Saint Venant's Approximation

Saint Venant represented the torsion constant of a solid section by a function relating the already known characteristic values of a cross section thus

For narrow rectangles (i.e. thin plates):

which reduces to

For circular sections

which is the polar moment of inertia.

It can be shown that for members composed of thin rectangles, the torsion constant is equal to the sum of the -values of component rectangles, except when the section is closed or ‘hollow’