ML20247B638
| ML20247B638 | |
| Person / Time | |
|---|---|
| Site: | Catawba  |
| Issue date: | 05/10/1989 |
| From: | DUKE POWER CO. |
| To: | |
| Shared Package | |
| ML20247B634 | List: |
| References | |
| CCCE-89-022, CCCE-89-22, NUDOCS 8905240184 | |
| Download: ML20247B638 (108) | |
Text
_ - - _ - _ - _ _ _ - - - _ - _ _ _ _ _ = _ __ ._ _-_ - - .. -_ . _. _ _ _ _
J CCCE-89-022 l
CATAWBA NUCLEAR STATIL.
DIRECT GENERATION OF RESPONSE SPECTRA Introduction The Catawba FSAR Section 3.7.2 describes the procedure for developing in-structure floor response spectra. This procedure utilites the time history analysis by considering four artificial time histories which envelope the #
design response spectra (ground response spectra). Methods, other than the I
time history analysis, are available, recognized and valid for this purpose.
Proposed revision 2 to Standard Review Plan (SRP) 3.7.2 Section 3.7.2.I.5, Development of Floor Response Spectra states:
"There are several methods for generating in-structure response spectra. One method makes use of time history analysis by considering a single. or multiple (real or artificial) ground time histories which, essentially, envelope the design response spectra. Another method involves a group of analysis ,
techniques, gener e.lly, referred to as the direct solution methods for the t generation of in-structure' response spectra. These techniques do not involve time history analysis. The basis and justification for the use of either of the above methods are reviewed."
The acceptance criteria for the direct solution technique is found in SRP Section 3.7.2.II.5, as follows:
"The use of direct solution methods is reviewed and accepted on a case-by-case basis. A demonstration of adequate theoretical basis and adequate comparisons of spectra (for selected representative locations) obtained from the direct solution method and the time history approach is required."
I l
Duke Power Company proposes to use a direct generation method to generate in-structure response spectra at Catawba Nuclear Station. The computer code used is called Equipment Dynamic Analysis Package (EDASP) . A number of submittals have been made by Duke Power Company to the NRC which describe this method and satisfy the areas normally reviewed under Standard Review Plan 3.7.2. The submittals, listed by date, are:
February 24, 1988 Initial Submittal July 5, 1988 Response to Additional Information Request September 16, 1988 Response to Additional Information Request October 27, 1988 Response to Additional Information Request i November 1 1988 Response to Additional Information Request November 21, 1988 Response to Additienal Information Request Two areas in the acceptance criteria with respect to the above referenced submittals will be reviewed and summarized in the discussion that follows.
8905240184 890510 <
PDR ADOCK 05000413 >
P PNU
v Demonstration of Adequate Theoretical Basis The theoretical basis of the technique is discussed in NUREG/CR-3480, which
-includes a general discussion of direct generation methods as well as comparisons between the method developed by Singh (Ref.1, 2) and time-history results. The concept of a spectrum-consistent power spectral density function was used in the development.of the Singh~ method. NUREG/CR-3480 states that the " method produces excellent, consistent. and repeatable results as compared .
to time-history approaches." It also notes that direct generation methods are
" Based upon sound theoretical backgrounds and are suitable for adaptation on .
computers."
The methods used in EDASP are based upon'the use of a spectrum-consistent power spectral density function. The basic equations and fundamental concepts -
used in EDASP are the same as those used by Singh. The procedures used in.
EDASP are identical to those recommended in NUREG/CR-3875, which were verified in 'the EDASP Theory and Verification Manual (Ref. 3) .
A copy of the EDASP Theory and Verification Manual (which also serves as a QA manual) was provided to the NRC on September 16,.1988.
A discussion of how the EDASP direct generation method compares to other direct generation methods and the limitation of the computer code is provided by Stevenson & Associates, on the following pages.
2 i
I COMPARISON OF EDASP WITH OTHER DIRECT RESPONSE SPECTRUM GENERATION METHODS INTRODUC"TTON Duke Power Company used the computer program EDASP of Stevenson & Associates to generate floor response spectra for the snubber reduction program in the Catawba Nuclear Station. During the NRC meeting on July 19, 1988, NRC has raised questions concerning the validity of the EDASP direct response spectrum seneration technique and how does it compare with other direct generation methods.
To answer these questions, the theoretical background of EDASP will be reviewed first, then followed by the comparison with other direct generation methods.
EDASP THEORETICAL BACKGROtJNQ To generate the elevated response spectrum (RS) from the base RS, EDASP performs the following three step:
(1) Convert the base RS into power spectral density function (PSD), =
(2) Calculate the elevated PSD, and (3) Convert elevated PSD to elevated RS.
The direct generation process in EDASP involves two major components, the RS/PSD , l conversion, and the computation of the elevated PSDs. The calculation of elevated PSDs will first be described.
The governing equations for a structural system subject to base excitation is:
( Af ]g + (C]r + (K]r, = -[M][Tle. (1) where (M).(C].and [K] are the mass, damping, and the stiffness matrices of the system, (T]is a N x 3 transformation matrix containirig the directional unit vectors for each degree of freedom, and u is a 3 x 1 vector containing the transnational base acceleration motion in three orthogonal directions.
Applying the modal transformation results in N decoupled equations:
a , - 2 4,w a , + w'a , = - f. , r,, d ,
l
~l
F i
whers r. is the participation factor of the ith modal system response due to base excitation in the kth direction.
Using the definition of
- ' I3)
- ,(w)=
w a w a+ 2it.w.w the response can be written (in the frequency domain) ac x.(W) * [ $.,#,(w)[ r,,d,(w) (4) where d,(w) is the Fourier transform of the base acceleration history in the kth direction.
Assuming the base motion input is a zero-mean stationary Gaussian random process, it
- can be represented by its acceleration power spectral density function alone. Pre-multiply both sides of Equation (4) by the complex conjugate of x.(w)and taking the ensemble average yieldt S,,,(w)- [ [ +,,6,,#,(w)#,'(w) { [ r,,r,,d,(w)g,' (w) (5)
. a s .
where the
- signifies the complex conjugate. Assuming the base excitations in all three directions to be uncorrelated allows the cross terms in the second double summation of Equation (5) to be ignored:
S,.,(w) . [ [ 6,,6,,#,(w)#,'(w) { r,,r,,s, ,(w) (6)
Equation (6) can be separated into its diagonal and cross-term components.
S,,(w)= 6,l#,(w)l' 8
r,8, S,. ,(w)
- 2 6,,6,, R e (#,(w)N'(w)} r,,r,,S,,(w)
Equation (7) represents the relative acceleration of the kth d base. The absolute acceleration response can be shown to be:egree o 9
Su
,,,3,,(m) - S,,,(w) . ( !
- 2 r., $,, R e (#,(w))]3, ,
g where r is tha global direction coincide with k.
between all the modes and, instead ,
of working ps ncludes full coupling on spectrum the rigid range. The elevated RS willrrection e reproduce in the modes in the frequency range of interest, even when i.e.,thsre whenare nothe structure The RS/PSD conversion equations will be derived in the follo i distribution of the maxima for a random process w ng section, se iswhere derived the ba d i probability of exceedance. The derivtuon pect to a follows mai Cartwright and Longuett-Higgins (2), and Kaul .
works (51of Rice (7],
Consider (f. / * , / ") is a zero-mean Gaussian randon rprocess ,
a f(t) the joint p ob b ty distribution of p(g ,, g,, g,) . I expf. N (** b 2*2IiI8**"I (2n)8'8(Am )"8 12m
,)k a
where (9) a .m m.-mj S
o
i i
- l l
~
)
l a
m = f".H(p.w)S(p)p dp = the nth spectral moment of the PSD S(p) 1 l
H(p,w)= **4*
(p * - w")*
- 4w*ttp3 l
The mean frequency for /(f) to be a maxima in the range (, < / < ti.dt, is f(4,)dt,-f (p(ti.0.(3)l4 ldt,Jdt, (10) 1 and the probability distribution of maxima is found by dividing this distribution by the total mean frequency of maxima, which is l
N,=f,.f,,.p(ti.0.(3)ltaldtid t, (II)
Substituting Equation '.9) into Equations (10) and (11), the probability distribution of the maxima is p(y) - - (12) v 2nm. .
s E(q/s) + a s E(q)f.. E(u)du, ,
in which I
E(u)= exp s
lu 2 .s 8 (I3) 9 " y/b (14) s' = 1 -mj/(mem.) (15) a = q/(1 - sa )t's (16) i I
The cumulative probability Q(y)is given by Q(y ) - -==g==
v(2n).fv.. E(u)du + 4(1 - s') E(q)f,, E(u)du.
t
l ..
?
1 .
Kaul(5) has shown that for large values of riand small s, which is true for taost cases, Equation (17) can be approximately written as Q(y)= V(1-s*)exp(-f q )
8 (II)
Consider a finito duration T of the random process. The expec:ed number of maxima in time T is given by N = f(m,/ma )"*T (I9)
The probability that the highest of these maxima in a sample of duration T having the value y as P(y.)= A dy[ t - Q(y))"
(20)
Define the response spectrum R(w)as the maximum response in duration T with probability.of exceedances of r, therefore r = ((P(y.)dy.= 1 -[1 -Q(R))" I2I) whence Q(R) = 1 -(1 -r)"" (22)
For large N we can write
- J I }
Q(R)=
s N>
In(1 -r)
Using Equations (14), (17), and (23) gives the response spectrum value at the osciMator frequency ua
i l
I -n (24)
R(w) = {-2me ln y(m /m )"81n(1-r)}i"8 e a
~ . . .
The deterucWon of RS from the PSD is straight forward using Equation (24). This is not true of the inverse problem in which one requires to obtain the PSD from its RS. In EDASP. the approximate solution derived in Kaul [5] is utilized as the initial guess. The approximate solution is based on the assumption that the acceleration exceedance level is high, i.e., the probability of exceedance is low, and that e is not too close to 1. The initial solution for the FSD is S(m)- 8 in(1-r) f }
- (w)/f-2in The above derivation is based on a random process with infinite duration. In reality, depending on the damping values of the system, within the duration of an earthquake, e the system may not be able to reach the steady state response. To correct for this finito duration problem, EDA $P uses an equivalent damping q. which is related to the actual damping 4 by the equation [8}
t,- 4 + 2/(w7)
(26) i ne computation of PSD from RS in EDASP following iteration process fR *8 (27) 3(w) . , - S(w).j g(w))]
where the hat indicates the ith estimate. The current PSD estimates are adjusted by the square of the ratio of the response spectra until a prescribed convergence bound is met or the maximum number of iterations is reached. The iteratiota process converges to a steady response spectrum very rapidly.
