Response spectrum of incompatible acceleration, velocity and displacement histories

The ground motions induced by an earthquake are expressed by the histories of acceleration, velocity and displacement. It is generally assumed that the acceleration, velocity and displacement histories contain identical information, i.e. the velocity history is obtained by integration of the acceleration history, and the displacement history is obtained by integration of the velocity history. However, this is not always true. In conventional processing of ground motion histories, additional corrections are applied to the velocity and displacement histories, which are not reflected in the acceleration history. As a result, the three ground motion histories contain slightly different information, or they are not fully compatible with one another. The structural response computed from the acceleration history, therefore, does not correspond to the processed velocity and displacement histories. The purpose of this paper is to underscore the engineering difficulties associated with incompatible histories and to provide a method of computing the response spectrum, which is compatible with the acceleration, velocity and displacement histories. Copyright © 2001 John Wiley & Sons, Ltd.