In response estimation of seismic control structures, it is necessary to consider the performance degradation of dampers due to long-period seismic motion. In this paper the focus is given to structures with shear strain dependent nonlinear viscoelastic dampers. A method is proposed to predict the damper dissipated energy considering performance degradation in earthquakes. The dissipated energy is used to predict the maximum deformation response of the structure using existing energy methods. New expression are proposed for the evaluation of the equivalent number of cycles and the effective damper deformation ratio. The accuracy of these prediction methods is then evaluated
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