Effective length factor of a non-symmetrical cross-bracing system with a discontinuous diagonal

Abstract

A non-rectangular frame panel usually contains an asymmetrical cross-bracing system with interrupted diagonals, leading to a more complicated buckling behavior than a symmetrical bracing system with continuous diagonals. There have been many studies of the stability theory of symmetrical cross-bracing systems, but few related to non-symmetrical systems. In this study, we analyzed elastic out-of-plane buckling of a general non-symmetrical cross-bracing system with a discontinuous diagonal. The discontinuous and continuous diagonals have different material and geometrical properties, and are not intersected at their mid-spans. A characteristic equation is presented to compute the critical loading of a non-symmetrical cross-bracing system when the supporting diagonal is under either compression or tension. The results show that the characteristic equation of a non-symmetrical bracing system can be transformed into a form the same as that of a geometrically mono-symmetrical system. To facilitate design applications, direct closed-form empirical equations of effective length factor are established for a general non-symmetrical cross-bracing case. The validity of the proposed empirical equations was verified by comparing predicted and theoretical results, and those from a stiffness approach.

抽象

目 的

非矩形平面框架致使其交叉斜撑体系具有非对称 性, 而采用了非连续支撑的非对称非连续交叉支 撑体系的面外稳定问题更为复杂。 本文旨在通过 建立无量纲稳定特征方程, 从理论上深入阐释该 交叉支撑体系的面外屈曲特征, 并为工程设计提 供显式的压杆计算长度系数的计算公式。

创新点

1. 建立一般情况下非对称非连续交叉斜撑体系的 无量纲特征方程; 2. 针对各种可能受力工况, 详 细分析该交叉支撑体系的面外屈曲特征, 并给出 理论解释; 3. 提出非对称非连续交叉斜撑体系中 压杆计算长度系数的显式经验计算公式。

方 法

1. 通 过对非对称非连续交叉支撑体系进行弹性面 外屈曲建模, 以及稳定平衡方程的无量纲化, 推 导出其相应的特征方程; 2. 通过变量替换, 揭示 其内在对称性, 从而为经验公式的构造提供依 据; 3. 针对各种受力工况, 进行求解域分析和确 定, 完成特征方程的求解, 以进行面外屈曲特征 分析, 并提出压杆计算长度系数的经验公式; 4. 利用经验公式对多个实例进行计算, 并与基于 有限元的刚度法结果以及以往的文献数据进行 比较, 以验证经验公式的可靠性。

结 论

1. 推导出了非对称非连续交叉斜撑体系的特征方 程; 采用无量纲参数后, 该方程具有一般性。 2. 通 过变量替换, 该方程可以转换为与单轴几何对称 交叉斜撑相同的特征方程形式。 3. 当交叉斜撑中 的连续杆和非连续杆同时受压时, 非连续杆将率 先失稳。 4. 针对各种受力工况, 提出了交叉支撑 体系的压杆计算长度系数的显式经验公式, 且计 算结果兼具可靠性和准确性。