Determining Equivalent Linear Parameters for Use in a Capacity Spectrum Method of Analysis

A new methodology for calculating equivalent linear parameters for use in predicting the earthquake response of structures is presented. The methodology is applied to single-degree-of-freedom inelastic structural models subjected to a suite of earthquake acceleration time histories. Error distributions over a two-dimensional parameter space of effective period and effective damping are analyzed through a statistical approach with an optimization criterion most applicable to structural design. Four hysteretic models are analyzed: bilinear, stiffness degrading, and two pinching models. Evaluation of the equivalent linear parameters is performed by two separate approaches. The first compares the maximum response of the equivalent linear system to the maximum response of the nonlinear system. The second compares the performance point displacement prediction calculated by the capacity spectrum method using the equivalent linear parameters developed in this paper to the maximum response of the nonlinear system. Results are compared to analysis using the existing equivalent linear parameters as set forth in Applied Technology Council-40 (ATC-40). The error analysis reveals that the ATC-40 equations are significantly unconservative at lower values of ductility and conservative at the higher values of ductility. The new equivalent linear parameters lead to a substantial improvement for both error measures over the entire ductility range.