Problem #$3(30$ points$)$: The stress strain curve for an aluminum rod is shown below on the left. A $15-mm$ diameter rod of this material is loaded as shown on the right.

a$)$ Determine the horizontal reaction $A_x$ at point $A.$

b$)$ Determine the axial force in segment $AB,$ indicate tension or compression.

c$)$ Determine the axial force in segment $BC,$ indicate tension or compression.

d$)$ Determine the maximum axial stress, $,$ in rod. Has the rod yielded?

e$)$ Determine the new length of the rod under the loading shown.

f$)$ If $v=0\mathrm{.}3,$ determine the new diameter in section $AB$ of the rod under the loading shown.