the elastic analyses of the stiff RHR system showed low stresses, well below yield, the input motions to the nonlinear analyses are increased by a factor 11.1 to ensure that significant yielding would occur.
This factor corresponds to the maximum stress of 60,000 psi in the elastic analysis of the stiff system.
5.2 ANSYS Math Model The ANSYS math model used to perform detailed nonlinear dynamic analysis is shown in Figure 5.9.
This model configuration corresponds exactly to the stiff model of the*RHR system, previously discussed in Section 3.1.
The ANSYS model used more dynamic degrees of freedom than the SUPERPIPE model in order to accurately capture the nonlinear behavior of the system. The model consists of elastic straight pipe elements (STIF9), plastic straight
01-0590-1135 Revision 0 Page 16 pipe elements (STIF20), and plastic elbow elements (STIF60).
All elbows used plastic elements, while straight pipe used plastic elements where yielding was expected.
Two elements were used to model 90 degree elbows. The accuracy of this assumption was confirmed by running a sensitivity study, comparing results from elbows modeled with two or four elements, as described in Section 4.0.
The stress-strain law used for straight pipe elements is based upon minimum code material strengths, at temperature, for A-106 Grade B, and are given in Table 5.1.
The material law for elbow pipe elements was modified so that the elbow behavior matched experimental results, as described in Section 4.0.
Damping for the SSE seismic event was incorporated using ALPHA-BETA damping, (using the current stiffness matrix) set to 2 percent, ranging from 0.2 to 33 Hz.
Seismic analyses were performed using motions in the N-S and E-W directions by the direct integration method.
Pressure, gravity and vertical earthquake stresses were not included. Pressure stresses cause actual increase in pipe elbow capacity (see discussion, Section 6.0) and hence are conservatively neglected. Gravity and vertical earthquake stresses are small (about 5000 psi) and would not significantly influence the piping system response behavior.
Thermal stresses are neglected at ASME level D limits.
5.3 PWHIP Math Model Due to the excessive computation costs associated with performing a dynamic analysis with the ANSYS model for a full 16 second earthquake motion, a similar nonlinear PWHIP model was developed.
(The time step integration using ANSYS was 0.001 seconds versus 0.020 seconds for PWHIP.)
The full 16 second time history analysis performed using PWHIP gave key results such as peak moments and displacements, and number of cycles where yield moment was reached; the ANSYS analysis extends past
01-0590-1135 Revision 0
_Pa ge _1_7 the time where critical moment was reached (at 3.28 seconds), and gives detailed results concerning moments and strains at elbow elements.
The PWHIP math model is shown in Figure 5.10.
The straight pipe shown has identical properties to the straight pipe ANSYS element; the length of the system is adjusted so as to give matching first mode (elastic) frequencies between the detailed ANSYS and simplified PWHIP systems% Table 5.2 compares the lower mode frequencies between the two models.
Dynamic analyses using both models showed extreme similarity in response:
first yield for both PWHIP and ANSYS models occurs at 3.22 seconds; response characteristics up to the time of yield are very similar; unloading after first yield occurs at 3.28 seconds for both systems. Figure 5.14 shows the comparison of time-varying moments on the yielding pipe elements. It is thus concluded that the simple PWHIP model can be used as an adequate predictor of the RHR system's overall behavior for the entire earthquake motion.
5.4 Response Results Basic response of the piping system is shown in Figures 5.11 through 5.14.
As can be seen in Figure 5.12, nonlinear analyses predict that peak pipe moments will occur between 3 and 5 seconds into the event. A total of seven excursions past yield are expected. After 5.
seconds, the system will continue to vibrate, although no further plastic excursions occur.
In comparison, by not allowing the system to yiel-d, substantially higher pipe moments occur in the system, as shown in Figure 5.12.
A comparison of peak pipe moments as determined by both elastic and nonlinear analysis methods is given in Table 5.3.
Results show that straight pipe moment reduces by 34 percent and elbow pipe moment reduces by 27 percent.
A similar reduction of moment is expected to occur for other piping systems not analyzed in this study for-the following reasons:
01-0590-1135 Revision 0
.Page 18 Pipe yielding increases the energy absorption of the system, hence reducing response.
Pipe yielding alters the system's dynamic
.characteristics, typically moving its response "frequencies" away from the peak input energy pulses causing the yielding.
Pipe yielding causes redistribution of moments in a indeterminantly supported system, thus limiting moments in highly stressed portions, while increasing moments in lower stressed portions.
