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

Abstract

A direct spectra-to-spectra method is developed for generating floor response spectra (FRS), which are used as input for seismic design and assessment of secondary systems in nuclear facilities, for structures under earthquake excitations at multiple supports. Only ground response spectra (GRS) and basic modal information of primary structures, including natural frequencies, modal damping ratios, modal participation factors, and mode shapes, which can be readily obtained from a modal analysis, are needed. The FRS are separated into two parts corresponding to dynamic response and quasi-static response, and are then combined by a new combination rule FRSMS-CQC, which is derived based on random vibration theory. FRSMS-CQC can account for the correlations between various components affecting FRS, i.e., 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, i.e., excitations at two supports are independent, and excitations in the same direction at two supports are identical, are considered. Numerical examples of a simple structure subjected to tridirectional seismic input at two supports are presented to demonstrated the superiority of the method. FRS from the proposed direct method agree extremely well with the numerical benchmark FRS obtained from a large number of sets of time history analyses. It is demonstrated that FRS determined by time history analyses have large variabilities, particularly at FRS peaks. The numerical examples show that combination rules have a significantly effect on the accuracy of FRS by a direct method, and the FRSMS-CQC can give accurate FRS.The proposed direct method, which avoids the deficiencies of time history methods, is of excellent accuracy, efficiency, and simplicity; it is convenient to implement in practice for generating FRS.