In the structure shown, a downward force $P$ is $10$ kN $,$ and the tie$-$back support $AC$ is a round steel rod having a diameter of $12$ mm and set at angle a $30.$ The steel strut $AB$ has a length of $2$ meters and a cross$-$sectional area of $550$ mm $2.$ Both members are hot$-$rolled $1040$ steel. Neglect the weight of the members. $(26$ points total$)$

a$.$ Find the total deformation in the support AC$.$

b$.$ Find the total deformation in the strut $AB.$

c$.$ If the factor of safety is $1\mathrm{.}8,$ is the design sound? Explain.