(Solved): 5.22. A uniformly loaded, simply supported rectangular beam has two \( 15-\mathrm{mm} \) deep vert ...

5.22. A uniformly loaded, simply supported rectangular beam has two \( 15-\mathrm{mm} \) deep vertical grooves opposite each other on the edges at midspan, as illustrated in Fig. P5.22. Find the smallest permissible radius of the grooves for the case in which the normal stress is limited to \( \sigma_{\max }=95 \mathrm{MPa} \). Given: \( p \) \( =12 \mathrm{KN} / \mathrm{m}, L=3, b=80 \mathrm{~mm} \), and \( h=120 \mathrm{~mm} \). Figure P5.22. Figure P5.23.