On torsion of cylindrical beams (Q1058889)

The problem of torsion of cylindrical beams with rectangular cross- sections with circular and elliptic ends and a pair of triangles under a terminal couple is studied. The method of solution is Saint-Venant's classical method. The shearing stresses, the torsional moment, the lines of shearing-stresses and the nature of distorted cross-sections have been obtained. The distorted cross-sections of the triangular and rectangular beams take the shape of hyperbolic curves. The shearing stresses are maximal at the mid-points of the sides of the triangle and the rectangle. Minimal shearing stresses occurs at the vertex of the triangular beam.