Analityczna Metoda Obliczania Nośności Granicznej Prętów Skręcanych

Owing to the analogies of Nadai and Sadowsky, the problem of calculation of the limit load of an isotropic homogeneous bar subject to torsion is reduced to that of computing the volume of a solid of uniform slope (a «sand hill»). The aim of the present paper is to derive general equations determining this volume. In Sec. 2 are given equations of discontinuity lines of stresses corresponding to regular arcs of the contour, one concave singularity and two concave singularities. These are, respectively, Eqs. (2.3), (2.4), (2.17) and (2.18). The volume of the sand-hill or part of it is determined by the respective general Eqs. (3.5) or (3.6), (3.9) or (3.13) and (3.15). As an example are given solutions for elliptic profiles, a semicircular profile, circle with a circular incision or with two circular incisions, a profile bounded by two cycloidal arcs and a cardioid.
The results are represented in the form of tables and graphs. In Sec. 6, the equations derived are applied to the computation of the limit load of anisotropic bars, because it has been shown by W.O. GEOGDŻAJEW, [S], that this problem can be reduced by substituting (6.4) to that of an isotropic bar with transformed contour. In Sec. 7, the equations derived are applied to the computation of the limit load of a non-homogeneous bar subject to torsion if the yield point depends only on the distance of the point from the contour of the section; this type of non-homogeneity may have a practical value in the case of surface heat treatment. The case of discontinuous non-homogeneity, is also considered.