Maximum mean square response and critical orientation under bi-directional seismic excitation

Power Spectrum Analysis (PSA) consists one of the seismic analysis methods proposed by modern code pro-visions. In the context of PSA, the computation of seismic behavior is achieved by a stochastic analysis that yields mean square values. A method that can be used for the determination of maximum or mean square response is the response history analysis. In the present study, analytical formulas are developed for the determination of the maximum mean square value and the corresponding critical incident angle of any scalar response quantity under two horizontal seismic components for any time interval of ground motion within the context of linear response history analysis. An R/C building is analyzed in order to demonstrate the variation of the maximum mean square response with the incident angle. The maximum mean square response values over all incident angles are calculated using the developed formulas. The results show that the application of the earthquake components along the structural axes can underestimate the mean square response.