Torsional rigidity of non-circular bars in mechanisms and machines

Determining the exact value of the torsional rigidity for cylindrical bars is limited to a few cross-sections. Exact solutions can be found in Mathematical Theory of Elasticity [Sokonlnikoff, Mathematical Theory of Elasticity, McGraw-Hill, New York, pp. 120] for the circle, ellipse and equilateral triangle. Good approximations for rectangular cross-sections are available in Theory of Elasticity, [Timoshenko, Goodier, Theory of Elasticity, McGraw-Hill, New York, p. 309] and approximations for various cross-sections such as trapezoids, isosceles triangle, semicircles, circles with a keyway, etc. are found in handbooks such as the one written by Roark [p. 309]. A method to approximate the torsional rigidity of any cylindrical solid cross-section is presented on this paper. Cross sections are classified by similarity to an ellipse, rectangle and/or a triangle. An aspect ratio of length to width is used as the second criteria to enter a graph where the torsional rigidity of the cross-section is given as a ratio to that of a circle of equal area.