The critical elements in the RHR piping system are the elbows. As elbows yield, they start to undergo large shape deformations:
if extensively yielded,the resulting ovality may cause a reduction in the pipe cross sectional area.
The detailed ANSYS model shows that the peak moment on the most highly loaded elbow was 42,580 lb-inch.
This moment is below the collapse load as calculated per-ASME Appendix F-1321.1(d) method. Further, the peak strain in the elbow associated with this moment was just slightly over 1 percent. Experimental tests on elbows by Greenstreet and others 5,8,9,10 have shown that elbows are well capable of yielding to strains in excess of 1 percent, without any
-significant flow restriction due to ovality changes.
01-0590-1135 Revision 0 Page 19 6.0 DISCUSSION The intent of this evaluation was to study the functionality of piping systems in response to the SSE event. The analyses performed have utilized the RHR piping system in Quad Cities Unit 1. By the use of detailed elastic and nonlinear analyses, this system has been shown to remain functional during the SSE event. This section of the report discusses the applicability of these results to -other piping systems in Quad Cities Units 1 and 2 and Dresden Units 2 and 3.
As discussed in Section 3.3, the use of detailed elastic analyses significantly reduces the peak stresses in the RHR system, as compared to values initially predicted by hand calculations. This is primarily due to the flexibility of this class-break system, which puts its first mode frequency at a point on the response spectrum of very low spectral acceleration. Review of the remaining five class-break systems shows that they are also flexible, and that they too can be analyzed using the low spectral accelerations of a flexible system. This has been done, in a simple manner, and results shown in Table 3.4.
While these results are not exact (they are still based on simple hand calculations of the class-break systems), they do show that seismic stresses are in the range of allowable levels.
To provide verification that class-break systems are not affected by the amplified portion of the response spectrum, an upper bound stiffness analysis of the RHR system was performed, by adding a fictitious support. Resulting stresses were confirmed to be at low levels, below code allowables.
Of further concern is the Recirculation system, which has previously been analyzed by response spectrum methods, and still shown to exceed a code allowable of 2.4 Sh.
To justify that this system would remain functional during the SSE event, as well as to determine a more reasonable functionality limit, nonlinear analyses have been performed on a piping system of similar dynamic characteristics; results show that internal pipe moments, as calculated by nonlinear methods, are 27% lower than those calculated by linear methods, while at the same time Apeak strains in elbow elements are limited to 1 percent, with no significant flow restriction. Of significance is the result that elbows, predicted to have 60,000 psi stress by elastic analysis, are below lowest bound collapse load and are shown functional by nonlinear analysis.
01-0590-1135 Revision 0 Page 20 Table 6.1 summarizes SSE stresses as pridicted by either hand calculation or response spectra analysis techniques. Hand calculation values have been adjusted to reflect SSE motion, (by use of multiplier of 1.6; Figure 5.8 suggests that a 2 percent SSE spectrum is approximately 80 percent of a 0.5 percent OBE spectrum. Hence, as SSE is twice the OBE zero period acceleration, use 1.6 = 2 times 0.8).
As can be seen in this Table, all elastically calculated stresses are below 60,000 psi.
This indicates that all the piping systems would remain functional during the SSE event.
Further, the following important conservatisms were not considered:
The code value of Sh is very conservative. A more realistic value of Sh is at least 20 percent larger.
Experimental test results have shown that elbows can strain in excess of 1 percent without loss of functionality.
The justification of an allowable stress level of 20 percent larger than 2.4 Sh is that:
In situ material yield strengths are 10 percent over code minimum.1 1,12 Strain rate effects increase nominal yield strengths by 10 percent.1 3,14 Other conservatisms not included in the analysis include:
Doubling gravity and pressure stress.
Actual component thickness.
Conservative modeling assumptions.
Collapse loads of pressurized elbows are significantly higher (on the order of 50 percent) than non-pressurized elbows, as verified by experimental results.5, 9,1 0 It is therefore concluded that all piping systems identified in Table 2.1 as being over original operability criteria would in fact remain functional during the SSE event.
01-0590-1-135 Revision 0 Page 21
7.0 CONCLUSION
A total of seven piping systems were identified by previous calculation to exceed operability limits. This report has studied one of these systems in depth, using both elastic and nonlinear methods. Results from these analyses show the following:
The analyzed RHR.class-break system has elastic stresses slightly in excess of code allowables, but remains functional during the SSE event when nonlinear effects are accounted.
