ML19221A910
| ML19221A910 | |
| Person / Time | |
|---|---|
| Issue date: | 02/28/1976 |
| From: | NRC OFFICE OF STANDARDS DEVELOPMENT |
| To: | |
| References | |
| REGGD-01.092, REGGD-1.092, NUDOCS 7907100336 | |
| Download: ML19221A910 (5) | |
Text
.
e Revision 1 U.S. NUCLEAR REGULATORY COMMISSION February 1976 REGLATORY GU DE OFFICE OF STANDARDS DEVELOPMENT REGULATORY GUIDE 1.92 COMBif4NG MODAL RESPONSES AND SPATIAL COMPONENTS IN SEISMIC RESPONSE ANALYSIS A. INTRODUCTION
- 2. Combining the maximum va!ues (in the case of time-history dynamk analysis) or the representative Criterion 2, " Design Bases for Protection Against maximum values (in the case of spectrum dynamic Natural Phenomena," of Appendix A " General Design analysis) of the response of a given element of a Criteria for Nuclear Power Plants," to 10 CFR Part 50, structure, system, or component, when such values are
" Licensing of Production and Uti'ization Facilities,"
calculated independently for each of the three orthogo-requires, in part, that nuclear power plant structures, nal spatial components (two horizontal and one wrtical) tystems, and components important to safety be de.
of an earthquake. The combmed value will be the signed to withstand the effects of earthquakes without representative maximum value of the combined response loss of capability to perform their safety functions.
of that element of the structure, system, or component Paragraph (a)(1) of Section VI, " Application to Enge to simultaneous iction of the three spatial components.
neenng Design," of Appendix A, " Seismic and Geologic Siting Criteria for Nuclear Power Plants," to 10 CFR The Advisory Committee on Reactor Safeguards has Part 100, " Reactor Site Criteria," requires, in part, that been consulted conceming this guide and has concurred structures, systems, and components important to safety in the regulatory position.
remain functional in the event of a Safe Shutdown Earthquake (SSE). It specifies the use of a suitable B. DISCUSSION dynamic analysis as or.e method of ensunng that the structures, systems, and components can withstand the
- 1. Combining Modal Responses seismic loads. Similarly, paragraph (a)(2) of Section VI of the same appendix requires, in part, that the To find the values of the response of different structures, systems, and components necessary for con-elements of a nuclear power plant structure, system, or tinued operation without undue risk to the health and component to a presenbed response spectrum,it is first safety of the public remain functional in a.a Operating necessary to calculate the mode shapes and frequencies Basis Earthquake (OBE). Again, the uz of a suitable of the structure, system, or component. This is done by ynamic analysis is specified as one method of ensuring sohing the following equation for the eigenvectors and that the structures, systems, and components can with-eigenvalues:
staad the seismic loads.
[Kl-4 [M] lc l= 0 staff fon
_ ( nl (1)
This guide desenbes methods acceptable to the NRC where [K] is the stiftness matnx, u is the natural n
frequency for the nth mode, [M] is the mass matrix, and
- 1. Combining the values of the response ofindividual modes in a response spectrum modal dynanuc analysis to
@n} is the eigenector for the nth mode.
find the representative maximum value of a particular response of interest for the design of a given element of a nuclear power plant structure, system, or component.
- Lmes mdicate substantive changes from previous issue.
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Note that it may not be necessary to solve Equation i
- 2. Combining Spatial Components for all modes. In many cases, determination of only those modes that are sipiilicant should be sufficier.t.
2.1 Response to Three Spatial Components Calcu-
- P*'* #
Die next tep is to detennine the maximum modal displacement relative to the supports. This is done as follows:
Regulatory Guide 1.60," Design Response Spectra for S
Seismic Design of Nutlear Power Plants," indicates that f4nf max " f" Onf h" (2) design of all Seisnue Category I structures, systems, or components should be based on three orthogonal com-ponent motions (two horizontal and one vertical) of a whe re qn max is the maximum displacement vector for prescribed design earthquake. Chu, Amin, and Singh the ntt m de, l'n is the modal participation facior for (Ref. 3) have concluded that the representative maxi-the nth mode and is expressed by mum value of a particular response of interest for design (e.g., stress, strain, moment, shear, or displacement) of a
?c IMI 1
@n I[M] I n,
pven element of a structure, system, or component c
!n subjected to the simultaneous action of the three t
components of the earthquake can be satisfactorily S is the va2ue of acceleration in the specified response obtained by tding the square root of the sum of the an spectrum correspondmg to w and desipi damping, and squares of corresponding representative maximum values n
supersenpt T desipiates the transpose. Other maimum of the spectrum response, or the maximum response values of the responses per mode such as stress, strain, values from time. history dynamic analysis, to each of moment, or shear can be computed from the appropriate the three components calculated independently.
by using the s iffness properties of the elements mn e structure, system, or component. Newmark (Ref.
