An M$12,$ Coarse$-$pitch, Class $-5\mathrm{.}8$ bolt $(E=206\mathrm{.}8$GPa$)$ with

a hexagonal nut is used to keep two machine parts together

as shown. Determine:

$($a$)$ the stiffness of the bolt and the member,

$($b$)$ the stiffness of the joint, $C_k,$

$($c$)$ the maximum external load that the bolted$-$joint

can support for a safety factor of $2\mathrm{.}0,$ and a

reused condition.