BRI Research Paper


Motions of Rigid Bodies and Criteria for Overturning by Earthquake Excitations.

Y.Ishiyama*1; January, 1984. 57p.


This investigation deals with motions of rigid bodies on a rigid floor subjected to sinusoidal and earthquake excitations, and 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 equations of motion, transitions of motion, and motions after impact between the body and the floor are studied. 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.

The computer program is developed to simulate the motions of bodies subjected to horizontal and vertical ground motions, numerically solving the nonlinear equations of motion. Several types of simulations are conducted and the following are found: The coefficient of friction must be greater than the breadth-height-ratio so that the body rocks. The motions after impact from translation jump are greatly influenced by the normal and tangent restitution coefficients.

Experiments and simulations of frequency sweep tests are conducted,and it is concluded that the horizontal velocity as well as the acceleration must be taken into account as criteria for overturning. Simulations by earthquake excitations show that the criteria are also applicable to the earthquake excitations. Therefore it is possible to estimate the lower limits of the maximum horizontal acceleration and velocity of the input excitations, from the overturning of bodies.

*1 Head, Building Engineering Division, International Institute of Seismology and Earthquake Engineering, Building Research Institute, Ministry of Construction

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