This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force F, bending moment M and distributed load q (or concentrated load P) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

中文翻译：

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横向固定端组合载荷下薄壁梁屈曲分析的显式表达式及其在锯片稳定性分析中的应用

本文研究了具有横向固定端部的薄壁梁的关键问题。阐明了组合荷载梁扭力矩公式的定义方法。在此基础上，建立了梁的控制微分方程。介绍了用能量法确定光束临界状态的程序。通过这个程序，在轴力等三种载荷下，相关梁的临界状态F, 弯矩米和分布式负载q（或集中负载磷) 被故意检查。结果以明确的封闭形式呈现，可以用 2D 和 3D 图表来说明。此外，获得的解析解与商业软件 NX Nastran 获得的数值一致。此外，直接应用解析解来探索偏心载荷下新型框架式锯床齿片的稳定性和设计优化。该结果还可用于研究具有横向固定端部的薄壁梁承受其他类型载荷的问题。