$1.$ A triple threaded steel bolt $($M$20,$ coarse$-$pitch, property class $12\mathrm{.}9)$ connects two identical elastic plates. After snug fit, the nut is turned $\backslash (\backslash$frac$\{1\}\{8\}\backslash )$ th of a full rotation. Resulting clamping force on plate is $80$ KN while the bolt elongates by $0\mathrm{.}70$ mm $.$

$($a$)$ Calculate stiffness of the bolt and members, and the joint constant

$($b$)$ Determine the external force that will cause the join of separation of this assemble.

$($c$)$ Evaluate if the material will fail at the separation or not.