双向荷载下单层平面索网结构静力解析方法:控制方程组与对数解

STATIC ANALYTICAL METHOD OF SINGLE-LAYER PLANE CABLE NET STRUCTURES UNDER BIDIRECTIONAL UNIFORM LOAD: BASIC CONTROL EQUATIONS AND LOGARITHMIC SOLUTION

单层平面索网玻璃幕墙结构主要承受面内均布恒载和法向风荷载。本系列研究将恒载和风载均等效为均布静载,以形成考虑幕墙恒载影响的单层平面索网结构的解析方法。该文基于连续化理论和在两个方向综合应用两种不同单索理论的思路,首次建立了考虑面内竖向恒载影响的单层平面索网结构静力平衡方程和适用于该类结构的变形协调方程;并阐述了竖向恒载影响挠曲变形的规律,建立系统科学的基本解析理论。根据单根横索和竖索的变形特性构造了含待定系数的挠曲面假定函数,并应用迦辽金法确定这些待定系数,给出了轮流迭代修正的求解方法。算例证明:该文解析方法得到的结果与有限元法吻合较好,最大挠度及位置的精度尤为突出,具有较强的工程应用价值。

The single-layer plane cable nets, which are the structure of a glass curtain wall, are mainly designed to bear the uniformly distributed vertical dead load and horizontal wind load. The paper aimed at presenting a complete static analytic method considered the vertical dead load effects for such kind of single-layer plane cable net facade. Firstly, such two kinds of loads are simplified to a uniformly distributed load and the basic assumptions are provided to analyze the net in this series of studies. Then, based on the continuous theory, the cable net is equivalent to an orthotropic membrane. Secondly, the static equilibrium equations considering the effects of the vertical dead load and the deformation compatibility equations are established. The compatibility equations respectively describe the deformation on two directions, which referred to two kinds of mature single cable theories. Finally, according to the deformation characteristics of single horizontal cable and vertical cable, the assumed function of the deflection surface is constructed, which include undetermined coefficients. They are determined by the application of a Galerkin method, and the loop iterative correction method for solving them was given. Numerical examples show that the analytical method results in a good agreement with that of the finite verifiedthat the theoretical analysis method is correct and the engineering applicability of which is very strong.