The remaining class-break systems all have approximately calculated stresses near code allowables, and remain functional during the SSE event when nonlinear effects are accounted.
The RRCI system has elastic stresses slightly in excess of code allowables, but remains functional during the SSE event when nonlinear effects are accounted.
As an outcome of this study, it is recommended that the simplified hand calculations used to analyze class-break systems on Quad 1 be modified to remove large conservatisms.
Based upon these conclusions, it is judged that the piping systems identified in this report would remain functional during an SSE event.
01-0590-1135 Revision 0 Page 22
8.0 REFERENCES
- 1. EDS Project Specific Instructions, Numbers 5.0, 6.0, 10.0 Job 0590-003.
- 2. Keith, Feibush Associates, Engineers letter of September 29, 1970, transmitting Quad I Response Spectra.
- 3. USNRC Regulatory-Guide 1.60, Revision 1, December 1973.
- 4. Commonwealth Edison Company Quad-Cities Station Units 1 and 2 Safety Analysis Report and Section 12, Question 12.3, Amendment 13.
- 5. Greenstreet, W. L., "Experimental Study of Plastic Responses of Pipe Elbows," ORNL/NUREG-24, February 1978.
- 6. Mashgiz, ed., Enziklopediceskii Spravocinik "Masinostroenie," Vol. 3 & 4, 1974.
- 7. EDS Nuclear "AED Technical Procedure8 -
Structural Analysis," May 1, 1979.
- 8. Evaluation of the Functional Capability of ASME Section III Class 1, 2 and 3 Piping Components Mark I Containment Program Task 3.1.5.4, Sargent & Lundy Engineers Report SL-3670, September 21, 1978.
- 9. Gross, Nicol, "Experiments on Short-Radius Pipe Bends,"
Proceedings Institution of Mechanical Engineers, (B), Vol.
1B, 1952-1953, p. 465.
- 10. Ellyin, Fernand, "An Experimental Study of Elasto-Plastic Response of Branch-Pipe Tee Connections Subjected to Internal Pressure, External Couples and Combined Loadings,"
Welding Research Council Bulletin 230, September, 1977.
- 11.
Calambos, T.V. and Ravindra, M. K., "Properties of Steel for Use in LRFD," ASCE JSD, September 1978.
01-0590-1135 Revision 0 Page 23
- 12.
Final Reaort on Bar Testsnfor the C6mmittee of Concrete Reinforcing Bar Producers, AISI, Wiff, Janfleg, Elstner and Associates, April 30, L970.
- 13.
"Determination of Break Locations and Dynamic Effects Associated with the Postulated Rupture of Piping," Section 3.6.2, Standard Review Plan, USNRC.
- 14.
Code Requirements for Nuclear Safety-Related Concrete Structures, ACI 349-76, Appendix C.
- 15.
EDS calculations 0590-013-456 A-001 Rev. 0:
Operability Assessment N-001 Rev. 0:
Time History Development N-002 Rev. 0:
SUPERPIPE Model N-003 Rev. 0:
Inelastic Elbow Verification N-004 Rev. 0:
ANSYS Model N-005 Rev. 0:
PWHIP Model N-006 Rev. 0:
Assessment of Q1-RBCW-02B N-007.Rev. 0:
PWHIP Analysis Results N-008 Rev. 0:
ANSYS Analysis Results
01-0590-1135 Revision 0 Page 24 IDENTIFIED PIPING SYSTEMS original EDS Problem No.
Method of Analysis QI-RRCI-01C Computer/Elastic Response Spectrum Ql-RHRS-03B
.Hand Calculation/Equivalent Static Method Ql-RHRS-02B Hand Calculation/Equivalent Static Method Ql-RHRS-09B Hand Calculation/Equivalent Static Method Q1-CCCD-02B Hand Calculation/Equivalent Static method Ql-RBCW-OlB Hand Calculation/Equivalent Static Method Ql-RBCW-02B Hand Calculation/Equivalent Static Method Abbreviations:
RRCI - Reactor Recirculation RHRS -
Residual Heat Removal CCCD -
Clean and Contaminated Drain RBCW -
Reactor Building Cooling Water Table 2.1
01-0590-1135 Revision 0 Page 25 RHR*FLEXIBLE SYSTEM FREQJENCIES Mode No.
