Vertical Seismic Load Effect on Hysteric Columns

An analytical method is developed to calculate the statistical properties of the response of hysteretic columns under earthquake excitations, with special emphasis on the effect of the vertical ground acceleration. Both the vertical and horizontal ground accelerations are modeled as amplitude-modulated Gaussian random processes, and the restoring force in a column is assumed to follow a functional relationship proposed by Hata and Shibata. Numerical results are presented for two columns, having two contrasting values of the post-yielding to pre-yielding stiffness ratio of 0.5 and 0.1, respectively. These results indicate that the vertical ground acceleration has an aggravating effect similar to that of the gravitational force in causing greater peak mean-square structural response than one induced by the horizontal ground acceleration alone. The time variation of the mean-square response is found to be extremely sensitive to structural parameters. For softer structures with a small post-yielding to pre-yielding stiffness ratio, large permanent deformations may remain after termination of the earthquake excitations.