Ditt tMKTONS OF TMF FDASP DIR Fr'1" GENER ATION MFTHODR
\
Since the direct generation method used in EDASP is based on general random vibration theories, it works in general for any frequency range, damping ratio, or earthquake characteristics.
One limit, concerning the validity of the equivalent damping equation in Equation (26),
the lowest frequency in the analysis should be at least several times the inverse of the duration of the seismic event.
The accuracy of the method, however, depends on the validity of the assumptions of the random process, such as stationarity, linearity, and the normal probability distribution properties forfaussian process, in our experience with EDASP, as well as in refer-ences Chen (3)r Kaul (5), Unruh (15,16), and Singh [13), the direct generation method has achieved comparable but more stable results than the time history method for a wide variety of acceleration time histories.
COMPARTRAN TO OTHER DrRFfT GENER ATf0N MFTHOIM Blame (1971) fil Kanur and than (1971) fd1 These early methods are semi-empirical in nature. In general they do not produce as ,
accurate results as the newer methods.
tinah (1975.19R0.1985) fil-131 Singh has developed the partial fraction form for the transfer functions and input PSD ,
to evaluate the elevated PSD. The peak factor was not evaluated and has been taken as a constant the PSD/RS conversion process, hreke and Gaenarini (1976) fl0.171 Professor Vanmcrcks has developed computer program SIMQKE for generating artificial time histories. The RS was converted to PSD first and then time hiatories were gener- I ated by adding random phase an61es and an envelope curve. The conversion procedure I of RS to PSD in SIMQKE is simdar to the direc? generation method in EDASP.
Recommended initial guess of PSD from RS to bc I * * **
C(w.) =
w,( *1;,- 1 ) L r -[* G(w)dw >
Suggested the iteration scheme used in EDASP, Equation (27). Suggested effective damping value as:
l l
l L
l l
E. - ( 1 - e'"*)" t !
K aul (197R) f 51 I 1
J Provided derivation for the PSD/RS conversion equations. Proposed an approximate and an exact (so-called) solutions to determine the PSD from RS. The approximate solution is implemented in EDASP, in which iterations were added. The exact solution consists of fitting multiple analytical functions to the PSD, where the form of the base functions remains to be verified.
8:nndararnian (198!) f f(1 The solution method is identical to that in EDASP.
Ifnruh and Kane (1981m 1981b) f15 161 The RS/PSD conversion implementation is identical to that of EDASP, in that the approximate initial solution derived by Kaul is used, iteration based on Equation (27),
and artificial damping in Equation (26).
- K iures hian heleman. and Naur Omid (1921) f61 Solved the, mass interaction problem of light equipment in structures. As for the direct generation of RS, only the mean value of peak response were examined. '
Rhinnvules Machin_ mnd hearma (19aa) r_91 Professor Shinozuka used the Vanmarcke method (SIMQKE) to generate the PSD, except that the exponent in the iteration process, Equation (27), from 2 to 2.5. The PSD generated is very similar to that of EDASP.
An alternate procedure is suggested to fit a Kanai-Tajimi form of curve to the PSD.
The Kanai-Tajimi forv is initially proposed for seismic PSD in Japan on a specific site.
The forts is simple to amplement and easy to derive close form statistical properties for the responses. However, most required response spectra are of the composite type, i.e.,
they are enveloped or broadened, like the NRC 1.60 response spectrum, which may be too complicated for a single Kanai-Tsjimi spectra to simulate. It might be more appro-priate to employ multiple Kanai-Tajimi functions similar to the exact solution of Kaul.
Chen (1988) r31 Chen uses the initial guess and artificial damping of Vanmarcke. The iteration process is performed directly on the initial guess.
I cONCLESTONS
Encept for the early semi-empirical methods, the direct generation methods for calculat-ing the elevated R$ from the base RS are based on rigorous random vibration theories.
Due to the satistical uncertainty of the input time history, the results from the direct generation method may not always match with the corresponding time history method.
The direct generation methods will match up better with the time history method statis-tically if a number of time histories were used to generate the response spectra.
The time history method is accurate only if the enact acceleration time history will occur in the future. In reality, the exact time variation is never known, and all we have is the statistical estimates of the seismic events. The direct generation methods, using the PSD as the intermediate step, provides more consisteet results than using the time history alone.
These direct generation methods are all derived from the same theoretical basis, they should all produce similar results. The difference lies in details of implementation, spe-cifically, during the RS to PSD conversion, the initial guess of the PSD from RS, the ,
iteration scheme, the effective damping value, and the numerical integration scheme.
REFER FNCE!L
- 1. Biggs, J. M., " Seismic Response Spectra for Equipment Design in Nuclear Power li Plants," Proceedings,1st International Conferosce on Structural Mechanics in Reac-tor Technology, Berlin, West Germany, September 1971, Paper K4/7. .
- 2. Cartwright, D. E. And M. S. Longuett-Higgins, "The Statistical Distribution of Marima of a Random Function," Proceedings of the Royal Society of London, Series A, Vol. 237,1956, pp. 212-232.
- 3. Chen, S. J., "A Practical Application of Spectrum-Consistent Power Spectral Density Function in Seismic Response of Structures," Proceedings of laternational Workshop on Seismic Design, Taipei, Taiwan, May 1988.
f
- 4. Kapur, K. K., And Shao, L. C., " Generation of Seismic Floor Response Spectra for Equipment Design," Proceedings, Specialty Conference on Structural Design of Nuclear Plant Facilities, Chicago, I111acis, December 1973.
- 5. Kant, M. K..Seochastic Characterization of Earthquakes Through Their Response Spectruan," Earthquake Engineering and Structural Dynamics, Vol. 6,1978, pp.
497-509.
- 6. Kiureshian, A. D., Sackman, J. L., And Nour-Omid, B., " Dynamic Analysis of Light Equipment in Structures: Response to Stochastic Input," Journal of the Engi- l neering Mechanics Division, Proceedings of the American Society of Civil Engi-neers, Vol 109, No.1, February 1983. j
- 7. Rice, S. O., " Mathematical Analysis of Random Noise," in Selected papers on Noise and Stochastle processes, Ed. N. Wax, Dover, New York,1954.
1
- 8. Rasenbleeth, E. And Elorduy, J., " Response of Lineer Systems to Certain Transient Disturbance," Proceedings, Fourth World Conference Earthquake Engineering, San-tiago, Chile, A-1,1969, pp.185-196.
j
- 9. - Shinoruka, M., Mochio, T., And Samaras, E. F., " Power Spectral Density Functions 1 Compatible With NRC Regulatory Guide 1.60 Response Spectra,' Department of Civil Engineering and Engineering Mechanics, Columbia University Report No.
NUREG/CR-3509, June 1933.
- 10. "SIMQKE: A Program for Artificial Motion Generation, User's Manual and Docu-mentation," Department of Civil Engineering, Massachusetts Institute of Technology, November 1976.
!!. Singh, M. P., " Generation of Seismic Floor Spectra *, Journal of the Engineering Mechanics Division, Proceedings of the American Society of Civil Engineers, Vol 101, No. EMS, October 1975.
- 12. Singh, M. P., " Seismic Design Input for Secondary Systems," Journal of the Stros-tural Division, Proceedings of the American Society of Civil Engineers, Vol.106, No. ST2, February 1980,
- 13. Singh, M. P., " Floor Spectra for Nonclassically Damped Structures," Journal of the ,
Structural Engineering, Vol. I11, No. I1, November 1945.
- 14. Sundararajan, C., "An Iterative Method for the Generation of Soisanc Power Spec-tral Density Functions," Proceedings, Civil Engineering and Nuclear Power, Knox-ville, Tennessee, September 1980 Vol. VI.
- 15. Unruh, J. F. And Kana, D. D., "An Iterative Procedure for the Generation of Con-sistent Power / Response Spectrum," Nuclear Engineering and Design, Vol. 66, 1981, pp.427-435.
- 16. Unruh, J. F. And Kana, D. D., 'A Power / Response Spectrum Consistent Procedure for Dynamic Qualification of Components," Southwest Research Institute, Interim Report, SwRI Project No. 02 9290, March 1981.
- 17. Vanmarcke, E. H. And Gasparial, D. A., "$1mulated Earthquake Ground Motions,"
Proceedings, 5th International Conference on Structural Mechanics in Reactor Tech-aclogy, Berlin, West Germany, September 1977. Paper Kl/9.
t I
em
- c Comparisons of Spectra Obtained for the Direct Solution Method and the Time History Approach The EDASP ' Theory and Verification Manual (Ref. 3) provided detailed comparisons between EDASP PSD generated response spectra and those generated by a_ time history method.
The test problem used in the EDSAP Theory and Verification Manual was an eight noded eccentric. frame. Modal analyses and time-history analyses were performed using the STARDYNE finite element computer code. Ten separate response spect:a analyses were performed using a' variety of input excitation directions and combinations. In each case the direct generation results showed an excellent agreement with the time-history results.
To illustrate further justification for the direct generation method a comparison is made between the direct generation method and the time history method. To provide the comparison a 0.5% damped response spectrum is generated from an artificial time history (one of the four Catawba artificial time histories). This response spectrum is then used as input to-the direct-generation method. The structure used for the comparison is the reactor building interior structure. The same seismic analysis model is used for both methods. Floor response spectra are generated at 0.5% and 5% critical damping.
at the following mass points:
Mass Point Elevation (ft + in) 3 562 + 0 7 595 + 4 11 628 + 8 15 662 + 0 19 691 + 2 21 713 + 1 The comparison of responses found in Table 1 contains information as follows:
Frequency columns: The EDASP column gives the frequency at which the acceleration (under the heading TH-EDAS) is computed.
The T.H. column under frequency lists frequencies near those used by EDASP for which responses were computed by the time history analysis.
Acceleration columns: The T. H. (AVE) column gives the acceleration for the frequency from the time history seismic analysis of the reactor building interfer structure, l
The TH-EDAS column gives the acceleration for the frequency developed from the EDASP program for the site ground response spectrum plotted from the time history.
(
13 l.-
-- _ _ _ _ _ - _ _ _ _ _ _ _ - _ _ = - _ _ - _ _ - _ _
Comparison of accelerations (peak and ZPA) for floor spectra generated by the time-history method and the direct generation method using the same response spectrum at the base of the structure is given below. (A positive sign indicates the direct generation results are larger):
Elevation % Peak Change % Change At (ft + in) ZPA (20 HZ) 0.5% 5% 0.5% 5%
562 + 0 +1.8 NA +4.5 NA 595 + 4 +5.1 +13.0 +30.0 +6.9 628 + 8 +7.6 +15.8 +23.8 +2.4 662 + 0 +9.4 +17.6 +5.7 0.0 691 + 2 +10.4 +17.6 +3.2 +3.2 713 + 1 +10.8 +17.5 +11.6 +4.3 The data presented in Table 1 is also provided in graphical form in Figure 1.
