Energy Response Spectra of Single-Mass Bi-Degrees of Freedom Systems for Hard Soil Site

The traditional energy response spectra depend on the single-directional earthquake excitations and two dimensional dynamic analyses, in which the imbalance and coupled characteristics of multi-dimensional responses of structures are not considered. So, the energy spectra of constant ductility facotors are developed by considering the single-mass bi-degrees of freedom systems subjected to perpendicular bi-directional earthquake motions. The restoring force rule of single-mass bi-degrees of freedom systems is assumed as two dimensional yield-surface plasticity function. The relative energy spectra for input energy, hysteretic energy, kinetic energy and damping energy are presented and analyzed based on 34 pair earthquake motion records of hard soil site. Analytic results show that the energy spectra for hard soil site have their own characteristics, and the spectral forms and values are affected strongly by vibration period, ductility factor and period ratio of single-mass bi-degrees of freedom systems.