$($b$)$ A single M$101\mathrm{.}5$ hexagonal head bolt is used to clamp together two $15$ mm steel plates. Young's modulus of the bolt and the plates can be taken as $207$ GPa $.$

$($i$)$ Determine a suitable length for the bolt.

$($ii$)$ Determine the bolt stiffness.

$[4]$

$($iii$)$ Determine the stiffness of the members.

$[4]$

$[6]$