PROBLEM $2$

For the steel truss and loading shown, determine:

a$)$ The minimum allowable diameter of the truss members, if all members must have the same diameter.

b$)$ The minimum allowable diameter of pins $\backslash ($ A $\backslash )$ and $\backslash ($ C $\backslash ),$ if both pins must have the same diameter and work in double shear.

The ultimate normal stress of the steel is $420$ MPa $,$ the ultimate shear strength of the pins is $900$ MPa and the safety factor is $3\mathrm{.}0.$