Evaluate the shape factor \(\phi_{B}^{f}\) for strength-limited design in bending of a square box section of outer edge-length \(h=100 \mathrm{~mm}\) 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 given in Table 10.3 of the text for the shape factors \(\phi_{B}^{f}\).

Data From Table 10.3

Section Shape a b a h Bending Factor Torsional Factor B Bending Factor Torsional Factor 03 1 2.38 1.6 1-0.58 b +0.6 (h>b) (h>b) = 1.15 0.832 = 0.658 0.83