The $d=15-mm-$diameter solid rod passes through a $D=20-mm-$diameter hole in the support plate. When a load $P$ is applied to the

rod, the rod head rests on the support plate. The support plate has a thickness of $b=15mm.$ The rod head has a diameter of $a=32$

mm $,$ and the head has a thickness of $t=8mm.$ If the normal stress produced in the rod by load $P$ is $125$ MPa $,$ determine

$($a$)$ the bearing stress acting between the support plate and the rod head.

$($b$)$ the average shear stress produced in the rod head.

$($c$)$ the punching shear stress produced in the support plate by the rod head.

Calculate the cross$-$sectional area of the rod.

Answer: $A_{\text{r}\text{o}\text{d}}=$

$m{m}^2$