Equivalent Linear SDF Response to Earthquakes

The objective of this paper is to examine the accuracy of an equivalent linearization method for prediction of maximum response of a single degree-of-freedom bilinear hysteretic oscillator subjected to earthquake input. Simple expressions are developed for equivalent linear frequency and damping in terms of maximum attained response ductility. Comprehensive numerical results are presented in which the effects on accuracy of elastic frequency, yield strength, bilinear hardening slope, initial viscous damping, and earthquake input are examined. The parameters that most strongly influence accuracy are the hardening slope of the bilinear hysteresis loop and the magnitude of the response ductility. Accuracy is poorest for nearly elastoplastic systems and moderate response ductilities. These trends are interpreted by examining in the frequency domain the response of the bilinear oscillator to simple inputs.