Response of simple yielding structures to earthquake excitation

Abstract

A method is developed for generating a random process that has the pertinent properties of recorded strong-motion earthquake accelerograms. The model accelerograms are sections of a stationary, Gaussian, random process with a power spectral density found from the average undamped velocity spectrum. Eight pseudo-earthquakes of thirty seconds duration are generated on the digital computer and the velocities, displacements, and velocity spectra calculated. The average velocity spectra of the real and pseudo- earthquakes correspond closely and the velocities, displacements, and velocity spectra of the real and pseudo-earthquakes exhibit similar statistical behavior. It is concluded that the pseudo-earthquakes are satisfactory models of strong-motion earthquakes for the purposes of structural analysis. A general nonlinear hysteretic force-deflection relation for dynamic studies is presented. The relation is a continuous, smooth function and includes the linear and elasto-plastic relations as limiting cases. The steady-state response to sinusoidal excitation is studied in detail and the results presented. It is concluded that the hysteretic relation is general enough to be useful in structural analysis and that comparison of test results and theory may enable the dynamic force-deflection relations of real structures to be approximated. A class of yielding structures suitable for earthquake response studies is defined by the geometry of the hysteresis curves and the law describing yielding behavior. The general yielding relation is included in this class as are the linear, the elasto-plastic and the bilinear hysteretic relations. The equation of motion and the energy equation for the response of yielding structures to earthquake motion are examined and a typical yielding structure is subjected to the ensemble of pseudo-earthquakes.