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Modal combination rules for multicomponent earthquake excitation
Author(s) -
Smeby Wiggo,
der Kiureghian Armen
Publication year - 1985
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290130103
Subject(s) - modal , random vibration , response spectrum , position (finance) , set (abstract data type) , vibration , ground motion , modal analysis , mathematics , principal component analysis , simple (philosophy) , mathematical analysis , computer science , structural engineering , engineering , physics , acoustics , statistics , polymer chemistry , philosophy , chemistry , finance , epistemology , economics , programming language
A response spectrum method for dynamic analysis of linear structures subjected to multicomponent seismic input is developed. The method is based on elementary concepts of stationary random vibration and assumes the existence of a set of principal directions along which components of ground motion are uncorrelated. Modal combination rules in terms of ground response spectra are developed for the mean and standard deviation of peak responses and for rootmean‐square responses. These rules account for correlations between modal responses of the structure, as well as correlations between the input components. When the position of principal directions is unknown, two alternative rules are proposed: one uses the direction which is most critical for the response quantity of interest, and the other considers the direction as a random variable. The proposed method is simple for practical implementation and gives more accurate results than other existing methods.