고체역학 (Beer) — Pure Bending: Problem 4.63

4.63 Semicircular grooves of radius \( r \) must be milled as shown in the top and bottom portions of a steel member. Knowing that \( M = 4 \text{ kip}\cdot\text{in.} \), determine the maximum stress in the member when the radius \( r \) of the semicircular grooves is (a) \( r = 0.25 \text{ in.} \), (b) \( r = 0.375 \text{ in.} \).