Maximum seismic displacement of inelastic systems based on energy concept

The energy balance and energy input of Single-Degree-of-Freedom (SDF) systems under earthquake motion is studied for elastic and inelastic systems. The maximum displacement of an inelastic system is related to that of an elastic system having the same initial stiffness and mass by considering the earthquake energy input per cycle of oscillation. With an assumption that the cyclic energy input is equal for both elastic and inelastic system for intermediate- and long-period systems, a simplified relation is suggested. Newmark's equal energy rule is shown to be the upper bound of the simplified relation; the lower bound of maximum response displacement is also derived in this paper. The numerical analysis results were mostly shown to fall between the proposed upper and lower bounds. A separate approximate relation is proposed for short-period systems. The reason for divergence from the suggested relations is discussed for short-period systems. Copyright (C) 1999 John Wiley & Sons Ltd.