Document: NUREG-0800
Document ID: 78905d69-1945-4638-99b9-2db68eb3da77
Document Type: srp
Title: SEISMIC SYSTEM ANALYSIS
Source: NUREG-0800
Source URL: https://www.nrc.gov/docs/ML0520/ML052070318.pdf
Revision Date: 2023-06
Chapter: 3
Section ID: 3.7.2
CFR Part: 
CFR Title: 

Content:
ation of modal responses is based on the premise that peak modal responses are randomly phased in time. This assumption has been shown to be adequate throughout the majority of the frequency range for earthquake-type responses. However, this premise is invalid at frequencies approximately equal to or greater than those at which spectral acceleration (S ) a roughly returns to the zero-period acceleration (ZPA). Phasing of the maximum response from modes at such frequencies (roughly 33 Hz and greater for the Regulatory Guide 1.60 response spectra) will be essentially deterministic and the structure simply responds to the inertial forces from the peak ZPA in a pseudostatic fashion. There are several solutions to the problem of how to combine responses associated with high- frequency modes when the lower-frequency modes do not adequately define the mass content of the structure. The following is one acceptable procedure for incorporating responses associated with high- frequency modes. Step 1. Determine the modal responses only for those modes that have natural frequencies less than that at which the spectral acceleration approximately returns to the ZPA (33 Hz for the Regulatory Guide 1.60 response spectra). Combine such modes in accordance with the methods delineated in Reference 8Regulatory Guide 1.92.82 Step 2. For each degree of freedom (DOF) included in the dynamic analysis, determine the fraction of DOF mass included in the summation of all of the modes included in Step 1. This fraction d for each DOF i is given by: i i 83 cn { n}T [m] {1} { n}T [m] { n} DRAFT Rev. 3 - April 1996 3.7.2-28 where n is order of the mode under consideration, N is the number of modes included in Step 1, is the nth natural mode of the system, and n,i c is the participation factor given by: n 84 Next, determine the fraction of DOF mass not included in the summation of these modes: e = d - i i ij where is the Kronecker delta, which is one if DOF i is in the direction of the ij i 85