A Method to Estimate Effective Viscous Damping Ratio and Restoring Force From the Dynamic Response Data of Structures

Dynamic response of structures is a complex process that is not well-understood. Seismic design codes allow structural systems of buildings to behave inelastically during strong ground shaking. While hysteretic energy dissipation due to inelastic behavior is rather well-understood, there exist other energy dissipation mechanisms which are not as well-understood. Energy dissipation due to mechanisms other than material non-linearity are often modeled in the form of a single, velocity proportional damping mechanism with an equivalent viscous damping ratio. In seismic design and dynamic analysis of structures, this equivalent viscous damping ratio is generally taken to be constant (e.g., 2 or 5% of the critical) regardless the response is elastic or inelastic. Instead of making such a strong assumption about the viscous damping ratio, which may have large influence on the peak response levels, it is advisable to use an effective viscous damping estimate based on studying the actual response of real structures responding to dynamic loads. Use of such obtained viscous damping will allow extraction of restoring forces from dynamic force estimates. At low strain-rate levels, such as those observed during seismic response, restoring forces match the resistance that develops during quasi-static loading, a method to estimate effective viscous damping and restoring force empirically from dynamic response of a structure is presented. The method considers inelastic response explicitly, i.e., no linearization assumptions are made for the load-deformation behavior of the structure. The presented method is tested on several computational simulation models with various hysteretic behaviors and a preset constant viscous damping ratio to verify that the algorithm (1) estimates a damping ratio close to the value used in the simulations, and accordingly, (2) captures the hysteretic behavior accurately. The method is illustrated using data obtained from reinforced concrete test specimens subjected to design-level base excitations on an earthquake simulator.