Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

中文翻译：

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不同端矩下悬臂圆拱的侧向屈曲

采用分析方法研究了悬臂圆拱在不同端力矩下的横向屈曲。考虑了三种类型的保守矩，即第1类和第2类的准切线矩和半切线矩。与经历 3 维旋转的每个力矩机构相关的诱导力矩包含在 Newman 边界条件中。利用可用于弯梁面外屈曲的微分方程，推导出悬臂圆拱的解析解，可作为其他分析方法校准的基准。