Stochastic Analysis of the Seismic Response of Secondary Systems

This thesis is concerned with the earthquake response of light equipment in structures. The motion of the ground during an earthquake is represented as a stochastic process in order to reflect uncertainty in the prediction of such motion. A number of different stochastic earthquake models are considered, and analytical methods are described for these models. The response of equipment in a structure to stochastic ground motion is derived, in the case of a single-degree-of-freedom secondary system (equipment) attached to a single-degree-of-freedom structure. The distribution of the envelope of the secondary system displacement is obtained for general transient ground motion. Closed form expressions are computed for the transient response to stationary ground motion. The effect of the interaction of equipment with the structure is described by the introduction of an equivalent non-interacting system. However, this method applies only to classically damped systems. The results are applied in a simple way to the problem of the computation of floor spectra. It is found that the ground spectrum is amplified in a simple way, except near resonance, where special considerations must be addressed.