On torsion of rectangular cylinders with grooves (Q1071563)

The torsion problem of a rectangular cylindrical beam under a terminal couple with triangular, circular, elliptic and parabolic grooves has been studied. The shearing stresses, the lines of shearing stress and the distorted cross-sections of the beam have been obtained by Saint-Venant's semi-inverse method. The minimum shearing stress occurs at the vertices of the grooves. The contour lines are straight lines. The lines of shearing stresses take the shapes of the grooves in the beam but in case of a triangular groove, they are hyperbolic curves.