Dual criterion equivalent linearization approach for yielding structures under earthquake excitation

In order to estimate both maximum displacement and maximum inertia force of bilinear hysteretic system subjected to earthquake motions, an equivalent linearization approach with new effective parameters is presented. Effective mass and effective damping ratio as pair of effective parameters instead of the effective period and effective damping ratio in existing equivalent linear systems are introduced. Two error measures for displacement and inertia force are defined. Error distributions over a two‐dimensional parameter space of effective parameters are analysed, and the parameters are determined through a statistical approach with a dual optimization criterion for displacement and inertia force errors applicable to structural design. Single‐degree‐of‐freedom systems with bilinear hysteretic model; natural periods from 0.1 to 3.0 s; linear damping ratios from 3 to 50%; ductility ratios from 1.5 to 6; and post‐yield slope ratios 0, 0.05, 0.1 are considered. Analytical expressions for the effective parameters, and the ratio of the maximum inertia force to the maximum restoring force as functions of response ductility, elastic damping ratio and natural period of inelastic system are proposed for different site conditions and post‐yield slope ratios. Evaluation of proposed equations is performed, which reveals that the linear parameters lead to permissible error ranges. Copyright © 2010 John Wiley & Sons, Ltd.