薄壁箱梁挠曲性能的矩阵分析

在选取薄壁箱梁剪力滞控制微分方程的齐次解作为单元位移函数建立形函数矩阵基础上,运用虚功原理推导竖向集中荷载作用下单元等效节点力公式,提出双室箱梁的合理剪滞翘曲位移函数。通过对变截面悬臂箱梁有机玻璃模型进行计算,验证提出的梁段单元对分析变截面箱梁的有效性。结合实际箱梁算例,分析预应力混凝土变截面连续箱梁的挠曲性能。研究结果表明:所提出的梁段单元用于变截面箱梁分析时,具有较高的计算精度;在竖向集中荷载作用下,箱梁剪滞力矩图是一条平滑曲线,任意截面处剪滞力矩均不大于弯矩;剪滞效应使连续箱梁的跨中挠度明显增大,工程实践中必须认真对待。

Matrix Analysis on Flexural Behavior of Thin-walled Box Girder

On the basis of the shape function matrix which is established through assuming the homogeneous solution to the governing differential equation for shear lag of the thin-walled box girder as the element displacement function,the formula of the equivalent nodal force of the element under vertical concentrated loads is derived by applying the principle of virtual work.The reasonable warping displacement function of shear lag is proposed for the box girder with the twin-cell cross-section.The plexiglass model of the cantilever box girder with variable cross-sections is calculated,thus validating the effectiveness of the finite segment element in analysis of the box girder with variable cross-sections.The flexural behavior of the prestressed concrete continuous box girder with variable cross-sections is analyzed through a practical example.The results show as follows: The finite segment element has high computing efficiency for the box girder with variable cross-sections;under the action of vertical concentrated loads,the shear lag moment diagram of the box girder is a smooth curve and the absolute value of the shear lag moment is not greater than that of the bending moment at any cross-sections;the shear lag effect increases the mid-span deflection of the continuous box girder significantly,which shall be treated seriously in engineering practice.