Seismic vulnerability assessment of multi-degree-of-freedom systems based on total input energy and momentary input energy responses

In energy-based seismic evaluation and design, input energy as a seismic demand parameter and hysteretic energy are two important factors. Previous studies for seismic assessment and design based on energy approach have been generally limited to single-degree-of-freedom (SDOF) structures. The purpose of this paper is to find a suitable energy-based parameter for estimation of the damaging potential of ground motion in reinforced concrete frames of multi-degree-of-freedom (MDOF) systems. In this regard, 40 common reinforced concrete frames subjected to four different earthquakes have been analyzed. The results indicate that maximum momentary input energy is a more appropriate parameter than maximum total input energy for estimation of structural damage in short-duration earthquakes or those in which the major damage to structures happens within a short duration of ground motion. In addition, in earthquakes with a wide frequency range, the predominant period of ground motion in Fourier spectrum is shown to be the period corresponding to maximum input energy.