The curves generated by the direct generation method shown results were conservative at the peaks particularly for the 0.5% curves. There is more variation away from the peak, but the direct generation method produces conservative results. The direct generation method using the EDASP program provides acceptable elevated response spectra for seismic design. Use of the direct generation method is also consistent with the recommendations in MUREG/CR-1161, " Recommended Revisions to Nuclear Regulatory Coomission Seismic Design Criteria".
Time History Comparisons Including High Frequency Energy Content Two additional time histories were chosen with different energy content to generate comparison spectra between the time history method and direct generation method.
The first time history was developed for Duke Power's Cherokee and Perkins projects. This earthquake envelopes the RG 1.60 spectra and includes significant high frequency content (Figure 2 titled "P81 Earthquake used for Comparisons"). The second time history was recorded during an actual earthquake. It does not envelop RG 1.60 but it has a high frequency centered at 20 Hz. (Figure 3 titled " Alternate Earthquake used for Comparisons").
Duke Power was not able to write or acquire the sof tware necessary to compute a power spectra directly from time history; therefore it could not be determined if either of these two time histories were acceptable under SRP 3.7.1, proposed revision 2. Duke Power is confident that comparisons using these two earthquakes adequately addrens concerns about the high frequency performance of EDASP.
Response spectra were computed at 0.5% and 5.0% damping for six floor elevations in the Catawba reactor building using STRUDL time history methods I
and EDASP power spectra methods. The EDASP PSDs were estimated from the P81 l
spectra and the Alternate spectra at 5.0% damping. See Figure 2, sheet 2 and Figure 3, sheet 2.
l l
14
)
L __ _ _ _ _ . _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ - _ _ - _ _ _ _ _ _ _ _ _ -
+
Comparisons of acce:erations using the P81 earthquake show that the EDASP spectra are consistent with the time history spectra. See Figure 4. In general, the EDASP spectra run along the center of the time history spectra in the low frequency range (0.2 Hz. - 5.0 Hz.) and exceed the time history spectts in the high frequency range ( 5.0 Hz.). Tabulated comparisons are provided for 0.5% and.5.0% damped spectra at elevations 628 + 8 and 713 + 1..
See Table 2. Comparisons using the Alternate earthquake show that the EDASP '
spectra consistently meet or exceed the time history spectra at a most points over the entire frequency range. See Figure 5.
Comparisons with Actual Earthquake and Time History Analysis for the Perry Containment A comparison was also made of the results from the direct generation method, time history method and an actual earthquake record information was received on the Perry containment stick model from Gilbert / Commonwealth. Inc. and the base mat recorded time histories from Stevenson & Associates. This information was used to perform an analysis similar to the one performed in Appendix A, paragraph A.2.1 of Reference 1. In that section, Gilbert / Commonwealth compared their analytical response spectra at elevation 688' + 6" of the Perry containment stick model with the recorded response spectra at elevation 686'. Figures 6 and 7 show the results.
The Perry containment model (natural frequencies, mode shapes, & nodal masses) was entered into EDASP and the base mat time histories were applied to the model. Response spectra in each direction were computed at the base of the model and at elevation 686' + 6" of the containment using time history analysis. The results of this and the Gilbert time history analysis were compared as a baseline check of the input time history and containment model.
Figure 8 shows the base mat response spectra along with the elevated (elevation 688' + 6") spectra computed by Gilbert / Commonwealth (from Figure 7) and the elevated spectra computed by Duke Power using time history analysis.
The base mat spectra compared well with the recorded base spectra shown in Figure 6. The elevated response spectra also compared well, showing similar frequency content and only slightly different peak responses. These comparisons showed that Duke was using the same base time histories and containment model as Gilbert.
Base Power Spectral Densities were computed from the base response spectra shown in Figure 8. The PSD's were then applied to the containment model and response spectra were computed at elevation 686' + 6". Figure 4 shows plots of the elevated recorded response spectra (from Figure 6 A.1, A.2, & A.3), the Gilbert / Commonwealth time history generated response spectra (from Figure 7),
and the Duke Power PSD generated response spectra. These figures shown that the PSD generated results compare at least as well as the time history results to the recorded spectra. This is in agreement with Duke's previous subrittals which showed that the PSD technique compared favorably with tire history techniques.
15
It is recognized that there are significant differences (particularly in the North / South direction) between the analytical response spectra and the recorded spectra. It is apparent that the error is due to the analytical model and not due to the analytical technique. This conclusion is supported by the fact that both the time history method and the direct generation method computed similar results. If either technique was required to more closely match the recorded spectra, a more detailed and complete model would be necessary. This model would need to include any factors significant to the seismic response of the containment including the soil characteristics and the soil-scructure interaction, details of the containment structure, information concerning structural loads and attachments on the containment, potential secondary systems interaction, and many others.
During the post earthquake evaluation, Gilbert / Commonwealth reviewed the containment structure and analytical model ard were unable to determine any reasons for the response spectra deviations. It would take months of analysis and investigation to review all of the potential factors. While this may be an interesting project for a national laboratory, it is beyond the scope of reviewing the EDASP response spectra generation technique.
Investigation of Structural and Response Spectra Damping The sensitivity of the EDASP Code to higher damping values was also investigated.
Two damping parameters were investigated; the structural damping and the response spectra damping. Response spectra were computed for two points in the Catawba auxiliary building with structural damping values from 3% to 7%
and response spectra damping values ranging from 0.5% up to 15%. The PSD computed from the P81 earthquake was used as input (Figure 2, sheet 2). The plots in Figure 10 show the results. The spectra show a good and consistent comparison over all three structural dampings (3%, 5%, 7%) and all three response spectra dampings (0.5%, 5%, 15%). No particular trends were noted with increasing structural damping or response spectra damping.
References:
- 1. M. P. Singh " Generation of Seismic Floor Spectra," Journal of Engineering Mechanics Division, ASCE EMS (October, 1975).
- 2. M. P. Singh, " Seismic Design Input for Secondary Systems", ASCE Mini-conference on Civil Engineering and Nuclear Power, Session 11, Boston, Massachusetts, April,1979, Volume II.
- 3. EDASP Version 1.1 Theory and Verification Manual. Stevenson & Associates, Woburn, Massachusetts, September 1, 1986.
4 The Cleveland Electric Illuminating Company Perry Power Plant Confirmatory Program of the January 31, 1986 Ohio Earthquake Effect, Gilbert / Commonwealth Report No. 2632, June 16, 1986, Docket Nos. 50-440; 50-441.
- 5. J. F. Unruh and D. D. Kana, "An Iterative Procedure for the Generation of Consistent Power / Response Spectrum".
16
4 Comments on NUREG/CR-3509 as Related to Duke Power's Discussions with the NRC Staff on Direct Generation of Response Spectra Proposed revision 2 of the Standard Review Plan Section 3.7.1 requires that design time histories produce a PSD that envelop the Kanai-Tajimi form developed in NUREG/CR-3509. The same section however, also states the following:
"For the cases where design response spectra do not correspond to RG 1.60 spectra, the target PSD function corresponding to the design response spectra and the demonstration of adequate energy in the frequency range of the interest are reviewed on a case-by-case basis.
(a number of techniques, e.g. Refs. 7, 8 and 9, are available to generate a PSD function consistent with a given response spectrum)."
Reference 8 ("An Iterative Procedure for the generation of Consistent Power / Response Spectrum" by J. F. Unruh and D. D. Kana) is the same process implemented in the EDASP program. Therefore, PSDs generated using EDASP i would be appropriate target PSDs.
Figures 11 and 12 show a comparison of the Kanai-Tajimi PSD with an EDASP generated PSD from RG 1.60 response spectra. Figure 11 shows the comparison in a semi-log format similar to NUREG/CR-3509. Figure 12 shows the comparison in a log-log format which permits a more complete evaluation. Each figure shows that the EDASP PSD is higher in the low frequency range and lower in the high frequency range.
Using the PSD/RS transformation in EDASP, the recommended Kanai-Tajimi PSD was transformed into response spectra. Figures 13, 14, 15 show the comparison of the Kanai-Tajimi derived response spectra with RG 1.60 spectra. These results show that the Kanai-Tajimi PSD is not consistent with RG 1.60 response spectra and therefore is not an appropriate target PSD for application in EDASP.
In general, the Kanai-Tajimi PSD appears to be too low (insufficient energy content) in the low frequency range and too high (too much energy content) in the high frequency range. The response spectra plots indicate that use of the Kanai-Tajimi PSD results in ground input requirements in the high frequency range in excess of RG 1.60. We do not believe it is the Staff's intent to require input levels above RG 1.60; therefore, the target PSD specified in NUREG/CR-3509 seems to be incorrect. Conversation with S. K. Shaukat indicates that the target PSD is being reconsidered by the Staff and a NUREG/CR will be published soon with the new requirements. It is expected that these new requirements will be consistent with current NRC input requirements.
17
__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ ____ _ i
4
Conclusion:
.The Standard Review Plan (proposed revision 2) requires that a direct generation technique demonstrate a valid theoretical basis and favorable results when compared to time history methods. Duke Power has provided the following theoretical basis for the code:
the EDASP Theory and Verification Manual, a comparison of the EDASP theoretical basis with that of other methods.
Procedures used in EDASP are identical to those recommended in NUREG/CR-3875.
Duke has also provided the following comparisons to time history analyses:
Compared EDASP PSD generated response spectra with time history generated response spectrc using one of the Catawba input time histories. These comparisons demonstrated a good correlation between the two analytical methods.
Compared EDASP PSD generated response spectra with time history generated response spectra using two input time histories with significant high frequency energy content. These comparisons demonstrated a good correlation between the two analytical methods.
Compared EDASP PSD generated response spectra with time history generated response spectra using structural dampings between 3% and 7%
and response spectra dampings between 0.5% and 15%. These comparisons demonstrated a good correlation between the two analytical methods.
Compared EDASP PSD generated response spectra with time history generated and actual recorded response spectra using the LeRoy Ohio earthquake and the Gilbert / Commonwealth Inc. containment stick model. This comparison showed that the EDASP response spectra matched the actual spectra at least as well as the time history spectra.
These comparisons have covered a variety of analytical models, input motions, structural dampings, and response spectra dampings. In each case, spectra ;
computed in EDASP compared well, if not exactly, with time history results. '
Duke Power believes that the Staff has been presented with sufficient documentation to review and approve the EDASP computer code.
