Combination of Modal Responses Consistent wtih Seismic Input Representation

The well-known modal superposition method for the evaluation of seismic response by the complete quadratic modal combination rule (CQC) is revisited. The most widely used version of the CQC rule utilizes correlation coefficients derived for white-noise excitation and neglects the influence of peak factor variation on the response. Here a simplified procedure for evaluation of correlation coefficients and peak factors consistent with the power spectral density of seismic excitation is proposed. The procedure is based on an approximate analytic expression for direct evaluation of the power spectral density of the excitation consistent with any prefixed response spectrum, and the evaluation of the consistent correlation coefficients and peak factors by using analytical expressions. The ranges of system dynamic parameters for which the correlation coefficients derived for white-noise excitation are not adequate are pointed out. Then the influence of the assumptions for CQC rule derivation on the evaluation of nodal response parameters is investigated, and the role played by the correlation coefficients and peak factors is pointed out.