Prediction of the "Average" Peak Nonlinear Seismic Response of Asymmetric Buildings Under Bi-directional Ground Motion Acting at an Arbitrary Angle of Incidence

In this study the "reduced response spectrum" is introduced for the prediction of the "average" response of all possible angle of incidence, and the "average" peak seismic response of an asymmetric building under horizontal bi-directional ground motion, acting at an arbitrary angle of incidence, is predicted based on the procedure proposed in Fujii (Bull Earthq Eng 12: 909-938, 2014). In this study, the following two definitions of the "reduced response spectrum" are examined; (A) the geometric mean spectrum of the horizontal major and minor components, and (B) the square root of the average of squares spectrum from all possible angle of incidence. In the numerical example, nonlinear time-history analyses of a four-storey torsionally stiff asymmetric building are carried out considering the various directions of seismic inputs, and these results are compared with the predicted results. The results show that the predicted "average" peak response displacement for the flexible-side frame satisfactorily agrees with the average of the time-history analyses results, either definition of the "reduced response spectrum".