集中荷载下矩形管翼缘组合梁侧扭屈曲研究

Research on Lateral-torsional Buckling of Rectangular Tubular Flange Composite Beams Under Concentrated Loads

摘要:

为研究集中荷载下跨中设置扭转支撑矩形管翼缘组合梁的稳定性能,采用"板-梁理论",建立了矩形管翼缘组合梁的弹性侧扭屈曲总势能方程,选取位移函数,运用能量变分法求解其屈曲方程,得到了矩形管翼缘组合梁弹性侧扭屈曲临界弯矩解析解。采用1stOpt软件,考虑多参数的影响,对不同截面尺寸、跨度、扭转支撑刚度下组合梁的弹性侧扭屈曲临界弯矩进行拟合,获得有无扭转支撑的组合梁弹性侧扭屈曲临界弯矩的计算公式,并与有限元分析结果进行对比,相对误差在5%以内,验证了计算公式的精确性。最后,分析混凝土强度、腹板高厚比、跨高比和上翼缘含钢率等参数对矩形管翼缘组合梁稳定性能的影响规律。研究发现,随着扭转支撑刚度的增加,组合梁的弹性侧扭屈曲临界弯矩逐渐增大,梁的稳定性得到提高;当扭转支撑刚度达到门槛刚度时,组合梁的弹性侧扭屈曲临界弯矩不再提高;改变混凝土强度或腹板高厚比不会使梁的弹性侧扭屈曲临界弯矩产生明显变化,而减小跨高比或提高上翼缘含钢率会明显增加该类组合梁的弹性侧扭屈曲临界弯矩。

Abstract:

To study the stability performance of rectangular tubular flange composite beams with torsional bracing set at the mid-span under concentrated loads, the "plate-beam theory" was adopted, and the elastic lateral-torsional buckling total potential energy equation of the rectangular tubular flange composite beam was established. The displacement functions were selected, and the energy variation method was used to solve the buckling equation, and the analytical solution for the elastic lateral-torsional buckling critical moment of the rectangular tubular flange composite beam was obtained. Then, using the 1stOpt soft ware, considering the influence of multiple parameters, the elastic critical moments of the composite beams under different cross-sectional dimensions, spans, and torsional bracing stiffness were fitted, and the calculation formulas for the elastic critical moments of the composite beams with and without torsional bracing were obtained. These formulas were compared with the finite element analysis results, and the error was within 5%, verifying the accuracy of the calculation formulas. Finally, the influence laws of parameters such as concrete strength, web height-thickness ratio, span-height ratio, and upper flange steel content ratio on the stability performance of the rectangular tubular flange composite beam were analyzed. The study found that as the torsional bracing stiffness increased, the elastic lateral-torsional buckling critical moment of the composite beam gradually increased, and the stability of the beam was improved; when the torsional bracing stiffness reached the threshold stiffness, the elastic lateral-torsional buckling critical moment of the composite beam no longer increased; changing the concrete strength or web height-thickness ratio would not cause significant changes in the elastic lateral-torsional buckling critical moment of the beam, while reducing the span-height ratio or increasing the upper flange steel content ratio would significantly increase the elastic lateral-torsional buckling critical moment of this type of composite beam.