Hysteretic Columns Under Random Excitations

Keywords: Hysteresis Models, Random Excitations, Columns, Horizontal Excitation, Vertical Excitation, Dissipation Energy Balancing, and Ground Motion.

Abstract: In a seismic event, the horizontal ground motion gives rise to an additive random excitation to a column, while the vertical ground motion gives rise to a multiplicative random excitation. The adjectives "additive" and "multiplicative" refer to the fact that these excitations appear in the governing equation as an inhomogeneous term on the right hand side and in a coefficient on the left hand side, respectively. In the present paper, the approximate method of dissipation of energy balancing, previously developed for randomly excited nonlinear systems, is applied to obtain the probability density for the response amplitude of a hysteretic column under such excitations. Both types of random excitations are idealized as Gaussian white noises. Three different hysteresis models are used in the formulation: the Hata-Shibata model, a general bi-linear model, and the Bouc-Wen model. Numerical results are obtained for wide ranges of excitation spectral levels and other physical parameters. To verify the accuracy of these results, the root-mean-square responses are also computed and compared with results from Monte-Carlo simulations and from the methods of equivalent linearization and Gaussian closure.