Estimating Effective Viscous Damping and Restoring Force in Reinforced Concrete Buildings

In seismic design, buildings are designed to respond to strong earthquake ground motions inelastically. The engineering norm followed in design and analysis is to use constant modal viscous damping ratios to account for all energy dissipation aside from that arising from material nonlinearity. In general, equivalent linear models, which aim to capture primarily the peak response with typically 2–5 % of critical damping are employed. In this paper, we show that the effective viscous damping ratio can be estimated from the dynamic response of actual building structural systems without linearization of the load-deformation characteristics. The empirical method we present, which estimates the effective viscous damping ratios of buildings, has been applied to several laboratory specimens and actual buildings. We show that the effective viscous damping ratio in a low to mid-rise reinforced concrete (RC) building responding at its dominant mode (equivalent of fundamental mode in linear elastic systems) varies linearly with the effective period of its dominant mode. The practical use of the method is demonstrated using acceleration records obtained in two 9-story small-scale RC laboratory test specimens during a series of strong base motions. Fundamental mode envelopes of hysteretic responses, that is, the backbone curves for both structures are estimated by excluding higher mode effects from the measured responses.