Parametric effect of vertical ground acceleration on the earthquake response of elastic structures

Abstract

An analytical procedure is presented for the calculation of the statistical properties of the response of a linear elastic tall building under earthquake excitation. Emphasis is placed on the effect of the vertical ground motion. The restoring force in each story of the structural model is assumed to arise from the bending deformation of the columns whose rigidities are subjected to a general reduction due to the combined action of gravitational forces and the random variations due to vertical ground acceleration. Since earthquakes are random phenomena, stochastic modelling of ground motion seems appropriate. Both the vertical and the horizontal accelerations are treated as amplitude-modulated Gaussian random processes. With these models, the techniques developed herein, using the concept of Markov processes and Itô's stochastic differential equations, may be applied. To illustrate the application of the method, numerical results are presented for a six-story building. For computational purposes, the structural properties are evaluated using the finite element method. Within the limit of linear elastic deformation, the vertical ground acceleration is shown to be capable of causing only a slight increase of 0.08% in the lateral displacement for this moderately tall building. The percentage is expected to be larger for a taller building and much larger when the deformations exceed the elastic limit. Key words: earthquake excitation, elastic frames, random vibration, Markov process, dynamic response.