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Transfer Matrix Method for Studying the In-plane Stability of Arch and Cable-arch

DOI：

 作者 单位 E-mail 刘利 湖南大学土木工程学院 liuli0909@hnu.edu.cn 康厚军 湖南大学土木工程学院 khjun@hnu.edu.cn 苏潇阳 湖南大学土木工程学院 丛云跃 湖南大学土木工程学院

为探究拱桥面内稳定问题求解的新途径，本文将应用传递矩阵法对径向均布荷载作用下的圆拱面内屈曲微分方程进行解答，利用边界条件导出其特征方程从而求得其屈曲荷载。同时，结合力法以及拱上荷载集度与轴力的关系，将该理论方法推广到承受集中荷载的变截面拱以及索拱组合结构的稳定分析中，并和有限元ANSYS计算结果进行对比，验证了本文理论和方法的正确性。最后研究了不同荷载工况下的边界条件、圆心角和截面惯性矩对拱结构面内稳定性的影响。结果表明，索拱结构的面内稳定性优于纯拱结构。

In order to explore a new way to solve the issue of in-plane stability of the arch bridge, the transfer matrix method is used to solve the in-plane buckling differential equation of a circular arch under the radial uniform load. Then, the characteristic equation of the circular arch considering its boundary conditions to obtain its critical load is derived. At the same time, by combining the force method and the relationship between the load concentrated on the circular arch and its axial force, the transfer matrix method is extended to analyze the in-plane stability of the variable cross-section circular arch and the cable-arch subjected to concentrated load. Comparing the results obtained by ANSYS and the proposed method shows a good agreement, which verifies the theory and method. Finally, the effects of boundary conditions, central angles and moment of inertia on the in-plane stability of the circular arch under different types of load are studied. The results show that the in-plane stability of the cable-arch is better than that of the pure arch.
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