Uniform deformation distribution of structures at different seismic hazard levels using endurance time method

This paper evaluates the application of the endurance time method in the optimum performance design of structures using the uniform deformation theory. The structures used in this study include shear-building systems with 5, 10, and 15 stories, and steel moment-resisting frames with 3, 7, and 12 stories. Initially, shear-building systems are optimized to have uniform story ductility ratios at low, moderate and high seismic hazard levels separately using three sets of ground motion records and a compatible series of endurance time acceleration functions. The effectiveness and accuracy of the endurance time method are assessed by comparing lateral force distribution obtained from this method with its corresponding attained from ground motion records. Moreover, as the number of stories and target ductility increases, the compatibility of these two methods improves. However, it is found that the optimum structure at one seismic hazard level does not necessarily lead to the optimum structure at other seismic hazard levels. Next, by adding dampers with gap to the systems, a procedure is suggested to optimize these structures at different seismic hazard levels simultaneously. These dampers are activated at moderate and high seismic hazard levels. Finally, similar optimization algorithm is used for steel moment-resisting frames to make their story drift ratios or plastic hinge rotations uniform along the height at different seismic hazard levels. Results show that combining endurance time method and uniform deformation theory leads to a promising optimization procedure that can significantly reduce computational costs with reasonable error.