On the Overturning Instability of a Rectangular Rigid Block Under Ground Excitation

ABSTRACT

This paper deals with the rocking response of a free-standing rectangular rigid block subjected to a ground acceleration assuming that the friction between the block and the ground is large enough so that there is no sliding. Particular attention is focused on the minimum acceleration amplitude which may lead the block to overturning instability. The conditions of such a critical state are properly established. Subsequently, two distinct modes of overturning instability under a one-sine ground pulse are examined: (1) overturning without impact and (2) overturning after one impact occurring either before or after the ground excitation expires. The effect of initial conditions on the minimum amplitude acceleration is also discussed in connection with a one-cosine and a one-sine pulse. The proposed technique is applied to various examples covering all possible cases of overturning instability.