Damping-adjusted combination rule for the response spectrum analysis of base-isolated buildings

Published online 9 May 2012 in Wiley Online Library (wileyonlinelibrary.com). The classical response spectrum method continues to be the most popular approach for designing baseisolated buildings, therefore avoiding computationally expensive nonlinear time-history analyses. In this framework, a new method for the seismic analysis and design of building structures with base isolation system (BIS) is formulated and numerically validated, which enables one to overcome the main shortcomings of existing techniques based on the response spectrum method. The main advantages are the following: first, reduced computational effort with respect to an exact complex-valued modal analysis, which is obtained through a transformation of coordinates in two stages, both involving real-valued eigenproblems; second, effective representation of the damping, which is pursued by consistently defining different viscous damping ratios for the modes of vibration of the coupled BIS-superstructure dynamic system; and third, ease of use, because a convenient reinterpretation of the combination coefficients leads to a novel damping-adjusted combination rule, in which just a single response spectrum is required for the reference value of the viscous damping ratio. The proposed approach is specifically intended for design situations where (i) the dynamic behaviour of seismic isolators can be linearised and (ii) effects of nonproportional damping, as measured by modal coupling indexes, are negligible in the BIS-superstructure assembly.