Frequency (cps)
Period (sec) 1
.205 4.8762 2
.266 3.7534 3
.465 2.1489 4
.820 1.2196*
5 1.033
.9678 6
1.294
.7728 7
1.471
.6797 8
1.668
.5996 9
2.037
.4909 10 2.158
.4634 11 2.311
.4327 12 2.527
.3957 13 2.610
.3832 14 2.625
.3810 15 2.677
.3735 16 2.783
.3593 17 3.070
.3257 18 3.618
.2764 19 4.150
.2410 20 4.413
.2266 C.
.0 45 10.642
.0940 Table 3.1
01-0590-1135 Revision 0 Page 26 RHR STIFF SYSTEM FREQUENiCIES Mode No.
Frequency (cps)
Period (sec) 1 2.365
.4228 2
5.510
.1815 3
8.086
.1237 4
9.022
.1108 5
9.269
.1079 6
16.342
.0612 7
18.263
.0548 8
23.539
.0425 9
25.741
.0388 10 27.515
.0363 T)
Table 3.2-
01-0590-1135 Revision 0 Page 27 PRELIMINARY CALCULATION OF STRESSES IN RHR SEISMIC PIPING Run 1 1-1067-3" Flexible System OBE Gravity Control
- Stress, Stress, Preliminary Point psi psi Stress, psi 100 5422 1019 7141 COlA, Elbow 5974 219 6893 C01B, Elbow 9066 246 10012 102 4224 202 5126 104 5173 2154 8027 CiXA, Elbow 11839 2443 14982 ClXB, Elbow 11648 1280 13628 106 7885 597 9182 CO2A, Elbow 16460 2991 20151 CO2B, Elbow 16809 2877 20386 108 8075 876 9651 Formula:
Preliminary Stress
=
OBE +
gravity +
pressure Pressure =
Pd
=
(210)(3.068)
= 697 psi 700 psi at all points D2 -d2 (3.5)2(3.068)2 B31.1 Code Criteria = 1.2 S
= 18000 psi Material A-106 Grade B
Reference:
OBE -
Computer run N-002-002 Gravity -
Computer run N-002-003 Table 3.3a
01-0590-1135 Revision 0 Page 28 PRELIMINARY CALCULATION OF STRESSES IN RHR SEISMIC PIPING Run 2 1-1065-3".
Flexible System OBE Gravity Control
- Stress, Stress, Preliminary Point psi.
psi Stress, psi 200 4088 2086 6874 CO5A, Elbow 7061 3694 11455 CO5B, Elbow 7158 3351 11209 C5XA, Elbow 7031 2537 10268 C5XB, Elbow 6970 2516 10186 201 4552 1440 6692 202 6311 1457 8468 CO6A, Elbow 14646 3417 18763 CO6B, Elbow 15677 3270 19647 204 8595 857 10152 206 9370 665 10735 Formula:
Preliminary Stress
=
OBE +
gravity +
pressure Pressure Stress = 700 psi at all points B31.1 Code Criteria = 1.2 S h 18000 psi Material A-106 Grade B
Reference:
OBE -
Computer run N-002-00 2 Gravity -
Computer run N-002-003 0r Table 3.3b
01-0590-1135 Revision 0 Page 29 PRELIMINARY CALCULATION OF STRESSES IN RHR SEISMIC PIPING Run 4 1-1066-3" Flexible System OBE Gravity Control
- Stress, Stress, Preliminary Point psi psi Stress, psi C38A, Elbow 15440 3062 19202 C388, El'bow 3315 19576 C39A, Elbow 15455 3345 19500 C39B, Elbow 12935 3503 17138 406 4478 2164 7342 C40A, Elbow 20320 4265 25285 C40B, Elbow 22227 4275 27202 C41A, Elbow 10446 5362 16508 C41B, Elbow 9328 5876 15904 408 4864 3310 8874 Formula:
Preliminary Stress
=
OBE +
gravity +
pressure Pressure Stress = 700 psi at all points B31.1 Code Criteria
= 1.2 S
= 18000 psi Material A-106 Grade B
Reference:
OBE -
Computer run N-002-00 2 Gravity -
Computer run N-002-003 Table 3.3c
