고체역학 (Beer) — Torsion: Problem 3.134

3.134 Each of the three aluminum bars shown is to be twisted through an angle of 2°. Knowing that \( b = 30 \text{ mm} \), \( \tau_{\text{all}} = 50 \text{ MPa} \), and \( G = 27 \text{ GPa} \), determine the shortest allowable length of each bar.