The allowable stress used in the design of a stecl bar is $80 \mathrm{MPa}$. Deter mine the largest couple $M$ that can be applicd to the bar (a) if the bar is designed with grooves having semicircular portions of mdius $r=15 \mathrm{mm}$ as shown in Fig $a,(b)$ if the bar is redesigned by removing the material to the left and right of the dashed lines as shown in Fig. $b$.