Equivalent Linearization for Seismic Responses. I: Formulation and Error Analysis

Abstract

A random‐vibration approach for uniaxial and biaxial nonlinear structures is presented based on the stochastic equivalent‐linearization method. By modifying and combining existing modeling techniques, a unified hysteretic modeling scheme is proposed. The method is applicable both to conventional uniaxial systems and general orthotropic systems, i.e., structural systems having different nonlinear characteristics in different directions. A significant attention is directed to the numerical errors associated with the equivalent‐linearization approximation. Numerical errors are classified as stationary and nonstationary errors. The mechanism of each error is carefully studied and quantitatively evaluated through a series of parametric studies. The postyield stiffness ratio, a, has been singled out as a key parameter in the error analysis. A practical error‐correction scheme is presented based on a large number of simulations.