DEPENDENCE OF GEOMETRICAL RIGIDITY OF TORSION RECTANGULAR SECTIONS FROM THEIR COEFFICIENT OF THE FORM AND RELATIONS OF CONFORMAL RADIUSES

Abstract

Structures experiencing torsion strains are widespread in construction, therefore, the development and improvement of methods for calculating such structures is one of the urgent problems of building mechanics and elasticity theory. Exact solutions can be obtained only for rods with an elliptical and rectangular cross-section; in other cases, it is necessary to resort to the use of approximate analytical or numerical methods, many of which are quite laborious. In this regard, the purpose of this article is the demontration of new possibilities of applying the interpolation methods to solving problems of free torsion of prismatic rods. The article compares the values of reduced geometric stiffness of straight-angle cross sections for free torsion of a rod, obtained using exact and approximate solutions. The exact solution is presented depending on the ratio of the sides of the rectangle, and the approximate solutions - depending on the geometric arguments - the shape factor and the ratio of the conformal radii (inner to outer). In the first case, for rectangular sections in the range 1 < a/b< 8, the error of the solutions obtained is 2%, and in the second case, 3.2%.