Stochastic Earthquake Response of Tapered Column

Abstract

This paper presents a stochastic analysis of a tapered column subjected to gravity as well as horizontal and vertical earthquake accelerations. The normal mode approach is used. The approach considers the effect of both non‐uniformity in column configuration and axial loading on mode shapes and natural frequencies. The earthquake accelerations are modeled as non‐stationary Gaussian random processes with either white or non‐white power spectra. This allows the statistical moments of column responses to be solved from a set of first order ordinary differential equations derived from the theory of Markov process. Both time histories of responses and spatial distribution of maximum responses along the elevation of the column are presented. Exact analytical sequences can be applied to handle problems of nonuniform columns.