$(25$pts$)$ A $40$ in long $A36$ steel pipe is filled with high strength concrete. The pipe has an outside diameter of $8$ in and an inside diameter of $7$ in $.$ A compressive load of $10$ kip is$.$ applied to the ends, and distributed such that the pipe and concrete inside are compressed by the same amount. Ignore effects of lateral expansion$/$contraction$.$

a$.$ Find the areas of the steel and of the concrete.

b$.$ Find the force supported by the steel and by the concrete.

c$.$ Find the stress in the steel and in the concrete

d$.$ Find the change in length for each material $($should be the same$).$

e$.$ Find the normal engineering strain in each material.