Hysteretic Energy Demand in SDOF Structures Subjected to an Earthquake Excitation: Analytical and Empirical Results

In energy-based seismic design approach, earthquake ground motion is considered as an energy input to structures. The earthquake input energy is the total of energy components such as kinetic energy, damping energy, elastic strain energy and hysteretic energy, which contributes the most to structural damage. In literature, there are many empirical formulas based on the hysteretic model, damping ratio and ductility in order to estimate hysteretic energy, whereas they do not directly consider the ground motion characteristics. This paper uses nonlinear time history (NLTH) analysis for energy calculations and presents the distribution of earthquake input energy and hysteretic energy of single-degree-of-freedom (SDOF) systems over the ground motion duration. Seven real earthquakes recorded on the same soil profile and three different bilinear SDOF systems having constant ductility ratio and different natural periods are selected to perform NLTH analyses. As results of nonlinear dynamic analyses, input and hysteretic energies per unit masses are graphically obtained. The hysteretic energy to input energy ratio (E_H/E_I) is investigated, as well as the ratio of other energy components to energy input. E_H/E_I ratios of NLTH analysis are compared to the results of empirical approximations related E_H/E_I ratio and a reasonable agreement is observed. The average of E_H/E_I ratio is found to be between 0.468 and 0.488 meaning nearly half of the earthquake energy input is dissipated through the hysteretic behavior.