剪力滞效应对箱形梁挠度影响的研究

从剪力滞翘曲应力的轴向平衡条件出发,选取双室箱梁的合理翘曲位移函数,引入相应于剪力滞翘曲变形的惯性矩和惯性积等几何特性,用能量变分法建立薄壁箱梁剪力滞效应分析的控制微分方程。通过求解控制微分方程,导出集中荷载和均布荷载作用下简支箱梁和悬臂箱梁的挠度公式及有限梁段单元刚度矩阵,模型试验和ANSYS壳单元计算结果证实了其正确性。结合简支、悬臂和连续箱梁数值算例,具体分析剪力滞效应对箱梁挠度的提高程度。结果表明,无论在集中荷载还是均布荷载作用下,剪力滞效应对简支箱梁的挠度均有显著提高。在集中荷载作用下,剪力滞效应对连续箱梁挠度的提高可达14%;对于跨宽比约为4.0～6.0的简支箱梁,可将按初等梁计算的跨中挠度乘以提高系数1.05～1.11;计算悬臂箱梁的挠度时,一般可以忽略剪力滞效应的影响。

Influence of shear lag effect on deflection of box girder

The warping displacement function for shear lag of twin-cell box girder is chosen upon the axial equilibrium of the relevant warping stress.Through defining the moment and product of inertia corresponding to the shear lag warping,the governing differential equations for shear lag analysis of thin-walled box girder are established by applying the energy variation method.The deflection formulas for simply supported and cantilever box girders under concentrated and uniform loads respectively and the finite segment element stiffness matrix are derived through solving the governing differential equations.Model test and ANSYS shell element results validate the formulas derived.The increase of deflection due to shear lag effect of simply supported,cantilever,and continuous box girders is numerically studied.It is shown that,the increase of deflection for simply supported box girder due to shear lag is remarkable under both concentrated and uniform loads.The increase of deflection for continuous box girder can reach 14% under concentrated loads.For a simply supported box girder with span-width ratio 4.0~6.0,the mid-span deflection calculated by elementary beam theory can be multiplied by 1.05~1.11.The influence of shear lag effect on the deflection of cantilever box girder can be generally ignored.