The Inelastic Input Energy Spectra for Main Shock–Aftershock Sequences

This study investigates the input energy spectra for inelastic single-degree-of-freedom (SDOF) systems under main shock–aftershock sequences. The input energy spectra quantitatively reveal the effects of aftershocks on input energy, which verifies the necessity of incorporating aftershocks in energy-based seismic design. The investigation selects the sequences including one aftershock or two aftershocks respectively, according to the proposed criteria for selecting earthquake records. Then, the input energy for sequences is normalized by mass, m, and expressed in terms of the equivalent velocity, V E, seq . Next, the variation of V E, seq is studied in consideration of the hysteretic models, ductility values, periods of vibration, site conditions, relative intensities of aftershocks and number of aftershocks. The results indicate that the effects of aftershocks on input energy are significant in almost the whole period region. Finally, a simplified expression of input energy is proposed for incorporating aftershocks in energy-based seismic design.