Bounds on Earthquake Response of Structures

Abstract

Dynamics of an elastic structure subjected to simultaneous horizontal and vertical earthquake ground accelerations are considered. The Liapunov method is used and several general bounds on the maximum responses are developed. Using a stored energy and an optimal Liapunov function, specific bounds on the motion of multidegree‐of‐freedom structures are obtained. Particular attention is given to the case of a single‐degree‐of‐freedom column structure subjected to horizontal‐vertical earthquake excitations. It is observed that the vertical acceleration enhances the peak horizontal response. The predicted bounds are compared with the response spectra of several earthquakes. It is shown that when an appropriate choice for the effective time duration is used the estimated maximum responses become quite reasonable.