01-0590-1135 Revision 0 Page 30 STRESSES IN RHR SEISMIC PIPING FLEXIBLE SYSTEM Preliminary Control OBE OBE SSE Point Stress, psi Stress, psi Stress, psi CO2A,. Elbow 20151 18217 27007 CO2B, Elbow 20386 20162 30233 CO6A, Elbow 18763 18322 27070 CO6B, Elbow 19647 14923 C38A, Elbow 19202 18499 27672 C38B, Elbow 19576 12741
- C39A, Elbow
.19500 12618 C40A, Elbow 25285 24558 36383 C40B, Elbow 27202 26801 40067 Formulas:
Preliminary OBE Stress:
=
OBE +
gravity +
pressure OBE Stress:
=1 (i)2(M yyBE + M
)
(MzzOBE 2
2 1/2
+ M 2+
(M
+ M
)2+
(pressure) zz,gravity tsOBE tgravity SSE Stress:
=
(i)2 (MyySSE
+ M yygravity 2 +
i) 2
~
L YSS yy~raviy 211/2 (MzzSSE + Mzz,gravity)2 + (Mt,OBE + M tgravity 2
+ (pressure)
(pressure) = 700 psi at all points Code Criteria:
OBE Str.ess -
1.2 Sh = 18000 psi SSE Stress -
2.4 Sh = 36000 psi
Reference:
OBE -
Computer run N-002-002 Gravity -
Computer run N-002-003
01-0590-1135 Revision 0 Page 31 STRESSES IN RHR SEISMIC PIPING STIFF SYSTEM Control OBE Case SSE Case Point Stress, Psi Stress, Psi 100 5507 7406 C01A, Elbow
.2987 3932 CO1B, Elbow 5316 7223 102 2954 3868 104 3939 4614
- CXA, Elbow 5791 7473 C1XB, Elbow 5773 7782 106 6937 9866 CO2A, Elbow 5241 6162 CO2B, Elbow 6183 7326 108 2676 3309 Formulas:
Stress
=1 M. (M
+ M 2+
W 2M S 13 2( yy,seismic yy,gravity 22 zzseismic
+ M
)2
+ (M+M2 2
+ (pressure) zz,gravity tseismic t,gravity Pressure = 700 psi at all points Code Criteria:
OBE Stress - 1.2 Sh = 18000 psi SSE Stress -
2.4 Sh = 36000 psi
Reference:
OBE -
Computer runs N-002-003 N-002-004 SSE -
Computer runs N-002-003 N-002-005 Table 3.3e
01-0590-1135 Revision 0 Page 32 System Original Stress/OBE Modified Stress/OBE(2 )
RRCI-01C 25,000 25,000 RHRS-03B(l) 102,155 26,800 RHRS-02B(l) 58,580 33,666 RHRS-09B(l) 124,358 14,544 CCCD-02B(l) 203,394 24,704 RBCW-01B (1)
Similar to RBCW-02B RBCW-02B(l) 301,000 30,000 Notes:
- l.
Original stress calculated using 1.5 peak spectral acceleration
- 2. Modified stress calculated using first mode spectral acceleration Table 3.4
01-0590-1135 Revision 0 Page 33 MATERIAL STRESS-STRAIN LAW Low Carbon Steel, A106 Grade B E
= 27,700,000 psi (at 2000)
Poisson's Ratio = 0.30 (elastic) varies to 0.50 at full plasticity Sy
= 31,900 psi ET
= (.01)E = 280,000 psi (at 2000)
Table 5.1
01-0590-1135 Revision 0 Page 34 DETAILED ANSYS AND SIMPLE PWHIP SYSTEM FREQUENCIES Mode Detailed ANSYS Modell Simple PWHIP Model 2 1
2.36 Hz 2.36 Hz 2
5.51 Hz 6.55 Hz 3
9.27 Hz 12.80 Hz
. References
- 1. Computer Run N-002-002
- 2. Calculation N-005 Table 5.2
01-0590-1135 Revision 0 Page 35 PIPE MOMENTS COMPARISJN Elastic Nonlinear Percent Analysis Analysis Reductions Straight Pipe 111.9 k-inl (64.9 ksi) 71.6 k-in 2 36 Elbow Pipe 53.8 k-in 3 (60.0 ksi) 42.6 k-in 4 21'
. Reference Computer Runs
- 1.
N-007-003
- 2.
N-007-00 2
- 3.
N-002-005
- 4.