18
1 A B uE: I. .S H T I c arisen er noe.en.e.:
Ofrect Generetten (EDASP) versus Time History 0.55 Critical Oesstnt et Elev. 562*0 Freouency (J) occeivation Frecuency (J) .acceleratten EDA 6p T. M. 7.N.(AVE) fl>60A5 . E0487. = f. N. T.N.(4WE) W f0A5 1.03 1.04 0.48 0.68 S.29 S.25 1.49 1.69 1.10 1.13 0.64. O.?$- S.50 S.41 ._ 1. 21 1.29 1.20 1.18 G.71 0.82 S.75 'S.73 0.80 0.96 1.30 1.32 0.62 0. 16 6.00 6.05 0.80 0.86 1.40 1.42 0.98 . 0,73 6.29 - 6.21 0.68 0.87 1.50 1.51 0.68 O.48 6.SG 6.53 0.79 0.af 1.60 1.61 0.76 0.98 6.75 6.68 0. 70 0.98 1.70 1.70 0.79 0.9s 7.00 7.00 0.88 0.93 1.00 1.80 0.90 1.12 7.25 7.32 0.81. 0.90 1.90' 1.89 1.00 . 1.21 7.90 F. 48 0.88 0.07 2.00 2.04 ' 1.03 1.14 7.75 - 1.80 0.64 8.87 2.10 2.09 0.94 ' 1.07 8.00 7.98 0.78 0.48 -
2.20 2.18 0.82 -1.19 8.90 8.44 0.86 0.88 :
2.30 2.32 1.07 1.29 9.00 9.07 0.70 0.81 2.40 2.42 1.10 1.25 9.90 9.98 0.62 0.70 2.50 2.52 1.03 1.23 10.00 9.87 0.62 0.73 2.60 - 2.61 1.01 1.26 10.90 10.39 0.61 0.64 2.70 2.71 1.10 1.33 11.00 10.90 0.62 0.64 2.88 2.80 1.20 1.31 11.50 11.62 0.51 0.67 2.90 2.90 1.04 1.23 12.00 11.94 0.51 0.62
- l. 3.00 2.99 0.88 - 1.17 12.50 12.57 0.48 0.S8
- 3. 15 3.14 1.12 1.22 13.00 12.09 0.47 0.54 3.38 3.34 1.06 1.30 13.50 13.$3 0.42 0.$2 3.00 3.46 1.09 1.25 14.00 13. 85 0.40 0.48 3.80 3.82 0.87 1.18 14.50 14.48 0.37 0.4l 4.00 3.98 0.93 1.20 15.00 15.12 0.30 0.43 4.20 4.14 1.18 1.31 16.00 16.07 0.25 0.39 4.40 4.46 1.19 1.35 17.00 17.03 0.23 0.30 4.40 4.62 1.10 1.of 17.45 17.35 0.22 0.35 4.to 4.78 1. f.7 1.61 18.00 17,99 0.23 C.33 S.00 4.93 1.41 1.72 20.00 19.09 0.22 0.23 1987 uncate 19
~
TABLEI SHT 2 e4. or . n...:
Co Of rect Generation (EDASP) Versus 7 fee History 0.55 Critical Desping 4t Elev. 595+4 Frequency (J) acceleration Frecuency (J) occeleratton
[0 Alp 7. N. 7. H. (4WE) 7M+(DAS [0 ASP 7. N.
T.N.(AVE) TH-(OA5 1.03 1.04 0.49 0.59 5.25 5.25 3.94 4. 12 1.10 1.13 0.65 0.77 5.50 5.41 2.84 4.14 1.20 1.18 0. 72 0.82 5,75 5. 73 1.63 2.10 1.30 1.32 0.43 0.77 6.00 6.05 1.09 1.32 1.40 1.42 0.60 0.74 6.25 6.21 0.77 0.94 1.50 1.51 0.70 0.09 6.50 6.53 0.61 0.44 1.60 1.61 0.79 0.98 6.75 6.88 0.54 0.61 1.70 1.70 0.81 1.01 7.00 7.00 0.54 0.59 1.80 1.80 0.93 1. 16 7.25 7.32 0.61 . O.58 1.90 1.09 1.13 1.28 7.50 7.44 0.54 0.58 2.00 2.04 1.08 1.19 7.75 7.88 0.50 0.40 2.10 2.09 0.99 1.12 8.00 7.98 0.57 0.62 2.20 2.18 0.88 1.26 8.50 8.44 0.48 0.6 2.30 2.32 1.14 1.37 9.00 9.07 0.68 0.64 2.40 2.42 1. 18 1.34 9.50 9.55 0.58 0.65 2.50 2.52 1.01 1.32 10.00 9.87 0.55 0.63 2.40 2.61 1.10 1.36 10,50 10.35 0.53 0.59 2.70 2.71 1.21 1.44 11.00 10.98 0.57 0.62 2.80 2.00 1.32 1.44 11.50 11.62 0.54 0.66 2.90 2.90 1.15 1.37 12.00 11.94 0.52 0.64 3.00 2.99 0.98 1.32 12.50 12.57 0.50 0.63 3.15 3.14 1.29 1.40 13.00 12.89 0.54 0.61
- 3.30 3.34 1.26 1.51 13.50 13.53 0.55 0.Il 3.40 3.64 1.37 1.52 14.00 13.85 0.51 0.60 3.00 3.82 1.10 1.49 14.50 14.44 0.45 0.59 4.00 3.98 1.21 1.57 15.00 15.12 0.43 0.60 4.20 4.14 1.60 1.81 16.00 16.07 0.35 0.63 4.40 4.44 1.78 1.94 17.00 17.03 0.32 0.72 1
4.60 4.62 1.75 2.35 17.45 17.35 0.31 0.71 4.00 4.78 2.44 2.85 18.00 17.99 0.32 0.
5.00 4,93 2.69 3.54 20.00 19.89 0.30 3. 3.
1987 uncats l 20
TABLEI SH T 3 Cossarison of Responses:
Of rect Generation (EDA 5P) versus 7 fan History 55 Critical Camping At Elev. 542*0 Frequency (J) Acceleration Frequency (J) ace,teragten EDASP T. H. f.N.(AVE) TH-EDAS EDASP T. H. T.N.(4VE) 7H.(0A$
1.03 1,04 N/A 0.32 5.25 5.25 N/A 0.61 1.10 1.13 N/A 0.37 5.50 5.41 N/A 0.50 1.20 1. 18 N/A 0.40 5.75 5.73 N/A 0.49 1.30 1.32 N/A 0.40 6.00 5.05 N/A 0.44 1.40 1. 42 N/A 0.39 8.25 6.21 N/A 0.42 1.50 1.51 N/A 0.42 8.50 S.53 N/A 0.41 1.60' 1.61 N/A 0.44 8.75 6.88 N/A 0.41 1.70 1.70 N/A 0.40 7.00 7.08 N/A 0.40 1.80 1.80 N/A 0.51 7.25 7.32 WA 0.40 1.90 1.89 M/A 0.54 7.50 - 7.40 WA 0.39 2.00 2.04 N/A 0.53 7.75 7.88 N/A 0.38 a 2.10 2.09 N/A 0.53 8.00 7. M N/A 0.38 2.20 2.18 N/A 0.54 8.50 8.44 N/A 0.37 2.30 2.32 N/A 0.54 9.00 9.07 N/A 0.34 2.40 2.42 N/A 0.54 9.50 9.55 N/A 0.35 2.50 2.52 h/A 0.56 10.00 9.87 N/A 0.33 2.00 2.51 N/A 0.54 10.50 10.35 N/A 0.32
- 2. 70 2.71 N/A 0.54 11.00 10. M N/A 0.31 2.80 2.80 N/A O.54 11.50 11.62 N/A 0.31
- 2. M 2. M N/A 0.55 12.00 11.94 N/A 0.30 3.00 2.99 N/A 0.54 12.50 12.57 N/A 0.29 3.15 3.14 N/A 0.54 13.00 12. 89 N/A 0.29
~
3.30 3.34 N/A 0.54 13.50 13.53 N/A 0.28 3.60 3.84 m/A 0.53 14.00 13.85 N/A 0.27 3.80 3.82 N/A 0.52 14.50 14.48 N/A 0.25 4.00 3. M N/A 0.53 15.00 15.12 N/A 0.26 4.20 4.14 N/A 0.54 15.00 16.07 N/A 0.25 4.40 4.44 N/A 0.54 17.00 17.03 N/A 0.24 4.60 4.62 N/A 0.59 17.45 17.35 N/A 0.24 4.80 4.78 N/A 0.61 18.00 17.99 N/A 0.23 5.00 4.93 N/A 0.53 20.00 19.99 N/A 0.22 1987 upcate 21
TABLE I S H T 4-Comparison of Aesponses:
}j Direct Generetten (EDA 5P) versus 7 fee Mistory 55 Critical Desping at Elev. 595+4 1
... t Freeuency (J) acceleration Feegwency (J) 'accelerecton, EDASP < 7. M. 7.P.(AVE) TN.E0A5 EDASP 7. M.
- 7. M. (4WE) '. 7N.(OA5 1.03 1.04 0.30 0. J2 5.25 5.25 1. 15 i
1.30-1.10 1.13 0.37. 0.38 . 5.50 5.41 1.10 1.27 '
1.20 1.18 0.38 0.41 5.75 5. 73 0.90 1.01 1.30 1.32 0.35 0.40 6.00 6.05 0.75. 0.41 1.40 1.42 0.40 0,40 6.25 4.21 0.67 0.66 1.50 1.51 0.43 0.44 6.50 6.53 0. M 0,57 1.60 1.61 0.45 0.47 6. 75 6.68 0.52 0.51 1.70 1. 70 0.44 0.50 7.00 7.00 0.40 0,44
- 1. m 1. = 0.48 0. u 7.25 7.32 0.4 0.
- 1.90 1.89 0.55 0.58 7.50 7.48 0.44 - 0.43 2.00 2.04 'O.59 0.56 7.75 7.80 0.41- 0.42 2.10 2.09 0.58 0.55 8.00 7.98 0.40 0.41 2.20 2.18 0.54 0.57 8.50 8.44 0.38 0 . 46 2.30 2.32 0.62 0.59 9.00 9.07 0.39 0.39 2.40 2.42 0.64 0.60 9.50 9.55 0.37 0.38 2.50 2.52 0.60 0.60 10.00 9.07 0.35 0.37 2.60 2.61 0.61 0.El 10.50 - 10.35 0.35 0.36 2.70 2.71 0. H 0.62 11.00 10.90 0.34 c.36
'2.80 2.80 0.65 0.62 11.50 11.62 0,34 0.36 2.90 .2.90 0.60 0.61 12.00 11.94 0.33 0.36 3.00 2.99 0.58 0.61 12.50 12.57 0.33 0.35.