Die SRSS procedure used by Newmark (Ref.1) and
- 1) has shown that the representative maximum value of Chu, Amin, and Singh (Ref. 3) for combining the values a particular response of interest for design (such as of the response to three components of an earthquake is components in given directions of stress, strain, moment, based on the consideration that it is very unlikely that shear, or d2splacement ) of a psen element can be peak values of a response of a pven element would occur obtained liom the conesponding maximum values of the at the same time during an earthquake.
response of individual modes as computed above by taking the square root of the sum of the squares (SRSS) of the maximum values of the response of these 2.2 Respon.se to Three Spatial Components Calcu-lated Simultaneously indmdual modes of the structure, system, or com.
ponent. The Newmar k study, however, does not address the problem of chiseiy spaced modes. Other studies (see The maximum value of a particular response of References 2 and 3) have shown that SRSS procedure interest for design of a given element can be obtained can significantly underestimate the true response in through a step-by-step method. Die time-history res-certain cases in which some of the modal frequencies of ponses from each of the three components of the a structural system are closely spaced (see regulatory earthquake motions can be obtained and then combined position 1.1 for delinition of cimety spaced modes).The algebraically at each time step or the response at each nuclear industry has used many different methods to time step can be calculated directly owing to the combme the response when closely spaced modes exist-simultaneeus action of three components. The max;.
Some of these methods can be found in References 2,4, mum response is deternuaed by scanning the combmud and 5. A recent unpublished study has shown that the time-history solution. When this method is used, ;he resultmg combined response of nuclear plant faci!ities earthquake monons specified in the three tffe.ent usmg any of the methods delineated in regulatory directions should be statistically independent. For a pm tio n 1.2, whhh covers a broad range of methods discussion of statistical independence, see Referer.cc 6.
t unen tly bemg used by the industry, is in good agreement u ith time-history response. Therefore, any of the methods psen m regulatory position 1.2 is C. REGULATORY POSITION au cptable f or combinmg the modal responses when timely spaced omdes exist.
The following procedures f or combining the values of it should he noted that,if the frequencies of a system the response ofindmdual modes and the response to the are all widely separated, all the terms in the second three mdependent spatial components of an earthquake summatmn sipi in Equations 4 and 5 of regulatory in a seismic dynanne analysis of a nuclear oower plant position 1.2 will v:mish, and these equations wdl structure, system, or component are acceptable to the degenerate to the SRSS method (Equation 3).
NRC staff:
ga I
\\
1.92-2
- l. Combination of Mo'dal Responses component should then be obtained by taking the square root of the sum of the squares of correspond.ng 1.1 With No Closely Spaced Modes representative nuximum values of the responu of the element attributed to each closely spaced group of in a response spectrum modal dynamic analysis,if the modes and the remaining modal responses for the modes modes are not closely spaced (two consecutive modes that are not closely spaced.
are defmed as closely spaced if their frequencies differ Mathematically, this can be expressed as follows; from each other by 10 percent or less of the lov er
- N P
j i
frequency), the representative maximum value of a particular response of interest for design (e.g., com-R=
R[ +
Req R E#* l4) m9 ponents of stress, strain, moment, shear, or displace-k=1 q=1 R=i m=i ment) of a given element of a nuclear power plant structure, system, or component subjected to a single independent spatial componerit (response spectrum) of a where R(q and R are modal responses, Rg and R mq m
within the 9th group, respectively;iis the number of the three-component earthquake should be obtained by mode where a group starts; j is the number of the mode taking the square root of the sum of the squares (SRSS) where a group ends; R, R, and N are as defmed k
of corresponding maximum values of the response of the previously in regulatory position 1.1 of this guide; and P element attributed to individual significant modes of the is the number of groups of closely spaced modes, structure, system, or component. Mathematically, this excluding mdividual separated modes.
can be expressed as follows:
1.2.2 Ten Percent Method
-N R=
R[
(3)
N
~%
~
R=
R[+2 R Rj itj i
(5)
_k=1 where R is the representative maximum value of a particular response of a given element to a given where R, R, and N are as defmed previously in k
component of an earthquake, R is the peak value of the k
regulatory position 1.1 of th s guide. The second response of the element due to the kth mode, and N is summation is to be done on all i and j modes whose the number of significant modes considered in the modal frequencies are closely spaced to each other. Let wj and response combination.
wj be the frequencies of the ith and jth mode. In order to verify which of the modes are closely spaced, the 1.2 With Closely Spaced Modes following equation wall apply:
In a response spectrum modal dynamic analysis, if some or all of the modes are closely spaced, any of the wj-wi (6) 50.1 following regulatory positions (i.e., 1.2.1, 1.2.2, or w
1.2.3) may be used as a method acceptable to the NRC staff to combine the modal responses.
