变刚度框架—剪力墙结构抗地震荷载剪力墙数量的优化分析

本文用微分方程法导出结构单元矩阵,根据相邻两个计算单元的协调条件推导出传递矩阵。以结构基础的边界条件为初始值,通过传递矩阵从下而上传导到结构的顶部,再由其顶部边界条件求出第一单元位移及内力,从而求出考虑剪力墙剪切、弯曲变形时的结构变形和内力。文中介绍了用矩阵传导法形成柔度矩阵,用迭代法求结构的自振周期,以及等效地震荷载的换算。在表达了目标函数和约束条件的式子以后,建立了确定剪力墙最优数量的数学模型。最后通过工程实例来说明本文的方法。

Optimal Analysis for Shear Wall Quantity of Frame-Shear Wall Structure with Variable Rigidities under Seismic load

In this paper,the structural element matrix is derived by the method of differential equation,and the transfer matrix is established by the compatibility conditions of two adjacent calculated elements. The boundary conditions at the base of the structure are taken as initial values and these values are propagated from base to top of structure by transfer matrix.Then by using the boundary conditions at the top of the structure, the deformations and internal forces of the first element are obtained, Hence the structural deformations and internal forces considering shear and bending deformations of the shear wall are determined.This paper also presents the formation of flexibility matrix by the method of matrix propagation,the determination of structural natural period by iteration, and the calculation of equivalent earthquake loading.The mathematical model for determining the optimal quantity of shear wall is thus established since the objective function and constraint conditions are formulated.Finally,a practical example is illustrated to show the application of the proposed method.