The shown closed thin-walled rectangular beam has constant thickness 2 mm, dimensions 400 mm × 100 mm, torque 3.2 kN m and shear modulus 25 GPa. Find twist per unit length in rad/m, to 3 decimals.
For a single closed thin-walled cell, $\theta\prime=T[\oint ds/t]/(4A_m^2G)$. Using mean-line dimensions 0.4 by 0.1 m gives Am = 0.04 m² and $\oint ds/t=2(0.4+0.1)/0.002=500$. Hence $\theta\prime=3200(500)/[4(0.04)^2(25\times10^9)]=0.010$ rad/m. The thin-wall approximation treats the drawn dimensions as mean-line dimensions.
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