高层建筑结构刚度退化与地震作用响应关系的理论分析

弹塑性分析方法是基于性能抗震设计的重要手段，由于影响该计算结果的因素较多，对分析结果可靠性的合理评判至关重要。从理论角度给出了高层建筑结构在地震作用下刚度退化系数和弹塑性耗能附加阻尼的定量关系，在此基础上推导了结构的内力响应和位移响应随刚度退化而发生变化的计算式，并分析了结构自振周期、初始阻尼比及场地特征周期等参数的影响规律。同时讨论了内力响应与位移响应趋势不一致以及弹塑性分析的基底剪力响应大于相应弹性结果等两类不满足基本规律的特殊问题。最后，通过对一个实际工程进行罕遇地震作用下的弹性与弹塑性时程分析，得到基底剪力和位移的响应，同时运用本文推导的理论计算式进行计算，结果显示，计算结果与有限元分析结果基本吻合。研究成果可为基于性能抗震设计以及弹塑性时程分析的结果评判提供参考。

Theoretical analysis about relationship between seismic response and structural stiffness degradation of high-rise building

Elasto-plastic analysis method is an important means in performance-based seismic design. Since there are many factors that will affect the calculation results, it is essential to give a reasonable judgment on the analysis results. The quantitative relationship between high-rise building structure’s stiffness degradation and additional damping ratio caused by elasto-plastic energy dissipation was discussed from the theoretical viewpoint. On this basis, the formula of changes in internal force response and displacement response with overall stiffness degradation was derived, and impact of some relevant parameters on the proposed formula was also discussed, such as vibration period, initial damping ratio, characteristic period of ground motion, etc. In addition, some special response problems, such as inconsistent internal force and displacement trends, and the greater magnitude of base shear response from elasto-plasitc analysis than that from elastic result, were also focused on and analyzed reasonably. At last, the elastic and elasto-plastic time-history analysis were conducted for an actual project, and the total base shear force and displacement response variation ratio were obtained. At the same time the coefficient was calculated by the proposed formula in this paper and the results show that both results are basically consistent. The research conclusions can provide theoretical reference to performance-based seismic design and elasto-plastic analysis results’ evaluation.