Simplified Analysis Method for Deflection of Thin-Walled Box Girder
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摘要: 为寻求考虑剪切变形影响的薄壁箱梁挠度计算简化方法，以单位力法为基础分析薄壁箱梁的挠曲变形. 首先，通过对薄壁箱梁挠曲剪应力分布模式的分析获取组成箱梁各壁板的剪切影响系数表达式，基于该剪切影响系数，利用Timoshenko梁理论导出简单箱梁挠度的解析表达式；其次，利用卡式第二定律推导出箱梁的梁段单元分析模型，编制了求解变截面箱梁等复杂结构的电算程序；最后，对等截面及变截面箱梁的算例模型进行了分析. 数值算例结果表明：程序计算的挠度与实测值及ANSYS空间有限元结果误差在3%以内；针对数值算例，剪切变形使箱梁挠度增大20%以上；随着宽高比的增大，翼板剪切产生的附加挠度会增大，而腹板情况与之相反.Abstract: In order to find a simplified method for calculating the deflection of the thin-walled box girder under the influence of shear deformation, the flexural deformation of the thin-walled box girder is analyzed on the basis of the unit force method. Firstly, by analyzing the distribution mode of the flexural shear stress of the thin-walled box girder, the expressions for the shear influence coefficients of each wallboard constituting the box girder are derived. With the shear influence coefficient, the analytical expression of the simple box girder deflection can be deduced by using Timoshenko beam theory. Secondly, the beam segment analysis model of the box girder is built by using the Castingliano’s second theorem and the program is compiled for solving the complex structure such as the box girder with variable sections. Finally, the example models of the box girders with constant and variable sections are analyzed. The results of numerical examples show that the error between the deflection calculated by the program and the measured and the ANSYS finite element results is within 3%. For the numerical example, the deflection of the box girder is increased by more than 20% due to the shear deformation. Parametric analysis also indicate that the additional deflection caused by the shearing of the flange increases with the width-to-height ratio, whereas for the web, the case is the opposite.
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表 2 跨中截面处挠度分析
Table 2. Mid-span deflection analysis
荷载 vc/mm vf/mm vw/mm （vf•vc−1）/% （vw•vc−1）/% 均布 0.228 0.087 0.072 38 32 集中 0.193 0.073 0.049 38 25 
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