$[30$ pts$]$ Three civil engineering students are asked to fabricate a hollow structure. The students used a hollow made from brass. They fastened the hollow brass $(E=15,000$ksi and $G=5600$ksi $)$ tube A with a $4-$in$.$ outside diameter and a $2-$in$.$ inside diameter to a solid $2-$in$.-$diameter steel $(E=30,000$ksi $)$ rod B$,$ as shown. Determine:

$($a$)$ The elongation of cross section a$-$a$.$

$($b$)$ The elongation of cross section $b-b.$

$($c$)$ The horizontal and vertical components of stress on an element on the outside surface of the tube and rod.

$($d$)$ The change in both the inside and outside diameters