Generalized Response Spectrum Analysis for Structures with Dampers

In this study, a computational seismic design routine is proposed based on a generalized response spectrum analysis for highly indeterminate structures with energy-dissipation members, such as viscous or elasto-plastic dampers. Complex stiffness terms are introduced to account for displacement-dependent damping, and a three-dimensional (3-D) element stiffness matrix with complex axial stiffness is proposed for elasto-plastic dampers. A modified complete quadratic combination method previously developed for real symmetric damped systems is extended to complex asymmetric damped systems, based on a theoretical analysis of eigenvalue equations. The response is evaluated by iteratively conducting complex eigenvalue analysis and modal combination. The accuracy is confirmed through comparison to nonlinear response history analysis of 2-D frame models. Finally, an example application is presented of a 3-D truss tower seismically retrofitted by replacing the braces with viscoelastic and then elasto-plastic dampers. The proposed design routine is used to rapidly identify novel and efficient damper arrangements and sizing distributions, avoiding computationally intensive nonlinear response history analysis.