Torsional index of an asymmetric building based on mode shape

Abstract

It is essential to carry out three-dimensional analyses considering all possible directions of seismic input, when conducting seismic assessment of an asymmetric building. For this purpose, the author has proposed a simplified procedure to predict the largest peak seismic response of an asymmetric building subjected to horizontal bi-directional ground motion acting at an arbitrary angle of incidence. In the proposed simplified procedure, the largest peak response is predicted from the response of two independent equivalent single-degree-of-freedom models representing the first and second modes and combination of pushover analyses. However, it is unclear which conditions an asymmetric building should satisfy for the applicability of the proposed procedure. In this study, a torsional index is defined based on each mode shape, and the applicability of the proposed procedure is discussed based on the torsional index. The advantages of the proposed torsional index are as follows: (a) it is related to the effective (equivalent) modal mass ratio which represents the contribution of each modal response to the whole response, and (b) it is easily extended for an multi-storey asymmetric building, and (c) there is the clear relationship between torsional indices of two different modes and the angle between the principal directions of two modes. The numerical results show that the proposed simplified procedure is at least applicable to torsionally stiff systems for both orthogonal directions, while it is questionable for torsionally flexible systems.