Problem $1(25$ points$)$:

Beam ABC $(2$ in wide $"$w$1"$ and $1$ in thick$)$ shown in figure is supported by hinge A and link BD $.$ Knowing that link BD is $1$ in wide $"w_2"$ and $0\mathrm{.}5$ in thick, and that all pins are in single shear and has $0\mathrm{.}3$ in diameter. Determine:

$($a$)$ Maximum normal stress in link BD$.$

$($b$)$ The pin where the maximum shear stress occurs and the magnitude of this stress.

$($c$)$ Factor of safety for bearing in beam ABC if the ultimate bearing stress in the wood is $60$ ksi.