Document: NUREG-0800
Document ID: c165ebfe-8431-4d56-8bc9-97c2227d45bb
Document Type: srp
Title: SEISMIC SYSTEM ANALYSIS
Source: NUREG-0800
Source URL: https://www.nrc.gov/docs/ML0706/ML070640311.pdf
Revision Date: 2023-06
Chapter: 3
Section ID: 3.7.2
CFR Part: 
CFR Title: 

Content:
r methods mentioned below is generally applicable if the composite modal damping exceeds 20 percent. A. Time domain analysis using complex modes/frequencies, B. Frequency domain analysis, or C. Direct integration of uncoupled equation of motion. For the composite modal damping approach, two techniques of determining an equivalent modal damping matrix or composite damping matrix are commonly used. They are based on the use of the mass or stiffness as a weighting function in generating the composite modal damping. The formulations lead to: where K* = {φ}T [K] {φ}, [K] = assembled stiffness matrix, β'j = equivalent modal damping ratio of the jth mode, [K'], [M'] = the modified stiffness or mass matrix constructed from element matrices formed by the product of the damping ratio for the element and its stiffness or mass matrix, and {φ} = jth normalized modal vector. For models that take SSI into account by the lumped soil spring approach, the method defined by equation (2) is acceptable. For fixed base models, either equation (1) or (2) may be used. Other techniques based on modal synthesis have been developed and are particularly useful when more detailed data on the damping characteristics of structural subsystems are available. The modal synthesis analysis procedure consists of (1) extraction of sufficient modes from the structure model, (2) extraction of sufficient modes from the finite element soil model, and (3) performance of a coupled analysis using the modal synthesis technique, which uses the data obtained in steps (1) and (2) with appropriate damping ratios for structure and soil subsystems. This method is based upon satisfaction of displacement compatibility and force equilibrium at the system interfaces and uses subsystem eigenvectors as internal generalized coordinates. This method results in a nonproportional damping matrix for the composite structure, and equations of motion have to be solved by direct integration or by uncoupling them by use of