Buckling loads of arches could be significantly affected by the assumptions made on the load behavior during buckling. For a funicular arch whose centerline coincides with the compression line, we may consider two types of load behaviors based on how the line of load action shifts during buckling. This paper presents the governing differential equations for the elastic in-plane buckling problem of funicular circular arches under uniform radial pressure based on the two different load behavior assumptions, as well as analytical and numerical methods for analysis. For the analytical method, buckling criteria of rotationally-restrained ended circular arches with an internal rotational spring are formulated by using the general solution of the governing differential equation. For the numerical method, the Hencky bar-chain model (HBM) and its simple matrix formulations for general funicular arches are established. The buckling loads and mode shapes of funicular circular arches are solved by using HBM and verified against exact solutions obtained from the analytical method. For funicular catenary arches and parabolic arches, the buckling load solutions by HBM with various number of segments are also obtained and compared with the solutions presented by the previous researchers.

中文翻译：

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索道拱门的弹性面内屈曲

拱的屈曲载荷可能会受到屈曲期间对载荷行为的假设的显着影响。对于中心线与压缩线重合的索道拱门，我们可以根据屈曲过程中载荷作用线的变化情况考虑两种类型的载荷行为。本文基于两种不同的载荷行为假设，以及分析和数值分析方法，提出了在均匀径向压力下索道圆拱弹性面内屈曲问题的控制微分方程。对于解析方法，利用控制微分方程的一般解，制定了具有内部旋转弹簧的旋转约束端部圆拱的屈曲准则。对于数值方法，建立了用于一般索道拱门的 Hencky bar-chain 模型 (HBM) 及其简单矩阵公式。使用 HBM 求解索道圆拱的屈曲载荷和振型，并根据解析方法获得的精确解进行验证。对于索道悬链线拱和抛物线拱，还获得了 HBM 不同段数的屈曲载荷解，并与前人提出的解进行了比较。