Energy Balance Equation for Estimating Overturning Potential of an Unanchored Rocking Body Subjected to Earthquake Excitation

Abstract

In this paper, the validity of the energy balance equation is verified by statistical analysis. An ensemble of two hundred artificial earthquakes are generated and used as input to a structure on whose floors unanchored bodies are placed. The equation of motion governing the rocking motion of an unanchored body is solved and the probabilities of overturning are obtained. This information is used to show that the energy balance equation proposed by Housner is indeed valid. A few examples are given to demonstrate the use of the energy balance equation.