$18-19$ A $30-$mm thick AISI $1020$ steel plate is sandwiched between two $10-$mm thick $2024-$T$3$ aluminum plates and compressed with a bolt and nut with no washers. The bolt is M$10$ xx$1\mathrm{.}5,$ property class $5\mathrm{.}8.$

$($a$)$ Determine a suitable length for the bolt, rounded up to the nearest $5$ mm$.$ Use the criteria that the bolt should go completely through the nut $($NOT needing an additional $2$ threads$)$

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

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