$(10$ Marks$)$ A bar ABC having two different solid circular cross sections is held between rigid support

$C$ and an elastic support A having spring constant $k=5{10}^{4}k\frac{N}{m}$ as shown. The properties are as

follows:

If only bar ABC is subject to a uniform temperature increase of $30C,$ determine

$(1)$ the normal stress in the aluminum rodBC;

$(2)$ the displacement ${}_n$ of noint $R.$