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Rectangular Sections

The torsion constant J is given by

J=Kb3bmaxJ = Kb^{3}b_{\max}

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

bmaxb\frac{b_{\max}}{b}KKbmaxb\frac{b_{\max}}{b}KKbmaxb\frac{b_{\max}}{b}KKbmaxb\frac{b_{\max}}{b}KK
1.00.1411.50.1962.80.25810.00.312
1.10.1541.80.2163.00.2630.333
1.20.1662.00.2294.00.281
1.30.1752.30.2425.00.291
1.40.1862.50.2497.50.305

or from the graph

rectangular-sections

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

Alternatively

K=13[10.63bbmax(1b412bmax4)]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 bmax>2bb_{\max} > 2b then

(1b412bmax4)1\left( 1 - \frac{b^{4}}{12{{b}_{\max}}^{4}} \right) \approx 1

and so

K=13[10.63bbmax]K = \frac{1}{3}\left\lbrack 1 - 0.63\frac{b}{b_{\max}} \right\rbrack