Marco de trabajo de COBIT

method for developing in structure spectra by scaling can be derived from random vibration theory. This is the basis for so called direct generation computer codes. However, inherent in the random vibration analysis, is a scale factor that is applied to the RMS response to obtain peak response. This scale factor often results in very conservative in-structure response if the absolute value is taken. A scheme to scale in-structure spectra that has been used successfully is to

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

compute in-structure spectra using random vibration theory for the original DBE ground motion spectra, and for the new UHS ground motion spectra. The ratio of these two in-structure spectra at different frequencies can then be used to scale the DBE in-structure response spectra to represent in-structure spectra for the UHS. The mathematical description of this process is contained in Appendix B. The process is most easily carried out using a direct generation computer code, but may also be done on a spread sheet using eigenvalues for modes of the most interest.

For this study we used a typical UHS for eastern US sites. The UHS has a peak ground acceleration of 0.1g compared to the 0.05g DBE but the peak occurred at 20 Hz as opposed to the 2.5 to 9 Hz amplified acceleration range for the RG 1.60 DBE spectrum. Figure A-10 compares these two spectra. Above 5 Hz the UHS spectral amplitudes are higher. Thus we would expect that high frequency modes would be greatly amplified by the UHS whereas there was not significant amplification for the DBE ground motion spectrum.

Figures A-11 and A-12 show the node 11 responses to the DBE and the UHS using the random vibration procedure described in Appendix B. The higher mode at about 18 Hz is highly amplified by the UHS. The ratios between these two spectra are shown in Figure A-13. These ratios, as a function of frequency, can then be used to scale the DBE in-structure response spectra. Figure A14 shows the scaled DBE spectrum to represent response to the UHS.

This method can be used if the participation factors and eigenvectors are available. In some cases, only frequencies and participation factors are tabulated in design reports. However, from the shape of the in-structure spectra and the participation factors, one can deduce the modes that are contributing significantly to response and to the shape of the in-structure spectra. If scale factors are developed at these significant modes and used to scale the DBE spectra, the resulting in-structure spectra for the UHS should be a reasonable approximation of UHS in-structure response spectra. This sample scaling might be considered applicable to capability Category 1 of the Standard. The next step was then to do this simple scaling for node 11 in the X direction and compare the results to the more rigorous scaling results.

If we examine the DBE spectrum for node 11, direction X, Figure A-2, we observe that the mode driving the peak of the spectrum occurs at about 6.6 Hz. This is mode 1. It then appears that there is another mode or modes less than 20 Hz that contributes to response. Examining the participation factors for the X direction we find that mode 6 at 18.5 Hz has a high participation.

Only modes 1 and 6 have significant participation. We would then select these two frequencies to scale the DBE spectrum. By comparing the UHS and DBE spectra in Figure A-10 at these two frequencies the resulting scale factors are:

Frequency Hz UHS Sa (g) DBE Sa (g) Scale Factor

6.6 0.16 0.136 1.18

18.5 0.24 0.077 3.12

The broadened DBE spectra from 5.8 to 7.2 Hz in Figure A-2 are then scaled up by the 1.18 scale factor determined at 6.6 Hz. At frequencies significantly below the broadened peak

frequency the UHS exhibits lower spectral acceleration than the DBE and the amplified peak can

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

conservatively be fared into the DBE spectra. From about 12 to 20 Hz the DBE spectra in Figure A-2 are flat. This is a result of broadening the peaks and smoothing. The scale factor of 3.12 should be applied to this part of the spectra. Between the broadened peak and 12 Hz the spectra should be fared using the same general shape as the DBE. The DBE zero period acceleration at 33 Hz should be scaled up by the ratio for the 6.6 Hz fundamental mode and from 20 Hz to 33 Hz the spectra should be fared.

This simple scaling is also plotted on Figure A-14 for comparison to the more rigorously scaled spectrum. As can be seen, the simple scaling results in conservative spectra through the

frequency range of interest. The zpa for simple scaling is about 15% lower than for the more rigorous scaling. Since the seismic issues are primarily with flexible equipment, the slightly lower zpa is of no consequence. Note that in Figures A-6 and A-7, the spectra from the recreated model were higher at about 18 Hz than the DBE spectra. This is also shown in Figure A-9 comparing the time history results using the eigensolutions to the DBE design spectrum.

However, when the simple scaling is done as shown in Figure A-14, the large scale factor at 18 Hz overcompensates for this and the resulting scaled spectra are conservative except in the rigid range.

This example of simple scaling for a case where more than one mode has significant response may be extended to address other cases of a dominant single mode or multiple modes of response.

The scaling process using the original eigensolutions and random vibration theory is considered to be acceptable for capability Category 1 and 2 of the Standard, when limited to fixed base models. The simplified Scaling based on identifying important modes by participation factors and spectral peaks is considered to be reasonable for capability Category 1 for fixed base models.

However, the analyst must be reasonably confident that the original analysis and resulting spectra to be scaled are realistic. In this case, they were shown to be conservative at the peak and slightly unconservative at higher frequency.

A.4. References

A1. EPRI NP-6041 SL, “A Methodology for Assessment of Nuclear Power Plant Seismic Margin (Revision 1),” EPRI, Palo Alto, California 1991.

A2. SAP 2000, “Three Dimensional Static and Dynamic Finite Element Analysis and Design of Structures,” Version 7.4, August 2000, Computers and Structures Inc., Berkeley, CA.

A3. Regulatory Guide 1.60, “Design Response Spectra for Seismic Design of Nuclear Power Plants,” US Nuclear Regulatory Commission, 1973.

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-1

Lumped Mass Model of Reactor Building

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-2

Reactor Building EQ Floor Spectra, Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-3

Reactor Building NS Floor Spectra, Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-4

Reactor Building Vertical Floor Spectra, Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-5

RG 1.60 Spectrum Compatible Time Histories

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-6

Reactor Building E-W Floor Spectra Reconstructed Model, Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-7

Reactor Building N-S Floor Spectra Reconstructed Model, Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-8

Reactor Building Vertical Floor Spectra Reconstructed Model, Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Design 11X

11X Modal Response @7%

Figure A-9

EW Floor Response Spectrum Developed From Eigensolution of DBE Analysis, Using RG 1.60 Time Histories

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

UHS

DBE

Figure A-10

Comparison of DBE with UHS

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-11

RB – Estimated SDOF Oscillator Response – Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-12

RB – Estimated SDOF Oscillator Response – Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Figure A-13

RB – UHS Scale Factors – Node 11

Benchmark Studies to Verify an Approximate Method for Spectra Scaling

Rigorous Scaling Simplified Scaling

Figure A-14

Scaled DBE Spectra – Node 11

B

DEVELOPMENT OF IN-STRUCTURE RESPONSE