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 post-yield 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 post-yield stiffness. Many materials, members and structures that incorporate both high-strength elastic materials and conventional materials show significant post-yield hardening (PYH) behaviors. The significant post-yield 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 post-yield stiffness may not be accurate for PYH structures. The post-yield 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-μp-T- 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.

中文翻译：

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包含高强度弹性材料的后屈服硬化单自由度系统的地震响应

延性设计提高了世界范围内结构的抗震能力已被广泛接受。然而，非弹性变形会导致结构发生严重损坏。先前的研究表明，一定水平的屈服后刚度可以减少结构的峰值位移和残余变形。近年来，已经开发了几种高强度弹性材料，如纤维增强聚合物（FRP）和高强度钢筋。这些材料的应用可以轻松提供具有更高和更稳定的屈服后刚度的结构。许多结合高强度弹性材料和传统材料的材料、构件和结构表现出显着的屈服后硬化 (PYH) 行为。PYH 结构显着的屈服后刚度有助于有效减少峰值变形和残余变形，为设计弹性结构提供了一种选择。然而，先前对具有完美弹塑性 (EPP) 行为或小屈服后刚度的结构的研究结果对于 PYH 结构可能并不准确。除了初始刚度、屈服强度和延展性之外，结构的屈服后刚度必须被视为重要的主要结构参数。在本文中，对 PYH 单自由度 (SDOF) 系统进行了广泛的时程和统计分析。获得并讨论了峰值位移和残余变形的平均值和变异系数。提出了 PYH 结构的新 R-μp-T-α 关系和损伤指数。还建立了残余变形计算的理论模型。这些模型为为 PYH 结构开发适当的抗震设计和性能评估程序提供了基础。