Evaluate the shape factor \(\phi_{B}^{e}\) for stiffness-limited design in bending of a square box section of outer edgelength \(h=100 \mathrm{~mm}\) and wall thickness \(t=3 \mathrm{~mm}\). Is this box shape more efficient than tube made of the same material with diameter \(2 r=100 \mathrm{~mm}\) and wall thickness \(t=3.82 \mathrm{~mm}\) (giving it the same mass per unit length, \(m / L\) )? Treat both as thin-walled shapes. Use the expressions in Table 10.3 of the text for the shape factor \(\phi_{B}^{e}\).

Data From Table 10.3

Section Shape a b h Bending Factor Torsional Factor 2.38 (h>b) Bending Factor Torsional Factor 1 h b 1-0.58 1.6. 1+0.6- (h>b) =1.15 0.832 30.658 0.83 a