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The following table from Ghali and Neville (1978) gives values of the torsion constant (J) for various cross-sectional shapes.

Shape	J
	$J = \frac{\pi r^{4}}{2}$
	$J = 0.1406b_4$
	$J = \frac{\pi\left( {r_{1}}^{4} -{r_{2}}^{4} \right)}{2}$
	$J = \left\lbrack \frac{1}{3} - 0.21\frac{b}{c}\left( 1 - \frac{b^{4}}{12c^{4}} \right)\right\rbrack$
	$J =\frac{\sqrt{3}b^{4}}{80}$
	$J =\frac{4a^{2}}{\int_{}^{}{\frac{1}{t}ds}}$ where $a$ is the area enclosed by a line through the centre of the thickness and the integral is carried out over the circumference
	$J = \frac{2t_{1}t_{2}\left( b_{1} - t_{2} \right)^{2}\left( b_{2} - t_{1} \right)^{2}}{b_{1}t_{2} + b_{2}t_{1} - {t_{2}}^{2} - {t_{1}}^{2}}$
	$J = \frac{b_{1}{t_{1}}^{3} +b_{2}{t_{2}}^{3} + b_{3}{t_{3}}^{3}}{3}$
	$J = \frac{b_{1}{t_{1}}^{3} + b_{2}{t_{2}}^{3}}{3}$
	$J = \frac{1}{3}\sum_{}^{}{b_{i}{t_{i}}^{3}}$

All the above assumes that the material is linear elastic.