Problem # $7$: For the truss structure shown in the figure, the pins for Joints A$,$ B$,$ C & D are all made from ASTM A$572$ high$-$strength low$-$alloy columbium$-$vanadium structural steel, Grade psi$).$ Pins at Joints A & C are in double shear and the load on them is static.

Determine the following for this structure.

A$)$ Reaction at support points $A$&$D=$ lbs$.$

B$)$ Axial forces in members $AD$&$DC=$ Ibs.

C$)$ Axial force in members $AB$&$BC=$ lbs$.$

D$)$ Axial force in member $BD=$ lbs$.$

E$)$ Yield strength in shear for ASTM A$572,$ Grade $50$ Pins $=S_{ys}=$ psi

F$)$ Design Shear Stress for pins $={}_d=\frac{S_{ys}}{N}=$ si

G$)$ Required cross$-$sectional area of pins at Joints $A$&$C=n^2$

H$)$ Required diameter of pins at Joints $A$&$C=-0\mathrm{.}192$ inch

Please show steps and explain