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基于能量变分原理,考虑箱梁横截面正应力轴向平衡条件和剪切变形的影响,构建了包含参数m的新剪力滞翘曲位移函数。以所得应力均方误差与挠度均方误差为精度标准,计算分析了不同m值(即不同幂次)抛物线下新构建剪力滞翘曲位移函数的适应性,得出了二次抛物线形式较为精确合理的结论。通过比较典型位置所得应力值,进一步分析了新构建剪力滞翘曲位移函数(m=2)的适应性和精确性。针对所得集中荷载作用下简支箱梁翼缘悬臂板最外端应力有较大偏差的情况,通过应力曲线拟合,得到了集中荷载作用下简支箱梁悬臂板的应力改进公式。将应力改进后新构建剪力滞翘曲位移函数与基本翘曲位移函数所得的应力与竖向挠度进行比较,论证了通过本文新构建的剪力滞翘曲位移函数推导计算所得的应力公式和应力改进公式的高精度。
Based on the theory of energy variation and considering the influence of axial stress and axial shear stress on the cross section of box girder, a new shear lag warping displacement function with parameter m is constructed. Based on the accuracy standard of mean square error and deflection mean square error of stress, the adaptability of newly constructed shear lag warp displacement function under parabola with different m values (ie different power) is calculated and analyzed. The quadratic parabola form is obtained Accurate and reasonable conclusion. By comparing the stress values of typical locations, the adaptability and accuracy of the newly constructed shear lag warp displacement function (m = 2) are further analyzed. Aiming at the large deviation of the outermost stress of the cantilever plate of the simply supported box girder under the concentrated load, the stress of the cantilever plate under the concentrated load is obtained through the stress curve fitting. After comparing the stress and vertical deflection of the newly constructed shear lag warpage displacement function with the basic warpage displacement function after the stress is improved, it is demonstrated that the stress formula derived from the newly developed shear lag warpage displacement function and the calculated stress formula High accuracy of stress improvement formula.