Generation of floor and tertiary response spectra of structures under seismic excitations at multiple supports

A direct spectra-to-spectra method is developed for generating floor response spectra (FRS) for structures under earthquake excitations at multiple supports in terms of ground response spectra (GRS). Only GRS, "t-response spectra" (tRS), and basic modal information of primary structures, which can be readily obtained from modal analyses, are needed. FRS are separated into dynamic part and quasi-static part, which are combined by a new combination rule FRSMS-CQC developed using random vibration theory. FRSMS-CQC can account for the correlations between various components affecting FRS, that is, the correlation between the responses of oscillators excited by any two vibration modes, the correlation between the response of an oscillator excited by a vibration mode and the response of an oscillator mounted directly on a support, and the correlation between the responses of oscillators mounted on two different supports. In particular, two special cases, that is, excitations in the same direction at two supports being fully correlated and excitations at two supports being uncorrelated, are considered. The direct method can also be applied to generate tertiary response spectra (TRS) from FRS at multiple supports of secondary structures. Numerical example of a piping system mounted on different buildings, which are subjected to tridirectional seismic excitations at the foundation level, is presented to demonstrate the superiority of the proposed method. It is shown that FRS/TRS determined by time-history (TH) analysis have large variabilities, particularly at FRS/TRS peaks. The proposed direct method, which avoids the deficiencies of time history methods, is of excellent accuracy, efficiency, and simplicity.