3.15 -3.14 0.59 ti. 62 13.00 12.89 0.35 0.35 3.30 3.34 0.59 0.63 13.50 13.53 0.38 0.35 3.60 3. M 0.67 0. H 14,00 13.85 0.35 0.34 3.80 - 3.82 0.64 0. H 14.50 14.48 0.33 0.34
. 4.00 3.98 0. M 0.70 15.00 15.12 0.33 0.34 4.2G 4.14 0.10 0.76 16.00 16.07 0.32 0.35 4.40 4.44 0.82 0.84 17.00 17.03 0.30 0.35 4.60 4.62 0.91 0.95 17.45 17.35 O.30 0.35 4.00 4.78 0.98 1.08 18.00 17.99 0.30 0.'
5.00 4.93 1.05 1.21 20.00 19.89 0.29 0.3.
1967 uncate 22
.m
i
.~ ; :
TA BLE I S'H T 5 coe cf n or n n .: 1 Of rect Generation (E04SP) versus 7 fee wfitory
- 0. 5 Critical Dae.Ing At Elev. 428+4 )
Frequency (J) Acceleretten Fesquency (J) Acceleregion E045P 7. N. 7.M.(Avt) Tk E045 E04SP T. N. T.H.(avt) Tk-EDA $
1.03 1.04 0.49 0.49 5.25 5.25 s.71 1.14 g 1.10 1. 13 0.64 0.78 S.50 5.41 .5.07 7 22 1.20 1.18 0.74 0. M 5.75 S. 73 3.21 4. 13 1.30 1.32 0.64 0.79 6.00 6.05 2.29 2.87 1.40 1.42 0.81 0.78 8.25 6.21 ' 1.61 2.14 1.w 1. n . 0.72 0.91 .. it .. u t.x
. 1.a 1.60 1,41 0.01 1.01 8.75 6.48 1.12 1.21 1.70 1. 70 0. M 1.08 7.00 7.00 0. 5 0.97-1.80 - 1.80 0.97 1.20 7.25 7.32 0.81': 0.86 1.N 1.09 1.18 1.31 7.50 7.48 0.75 0.74 2.00 2.04 1.11 1.24 7.75 7.00 0.68 0.06
'2. 10 2.09 1.05 1. 18 4.00 7.N 0.43 0.62 2.20 2.14 0.92 1.33 4.M 8.44 0.57 0.57 2.30 2.32 1.32 1.45 9.00 9.07 0.80 0.99 2.40 2.42 1.27 1.43 9.50 9.95 0.54 0.54 2.50 2.52 1.13 1.42 10.00 9.87 0.52 L. 54 2.80 2.81 1.20 - 1.48 10.50 10.35 0.50 0.53-2.70 2.71 1.32 1.59- 11.00 10. N 0.50 0.54 2.80 2.80 1.46 . 1.58 11.50 11.62 0.51 0.57 2.M 2. N 1.28 1.51 12.00 11.94 0.52 0.57 3.00 2.99 1.09 1.47 12.50 12.57 0.49 0.57 3.18 3.14 1.46 1. M 13.00 12.09 0.55 0.57 3.30 3.34 1.47 1.73 13.50 13.53 0.50 0.57 l~ 3.80 3.06 1.67 1.81 14.00 13.86 0.53 0.54 3.80 3.82 1.37 1.81 14.50 14.48 0.50 C.59 4.00 3.W 1.54 1. 98 15.00 15. 3 0.57 0.60 4.20 4.14 2.05 2.35 18.00 16.07 0.44 0.66 4.40 4.46 2.43 2.68 17.00 17.03 0.44 0.78 l 4.60 4.62 2.53 3.34 17.45 17.35 0.44 0.81 4.00 4.78 3.52 4.27 18.00 17.99 0.43 0.80 5.00 4.93 4.13 S.73 20.00 19.89 0.42 0.52 1947 Update
4 I !
. 1 TA B LE I SHT 6 cc ri .n ., no. n...: .
Of rect Generetton (EDA 5P) versu. 7ine History {
55 Critical casetng At Elev. 628+8 i F*eouency (J) Acceleration Frecuency (J) Acceleration EDASP 7. H. 7.H.(AVE) 7H*EDAS EDA 57 7. M. 7.M.(Avf) 7W f0A5 1.03 1.04 0.31 0.32 5.25 5.25 1.90 2.19 1.10 1.13 0.37 0.38 5.50 5.41 t.87 2.20 1.20 1. 18 0.38 0.42 5.75 5.73 1.60 1. 8 L 1.30 1.32 0. 34 0.41 6.00 6.05 1.31 1.47 1.40 1.42 0.41 0.41 6.25 6.21 1. 16 1.20 1.50 1.51 0.45 0.45 6.50 6.53 0.93 1.02 1.60 1.61 0.47 0.44 6.75 6.64 0.85 0.89
- 1. TO 1.70 0.44 0.51 7.00 7.00 0.13 0.79 1.80 1.80 0.50 0.58 1.25 7.32 0.47 0.72 1.90 1.89 0.57 0.54 7.50 7.48 0.86 0.67 2.00 2.04 0.63 0.54 7.75 7.00 0.42 0.63 2.10 2.09 0.62 0.54 8.00 1.96 0.84 0.00 2.20 2.18 0.54 0.61 8.50 8.44 0.56 0.55 2.30 2.32 0.64 0.63 f, 30 9.07 0.52 0.5 2.40 t.42 0.69 0.64 9.50 9.55 0.49 0.50 2.50 2.52 0.64 0.65 10.00 9.07 0.44 0.49 2.60 2. El 0.67 0.64 10.50 10.35 0.47 0.47 2.70 2.71 0. 72 0.68 11.00 10.98 0.45 0.44 2.80 2.80 0.72 0.68 11.50 11.62 0.43 0.46 2.90 2.90 0.67 0.64 12.00 11.94 0.44 0.45 3.00 2.99 0.64 0.64 12.50 12. 57 0.44 0.45 3.15 3.14 0.67 0.70 13.00 12.89 0.45 0.44 3.30 3.34 0.68 0.74 13.50 13.53 0.44 0.44 3.60 3.64 0.42 0.78 14.00 13.85 0.44 0.44 3.90 3.82 0.79 0.83 14.50 14.44 0.45 0.44 4.00 3.90 0.80 0.91 15.00 15.12 0.44 0.44 4.20 4.14 0.92 1.03 16.00 16.07 0.43 0.44 4.40 4.44 1. 16 1.19 17.00 17.03 0.43 0.45 4.60 4.62 1.32 1.40 17.45 17.35 0.42 0.45 4.00 4.78 1.44 1.64 10.00 17.99 0.42 0.45 5.00 4.93 1.64 1.95 20.00 19.89 0.41 0.
1987 up st 24
SHT TA BL E I 7 ca . orn .a er s.o ...:
Ofroct Generetten (EDA 57) versus Ties History O.55 Crftfcol 04mpiat at Elev. 642*0 F w (J) Acceleration Frecu*acy (J) ACCeleretten EDASP T. N. 7.M (AVf) 7N=(DA5 EDA 57 7. M.
7.M.(AVE) n+-(045 1.03 1.04 0.50 0.70 5.25 5.25 9.44
- 10.18 1.10 1. 13 0.67 0.79 5.50 5.41 7.33 10.39 1.20 1.14 0.75 0.85 - 5.75 5.73 4.85 6.37 1.34 1.32 0.64 0.80 6.00 6.09 3.57 4.54 1.40 1.42 0.62 0.78 6.25 6.21 I 2.56 3.52 1.50 1.51 0.73 0.93 6.$0 6.53 2.22 2.61 ,
1.60 1,61 0.46 1.03 6. 75 6.64 1.97 2. 17 1.70 1.70 0.47 ' 00 7.00 7.00 1,43 1.76
- 1. = 1. m t. 00 1. u 7.25 7.n 1.42 1.. j 1.m 1.n 1.u 1.x 7.m 7. 4 t.n 1.n 2.00 2. u ,.20 1. n 7.n 7.00 1.01 1.u ;
2.10 2.09 1.10 1.23 8.00 7. M 1.00 ' 1.08 )
2.20 2.14 0. M 1.40 8.90 8.44 0.80 0.92 1 2.?0 2.32 1.30 1.53 9.00 9.07 0.00 0.82 l
2.40 2.42 1.35 1,51 9.50 9.58 0.76 0.75
]
2.50 2.52 1.26 ' 51 10.00 9.87 0.69 0.70 2.60 2.61 1.29 1.54 10.50 10.35 0.65 0.64 l 2.70 2.71 1.42 1.71 11.00 10.98 0.63 0.63 2.80 2.80 1.59 1.71 11.50 11.62 0,60 0.61 2.90 2.90 1.37 1.65 12.00 11.94 0.59 0.60 3.00 2.99 1.20 1.61 12.50 12.57 0.54 0.59
- 3. 15 3.14 1.63 1.15 13.00 12,89 0.54 0.58 3.30 3.34 1.67 1.94 13.50 13.53 0.58 0.57 3.60 3.64 1.95 2.00 14.00 13.85 0.57 0.57 3.00 3.82 1.62 2. 12 14.50 14.48 0.55 0.57 4.00 3.90 1. 8S 2.34 15.00 15.12 0.56 0.57 4.20 4.14 2.44 2.84 16.00 16.07 0.54 0.58 4.40 4.44 3.07 3.37 17.00 17.03 0.54 0.61 1 4.60 4.62 3.31 4.35 17.45 17.3S 0.54 0.63 4.00 4.73 4.60 5.67 18.00 17.99 0.54 0.63 5.00 4.93 5.64 7.89 20.00 19.89 0.53 0.56 1947 Update 25
I TABLE I SHT 8 Commertson or Responses:
Of rect Generation (E0A57) versus rfe. History )
. 53 Critical Camping At Elev. 642+0
- rsouency (J) Acceleration Frequency (J) acceleration EDASP 7. N. 7. N. ( AW() 7M.(043 EDA $P 7. N. T. N ( Avg) TH.ggAg 1.03 1.04 0.31 0.33 5.25 5.25 2.64 3.09 1 1
1.10 1.13 0.38 0.39 5.50 5.41 2.67 3,14
^
1.20 1.18 0.39 0.42 5.75 5.73 2.34 2.65 1.30 1.32 0.34 0.42 6.00 6.09 1.93 2.17 !
