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提出一种考虑翘曲扭转(W型钢)的新型线弹性三维Timoshenko梁单元。它适用于分析由开口和中空截面(HCS)梁组成的空间结构。通过二阶梁理论(轴心受拉)与扭转(包括翘曲)的类比,建立非均匀扭转方程。局部梁单元刚度矩阵考虑二阶扭矩和剪力对变形的影响。将扭转角一阶导数的翘曲部分作为节点单元的附加自由度,该自由度代表双弯矩引起的扭转角。对数值分析结果进行讨论、比较和评价,对计算结果进行了试验验证,表明分析HCS梁应力-变形时考虑翘曲的重要性。
A new linear elastic three-dimensional Timoshenko beam element considering warpage (W-section steel) is proposed. It is suitable for analyzing spatial structures consisting of open and hollow cross-section (HCS) beams. Through the analogy between the second-order beam theory (axial tension) and torsion (including warping), a non-uniform torsion equation is established. Local Beam Stiffness Matrix Considering second order moment and shearing forces on deformation. The warped part of the first derivative of the twist angle is taken as an additional degree of freedom for the node element, which represents the twist angle caused by the double bending moment. The results of numerical analysis were discussed, compared and evaluated. The calculated results were verified by experiments, which showed the importance of considering warpage in stress-strain analysis of HCS beams.