The Rocking Response of an Unanchored Body Subjected to Simulated Excitation

Abstract

The rocking response of rigid bodies with rectangular footprint, freely standing on a horizontal rigid plane is studied analytically. Rigid bodies are subjected to simulated single component of horizontal earthquake time histories. The effect of the baseline correction, applied to simulated excitations, on the rocking response is first examined. The sensitiveness of rocking motion to the details of simulated earthquakes and the geometric properties of rigid bodies (i.e., slenderness ratio and sizeparameter) as well as the coefficient of restitution is investigated. Because of the demonstrated sensitivity of rocking response of rigid bodies to these factors, prediction of rocking stability must be made in the framework of probability theory. Therefore, using a large number of simulated earthquakes, the effects of duration and shape of intensity function of simulated earthquakes on the overturning probability of rigid bodies are next studied. In the case when a rigid body is placed on any floor of a building, the corresponding overturning probability is compared to that of a body placed on theground. For this purpose, several shear frames with fundamental natural period of vibration ranging from 0.5 sec(stiff) to 2.0 sec (flexible) are employed. Finally, the viability of the energy balance equation which was introduced by Housner in 1963 (The behavior of inverted pendulum structures during earthquakes, Bulletin of Seismological Society of America, 53, 2, 403-417) and widely used by the nuclear power industry to estimate the rocking stability of rigid bodies is evaluated.