基于设计反应谱的空间结构弹塑性地震反应分析方法

空间结构非线性等效单自由度体系的荷载-位移曲线后屈服段较短，采用等能量方法将其转化为双折线时易产生较大计算误差，且双折线拐点需迭代确定。针对此问题，采用Ramberg-Osgood模型描述空间结构等效单自由度体系荷载-位移滞回曲线；基于等效线性化方法，采用最大位移对应的割线刚度作为等效线性体系刚度k_e；对滞回曲线积分得到滞回环面积，令滞回耗能与等效线性体系阻尼耗能相等，导出等效黏滞阻尼ζ_e。将线性加速度设计反应谱变换为T(周期)-ζ(阻尼比)-d(位移)格式，与空间结构等效线性体系的T_e(等效周期)-ζ_e-d曲线联立，用图解法直接计算等效线性体系的地震位移反应，并进一步得到空间结构的整体地震反应。采用所提出的方法计算柱面网壳和球面网壳结构的非线性地震反应。结果表明：该方法简洁高效，无需迭代，易于编程实现，对空间结构地震位移反应求解精度较高。

A procedure for elasto-plastic seismic response analysis of spatial structures based on design response spectra

For the equivalent single-degree-of-freedom (ESDF) system of a spatial structure, the post-yielding stage of its load-displacement curve is relatively short, therefore, large errors would occur as the force-displacement (F-d) curve being bi-linearized via conventional methods. Besides, some iterative processes are needed in determining the inflection point of the F-d curve herein. In view of these problems, the Ramberg-Osgood model is adopted to describe the hysteretic curves of the ESDF systems of spatial structures. Based on an equivalent linearization procedure, the stiffness of the equivalent linearized system is set equal to the secant stiffness of the nonlinear ESDF system at its maximum displacement. The area of a hysteretic loop of the nonlinear ESDF system is calculated through integration of the hysteretic curve, and the equivalent viscous damping is derived by setting the energy dissipated equal to that dissipated by hysteresis. By transforming the linear acceleration response spectra into the period-damping ratio-displacement format, and solving the simultaneous formulas consisting of the transformed spectra and the equivalent period-damping ratio-displacement curve of the equivalent linear system through a graphic method, the seismic responses of the equivalent linear system is obtained. Accordingly, the overall seismic response of the spatial structure is got. Nonlinear seismic responses of a cylindrical latticed shell and a spherical latticed shell are computed by means of the proposed method. Results demonstrate that the proposed method is simple, efficient and involves no iteration. In addition, this method is easy for execution via computer programing, and could yield relatively accurate seismic displacement responses for spatial structures.