$(35$ Points$)$ A composite structure is illustrated consisting of a tubular shell $(1)$ bonded

to the section $AB$ of a continuous solid rod that extends from $A$ to $C.$

Core Properties:

The diameter of the core, $d_{\text{c}\text{o}\text{r}\text{e}}=40mm.$

$E_{\text{c}\text{o}\text{r}\text{e}}=73\mathrm{.}1$GPa

Shell Properties:

The shell outer diameter, $d_0=60mm$

$E_{\text{s}\text{h}\text{e}\text{l}\text{l}}=200$GPa

Determine the following:

$[$a$]$ The normal forces in the shell $(1)$ and the core $(2).$

$[$b$]$ The normal stresses in the shell $(1)$ and the core $(2).$

$[$c$]$ The deflection of $C$ relative to $A,$ C$/$A$.$