Abstract
This study is concerned with the conditions for the initiation of various modes of response of a freeβstanding rigid body, initially at rest, placed on a frictional horizontal base which undergoes earthquakeβlike accelerations in both the horizontal and vertical directions. These conditions are derived using equations of motion appropriate for each mode of motion. The analysis shows that an equivalent horizontal base acceleration may be constructed by dividing the time history of horizontal base acceleration by the sum of gravitational acceleration and the time history of vertical base acceleration. The criteria governing each mode of response of a body of given aspect ratio are then presented graphically with the magnitude of the equivalent base acceleration as abscissa and the coefficient of friction between the body and the base as ordinate. The study shows that a body is more stable while the vertical base acceleration is upwards than when it is absent as expected. When the vertical base acceleration is downwards, although the body is very likely to be lifted off the base, it is nevertheless possible to rock, and slide and rock simultaneously provided the value of coefficient of friction is sufficiently high and the downward vertical base acceleration is not too different from gravitational acceleration. Copyright Β© 2007 John Wiley & Sons, Ltd.