Rocking Response and Overturning of Equipment under Horizontal Pulse-Type Motions

In this report the transient rocking response of electrical equipment subjected to trigonometric pulses and near-source ground motions is investigated in detail. First the rocking response of a rigid block subjected to a half-sine pulse motion is reviewed. It is shown that the solution presented by Housner (1963) for the minimum acceleration amplitude of a half-sine pulse that is needed to overturn a rigid block is incorrect. In reality, under a half-sine pulse, a block overturns during its free vibration regime and not at the instant that the pulse expires, as was assumed by Housner. Within the limits of the linear approximation, the correct conditions for a block to overturn are established and the correct expression that yields the minimum acceleration required to overturn a block is derived. Subsequently, physically realizable cycloidal pulses are introduced and their resemblance to recorded near-source ground motions is illustrated. The study uncovers the coherent component of some near-source acceleration records, and the overturning potential of these motions is examined. The rocking response of rigid blocks subjected to cycloidal pulses and near-source ground motions is computed with a linear and nonlinear formulation. It is found that the toppling of smaller blocks depends not only on the incremental ground velocity but also on the duration of the pulse, whereas the toppling of larger blocks depends mostly on the incremental ground velocity. The kinematic characteristics of recorded near-source ground motions are examined in detail. It is found that the high frequency fluctuations that occasionally override the long duration pulse will overturn a smaller block, whereas a larger block will overturn due to the long duration pulse. A method to determine the cut-off frequency is developed and illustrated through examples. In this light, the rocking response of electrical equipement subjected to nearsource ground motions is shown to be quite ordered and predictable. TABLE OF CONTENTS ABSTRACT ................................................................................................................................ 2 TABLE OF CONTENTS ............................................................................................................ 3 LIST OF FIGURES ..................................................................................................................... 4 LIST OF TABLES ....................................................................................................................... 8 ACKNOWLEDGMENTS ........................................................................................................... 9 CHAPTER