Critical response evaluation of damped bilinear hysteretic SDOF model under long duration ground motion simulated by multi impulse motion

Abstract

Multi impulse is used as a representative of a series of many-cycle harmonic waves which substantially simulate the long-duration earthquake event. An analytical formulation is developed for the elastic-plastic response of a single-degree-of-freedom (SDOF) damped structure with bilinear hysteresis under the critical multi impulse condition. Following the procedure for elastic-perfectly plastic models, a novel procedure using an energy balance law is introduced. In this procedure, under the multi impulse condition, only the free-vibration exists, hence the energy balance law can be applied easily. An approximate but effective treatment of the energy dissipated by the viscous damping is a new perspective. It is shown that based on an analytical solution, the critical maximum plastic deformation and the corresponding critical impulse timing can be determined in the steady state condition depending on the input values. To investigate the reliability and accuracy of the proposed approach, a comparison is made with the response analysis outcome to the corresponding sine wave as a representative of the long-duration earthquake ground motion (GM).