1.40 1.42 k 0.41 0.42 6.25 6.21 1.70 1.40 1.50. 1.51 0.44 0.44 6.50 6.53 1.37 1.52 1.60 1.61 0.44 0.50 6.75 6.64 1.20 1.33 1.70 1.70 0.44 0.53 7.00 '7.00 1.06 1.13 1.80 1.00 0.53 0.57 7.29 7.32 1.01 1.00 1.90 1.89 0.00 0.00 7.50 7.44 0.97 0.M 2.00 2.04 0.64 0.41 7.75 1.80 0.90 0.98 2.10 2.09 0.64 0.61 8.00 1.98 0.87 0.87 2.20 2.18 0.61 ' O.64 8.50 8.44 0.70 0.k 2.30 2.32 0.71 0.67 9.00 9.07 0.73 0.74 2.40 2.42 0.14 0.64 9.50 9.55 0.70 0.70
- 2. 5C 2.52 0.69 0.69 10.00 9.87 0.67 0.67 2.60 2.61 0.13 0.71 10.50 10.35 O.64 0.64 2.70 2.71 0.79 0.73 11.00 10.98 0.62 0.62 2.80 2.80 0.78 0.74 11.50 11.62 0.60 0.61 2.90 2.90 0.73 0.75 12.00 11.94 0.59 0.50 3.00 2.99 0.71 0.76 12.50 12.57 0.54 0.59
- 3. 15 3.14 0.75 0.79 13.00 12.89 0.57 0.58 3.30 3.34 0.79 0.64 13.50 13.53 0.57 0.57 3.60 3.64 0.96 0.92 14.00 13.85 0.54 0.54 3.80 3.82 0.93 1.00 14.50 14.48 0.54 0.56 4.00 3.94 0.97 1.12 15.00 15.12 0.56 0.55 4.20 4.14 1. 14 1.30 16.00 16.07 0.55 0.55 4.40 4.de 1.50 1.54 17.00 17.03 0.54 0.54 4.60 4.62 1.73 1.85 17.45 17.35 0.54 0.54 4.80 4.70 1.99 2.25 18.00 17.99 0.54 0.!
5.00 4.93 2.23 2.67 20.00 19.89 0.53 0.53 1947 Uncata
TABLE I SHT 9 Come4 risen of Reseenses:
Otreet Generetten (EDA 57) versus Tfee History 0.55 Critical Caseing At Elev 691+2 Froovency (J) Acceleretten Frecuenc/ (J) acceleration (DASP T. H. T.H.(AVE) TM-EDAS E0A57 T. H. T.H.(AVE) TH-EDAS 1.03 1.04 0.50 0.71 5.25 5.25 11.62 12.60 1.10 1.13 0.67 0.80 5.50 5.41 9. 12 12.83 1.20 1.18 0.76 0. SS 5.75 5.13 6. 14 8.12 1.30 1.32 0.67 0.01 6.00 6.06 4.59 5.89 1.40 1.42 0.83 0.79 6.25 6.21 3.35 4.63 1.50 1.51 0.75 0.94 8.50 6.53 2.93 3.50 l
1.60 0.88 1.61 1.09 6.75 6.80 2. M 2.97 1.70 1.70 0.89 1.10 7.00 7.00 1.99 2.45 1.80 1.80 1.03 1.27 7.25 7.32 1.96 2.15 1.90 1.89 1.14 1.40 7.50 7.48 1.80 1.Os 2.00 2.04 1.24 1.33 7.75 7.80 1.39 1.84 2.10 2.09 1.14 1.27 8.00 7.96 1.54 1.58 2.20 f.18 1.00 1.45 8.50 8.44 1.28 1.33 2.30 2.32 1.34 1.59 9.00 9.07 1.24 1.18 2.40 2.42 1.41 1.57 9. LJ 9.56 1.07 1.07 2,50 2.52 1.32 1.54 10.00 9.87 1.00 0.99 2.80 2.61 1.34 1.64 10.50 10.35 0.91 0.91 2.70 2.71 1.51 1.80 11.00 10.98 0.87 0.87 2.80 2.80 1.69 1. n. 11.50 11.62 0.83 0.85 2.90 2.90 1.45 1.75 12.00 11.94 0. 77 0.82 3.00 2.99 1.28 1.72 12.50 12. 5 7 0.80 0.79 3.15 3.14 1.76 1.89 13.00 12.89 0.75 0.77
^
3.30 3.34 1.83 2.10 13.50 13.53 0.14 0.75 3.60 3.64 2.la 2.29 14.00 13.SS 0.72 0.74 l 3.80 3.82 1.82 2.37 14.50 14.44 0.70 0.72 4.00 3.98 2.10 2.69 15.00 15.12 0.64 0.71 4.20 4.16 2.82 3.30 16.00 16.07 0.64 0.70 4.40 4.44 3.54 3.91 17.00 17.03 0.64 0.71 4.60 4.62 3.92 5.12 17.45 17.35 0.63 0.70 4.00 4.78 5.45 6.78 18.00 17.99 0.63 0.70 1 5.00 4.93 6.79 9.60 20.00 19.89 0.62 0.64 1947 Uncat
TA BL E I S H T 10 1
\
c ori.en e7 n..e.n.e.: y 01 rect Generetten (t0Ap) versus 7(es Mistory j 55 critical Campin9 At Elev. 691+2 Frequency (J) Acceleretten Frecuem.'y - (J) AC celeretten EDAp 7. H. 7.N.(Avt) FN=(OAS E0 ASP T. H. 7.N (AVI) -TN.f0A$
1.03 1.04 0.32 0.33 5.29 S.25 3.27 3.82 1.10 1.13- 0.38 0.39 5.50 5.41 3.30. .' 3. 88 1.20 1. 14 0.39 0.43 5. 75 S.73 2.94 3.32 1.30 1.32 0.37 0.42 6.00 .6.09 2.43 2. 74 - -
1.40 1.42 0.42 0.43 6.25 6.21 2. 15 2.28 l
~
1.50 1.51 0.47 0.47- 6.Sc 6.13 . 1.74 1.94 1.60 1.61 0.49- 0.51 6.75 6.88 1.e6 1.70 1.70 1.70 0.49. 0.54 7.00 7.00 1.38 1.52 - !
1.80 1.40 0.51 0.99 7.25 7.32 1.30- 1.38 1.M 1.89 0.62 0.62 7.50 ' 7. 48 - 1.29 1.27 2.00 2.04 0.69 ' O.43 7. 7S 7.80 1.18 1.18 .
2.10 .2.09 0.48 0. M 8.00 7.98 1.11 1.11 'i 2.20 2.12 0. M - 0. H 8.50 8.44 1.00 1.03 - I 2.30 2.32 0.74 0.70 9.00 9.07 0.93 0.9.
2.40 2.42' O. 78 0.72 9.50 9. SS 0.90 0.88 2.50 2.52 0.72 0.73 10.00 9.87 0. M ' O.M ,
2.60 2 61 0.78 0.75 10.50 10.35 0.80 0.80 2.70 2.71 0. M 0.78 11.00 10.90 0.78 0.18
- l. i 2.80 2.80 0.83 0.79 11.50 11.62 0. 74 0. 76 l
2.90 2.90 0.70 0.40 12.00 11.94 0.75 0.74 3.00 2.99 0.75 0.82 12.50 12.57. 0.73 0.72
- 3. 15 3.14 0, at O.86 13.00 12.89 0.71 0.71 -
3.30 3.34 0.88 0.92 13,50 13.53 0.69 0.70 i 3.60 3.M 1.07 1.03 14.00 13.85 0.67 0.69 3.80 3.82 1.06 1.13 14.50 24.48 0.64 0.64 4.00 3.98 1.11 1.29 15.00 15.12 0.64 0.M 4.20 4.14 1.34 1.52 16.00 16.07 0.65 0.67 4.40 4.46 1.77' 1.82 17.00 17.03 0M 0.66 4.60 4.62 2.05 2.22 17.45 17.35 0. H 0.65 4.00 4.78 2.33 2.72 18.00 17.99 0.63 0.65 5.00 4.93 2.71 3.29 20.00 19.89 0.62 0.
1987 unaste 28 \
_ m
i TABLE I SH T 11 l
Comperisen of Responses:
Ofrect Generation (ESA57) versus Tfee History
. 0.55 Critteel Camping 4t Elev. 7131 Frequency (J) Acceleration Frequency (J) acceleration E0A57 T. H. T.N.(AVE) TN EDAS EDA $P r. M. T.M.(4vt) TH. EDA 5 l 1.03 1.04 0.51 0.71 5.25 5.25 13.00 14.14 1.10 1.13 0.64 0.00 5.50 5.41 10.26 14.41 1.20 1. 18 0.74 0.87 5.75 5.73 6.97 9.23 1.30 1.32 0.67 0.32 6.00 4.05 5.25 6.75 1.40 1.42 0.63 0.79 6.25 6.21 3.es 5.35 1.50 1.51 0.76 0.96 6.50 6.53 3.39 4.00 1.60 1.61 0.07 1.06 6.7t 6.08 3.14 3.49 -
1
- 1. 70 1.70 0.90 1.11 7.00 7.00 2.37 2.96 1.80 1.80 1.04 1.29 7.25 7.38 2.31 2.55 1.90 1.89 1.28 1.42 7.58 7.48 2. M 2.24 2.00 2.04 1.27 1.35 7.N 7.00 1.43 1.99 2.10 2.09 1.17 1.30 8.00 7.96 1.83 1.86 2.20 2.14 1.03 1.48 8.50 8.44 1.57 1.60 l 2.30 2.32 1.40 1.63 9.00 9.07 1.52 1.43 2.40 2.42 1.44 1.62 9.50 9.55 1.27 1.31 2.50 2.52 1.34 1.83 10.00 9.87 1.20 1.20 2.60 2.61 1.41 1.71 10.50 10.35 1.11 1.09 2.70 2.71 1.54 1.86 11.00 10.98 1.04 1.05 2.80 2.80 1.75 1.88 11.50 11.62 0.99 1.05 2.90 2.90 1.51 1.82 12.00 11.94 0.91 1.00 3.00 2.99 1.33 1.79 12.50 12.57 0.97 0.96 3.15 3.14 1.44 1.98 13.00 12.09 0.90 0.94 3.30 3.34 1.93 2.21 13.50 13.53 0.90 92 3.60 3.64 2.32 2.43 14.00 13,84 0.87 0.90 3.80 3.42 1.94 2.53 14.50 14.48 0.83 0.89 I 4.00 3.98 2.25 2.90 15.00 15.12 0.77 0.98 4.20 4.14 3.04 3.57 16.00 16.07 0.71 0.89 4.40 4.44 3.88 4.26 17.00 17.03 0.71 0. 34 4.60 4.62 4.32 5.62 17.45 17.38 0.70 0.95 4.80 4.78 6.00 7.49 18.00 17.99 0.70 0.95 5.00 4.93 7.53 10.70 20.00 19.09 0.69 0.77 gg 1987 Unca'
l TABLE 1 SHT 12 Caesarisen of 8esponses: ~
Of rect Generation ((OASP) versus 7 fee Mistory SI Cattical Caseing at Elev. 7131 1
Frequency (J) occeleretten Frequency (J) occelereglen !
