An evaluation of inelastic responses of hysteretic systems under bidirectional seismic excitations

An assessment of the statistics of peak displacement ductility demand aimed at developing simple equations for estimating ductility demand of structures under bidirectional seismic excitations is carried out for idealized inelastic 2-degree-offreedom systems. The hysteretic behavior of the structural system is represented by the Bouc-Wen model with biaxial interaction. Based on the dynamic analysis results, it was concluded that in general the ductility demand under bidirectional seismic excitations are much higher than that under unidirectional excitations. Therefore, underestimation of the damage and seismic risk is likely to occur if the effect of bidirectional excitations is ignored. Simple approximate equations are proposed for estimating the ductility demand and normalized dissipated hysteretic energy. These approximations used the results of unidirectional excitations for single-degree-of-freedom systems. Nonlinear dynamic responses obtained for the considered records suggest that the proposed approximations are adequate. The results also shown that the ductility demand under bidirectional excitations can be modeled by a lognormal or Frechet variate, depending on the vibration period, and that the coefficient of variation of ductility demand under bidirectional excitations is comparable to that obtained under unidirectional excitations.