The bar$-$shaped plate is loaded at its ends by a pair of $4$ kN loads. At each end of the bar, there is a hole in which a pin loaded by a $0\mathrm{.}5$ kN load is inserted. Given the dimensions as $a=40mm,w=22mm,D_1=25mm,D_2=15mm$ and $t=10mm,$ determine $($a$)$ the maximum average normal stress in the bar, and $($b$)$ the average bearing stress on the pin$-$plate bearing surface. $[2$ Marks$]$