Problem $3.[40$ pts$]$ A composite circular rod made of three materials is fixed at A and $D$ as shown in the figure below. One $(1)$ external force of $15$ kN is applied at C $.$

$($a$)$ Calculate the reactions at the wall support at pt$.$ A and pt$.$ D$.$

$($b$)$ Calculate the displacement of point $B({}_B)$ only.

$($c$)$ Calculate the internal normal stress in each material ${}_{\text{b}\text{r}\text{o}\text{n}\text{z}\text{e}},{}_{\text{s}\text{i}\text{l}\text{v}\text{e}\text{r}},{}_{\text{g}\text{o}\text{l}\text{d}}.$

The Young's Modulus or stiffness of each material are: $E_{\text{b}\text{r}\text{o}\text{n}\text{z}\text{e}}=95$GPa,$E_{\text{s}\text{i}\text{l}\text{v}\text{e}\text{r}}=83$GPa and $E_{\text{g}\text{o}\text{l}\text{d}}=74$GPa.