Standard hysteretic energy spectra of constant ductility factors for bi-directional earthquake motions

The current theory of hysteretic energy response spectra depends on the theory of single degree of freedom system subjected to single directional earthquake motion,in which the imbalance and coupled characteristics of multi-dimensional responses of structures are not considered. So,the standard hysteretic energy spectrum is presented by considering the single-mass bi-degrees of freedom system subjected to bi-directional earthquake motions. The spectral values between bi-degrees of freedom system and single degree of freedom system are compared and the results show that the latter are lower in some cases. The statistical average spectra for hard soil site,medium soil site and soft soil site are established and analyzed on the basis of 178 earthquake motion records. Analytic results show that: the standard hysteretic energy spectra for each soil site have their own characteristics; the influence of ductility factor on spectral value is obvious in soft soil site,but it is not obvious in hard and medium soil sites.