EDAW f. N. 7.H.(4WE) 7N-f0AS EOASP 7. M. 7.H.(4VE) 7M.E045 1.03 1.04 0. 32 0.33 S.25 S.25 3.69 : 4.28
- 1. 10 1.13 0.30 0.39 S.50 - S.41 3.71 4.36 i 1.20 1.18 0.40 0.43 S.75 S.73 3.32 3.75 1.30 1.32 0.37. 0.43 8.00 8.05 2.75 3.11 1.40 1.42 0.42 0.43. 6.25 - 6.21 2.43 2.59 1.50 1.51 0.48 - 0.47 6.90 6.53 1.98 ' 2.21 1.60 1.61 0.50 0.52 8.75 6.48 1.75 1.94 1.70 1.70 0.90 0.59 7.00 7.00 1.58 1.74 1.80 1.80 0.SS 0.80 7.25 7.32 1. M 1.97-
- 1. M 1.89 0.63 0.63 7.54 7.44 - 1.43 1.48 2.00 '2.04 0.71 0. M 7. 75 7.88 1.32 1.39 2.10 2.09 0.70 0.68 6.00 7. M 1.27 1.27-2.20 2.18 0. M 0.58 8.30 :8.44 '1. 14 1.1! .
2.30 2.32 0.76 0.72 1.00 - 9.07 1.07 1.07
( 2.40 2.42 0.80 0.74 9.90 9.55 1.03 1.00 2.50 2.52 0.75 0.75 10.00 9.87 3.97 0.95 2.00 2.61 0.81 0./8 10.90 10.38 0.92 0.91-2.70 2.71 0.87 0.81 11.00 10.90 0. M 0.88 2.80 2.80 0.86 0.83 11.50 11.62 0.88 0.86
- 2. M 2. M 0.81 0. M 12.00 11.94 0.87 0. H 3.00 2.99 0.78 0.86 12.50 12.57 0. M 0.82
- 3. 19 3.14 0.86 0.91 13.00 12.89 0.82 0.81 ll
- 3.30 3.34 0.94 0.97 13.50 13.53 0.79 0.80 -
3.60 3.88 1.14 1.10 14.00 13.85 0.78 0.79 3.80 3.82 1.12 1.22 14.50 14.48 0.78 0.78 4.00 3.98 1.20 1.40 15.00 15.12 0.74 0.77 7-4.20 4.14 1.47 1.66 16.00 16.07 0.72 0.76 4.40 4.48 1.94 2.00 17.00 17.03 0.71 0.75 4.60 4.62 2.25 2.45 17.45 17.35 0.71 0.75 4.00 4.78 2.58 3.02 18.00 17.99 0.70 0.**
S.00 4.93 3.01 3.87 20.00 19.89 0.59 0.r.
1987 una4te 30
.... TABLE 2 SHT I Time History vs Pouer spectre Tectaignes P81 Earth pake Iaput, output at Devotias 620+8
- Reapamme t estra at 0.96 Dampimp Time matarr pesar spectr e Time 81 story Pouer specta n Freq(us) Assel(4) Frug (as) noon 1(8) % Differ. Freq(Ns)Accal(8)Freq(Ms) noon 1(8)% Differ.
. ._ - .~._.
0.20 0.069 0. M 0.068 -1.E 6.75 1.076 6.75 L.177 9.35 0.30 0.125 7.00 0.923 7.00 L019 10.33 0.40 0. 223 0.6 0.183 -17.68 7.3 0.821 7.25 0.864 4.98 0.50 0.282 7.50 0.869 7.50 0.741 10.70 0.60 0.372 0.40 ' O.218 - 3 .22 7.M 0.643 7.75 0.678 5.52 0.70 0.22B 8.00 0.557 8.00 0.C32 13.31 0.80 0.383 0.00 0.291 -25.87 8.3 0.401 0.90 0.349 8.50 0.53 8.50 0.583 12.17 1.00 0.68 1.00 0.421 -7.99 8.75 0.!I75 1.10 0.483 9.00 0.515 9.00 0.582 12.98 1.20 0.421 1.3 0.5M 3 .65 9.3 0.584 1.30 0.611 9.50 0.536 9.50 0.982 . 10.38 1.40 0.436 1.e 0.463 -77.15 9.M - 0.990 1.50 0.F70 10.00 0.000 10.00 0.5M -4.07 1.50 0.645 1.60 0.742 15.01 10.50 0.640 10.50 0.55 13. s 1.70 0.00 11.00 0.646 11.00 0.500 -10.10 1.80 0.643 1.80 0.795 23.52 11.50 0.6M 11.50 0.731 8.10 1.90 0.748 12.00 0.72F 12.50 0.588 3 .16 2.00 1.345 2.00 0.909 -32.C 12.50 0.7M 2.10 1.255 13.00 0.780 13.00 1.040 23.M 2.20 0.912 2.20 1.190 30.e 13.50 0.802 13.50 1.083 22. 5 2.30 0.M3 14.00 0.76 14.00 1.195 E.M 2.# 1.63 2.40 1.13 -30.3 14.50 0.940 14.50 L305 38.96 2.50 1.6E3 15.00 1. 776 15.00 1.521 19.19 2.40 1.768 2.50 1.2M -30.M 16.00 1.250 . 16.00 1.970 40. 3 2.70 1.13 16.50 2.G4 2.80 1.313 2.00 1.551 18.19 17.00 2.011 17.00 2.848 e.19 2.90 1.487 17.95 1.997 17.50 2.959 e.17 3.00 1.347 3.00 1.533 14.18 18.00 1.514 18.00 2.619 72.92' 3.15 1.258 3.3 1.585 25.00 19.00 1.999 3.30 1.M9 3 .00 0.912 20.00 1.03 12.50 3.45 1.704 3.e 1.677 -1.M 22.00 0.443 22.00 0.7M 14.07 3.60 1.983 3.00 1.925 -3.M M.00 0.453 M.00 0.702 H.90 3.00 1.640 3.80 2.34 M.37 3 .00 0.45 25.00 0.640 50.48 4.00 2.245 4.00 2.115 -5.M 28.00 0.504 4.20 1.633 4.3 1.7E 9.04 30.00 0.404 .10.00 0.444 9.91 4.e 2.154 4.e 1.904 -11.E 32.00 0.G2 32.80 0.480 9.17 4.80 2.735 , 4.80 2.482 -3.05 33.14 0.390 4.88 3.483 4.5 4.032 16.M M.00 0.31 M.00 0.442 12.91 5.00 5.806 5.00 5..u -4.25 35.00 0.388 35.00 0.uS 7.M 5.3 5.239 5.3 6.391 21.97 38.00 0.386 30.00 0.G2 6.M 5.33 4.703 5.# 6.500 e.35 e.00 0.384 e.00 0.u0 6.66 5.50 4.33 5.80 5.374 3.e G.00 0.382 G.00 0.68 6.67 5.75 2.875 5.80. 4.0M e.33 44.00 0.381 i
6.00 2.05 6.00 2.9E G.M 46.80 0.379 46.00 0.404 4.0 l 6.3 1.881 6.3 1.M7 3.5 48.00 0.378 4.50 1.518 6.50 1.489 -3.90 50.00 0.3N 50.00 0.402 6.M
! Sverspe 31ffer. 14.97 1
3I
l-t . j TABLE 2 SHT 2 Tian l'istory
. vs Pouer Spectrum 1 ten 14888 PS1 Berthpahn Igut, Output at $1avutlas 6 3+4
- Responen testre et 5.04 Desing 71st Estauf Puumr spectru 71am nistarf Pouer spectr e Pres (ms) assal(G) Freq(as) noon 1(6) % Differ. Freq(Ns) less1(0) Freq(us) & coal (0) % Differ.
0.20 0.054 0.20 'O.054 -0. M 6.75 0.798 6.75 0.891 11.62 0.30 0.102 7.00 0.726 7.00 0.797 9.64 0.40 0.136 0.40 0.137 0.77 7.25 0.646 7.25 0.728 12.59 0.50 0.179 7.50 0.613 7.50 0.675 10.13 0.80 0.192 0.00 0.191 -0.82 7.75 0.578 7.75 0.634 9.77 0.70 0.1M 8.00 0.539 8.00 0.663 11.30 0.80 0.198 0.00 0.201 1.43 8.3 0.578 0.90 0.233 8.50 0.408 8.50 0.558 14.39 1.00- 0.259 1.00 0.200 0.68 8.75 0.542 1.10 0.3E3 9.00 0.462 9.00 0.530 14.69 1.3 0.337 1.3 0.317 -4.04 9.25 0.53 1.30 0.257 9.50 0.e4 9.50 0.511 10. 3 1.e 0.36 1.e 0.300 4.73 9.75 0.504 1.50 0.300 10. 5 0.474 10.00 0.65 5.02 1.60 0.362 1.00 0.3E2 5.57 10.50 0.69 10.50 0.409 6.86 1.70 0.408 11.00 0.442 11.00 0.400 10. 8 1.00 0.433 1.80 0.43 -3.11 11.50 0.440 11.50 0.99 13.47 +
1.90 0.421 12.00 0.427 12.50 0.534 3 .07 2.00 0.463 2.00 0.471 1.74 12.50 0.40 2.10 0.400 13.00 0.509 13.00 0.549 7.05 2.30 0.586 2.20 0.56 -4.19 13.50 0.563 2 50 0.566 0.57 2.30 0.615 14.00 0.586 14. 0 0.991 1.02 2.40 0.500 2.40 0.565 -4.3 14.50 0.573 14.50 0.43 9.34 2.50 0.517 15.00 0.567 15.00 0.669 - 17.96 2.60' 0.55 2.40 0.000 3.96 16.00 0.664 16.00 0.780 17.53 2.70 0.657 16.50 0.842 2.80 0.713 2.50 0.644 -4.06 17.00 0.324 17.00 0.890 7.93 2.90 0.703 17.55 0.055 17.50 0.904 5.75 3.00 0.700 3.00 0.712 1.44 18.00 0.790 18.00 0.879 11.23 3.15 0.774 ' 3.3 0.736 -4.97 19.00 0.753 3.30 0.760 3 .00 0.535 20.00 0.635 18.70 3.45 0.779 3.9 0.775 -0.10 22.00 0.62 22.00 0.536 7.00 3.60 0.900 3.00 0.846 4.19 24.00 0.442 24.00 0.490 10.73 3.80 0.956 3.00 0.909 -5.00 26.00 0.419 26.00 0.466 11.20 4.00 0.93 4.00 0.532 0.44 25.00 0.445 4.30 0.908 4.3 0.966 6.3 'J0.00 0.390 30.00 0.431 8.21 4.5 1.051 4.5 1.053 -2.50 32.00 0.394 32.00 0.422 6.99 4.9 1.34 4.5 1.277 1.00 33.14 0.391 4.5 1.4N
- 4.5 1.994 0.04 34.00 0.390 34.00 0.419 7.42 5.00 1.745 5.5 1.923 10.33 36.00 0.387 36.00 0.414 7.06 5.3 1.784 5.3 2.142 20.07 30.00 0.384 38.00 0.411 6.M 5.33 1.726 5.e 2.171 3.E2 e.00 0.3E2 40.00 0.408 6.74 5.50 1.774 5.00 2.010 13.32 42.00 0.381 42.00 0.40$ 6.5 5.75 1.610 5.00 1.749 8.66 44.00- 0.380 6.00 1.30 6.00 1.478 14.73 45.00 0.379 46.00 0.403 6.4 6.25 1.077 6.25 1.38 12.13 e.00 0.375 6.50 0.936 6.50 1.03 9.09 50.00 0.377 50.00 0.401 6.40 hverage Differ. 5.86 32
- s. j TABLE
. 2 SHT 3 71am K1 story vs Paume 8psett e Technigmas PS1 Earthquets Iget, Output at E3evotias 7D*1
.]
