Geometric rigidity of sections in the form of in torsion

This article is a generalization of known solutions to the problem of determining the reduced geometric stiffness of sections of elastic prismatic beams using geometric arguments: the shape coefficient and the ratio of conformal radii (internal to external). Analytical dependences are constructed for all considered sections (regular polygons, ellipses, rectangles, isosceles and right triangles): reduced geometric stiffness is the coefficient of shape and reduced geometric stiffness is the ratio of conformal radii. Formulas in the form of polynomials for determining the ratio of conformal radii are also constructed for these sections. An analysis of the changes in both arguments under various geometric transformations showed that the ratio of conformal radii has similar isoperimetric properties as the shape coefficient. This allows to determine the geometric torsional stiffness of the sections by interpolation.