Problem $1$:

A cantilever beam is bolted to a $\backslash (152\backslash$times $76\backslash )$ vertical channel using three M$10$ x $1\mathrm{.}5$ ISO $9\mathrm{.}8$ bolts as shown in the right. The material for the channel and the beam is AISI $1020$ hot rolled steel. Find the force F that can be applied to the cantilever without causing failure to the joint. The design factor $\backslash ($ n$\_\{$d$\}=2\mathrm{.}0\backslash ).$ The thickness of the channel is $6\mathrm{.}4$ mm $.$ You must check for shearing of the bolts, bearing of the bolts and the channel, and the bending of the cantilever. $(12$ pts$)$