Interrelation of rigidness of triangular cross-sections under bar torsion with conformal radii relation

Abstract

Abstract The investigated problems of interrelation of the given geometrical rigidness of bars cross-sections of pure torsion with the geometrical characteristic of cross-sections – the relation of the internal conformal radius to the external conformal radius are covered in the article. Formulas for calculation of values of internal, external conformal radii and their relations for arbitrary, isosceles and rectangular triangles are given and the approximating functions for definition of these geometrical characteristics for triangles of any form are constructed. The graphic analysis of the obtained values shows that all variety of the relations of conformal radii presented graphically depending on one of the triangle corners falls into two subsets. One of them includes all variety of acute triangles, which is limited to isosceles acute triangles and rectangular triangles, and another one is limited with isosceles obtuse triangles and rectangular triangles. The graphic analysis of the whole variety of the known values of the given geometrical rigidness of triangular cross-sections at torsion, presented depending on one corner of a triangle, demonstrates that this geometrical characteristic is functionally connected with the relation of conformal radii; the corresponding approximating functions have linear character.