The two$-$segment statically indeterminate bar in the following figure has a constant cross$-$sectional area $A=0\mathrm{.}8i{n}^2.$ It is made entirely of material that has elastic, perfectly plastic behaviour with $y=36$ksi and $E=20{10}^3$ksi. If $P=45$kip is applied to the bar and then removed

a$)$ Determine the residual stress in each segment.

b$)$ Find the permanent deformation at point

B$.$

c$)$ Determine the smallest load $P$ needed to cause segment CB to yield.