PROBLEM $1(40$P$).$ In the rocket launch system shown in the figure, the rocket launch case is fixed with pin $C$ and $AB$ bar.

a$)$ Calculate the forces acting on the supports $B$ and $C$ and show the internal forces in section E $.$

b$)$ Since it is known that A$,$ B and C pins are made of A$304$ stainless steel, determine the diameters of A and $C$ pins with a safety factor of $1\mathrm{.}5.$

c$)$ What is the diameter of AB bar