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:
o account for element-associated damping. Use of composite modal damping for computing the response of systems with nonclassical modes may lead to unconservative results (Reference. 1014 ). Therefore, 51 the composite modal damping approach is acceptable provided the composite modal damping is limited to 20 percent. One of the other 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* = { } [K] { }, T DRAFT Rev. 3 - April 1996 3.7.2-18 [K] = assembled stiffness matrix, = equivalent modal damping ratio of the j mode, j th [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 { } = j normalized modal vector. th For models that take the soil-structure interaction into account by the lumped soil spring approach, the method defined by equation (3) is acceptable. For fixed base models, either equation (2) or (3) 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