Hysteretic Column under Earthquake Excitations

Abstract

A hysteretically nonlinear column subjected to earthquake excitations is considered. The horizontal and vertical earthquake ground accelerations are modeled by segments of stationary and nonstationary Gaussian white noise and filtered white noise processes. The method of equivalent linearization is used, and the time‐dependent equivalent parameters in terms of response moments are evaluated. 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 effects of the vertical ground acceleration. It is shown that the effect of the vertical ground motion is usually insignificant, unless the load coefficient is quite large.