A solid steel shaft with the diameter $30\mathrm{.}2$ mm is assembled into a brass collar $($tube$)$ with the nominal outer diameter $50$ mm and the inner diameter $30$ mm via shrink$-$fitting at room temperature $(25C).$ The material properties and geometries are tabulated below. $($a$)$ Find the interfacial contact pressure $p,$ tangential stress ${}_{}$ and normal stress ${}_{rr}$ on both sides of the fitting surfaces at room temperature after assembly; $($b$)$ Determine the interfacial contact pressure $p$ if the temperature drops uniformly to $0C.$

$\backslash$table$[[$Materials$,$Brass collar $($Outer$),$Carbon steel $($Inner$)],[$Young$\text{'}$s modulus,$E_0=97\mathrm{.}0{10}^3$MPa,$E_i=207{10}^3$MPa