also 15 i < j $ N (7) 1.2.1 Grouping Method 1.2.3 Double Sum Method Closely spaced modes should be divided into
- N N
~%
groups that include all rnodes having frequencies lying R=
Rk R 4s (8) s between the lowest frequency in the group and a l frequency 10 percent higher.' The representative
,k=1 s=1 maximum value of a particular response of interest for R, R, and N are as de t.med previously in w here k
the design of a given element of a nuclear power plant regul tory positten 1 of this guide. R is the peak value structure, system. or component attributed to each such 3
f the response of the element attributed to sth mode.
group of modes should first be obtained by taking the sum of the absolute values of the corresponding peak (4 - d )
2 a
S
,W values of the response of the element attributed to qS i+
=
individual modes m that group. The representative g' wk + k ud maximum value of this particular response attributed to L
all the significant modes of the structure, system, or in w hich 0
' Groups should be formed staJting from the lowest frequency w( = q
] _g (jg) and working towards successively higher frequencies. No one frequency is to be in more than one group.
l 126 073 1.92-3
responses are calculated using the time-history method O, = Ok +
instead of the spectrum niethod.
L 4y;)
t Wk d
where w( and #k are the modal frequency and the
- b. When the time-history responses from each of t:ie i
ee c mponen s e er qua m tion are damping ratio in the kth mode, respectively, and tds the duration of the earthquake.
calculated by the step-by-step method and combined algebraically at each time step, the maximum response 2.
Combination of Effects Due to Three Spatial Com.
can be obtained from the combined time solution.2 ponents of an Earthquake
- 3. If the applicant has used the methods desenbed in Dependmg on which basic method is used in the this gmde, the Preluninary Safety Analysis Report seismic analysis, i.e., response spectra or time-history (PS AR) should indicate in each applicable section which method, the following two approaches are considered of the alternative acceptable methods were used for the acceptabL fo; the combir.ation of threc-dimensional structures, systems, or components covered by that earthquake effects.
section.
2.1 Response Spectra Method D. IMPLEMENTATION When the response spectra method is adopted for The purpose of this section is to provide infonuation seismic analysis, the representative maximum values of to appheants and licensees regarding the NRC staff's the structural responses to each of the three components plans for utilizing this regulatory guide.
of earthquake motion should be combined by taking the square roo' af the sum of the squares of the maximum Except in those cases in which the applicant proposes representative values of the codirectional responses an alternative method for complying with specified caused by each of the three components of earthquake portions of the Commission's regulations, the methods motion at a particular point of the structure or of the described herein wtll be used by the staff in the mathematical model.
evaluation of submittals for construction permit applica-tions docketed after the date ofissue of this guide.
2.2 Time-liistory Analysis Method If an appheant wishes to use this regulatory guide in When the time-history analysis method is employed de eelopmg subnuttals for applications docketed on or for seismic analysis, two ty,es of analysis are generally before the date of issue of this guide, the pertinent r
performed depending on the complexity of the problem:
portions of the application will be evaluated on the basis of this guide.
- a. When the maximum responses due to each of the three components of the carthquake motion are 2"*"*""'*
d " '* d ' * * * *'
- 4 " * " " "' ' P" U# d '"
calculated separately, the method for combininE the the three different directions should be statisucally indepen-three-dimensional effects is identical to that described in dent. For a discussion of statutical independence, see Refer-regulatory position 2.1 except that the maximum ence 6.
O 1.92-4 126 074
REFERENCES
- 1. R. L. Wiegel, editor, Earthquake Engineering,
- 4. E. Rosenblueth and J. Elorduy, " Response of l Englewood Cliffs, N.J., Prentice-Hall, Inc.,1970, chapter Linear Systems to Certain Transient Disturbances."
by N. M. Newmark, p. 403.
Proceedings, Fourth World Conference on Earthquale
- 2. A. K. Singh, S. L. Chu, and S. Singh, " Influence of Closely Spaced Modes in Response Spectrum Method of Analysis," Proceedings of the Specialty Conference on
- 5. N. C. Tsai, A. H. Hadjian et al.," Seismic Analys:s Structural Design of Nuclec Plant Facilities, Vol. 2, of Structures and Equipment for huclear Power Plants,"
Chicago, December 1973. (Published by American Bechtel Power Corporation Topical Report 4 A, Resi-Society of Civil Engineers, New York, New York.)
sion 3, November 1974.
- 3. S. L. Chu, M. Amin, and S. Singh, " Spectral Treatment of Actions ofihree Earthquake Components
- 6. C. Chen, " Definition of Statistically Independent on Structures," Nuclear Engineering and Design,1972, Time Histories," Journal of the Structural Division, Vol. 21, No.1, pp.126-136.
ASCE, February 1975.
126 075
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