In the analysis of thin-walled members, some types of boundary conditions met in practice cannot be correctly represented by conventional line (1D) models. Of course, both shell models or advanced line models (such as generalised beam theory, GBT, among others) can accurately tackle this type of problems – at the cost, however, of the simple interpretation of results provided by conventional line models. This paper investigates the combined bending and twisting of doubly symmetric I beams supported along a single flange. This type of support precludes the application of the conventional Vlasov’s theory, because it ignores the distortion of the cross section. A simple line model which accounts for web distortion is developed and a mixed 3-field finite element – which can achieve any required accuracy on very coarse meshes – is derived for its numerical implementation. Illustrative examples are also presented.

在薄壁构件的分析中，在实践中遇到的某些类型的边界条件不能用传统的线 (1D) 模型正确表示。当然，壳模型或高级线模型（例如广义梁理论、GBT 等）都可以准确地解决此类问题 - 然而，代价是传统线模型提供的结果的简单解释。本文研究了沿单个翼缘支撑的双对称工字梁的组合弯曲和扭转。这种类型的支撑排除了常规 Vlasov 理论的应用，因为它忽略了横截面的变形。开发了一个考虑腹板变形的简单线模型，并导出了一个混合 3 场有限元——它可以在非常粗的网格上达到任何所需的精度——用于其数值实现。还提供了说明性示例。