Torsion of a Rectangular Prismatic Bar: Solution Using a Power Fit Model

Abstract

The torsion problem of a rectangular prismatic bar is solved using the Saint-Venant’s warping function method and analytic solutions to the twisting moment and the non-vanishing shear stresses are presented. Approximate solutions to the torsion problem are derived by curve-fitting the analytic solutions using a power fit model with the lengths of the rectangle sides as parameters. Errors observed did not exceed 0.6%. The study successfully presents a solution to the maximum non-vanishing shear stress at the narrow side of the rectangular section. Such a solution will be useful for the assessment of the critical points on a section that experiences combined bending and torsion loads.

Keywords: torsion, rectangular section, Saint-Venant, warping function, twisting moment, shear stress