Calibration of a damping law to predict probabilistic seismic capacity by nonlinear static analysis

Under strong earthquakes, real structures generally experience significant dynamic response and their members perform in the nonlinear range of behaviour. To this end, nonlinear dy-namic analysis is widely recognised as the most accurate tool to predict all the aspects of the structural response demanded by the single ground motions. However, many uncertainties af-fect the seismic response of the structure and the related performance. Among these uncertain-ties, the feature of the ground motions is the most important one. Hence, probabilistic ap-proaches for the evaluation of the seismic performances, based on Incremental Dynamic Analysis and fragility curves, has recently gained popularity in the scientific community. On the other hand, computational cost of these analyses is still too high to be suitable for profes-sional purposes. For this reason, nonlinear static methods of analysis still represent a com-promise between accuracy and computational burden. Unfortunately, the capacity assessed by nonlinear static methods of analysis often underestimates that predicted by probabilistic ap-proaches and nonlinear dynamic analysis. This is due to the fact that nonlinear static methods of analysis do not account adequately for the increase of energy dissipation induced by the structural damage. In this framework, a new damping law is formulated, calibrated and in-corporated in the nonlinear static method of analysis to predict accurately the capacity of RC framed structures determined by the probabilistic approach. To this end, a set of frames repre-sentative of buildings with RC framed structure have been designed, numerically modelled and assessed by incremental nonlinear dynamic analysis and nonlinear static analysis.