Rectangular Sections

The torsion constant J is given by

$$J = Kb^{3}b_{\max}$$

where $K$ is a constant depending on the ratio of $\frac{b_{\max}}{b}$, which can be read either from the table below. Linear interpolation may be used for intermediate values.

$\frac{b_{\max}}{b}$	$K$		$\frac{b_{\max}}{b}$	$K$		$\frac{b_{\max}}{b}$	$K$		$\frac{b_{\max}}{b}$	$K$
1.0	0.141		1.5	0.196		2.8	0.258		10.0	0.312
1.1	0.154		1.8	0.216		3.0	0.263		∞	0.333
1.2	0.166		2.0	0.229		4.0	0.281
1.3	0.175		2.3	0.242		5.0	0.291
1.4	0.186		2.5	0.249		7.5	0.305

or from the graph

Note that K converges to 1⁄3 for narrow rectangles.

Alternatively

$$K = \frac{1}{3}\left\lbrack 1 - 0.63\frac{b}{b_{\max}}\left( 1 - \frac{b^{4}}{12{b_{\max}}^4} \right) \right\rbrack$$

generally, or if $b_{\max} > 2b$ then

$$\left( 1 - \frac{b^{4}}{12{{b}_{\max}}^{4}} \right) \approx 1$$

and so

$$K = \frac{1}{3}\left\lbrack 1 - 0.63\frac{b}{b_{\max}} \right\rbrack$$