$(30$ Points$)$ A simple structure is loaded as illustrated and is in equilibrium.

a$.$ If the yield stress for the material of cable $AB$ is ${}_y=345$MPa and a factor of

safety on yield of F$.$S$.$y $=2\mathrm{.}5$ is required, determine the minimum required

diameter of cable AB$.$

${\mathrm{.}1}^{\frac{14}{1}}m$

b$.$ Determine the minimum diameter of pin $C$ if the allowable shear stress is

${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=85$MPa.

$\mathrm{.}044$ m

$gra{d}_{GB}=345$MPa$25$

$=62\mathrm{.}5$