Response Spectrum Analysis of Class of Torsionally‐Coupled Buildings

An effective procedure is developed for estimating the maximum response of a class of torsionally‐coupled, multistory buildings due to earthquake ground motion characterized by smooth response spectra. Several properties characterize this class of buildings, the most important of which is that all frames (spanning along either of two orthogonal directions) have proportional lateral stiffness matrices. It is demonstrated that the maximum response of such a torsionally‐coupled, N‐story building in its njth mode of vibration can be determined exactly by analyzing: (1) The response in the jth vibration mode $(j=1\text{,}2\text{,}\dots \text{,}N)$ of the corresponding torsionally‐uncoupled, N‐story system; and (2) the response in the nth vibration mode $(n=1\text{,}$ 2 for a one‐way symmetric plan) of an associated torsionally‐coupled, one‐story system. The total response is then determined by an appropriate modal combination rule.