Response of structures subjected to horizontal-vertical random earthquake excitations

Abstract

A single-degree-of-freedom column subjected to horizontal and vertical earthquake excitations is considered. The earthquake ground accelerations are modelled by segments of stationary and nonstationary Gaussian white noise processes. The Fokker-Planck equation governing the transition probability density of the response is described and the associated second moment equations are derived. The transient and nonstationary response statistics for a range of values of parameters are obtained. A Monte-Carlo digital simulation study is also performed. The results are compared with the theoretical findings and good agreement is observed. Particular attention is given to the amplification effect of the vertical ground acceleration. It is shown that the effect of the vertical ground motion is significant when the load ratio is relatively large. Based on the presented statistical analysis, peak velocity responses for a range of natural periods are estimated. The results are compared with the combined horizontal-vertical response spectra of El Centro 1940 earthquake and reasonable agreement is obtained.