МODELING OF A CROSS-SECTION CORE FOR A ROD WITH A COSINE-SHAPED CROSS-SECTION
In this paper, an example of constructing a cross-section core for rods with a curved cross-section shape is given. A detailed description of this method is given in the last two sources listed in the list of references to this article. In addition, this article presents the derivation of the equation of the tangent to the core of the section, which was absent in previous sources. The applied method of constructing the cross-section core is original. It uses the replacement of the graphical representation of the tangent to the contour of the cross section with an analytical one, based on the geometric meaning of the first derivative of the function describing the equation of the corresponding contour. This equation is written in relation to the main central axes of inertia of the cross section. Previously, it is necessary to calculate the following geometric characteristics: the cross-sectional area, the main central moments of inertia (using integral dependencies) and the squares of the radii of inertia. This method of constructing the cross-section core is convenient to use if one or two main central axes are axes of symmetry. In this paper, a sinusoid (cosine) is considered as a symmetric function.