H$.$W $1$: For the structure below, the area of section $BC=75\mathrm{.}29i{n}^2,$ the allowable shear stress of

pin $A=9\mathrm{.}1$ psi. and the ultimate shear stress of pin $C=46$ psi with $F.S=2,$ calculate:

$1-$ The normal stress in member $BC.$

$2-$ The diameter of pin C if the lap joint is single shear.

$3-$ The diameter of pin A if the lap joint is double shear.

$4-$ If the thickness of the plate in lap joint $A=3in,$ calculate the bearing stress in this lap joint.