고체역학 (Beer) — Pure Bending: Problem 4.108

4.108 A milling operation was used to remove a portion of a solid bar of square cross section. Forces of magnitude \( P = 18 \text{ kN} \) are applied at the centers of the ends of the bar. Knowing that \( a = 30 \text{ mm} \) and \( \sigma_{\text{all}} = 135 \text{ MPa} \), determine the smallest allowable depth \( d \) of the milled portion of the bar.