- angsans Spastre et 0.m Omgins Tsse utsessy pesar 8psettua fian mistar; pouer synetrum Freq(us)Assal(4)Pseq(us)noen1(G)% Differ. Freq(us) & coal (0) Freq(Ns) & coal (G) % Differ.
0.3 0.000 0.3 0.068 -1.37 6.75 2.781 6.75 3.382 21.58 0.30 0.127 7.00 2.900 7.00 3.078 4.70 )
0.# 0.2M 0.40 0.1M -17.45 7.5 2.M3 7.5 2.714 21.01 I 0.50 0.34 7.30 2.167 7.50 2.318 6.99 0.60 0.375 0.00 0.31 -3.19 7.75 2.092 7.75 2.15 2.u 0.70 0. 231 B.00 1.964 0.00 2.006 1.09 1 0.80 0.390 0.80 0.296 -25.59 8.25 1.8N 0.3 0.3. 8.. i.m 8.3 i.75
{
0.3 1.00 0.489 1.00 0.432 -7.80 8.75 1.683 1.10 0.507 9.00 1.32 9.00 1.656 31.10 )
1.3 0.434 1.3 0.595 3 .90 9.25 1.06 {
1.30 0.G8. 9.50 1.2H 9.50 1.51 22.74 1.6 0.868 1.40 0.406 -27.27 9.75 1.511 i 1.50 1.014 .10.00 !!446 10.00 1.33 4,5 1.00 0.EE3 1.40 0.786 15.00 10.50 1.37 10.50 1.1# ~12.10 1.70 0.917 11.00 1.28 11.00 1.15 -11.74 1.00 0.887 1.00 0.855 M.3 11.50 1.121 11.50 1.270 13. 3 1.90 0.825 12.00 1.158 2.5 1.461 2.00 0.995 -31.88 12.50 1.246 12.50 1.516 3 .79 2.10 1.439 13.00 1.lu 13.00 1.483 3.M 2.3 1.03B 2.20 1.325 27.61 13.50 1.046 13.50 1.G2 M.99 2.30. 1.000 14.00 1.059 14.00 1.463 3 .87 2.40 1.853 2.40 1.31 -30.5 14.50 1.118 14.50 1.53 3 .53 2.50 1.004 15.00 1.436 15.00 1.861 15.71 2.5 2.039 2.50 1.427 -30.02 16.00 1.402 14.00 1.900 30.39 2.70 1.319 16.50 2.31 2.80 1.532 2.80 1.848 20. 0 17.00 1.864 17.00 2.549 3 .77 2.90 1.753 17.55 1.876 17.50 2.623 39.77 3.00 1.05 3.00 1.879 14.96 18.00 1.395 18.00 2.302 H.99 3.15 1.606 3.3 1.995 24.21 19.00 1.51 3.30 2.144 2 .00 0.904 3 .00 1.073 9.04 3.46 2.200 3.# ' 2.100 -2.66 22.00 0.766 22.00 0.894 16.00 3.80 2.677 3.00 2.999 -2.94 M.00 0.657 M.00 0.890 35. 0 3.80 2.279 3 .00 0.637 26.00 0.870 3.6 4.00 3.35 4.5 3.53 -4.52 3 .00 0.686 3 .00 0.786 19.91 4.3 2.536 4.3 2.75 8.3 30.00 0.623 30.00 0.7e 18.81 4.5 3.25 4.e 3.052 -4.10 32. 5 0.85 32.00 0.W8 3 .72 4.00 4.50 4.5 4.518 0.0 33.14 0.697 4.M 6.05F 4.5 7.213 3 .07 M.R 0.646 M.00 0.806 M.09 5.5 10.W5 5.5 10.187 -2.92 3 .00 0.809 3 .00 0.770 26.53 5.5 9.9f7 5.3 12.336 25.# 30. 3 0.621 30.00 0.73 15.93 5.33 9.31 5.# 13.515 46.00 e.M 0.003 e.00 0.704 16.67 I 5.50 8.958 5.00 11.eu 27.73 C.00 0.002 C.00 0.488 16. 3 5.75 6.340 5.80 8.910 40.54 44.00 0.600 6.00 4.904 6.3 6.891 m.53 46.0B 0.999 46.00 0.091 15.C 6.3 4.8R1 6.3 4.864 4.M 48. 3 0.538 6.50 3.933 6.50 3.918 -1.06 50. 5 0.588 50.00 0.488 11.10 Averups Differ. 14.52 l
33 I
i
. TABLE 2 SHT 4 Tias History vs Pouer Spectre 7echniques 781 Barthqueha Input, output at Elevetim 713+1 Bespense apostra at 5.06 Ommpias 71ss materF Dauer 8pmetr e 71m nisterr Pouer spectra Freq(Os)assel(4)Freq(Os)& coal (G)% Differ. Frsq(Ms) nosel(0) Freq(Hs) & coal (G) % Differ.
0.30 0.0546 0.20 0.053M9 -1.19 6.75 1.0627 6.75 1. M7451 5.62 0.30 0.1027 7.00 1.7201 7.00 1.771169 2.6 0.40 0.D68 0.40 0. D8019 0.M 7.3 1. # 46 7.25 1.61M1 0.16 0.50 0.1805 7.50 1.3899 7.50 1.#1843 7.33 0.60 0.195 0.40 0.193000 -1.02 7.75 1.3167 7.75 1.39237 5.74 0.70 0.1998 8.00 1.2142 0.00 1.312786' 7.M 0.00 0. 3 11 0.00 0.204763 0.82 8.25 1.348151 0.90 0. 3 89 B.50 1.0861 8.501.1M766 13.13 1.00 0. 3 75 1.00 0.37930 0.16 8.75 1.150 0 1.10 0.3133 9.00 0.904 9.00 1.113551 13.17 1.30 0.3804 1. 3 0.3 3930 -4.13 9.25 1.001351
-1.30 0.3039 9.50 0.8939 9.50 1.0512f7 17.61 1.# 0.304 1.40 0.31712 4.32 9.75 1.02D47 1.50 0.3978 10.00 0.9335 10.00 0.99453 6.M 1.60 0.3848 1.00 0.408919 6.27 10.50 0.8973 10.50 0. M7936 5.M 1.70 0.4433 11.00 0.85M 11.00 0.91M G 7.3 1.00 0.4777 1.80 0.457243 -4.3 11.50 0.7812 11.50 0.91133 M.06 1.90 0.4871 12.00 0.00M 2.00 0.5034 2.00 0.52 M73 4.19 12.50 0.8485 12.50 0.913174 7.62 2.10 0.54G 13.00 0.8883 13.00 0.9M875 4.00 2.3 0.6777 2.30 0.620573 -8.43 13.50 0.85 3 '13.50 0.90 3 8 5.91 2.30 0.7056 14.00 0.81M 14.00 0.904259 10.80 2A3 0.0615 2.40 0.6535 3 -1.20 14.50 0.7757 14.50 0.913 32 17.74 2.50' O.631 15.00 0.7116 13.00 0.9 3707 30.51 2.60 0.489 2.50 0.723756 5.04 16.00 0.861 16.00 0.977000 15.06 2.70 0.7756 16.50 1.000008 2.80 0.8H4 2.00 0.8325M -3.68 17.00 0.9315 17.00 1.0 31W 10.38 2.90 0.8691 17.55 0.9452 17.50 1.0304 8.95 3.00 0.8788 3.00 0.99213 1.52 18.00 0.9288 18.00 1.0067 3 8.27 3.15 0.98 3 3.3 0.95BM3 -2.86 19.00 0.919171 3.30 0.W25 20.00 0.7421 20 30 0.8M112 13.75 3.45 1.1153 3.40 1.045759 -5.M 22.00 0.7121 22.00 0.77793 9.24 3.60 1.3109 3.00 1.18 W12 -9.93 M.00 0.6599 24.00 0.733M 15.17 3.00 1.3904 3 .00 0.6351 26.00 0.7412 3 16.71 4.00 1.35 3 4.00 1.413953 2.3 3 .00 0.6346 3.00 0.72M M 16. 6 4.5 1.447 4. 5 1.577323 9.01 30.00 0.6181 30.00 0.718E25 16.30 '
4.e 1.7732 4. 5 1.79 8 19 1.22 32.00 0.6133 32.80 0.73988 17.M 4.80 2.2BM , 4.8 2.271 3 8 1.78 13.14 0.6109 4.00 2.8889 4.5 2.930916 10.31 34.00 0.8052 34.00 0.7E038 18.19 5.00 3.34E1 5.00 3.639469 9.70 36.00 0.8071 36.00 0.711432 17.19 5.3 3.513 5.3 4.1M16 20.71 38.00 0.8051 30.00 0.7027W 16.15 5.33 3.4314 5.40 4.333118 26. 3 40.00 0 GGM 40.00 0.IW555 15.40 5.50 3.6117 5.60 4.108344 13.75 42.00 0.0018 42.00 0.694277 15.37 5.75 3.3055 5.00 3.H7962 10.M 44.00 0.0007 6.00 2.6372 6.00 3.133954 18.M 5 .00 0.59W M.00 0.690211 15.09 6.5 2.518 6.5 2.00535 13.18 e.00 0.5939 6.50 2.099 6.50 2.23109 4.52 50.00 0.5883 50.00 0.687E23 14.93 Average Oiffer. 6.85 34
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