Toppling Fragility of Unrestrained Equipment

Abstract

Block-type equipment without restraining devices and under earthquake loads can effectively be modeled as freestanding rigid blocks resting on supporting bases subjected to base excitations. Once the peak values of base excitation levels, the aspect ratio of the bock, and the static friction coefficient between the block and the supporting base are known, the motion type of the block that will be initiated under base excitation can be determined. One of the possible motion types is rocking. When rocking is initiated, the block may topple and suffer severe damage and permanent loss of function. The emphasis of this study is placed on quantifying the possibility of toppling of a rigid block during rocking motion given its geometry and design earthquake environment. Using floor response spectra to characterize excitation inputs, results are given in the form of toppling fragility curves, i.e., probability of toppling as a function of peak ground accelerations. Parametric sensitivity studies are also carried out to show the effects of several key parameters on the fragility results.