非线性温度梯度作用下简支箱梁的剪力滞效应

Shear lag effect on the cantilever box girder under nonlinear temperature gradient

摘要:

为分析非线性温度梯度作用下箱梁的自应力分布,考虑上、下翼板剪切转角的最大差值幅值和相位的不同及截面的内力平衡,提出应力平衡的双参数剪力滞翘曲位移函数.在此基础上,根据最小势能原理,建立简支箱梁的微分方程和边界条件.随后计算非线性温度作用下简支箱梁的自应力,并与有限元结果进行比较.算例分析结果表明,在非线性温度梯度作用下,双参数法所得计算结果与有限元分析结果一致,且满足全截面轴力自平衡的双参数法计算精度高于直接双参数法的计算结果.简支箱梁在非线性温度梯度下的温度自应力导致端部产生剪力滞效应,温度剪力滞效应的影响范围约为1.5倍箱梁宽度,且应力结果大于基于平截面所得的应力.对于截面上下对称的无悬臂翼板箱梁,考虑剪力滞效应的跨中应力和平截面假定的计算结果相同；对于截面上下不对称的带悬臂翼板箱梁,由于非线性温度引起剪力影响截面的曲率,即使在跨中区域平截面假定所得的温度应力依然小于精确解,双参数法修正了剪力对截面曲率的影响而显著提高了计算精度.

Abstract:

Considering the difference of the maximum amplitude and phase of the shearing angle of top and bottom flanges as well as the equilibrium of the internal force of the section, the two-parameter shear lag warpage displacement function of the stress balance was proposed. On this basis, the differential equations and boundary conditions of simply supported box girder were established based on the principle of minimum potential energy. Then, the self-equilibrating stress of the simply supported box girders at nonlinear temperature was calculated and compared with the finite element results. Numerical analysis show that results of the two-parameter method were consistent with those of the finite element analysis, and the calculation accuracy of the two-parameter function satisfying the axial force self-balance of section was higher than that of the direct method. The self-equilibrating stress of the simply supported box girder in the nonlinear temperature gradient led to the shear lag effect at the end. The influence range of the temperature shear lag effect was about 1.5 times of the width of the box girder, and the stress result was greater than the stress based on the plane cross-section assumption. For the cantilever box girder with symmetry section, the calculation results of the stress in the span considering the shear lag effect were the same with the results obtained based on the plane cross-section assumption. For the cantilever flanged box girder with asymmetric section, the plane section method neglected the modification of section curvature which was caused by shear force due to nonlinear temperature, so the calculation error of the mid-span stress by plane section method was still smaller than the exact solution. While the two-parameter method modified the influence of shear force on section curvature and improved the calculation precision.