考虑压-弯-扭耦合作用的开口截面杆件非线性静力模型

针对温室结构中檩条受力变形复杂且失稳现象严重的问题,对温室结构中开口截面檩条的力学性能进行研究。鉴于其受力变形的复杂性,将其按压弯扭杆件进行分析,综合考虑压-弯-扭耦合作用、约束翘曲、剪切变形因素,阐明二阶内力产生原理并建立杆件微段隔离体平衡方程;结合物理方程与几何方程,推导出关于扭转角和挠度的位移控制方程,进而获得压-弯-扭耦合作用下杆件位移及内力的几何非线性计算模型,同时给出其计算步骤。计算了开口截面杆件在集中扭矩、分布扭矩、压扭、弯扭、压弯扭5种荷载工况作用下的位移、变形及内力,并与理论解析解进行对比与分析,验证了计算模型的适用性及精确性。结果表明:本研究得到的非线性静力模型可用于温室结构中开口截面檩条在任意荷载工况组合条件下的位移、变形及内力计算。

Nonlinear static model for the bar with open section considering pressure-bending-torsion coupling

In view of the complex deformation and serious instability of purlin in greenhouse structure, the mechanical properties of open section purlin in greenhouse structure was studied. The open section purlin was taken as pressure-bending-torsion bar due to the complexity of mechanical deformation. Firstly, the second order internal force was discussed and equilibrium equations of bar microsegment isolator were established by considering the pressure-bending-torsion coupling, constraint warping and shear deformation. The displacement control equations in regard to both torsion angle and deflection were then deduced by combining with physical equations and geometric equations, and the geometric nonlinear calculation model for displacement and internal force of bar under the pressure-bending-torsion coupling was obtained. At the same time, a calculation procedure was put forward, the deformation, displacement and internal force of the bar with open section under concentrated torque, distributed torque, compression-torsion load, bending-torsion load and pressure-bending-torsion load were calculated, respectively. The calculation values were compared with the theoretical values to verify the applicability and accuracy of the model. In conclusion, the nonlinear static model in this study is suitable for the calculation of displacement, deformation and internal force of open section urline in greenhouse structure under any load condition.