Statistics of inelastic responses of hysteretic systems under bidirectional seismic excitations

This study attempts to assess characteristics of the peak ductility demand and damage index, and to develop simple equations for estimating ductility demand of structures under bidirectional seismic excitations. To achieve these goals, parametric studies by considering 381 California records from 31 seismic events are carried out for idealized inelastic 2-degree-of-freedom systems whose hysteretic behavior is represented by the Bouc–Wen model with biaxial interaction. Use of the Bouc–Wen model to represent inelastic behavior of structural systems is advantageous as the model can incorporate strength/stiffness degradation and take into account different degrees of biaxial interaction. Based on the results of nonlinear dynamic analysis, it was concluded that, in general, the ductility demand under bidirectional seismic excitations are higher than that under unidirectional excitations. Simple approximate equations are proposed to estimate the ductility demand and normalized dissipated hysteretic energy. Nonlinear dynamic responses obtained for the considered records suggest that the proposed approximations are adequate, 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.