Motions of rigid bodies and criteria for overturning by earthquake excitations

Abstract This investigation deals with motions of rigid bodies on a rigid floor subjected to earthquake excitations, and criteria for overturning of the bodies. In order to study any motions of a body in a plane, the motions are classified into six types, i.e. (1) rest, (2) slide, (3) rotation, (4) slide rotation, (5) translation jump and (6) rotation jump. Then, the following are studied: the equations of motion, transitions of motion, and motions after impact between the body and the floor. One of the features of this investigation is the introduction of the tangent restitution coefficient which enables us to estimate the magnitude of the tangent impulse at the instant of impact. A computer program was developed to simulate the motions of bodies subjected to horizontal and vertical ground motions, numerically solving the non‐linear equations of motion. Several types of simulation were carried out and the following conclusions were found. The coefficient of friction must be greater than the breadth—height‐ratio in order for the body to rock. The motions after impact from translation jump are greatly influenced by the normal and tangent restitution coefficients. As criteria for overturning of bodies, at least two factors must be taken into account: the horizontal acceleration and the velocity of the floor. Then it is possible to estimate the motions of the floor from the overturning of bodies in a more reliable manner than before.