N-008-005 Table 5.3
01-0590-1135 Revision 0 Page 36
SUMMARY
STRESSES Elastic SSE Stress System psi (3)
RRCI-01C Note 1 43,000 RHRS-03B Note 1 40,087 RHRS-02B Note 2 53,865 RHRS-09B Note 2 23,270 CCCD-02B Note 2 39,526 RBCW-01B Note 2 similar to RBCW-02B RBCW-02B Note 2 5Q,694 Notes
- 1. By response spectra analysis
- 2. By static hand calculation using first mode spectral acceleration
Table 6.1
rtoo Flexible RIR piping systen SUPERPIPE Math Model as I. N PHOOLEM M9VISION NUNUE OK 3
.s 41s ft-f WI O
VI S
gIl V,
ird"Vti 646 aM P-1 is USIAI 01-0590-1135 figure 3.1 RevisionA0 Page 37
Stiff RHR piping system SUPERPIPE Math Model 124 122 ol IV2Vt6, t'tIMIIAL 1jA1,3#6 F
- e.
- Cft (6919009 B
LY 0Aff
'00 Ao.
A 0
NT. JE V.
c 7
o..
0680ooI-0456
,d.VOt-4 A
01-0590-1135 toi
(,Ot4 W
V~f-4 II W
01idC
.ad0 lJ~t4hOC-C-VAI11' IIOA e-rfrvtt Vj QtL IVA(t:'c~ajA
&4.al6 05w.013-46 VII
- 04 01-090-13 5Figure 3.2 Page 38 Revision 0
ANSYS Correlation Study with a 6" Elbow 14000 13000 1300 Deflection at node 9 12000--
ANSYS Experimental theoretical collapse load 11000 ----
7 10000 Deflection at node 10 9000-theoretical y eld load 8000--
7000--
8 9
10 11 12
@6 6000-5 927.S" 2@5" Model::
4
-f 5000./
6" Sch 80
- 1.
3
.4000-X-Node No*
( )
3@6"=18" X - Element No.
2 3000-(0 2
j 2000--1 Reference Computer Run N-003-003 1000--I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Deflection (in) 01-0590-1135 Revision 0 Figure 4.1 Page 39
Mment-Deflection Curve for a 3" Scnedule 40 Long Radius Elbow 45000 ASME Appendix F Collapse Load (2xDistortion at Yield)(43,500 lb-in)
Theoretical Collapse Load (41,000 lb-in) 36000 Theoretical Yield Load (31,000 lb-in) 10 I @
27000 18000 Model:
3" Sch 40 X.- Node No.
- ElementNO 9000 Referenoe Computer Run N-003-006 I
I I
I I
I 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 Deflection of Point 9 (in)
Figure 4.2; 01-0590-1135 Revision 0 Page 40
Required Input Spectrum for RHR System TLn SCALE HORIZONTAL I INCH = 0.2 SECONDS VERTICAL I INCH - 0.2 GRAVITY z zri c
cc I-toU)
- c.
S 1.111 GRAVITY AT tu3)tn 0C 1.2 T
- 0. 111 SECONDS z 7t.
o U
(a (nz 0
a-c)ZC IU I,'
CC-UI--*
DD i (-
j ar
.n Ln Z
oc a) 4j 0.6 (1.
(ccr0 i/i ILiJL I-
- 0.
E O TEU cc:
Uc /
/
.)
U Z co Reiso
- 0.
Figre
.1PaL)4 1..
1 U
MF ID (f)
I Ld F
~j 02 0
cc:
LUJ 0.0 0.2 0.11 U. 6 0.0 1.0 1.2 1.14 1.6 1.8 2.0 PERI100.
T (SECONDS)
Revision 0 Figure 5. 1 Page 41
Acceleration Time History Based on El Centro Record 0.30-(Note: This time history is increased 11.1 times for nonlinear analyses.)
0.20- -
C G JC
-0.20 Lii Lr
-0.30 0.0 2.0 43
.0 c
- q.
- o.
1..0 14 3 16.0 01-0590-1135 TIME (SEL-I Page42 Revision 0 Ficgure 5. 2
Is 0 Displacent Time History Based on El Centro Record (Note:
This time history is increased 11.1 times for nonlinear analyses.)
U LE L3
-60 0.0 2.0 4.0 6 C
.0 q-0.0 12.0 14.3 16.0 01-0590-1135 Revision 0 1Pg Figure 5. 3
Acceleration Time History Based on Pacnirra Dam Record (Note: This time history is increased 11.1 times for nonlinear analyses.)
C,.10-0-
U CE
-*~0.0-
- 0. 0~
2.o 4.0 ho 0o f3.o.3
- 12.
