The paper addresses the theoretical framework and the numerical procedure developed to carry out the sectional analysis preliminary to the use of a recently formulated isotropic and homogeneous beam model consistently derived from the Saint Venant solid one.

Specifically, in order to ensure the equivalence of the new beam model with the 3D solid one, both in terms of elastic energy and displacements of the beam axis, one requires the evaluation of a symmetric second-order tensor, accounting for the shear deformation, besides the center of twist and the torsional stiffness factor.

Common property to such geometrical quantities is to be expressed as integrals of harmonic functions solution of Neumann problems that are defined over the section domain. Hence, with a view towards numerical applications, they are reformulated as integrals defined over the section boundary, assumed to be of arbitrary polygonal shape.

The numerical evaluation of the resulting line integrals is obtained by exploiting a recently formulated boundary element approach in which the harmonic potential functions are expressed as polynomials defined on suitably defined subsets of each edge of the section boundary.

As an outcome of the extensive numerical tests that have been carried out on compact and thin-walled sections a general criterion, established elsewhere for properly selecting the best combination of polynomial degree and edge discretization, is shown to be successful also for carrying out the shear analysis of beam sections having arbitrary shape.

本文介绍了为进行截面分析而开发的理论框架和数值程序，该分析是使用从圣维南实心模型一贯导出的最近制定的各向同性和均质梁模型开始的。

具体来说，为了确保新的梁模型与3D实体模型等效，无论是在弹性能还是在梁轴线的位移方面，都需要评估对称的二阶张量，考虑到剪切变形，除了扭转中心和扭转刚度因子。

这种几何量的共同性质将表示为在截面域上定义的Neumann问题的谐波函数解的积分。因此，考虑到数值应用，将它们重新构造为在截面边界上定义的积分，假定为任意多边形。

通过采用最近制定的边界元方法，可以得到结果线积分的数值评估，其中谐波势函数表示为在截面边界的每个边的适当定义的子集上定义的多项式。

作为在紧凑和薄壁截面上进行的大量数值测试的结果，在其他地方建立的，用于正确选择多项式度和边缘离散化的最佳组合的一般准则也显示出对剪切的成功。分析具有任意形状的梁截面。