Equivalent linearization applied to earthquake excitations and the R-μ-T₀ relationships

This paper uses the equivalent linearization approach to derive the approximate harmonic equivalent stiffness and damping for bilinear systems in the context of earthquake resistant design. Whereas the resulting stiffness is identical to that in published works, the damping herein depends on the harmonic output frequency as well. This additional dependence produces an efficient method, which, although deterministically derived, predicts quite well the maximum output displacements for earthquake excitations. Two methods for choosing output frequencies are described. The results from these two methods are compared to those from several available approximation methods for 16 separate cases for an ensemble of 20 earthquake time history records. For the bilinear systems studied the methods presented in this paper give in most cases more accurate results. These results can also be used for evaluating the strength reduction factor R for given ductility or vice versa-the R-μ-T₀ relationship-and hence improve the accuracy of the simplified procedures now used for displacement-based design.