Seismic responses of postyield hardening single–degree-of-freedom systems incorporating high-strength elastic material

It is widely accepted that ductility design improves the seismic capacity of structures worldwide. Nevertheless, inelastic deformation allows serious damage to occur in structures. Previous studies have shown that a certain level of postyield stiffness may reduce both the peak displacement and residual deformation of a structure. In recent years, several high-strength elastic materials, such as fiber-reinforced polymer (FRP) and high-strength steel bars, have been developed. Application of these materials can easily provide a structure with a much higher and more stable postyield stiffness. Many materials, members, and structures that incorporate both high-strength elastic materials and conventional materials show significant postyield hardening (PYH) behaviors. The significant postyield stiffness of PYH structures can help effectively reduce both peak and residual deformations, providing a choice when designing resilient structures. However, the findings of previous studies of structures with elastic-perfectly plastic (EPP) behavior or small postyield stiffness may not be accurate for PYH structures. The postyield stiffness of a structure must be considered an important primary structural parameter, in addition to initial stiffness, yielding strength, and ductility. In this paper, extensive time history and statistical analyses are carried out for PYH single–degree-of-freedom (SDOF) systems. The mean values and coefficients of variation of the peak displacement and residual deformation are obtained and discussed. A new R-μ_p-T-α relationship and damage index for PYH structures are proposed. A theoretical model for the calculation of residual deformation is also established. These models provide a basis for developing the appropriate seismic design and performance evaluation procedures for PYH structures.