Abstract This paper presents a new general methodology to obtain an approximate analytical expression of the Saint-Venant's torsion. The shear stress in each of the principal Cartesian directions is obtained by the derivation of the stress function, whose analytical expression is obtained from the Prandtl analogy. The proposed methodology uses two variables quadratic piecewise functions to define the Prandtl membrane. This document shows that the approximate procedure is especially suitable for steel shapes, giving values very close to those obtained with more precise methods. The main advantage of the presented methodology is its simplicity, which makes it useful for both pedagogic and practical applications. Several examples are developed.

中文翻译：

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普朗特膜类比在开放薄壁截面和正多边形的线弹性纯扭转中的近似表达

摘要 本文提出了一种新的通用方法来获得圣维南扭转的近似解析表达式。每个主要笛卡尔方向上的剪应力是通过应力函数的推导获得的，其解析表达式是从 Prandtl 类比中获得的。建议的方法使用两个变量二次分段函数来定义 Prandtl 膜。该文件表明，近似程序特别适用于钢型材，其值与使用更精确方法获得的值非常接近。所提出的方法的主要优点是它的简单性，这使得它对教学和实际应用都很有用。开发了几个示例。