A class $8\mathrm{.}8,M273$ ISO bolt has rolled threads and is used to clamp two rigid

members together so that $k_c=6k_b.$ There is an external force fluctuating rapidly

between $0$ and $20kN.$ The construction and precision of manufacture are such

that there is a possibility of slight bolt bending. Bolt material exhibits an

idealized elastic, perfectly$-$plastic stress$-$strain curve.

Answer the following two questions for the initial tension of regular value that a

mechanic would apply using a torque wrench, i$.$e$.F_i(N)=2800d(mm)$

a$)$ Make a force$-$versus$-$time plot showing the fluctuating external load, bolt

force and clamping force.

b$)$ Analyze bolt failure. Consider both separation and eventual fatigue

failure. Provide safety factors when applicable.