Problem $4[35$ points$].$ The bar has a cross$-$sectional area of $0\mathrm{.}5i{n}^2$ and is made of a material that has stress$-$strain diagram approximated by the two line segments, shown in the figure.

a$)[12$ points$]$ Determine the elongation of the bar due to the applied loading $($loads at $B$ and $C).$

a$)[13$ points$]$ If all the loads $($in part a$)$ are removed, determine the permanent displacement of point $C.$

b$)$ points