14 s.0 16.0 01-0590-1135.
Revision 0 TIME 1SEC. I Page 44 Figure 5. 4
Displacement Time History Based on Paoina Dam Record (Note: This time history is increased 11.1 times for nonlinear analyses.)
10.0-LLJ (L
U I-5.C
- 0.0-Li I.0 0 IC 3
.4 01 12.
14.0 Il 01-0590-1135 TI ME ( SEC.1 Page 45 Revision 0 Ficture 5. 5
Response Spectra Based on El Centro Record 2.bO 0.5% Danping z
C I
KFAE Quad 1 OBE Spectrun 1.0% Damping L-(0.5% Danping) 2.0% Damping Li Li LE 0.53 USNBC Reg. Guide 1.60 Spectrun (0.
5% Damping) o.,
oo FREQUENCY (CP51 01-0590-1135 Revision 0 Figure 5.6 Page 46
Response Spectra Based on Pacoima Dam Record 2.00 I 1.50 Cl 0.5% Danping KFAE Quad 1 OBE Spectrurn ILJ (0.
5% Danping) 1.00 a
IiL 1.0 (0.5mDpiing 2.0% Danping o*0 USNC Reg. Guide 1.60 Spectrui (0.5% Danping) 0.1
-+
+H
+
+ +
-O15 Hd 01-0590-113 5
FREQUENCY (CP51 Revision 0 Fiqure 5.7 Page 47
omparison of Damping Levels in Response spectra Response Spectrum for the Residual Heat Removal System 2.00-A 2 %
Period Frequency A. 5 %
.000 1.00
.050 20.00
.95
.070 14.29
.82 1.AC
.080 12.50
.82
.100 10.00
.69
.140 7.14
.65
.180 5.56
.65
.181 5.52
.77
.190 5.26
.77 1.20
.191 5.24
.77 z
.230 4.35
.75
.270 3.70
.74 0.5% Damping
.830 3.03
.77
'4
.390 2.56
.76
.620 1.61
.77 1.0% Damping 0 O 2.0% Damping FREOUENEY (PSI 01-0590-1135 Figure 5.8 Revision 0 Page 48
Math Model for ANSYS Analysis RIlR System z
F
- 5.
1049 too Opa 41 0
49 e
-444 Figure 5.9 01-0590-1135 Re.visi.n 0 Page 49
01-0590-1135
-Revision 0 Page 50 Math Model for PWHIP Analysis 1
2 3
4 5
6 7
8 9
10 1
10 051.5 in. =515 in.
Figure 5.10
PWHIP Nonlinear Analysis o
Mid-Span (Node 6) Displacement Relative to Ground (NUE: Math Model is shown in Figure 5.10.)
0 C3 0
C>
00 O0 O 0
O I B I
Time (sec) 01-0590-1135 Figure 5.11 Page 51 R#-IisiIn 0 1
PWiljP Anal o
End Moment (Node 11)
(Note:
Math Model is shown in Figure 5.10) oF II3' Linear Analysis C!
I Nonlinear Analysis yield momnent I'
II (62,200 lb-in)
"'A I
I 00 I
O Tes yield nonent
~~'
(62, 200 1b-in) 0 5.12,
- a 52 Oi I
(9 I
'1i 0I Revision y0elguneo5.n2 Pae5
ANSYS Analysis cono Moment in Elbow from Node 39 to 40 (Note: Math Model is shown in Figure 5.9) 24000 ac()
If000 8-6000 M
-24000
-3200C
-40000
-4a000 lilillik IfulE
.,a
.40
.00 1.0 1.60 2.00 2.40 2.f00 3.20 3.60 4.00 fCt0/NC NINE.9 PIPE ANALYSIS N S 01-0590-1135 Figure 5.13 Revision 0 Page 53
Itment at Anchor Node 51 soooo (Note: Math Models are shown in Figures 5.9 and 5.10)
PWiIP Analysis (Node 11) 75000 ANSYS Analysis 60000 45000 m
By I5000 L.-
B-M 15000 I
J J
-30000
-45000
-60000
.00
.40
.00 1.20 1.60 2.00 2.40 2.00 3.20 3.60 4.00 CfE0/NONLINEqR PIPE ANALYSI S 01-0590-1135 Figure 5.14 Revision 0, Page 54
01-0590-1135 Revision 0 Page A-1 APPENDIX A COMPUTER PROGRAM DESCRIPTIONS