斜靠式拱桥结构侧倾失稳分析的Ritz法

Ritz method of the analysis of lateral buckling for leaning-type arch bridge

采用Ritz法,首次推导了主拱肋拱脚铰接、稳定拱肋拱脚固接边界条件下,斜靠式拱桥的侧倾失稳临界荷载系数的计算公式,并通过有限元法验证了该计算公式的正确性。进一步分析了稳定拱肋弯曲变形能和扭转变形能、主拱肋与稳定拱肋间横撑切向和径向弯曲变形能及吊杆非保向力位势和桥面系侧向弯曲变形能对斜靠式拱桥侧倾失稳临界荷载系数λcr的影响。研究结果表明:稳定拱肋的侧向弯曲变形能对斜靠式拱桥侧倾失稳临界荷载系数λcr有一定的影响,而扭转变形对侧倾失稳临界荷载系数λcr影响甚微;若忽略横撑的所有变形能,侧倾失稳临界荷载系数λcr降低65%～83%,即横撑对斜靠式拱桥侧倾失稳临界荷载系数λcr的影响非常显著;随着稳定拱肋倾角的增加,侧倾失稳临界荷载系数λcr呈增大趋势,且增设稳定拱肋对提高斜靠式拱桥的侧向稳定性大有帮助。

Based on Ritz method, the calculation formula of the critical load coefficient about leaning-type arch bridge has been first derived under the hinged boundary condition at the main arch ribs springers and clamped boundary condition at the stable arch ribs. And compared it with the result obtained from FEM,it is verified that the formula presented in this paper is accurate. Furthermore,those effect factors are analyzed, such as the bending deformation energy and torsional deformation energy of the stable arch ribs, the tangential the radial bending deformation energy of transverse braces, the potential energy of non-directional load of hangers and the bending deformation energy of bridge deck on the critical load coefficient λcr of leaning-type arch bridge. It is shown from the research results that：The bending deformation energy of the stable arch ribs have some influence on the critical load coefficient Act while the torsional deformation energy have little influence on it; If the tangential the radial bending deformation energy of transverse braces are ignored, the critical load coefficient λcr will decrease by approximately 65% to 83%, so the transverse brace between the main arch rib and stable arch rib have significant impact on the critical load coefficient λcr ; The leaning-type arch bridge＇ s critical load coefficient 2. increases effectively with the increasing of stable arch rib＇s inclined angle, and adding the stability of arch rib is a great help for the lateral stability of leaning-type arch bridge.