Equivalent Static Factor

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US-NRC requirement on the equivalent Static coefficient when converting from dynamics analysis to static equivalent.

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    10Page iii of ASCE 43-05 lists current ASCE Standards with their dates. However, this cannot beconsidered an endorsement since (a) this page is not part of Standard 43-05, and (b) all ASCE standardsare listed, including those that are irrelevant to NPP construction.

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    4 Seismic Demand, Capacity, and Acceptance Criteria

    4.1 Seismic Demand

    Section 3.1 of ASCE/SEI Standard 43-05 stipulates that seismic demand for SSCs shall becomputed in accordance with the requirements of ASCE Standard 4, Seismic Analysis of

    Safety-Related Nuclear Structures. In applying ASCE Standard 4, ASCE 43-05 allows the useof linear equivalent static analysis, linear dynamic analysis, complex frequency responsemethods, or nonlinear analysis methods.

    4.1.1 Acceptable Editions of Industry Codes and Standards

    As indicated in Section 2.3 of this report, in most cases the Standard does not identify the dateor edition of the applicable code or standard (such as ASCE Standard 4 in this case) 10. Thiscan lead to potential problems in the future when newer editions of these codes/standard areutilized for design without the opportunity of the NRC to review their acceptance. Therefore, thespecific dates or editions of codes and standards referenced in Section 1.2 of ASCE 43-05should be identified to allow confirmation that these codes and standards have been endorsedby the NRC for the seismic design of NPPs.

    4.1.2 Technical Adequacy of ASCE Standard 4

    Most of the analysis methods described in ASCE Standard 4 (the latest version is 1998) areconsistent with the accepted methods in NRC regulatory guidance documents such as theStandard Review Plan (NUREG-0800) (SRP) and Regulatory Guides. However, the NRC hasnot officially endorsed or generically accepted the use of ASCE Standard 4. NRC is currentlyupdating Regulatory Guides such as RG 1.92 and RG 1.61, and NRC is also undertaking anupdate of the SRP, in order to have updated guidance in place prior to the anticipated submittalof new reactor applications. However, a review by the NRC for generic acceptance of ASCEStandard 4 at this time is not anticipated, and a complete technical review of ASCE Standard 4is beyond the scope of this study. Therefore, for purposes of this study, a number of areaswhere the Standard specifically references ASCE Standard 4 for analysis methods have beenreviewed and compared with the guidance presented in NRC regulatory documents. Thesedifferences are discussed in this report. The NRC may want to consider a future activity toreview the current ASCE Standard 4 for generic acceptance. This would avoid the need toreview selected applications of the analysis methods contained in ASCE Standard 4 on a case-by-case basis each time it is referenced in licensing applications.

    4.1.3 Linear Equivalent Static Analysis Methods

    Section 3.2.1 of the Standard describes an equivalent static analysis method to evaluate single-point-of-attachment cantilever models with essentially uniform mass distribution, or other simplestructures that can be represented as single degree-of-freedom systems. The equivalent staticload base shear is determined by multiplying the cantilevered structure, equipment, or

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    component masses by an acceleration equal to the peak of the input response spectrum. Thebase moment is determined by using an acceleration equal to 1.1 times the peak of theresponse spectrum and applying the resulting load at the center of gravity of the structure.Reviewing NRC regulatory guidance documents, the equivalent static load method is describedin Section 3.7.2, II, 1, b of the SRP for seismic analysis of SSCs. However, this section of theSRP requires that a factor of 1.5 be applied to the peak acceleration of the applicable floor

    response spectrum. According to the SRP, a factor of less than 1.5 may be used if adequatejustification is provided. In SRP 3.9.2, II, 2, a, (2), which addresses dynamic testing andanalysis of systems, components, and equipment, the same guidance is provided as in Section3.7.2, II, 1, b of the SRP. However, SRP 3.9.2, II, 2, a, (2), also indicates that for equipmentwhich can be modeled adequately as one-degree-of-freedom systems, the use of a static loadequivalent to the peak of the floor response spectra is acceptable. Thus, it can be concludedthat the equivalent static approach contained in the Standard is acceptable; however, adequate

    justification needs to be provided that the SSC can be modeled as a one-degree-of-freedomsystem or that a factor of less than 1.5 is still conservative.

    Section 3.2.1 of the Standard also describes the use of an equivalent static analysis method forcantilevers with nonuniform mass distribution and other simple multiple-degree-of-freedom

    structures. If the predominant or fundamental mode shape of the structure has a curvature inone direction only (e.g., cantilever mode), the equivalent static load is determined as theproduct of the structure, equipment, or component masses by an acceleration equal to 1.5times the peak acceleration of the response spectrum. The Standard also indicates that asmaller factor may be used, if justified. This approach is consistent with the guidance providedin Sections 3.7.2, II, 1, b and 3.9.2, II, 2, a, (2) of the SRP which were discussed above. Also,IEEE Std 344-1987 (formally accepted by RG 1.100, Rev.2) and the 2004 edition (not yetaccepted by NRC) basically describe the same approach for seismic qualification of Class 1Eequipment for NPPs. IEEE Std 344 states that the 1.5 static coefficient factor was determinedfrom experience to take into account the effects of multifrequency excitation and multimoderesponse for linear frame-type structures (similar to beams and columns), which can berepresented by a simple model. Based on the above discussion, this second equivalent static

    method is considered acceptable.

    A third equivalent static method is described in Section 3.2.1 of the Standard. If a modalsolution has been performed in accordance with ASCE Standard 4, then the spectralacceleration value at the fundamental frequency of the structure may be used. The 1.1 factorfor the base moment or the 1.5 factor defined for the nonuniform mass distribution and othersimple multiple-degree-of-freedom structures shall be applied to the acceleration valuedetermined at the fundamental frequency. This approach is not described in ASCE Standard 4,SRP 3.7 and 3.9, and in IEEE Std 344-1987 or -2004. In some cases this may be anacceptable approach; however without further guidance, this approach could under-predict thetrue response. For example, if the fundamental frequency of the SSC were to fall on the softside of any peaks in the spectra, this approach could lead to unconservative member forces if it

    turns out that the SSC had a somewhat higher fundamental frequency or the SSC has highermodes with frequencies corresponding to accelerations greater than that at the fundamentalfrequency. Also, the use of the 1.1 factor rather than 1.5, for base moment, would have to be

    justified. Therefore, it is recommended that this approach not be generically accepted withoutfurther guidance; its application should be reviewed on a case-by-case basis.

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