箱形梁剪力滞和剪切效应引起的附加挠度分析

将箱形梁腹板剪切变形纳入初等梁挠曲变形,在全截面上引入剪力滞翘曲修正系数,重新定义了剪力滞翘曲位移模式。选取剪力滞效应引起的附加挠度为广义位移,计算外力势能时考虑剪力滞广义位移的影响,应用能量变分法建立了反映剪力滞和剪切效应的控制微分方程,并导出了均布荷载作用下简支箱梁和两跨连续箱梁剪力滞和剪切效应附加挠度的解析解。数值算例表明,本文方法计算的总挠度值与有限元数值解吻合良好,从而验证了本文方法的合理性。算例箱梁剪切附加挠度明显大于剪力滞附加挠度;简支箱梁跨中截面的剪切和剪力滞附加挠度分别占初等梁挠度的2.50%和1.97%,两跨连续箱梁距中支点9l/16截面分别占27.45%和16.87%。

Analysis on additional deflection induced by effects of shear lag and shear deformation in box girders

The shear deformation of the webs of box girders was incorporated into the flexural deformation of the primary beam and the shear lag warping displacement mode was refined by introducing shear lag warping correction factor for the wholes cross section.The additional deflection induced by shear lag effect was chosen as generalized displacement.The influence of generalized displacement for shear lag was considered in calculation of potential energy.The governing differential equations for reflecting shear lag and shear deformation were established by applying energy variation method.The analytical solution of the additional deflection for shear lag and shear deformation of simply supported and two-span continuous box girders under uniform load was derived.Numerical examples show that the total deflections calculated in the present method are in good agreement with those by finite element method,validating the rationality of the present method.It is shown that the additional deflection caused by shear deformation is larger than that by shear lag for the box girder examples.The additional deflection for shear deformation and shear lag reaches respectively 2.5% and 1.97% of the primary beam deflection at the mid-span cross section of the simply supported box girder.For the two-span continuous box girder,the additional deflection reaches 27.45% and 16.87% of the primary beam deflection respectively at the cross section 9l/16 from the middle support.