Equivalent damping ratios of nonclassically damped structures composed of two substructures along the height by using equivalent two-degree-of-freedom systems

The nonconventional damping properties of structures, composed of two substructures with different damping ratios along the height, make an exact seismic analysis very complex. Determining an equivalent damping ratio for such structures makes the time-history analysis (THA) possible through conventional analysis methods. In this study, this issue is addressed using a novel analytical method that computes the equivalent damping ratios of arbitrary mixed structures composed of two different parts with arbitrary damping ratios. The accuracy of the method is verified by two studies already published in the technical literature that are based on the semiempirical analysis methods. Furthermore, the method is applied to two vertically irregular 15-story frames composed of steel and reinforced concrete substructures. The seismic responses obtained from the THA using the proposed equivalent damping ratios are compared with those from the THA performed on the main structure with a nonclassical damping matrix. The latter analysis is implemented in the state space as a benchmark solution. The results indicate that the proposed formula generates accurate seismic responses. The advantages of the proposed analytical method are its ease of use, accuracy, and the capacity of application to arbitrary mixed structures composed of two parts with arbitrary damping ratios.