考虑翼板局部弯曲及剪力滞效应的波形钢腹板组合箱梁挠度分析

Deflection Analysis of Composite Box Beam with Corrugated Steel Webs Considering Local Bending of Flange and Shear Lag Effect

在位移场中引入挠度1阶导数考虑翼板局部弯曲,添加剪力滞强度函数和截面转角计入翼板剪力滞效应和波形钢腹板剪切变形,基于能量变分原理获得波形钢腹板组合箱梁的控制微分方程,进而推导包括挠度在内的综合考虑翼板局部弯曲、剪力滞效应和波形钢腹板剪切变形的位移变量解析解,并分析翼板局部弯曲和剪力滞效应对不同高跨比、腹板高度占比、宽跨比、板宽比组合箱梁挠度的影响。结果表明:该解析解能较精确地计算组合箱梁的挠度;忽略翼板局部弯曲和剪力滞效应将导致组合箱梁的挠度计算结果误差过大;对于波形钢腹板组合箱形连续梁,不考虑翼板局部弯曲和剪力滞效应,跨中挠度将分别被高估13.0%和低估7.0%;剪力滞效应对翼板与波形钢腹板间的剪力分配几乎无影响,翼板局部弯曲会显著降低波形钢腹板剪力承担比,大大减小梁体挠度;剪力滞对挠度的放大效应随宽跨比的增大而增大,而翼板局部弯曲对挠度的减小作用随着高跨比和宽跨比的增大及波形钢腹板高度占比的减小而显著提高;翼板局部弯曲和剪力滞效应对连续梁挠度的影响比简支梁更大。

The local bending of flange is incorporated by introducing the first derivative of the deflection to the displacement field.The shear lag effect of flanges and the shear deformation of corrugated steel webs(CSWs)are calculated by adding the shear lag intensity function and the cross-sectional rotation.The governing differential equations for composite box beams with CSWs are obtained according to the energy variational principle.And the closed-form solutions to all the displacement variables including the deflection are then derived with the comprehensive consideration of local bending of flange,shear lag effect as well as the shear deformation of CSWs.The local bending of flange and shear lag effects on the deflections are subsequently analyzed for composite box beams with different depth-span ratios,web-to-slab depth ratios,width-span ratios,slab width ratios.The results demonstrate that the deflections of composite box beams can be well predicted by the closed-form solutions.The ignoration of flange local bending and shear lag results in considerable errors in the deflection computation of composite box beams.For the continuous composite box beam with CSWs,the mid-span deflections without considering flange local bending and shear lag can be overestimated by 13.0%and underestimated by 7.0%,respectively.The shear lag has almost no effect on the shear force allocation between the flanges and the CSWs,while the flange local bending can significantly alleviate the beam deflection through reducing the shear bearing ratio of CSWs.The amplification effect of shear lag upon the deflections enlarges with the increase of the width-span ratio,whereas the reduction impact of flange local bending on the deflections substantially enhances with the increase of the depth-span and width-span ratios,also with the decrease of the web-to-slab depth ratio of CSWs.The impacts of flange local bending and shear lag on the deflections of the continuous beam are more significant,in comparison with the case of the simply-supported beam.