$(8-47)$ The upside$-$down steel A frame shown in the figure is to be bolted to steel beams on the ceiling of a machine room using ISO grade $8\mathrm{.}8$ bolts. This frame is to support the $40-kN$ vertical load as illustrated. The total bolt grip is $48$ mm $,$ which includes the thickness of the steel beam, the A$-$frame feet, and the steel washers used. The bolts are size M$20$x$2\mathrm{.}5.$

$($a$)$ Determine the bolt stiffness

$($b$)$ Determine the stiffness of the material of the joint

Problem $8-47$