Evaluation of equivalent linear methods for estimating target displacements of existing structures

This paper presents a statistical study that evaluates the accuracy of four equivalent linear methods which allow the maximum deformation demands of nonlinear structures to be estimated from the maximum deformation demands of the equivalent linear ones. Three of them are defined by displacement ductility ratios, and the other is defined by lateral strength ratios. It is shown from the study that conclusions for the approximate displacements derived from structures with known displacement ductility ratios (new structures) such as the work done by Miranda and Ruiz-Garcia in 2002 [16] are not applicable to structures with known strength ratios (existing structures). The equivalent damping of the equivalent linear systems is usually greater than 5% and the design response spectra specified in codes have a viscous damping ratio of 5% only. Therefore, the highly damped maximum displacement responses of the equivalent linear systems in this study are derived from both damping reduction factors and linear response-history analyses to discuss the effect of different damping reduction factors. Elastoplastic single-degree-of-freedom systems with periods between 0.1 and 3.0 s are considered when subjected to 72 earthquake ground motions recorded on firm sites in California. Mean ratios and the dispersion of approximate to exact maximum inelastic displacements for each method are computed as functions of periods of vibration and strength ratios. This study focuses on existing structures, which already have known vibrating periods and strength ratios.