Influences of bidirectional seismic excitations and P-Δ effect on ductility demand

A new biaxial Bouc-Wen model for seismic dynamic analysis of an inelastic Two-Degree-of-Freedom(2DOF) system under bidirectional horizontal excitations was developed by adopting the normalized displacement as a governing parameter and taking P-Δ effect, strength deterioration, stiffness degradation and strain hardening into account. In this model, the circular yield surface was used to describe the coupling effect between orthogonal normalized restoring forces. The influences of bidirectional excitations and P-Δ effect on statistical characteristics of seismic ductility demand of the inelastic 2DOF system were quantitatively investigated using 69 earthquake records. Analysis results showed that bidirectional excitations and P-Δ effect can significantly affect seismic ductility demand of the inelastic 2DOF system depending on structural parameters; the seismic ductility demand of systems with long period can be described as either Lognormal or Frechet distribution variable, while Frechet distribution is preferred for systems with short period; the seismic ductility demand of the inelastic 2DOF system under bidirectional excitations can be described as a square root of the square sum of seismic ductility demands of single-degree-of-freedom (SDOF) systems under unidirectional excitation.