Problem $1(25$ Points$)$: The hydraulic cylinder CF$,$

which partially controls the position of the rod DE

through the rigid member BCD $,$ has been locked in

the position shown. The angle $=60.$ The link

AB has a width of $20mm$ and is $5mm$ thick and is

made of steel with ultimate tensile strength $({}_{\text{u}\text{l}\text{t}})$

sutatof $650$ MPa $.$ The pins at A and $B$ are $8$ mm in

diameter, experiencing single shear, and made of

steel with an ultimate shear strength $({}_{\text{u}\text{l}\text{t}})$ of fi

$410$ MPa $.$ Pins C and D as well as the member DE

are adequately reinforced. If a Factor of Safety

$($FS$)$ of $2\mathrm{.}5$ is used:

a$-$ what is the maximum load, $P,$ that can be

applied to DE$?$

b$-$ What is the resulting shear stress in Pin C$?$

if it is $10mm$ in diameter and experiencing

single shear.