Problem $1.(50$ pts$.)$

The truss ABC is loaded as shown in the figure below. All of the bars have the cross$-$section indicated

in the figure. The critical components of this structure are the bar BC and the pin at A$.$

a$)$ The the bar BC is made of steel $(E=30$Msi,${}_Y=40$Ksi $)$ What is the Factor of Safety of

bar BC with respect to yielding?

b$)$ The pin at A is loaded in double shear, and is made from a steel with an ultimate shear strength

of ${}_{\text{U}\text{L}\text{T}}=60$Ksi. What is the minimum diameter of the pin at A to provide a factor of safety

$($F$.$S$.)$ of at least $3\mathrm{.}3$ with respect to failure?