ㄇ形梁剪力滞效应的解析解

精确分析ㄇ形梁在纵横向荷载共同作用下,其横断面上正应力分布规律对于计算其有效宽度有重要意义,应用力法原理,先将ㄇ形梁和翼板截开成矩形截面梁和平面应力板,在截面上代之以赘余的分布剪力,对于平面应力板,通过利用板变形的对称性来简化其边界条件,然后假设一个满足板的控制方程的Airy应力函数求得板的应力和位移,再利用Timoshenko梁理论求得梁的挠度和转角,根据截面上梁与板的纵向位移相等的变形协调条件便可最终确定截面上的分布剪力,给出的数值算例验证了方法的有效性,并与铜陵长江公路大桥主梁的模型有限元结果和试验结果作了对比,解析解法还可用来检验其他各种数值计算方法的精度,并可推广到其他多跨薄壁结构梁桥的膜应力分析中。

AN ANALYTICAL SOLUTION FOR SHEAR LOG EFFECTS OF FLAT-ARCH-SHAPED BEAM BRIDGE

Exact analysis of membrane stress distribution of thin-walled beam bridge under both vertical and horizontal loading is significant for the calculation of shear log and will be beneficial for finally determining the efficient width of bridge wing for practical design purpose. By generalizing force method into a 2-D structural problem, a typical flat-arch-shaped beam bridge is divided into a slab of plane stress and 2 beams of rectangular cross section. Consequently, an unknown distributive shear is assumed on longitudinal intersection of both beam and slab. By adapting elasticity theory, a complete system of Airy stress functions, which satisfies both biharmonic controlling equation of 2-D plane stress problem and its boundary conditions, is employed for the analysis of stresses and displacements of slab. The beam ribs are also analytically solved for their deflection and rotation displacements by Timoshenko抯 theory. The deformation compatibility, that the longitudinal displacements of both beams and slab are equivalent to each other at the longitudinal intersection, is used to finally determine the unknown shear. The efficiency of analytical solution procedure is verified and demonstrated by examples and an excellent agreement is reached with the results of FEM and model experiment of Yangtse Highway Bridge at Tongling.