The torsional rigidity of a circle, an ellipse, and an equilateral triangle (Fig. 6.11)...

The torsional rigidity of a circle, an ellipse, and an equilateral triangle (Fig. 6.11) are denoted by and respectively. If the cross-sectional areas of these sections are equal, demonstrate that the following relationships exist:

where a and b are the semiaxes of the ellipse in the x and y directions.