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本文从三维动力方程出发,应用反应谱理论推导了空间结构在任意方向地面运动作用下结构变形与内力的计算方法。所得到的算式是十分简单、实用的。这套公式对于空间问题自然地计及了扭转效应,而对于平面模型的处理则与当前规范完全一致。可以说,这是当前抗震规范所规定的反应谱方法在三维结构分析中的自然推广及理论论证。 三维反应谱方法已在高层建筑专用程序DASTAB上实现。动力分析可以采用与静力分析同样复杂、细致的模型。国内许多大设计院用DASTAB程序对多种形式的三维结构模型进行抗震计算(包括水平面内0°,45°,90°方向的地震作用),均对计算结果表示满意。由于应用了多层子结构,多级主从关系等技术,从而大大减少了数据准备及计算工作量。
In this paper, starting from the three-dimensional dynamic equation, the response spectrum theory is used to derive the calculation method of the structural deformation and internal force of the spatial structure under the action of ground motion in any direction. The resulting formula is very simple and practical. This set of formulas naturally accounts for the torsional effect of the space problem, while the handling of the planar model is exactly the same as the current specification. It can be said that this is a natural promotion and theoretical proof of the response spectrum method specified in the current seismic code in the three-dimensional structure analysis. The three-dimensional response spectrum method has been implemented on the high-rise building dedicated program DASTAB. Dynamic analysis can use the same complex and detailed model as static analysis. Many large design institutes in China use the DASTAB program to perform seismic calculations on various forms of three-dimensional structural models (including the 0°, 45°, and 90° directions of seismic motion in the horizontal plane), and both of them are satisfied with the calculation results. Due to the application of multi-level sub-structures, multi-level master-slave relationships and other technologies, data preparation and calculation workload are greatly reduced.