Two $10"$ wide by $\frac{3}{4}"$ thick plates are joined together by means of two cover plates each $\frac{1}{2}"$ thick, as shown in the diagram below. Eight ordinary $7/8"$ bolts are used on each side of the joint in tight$-$fitting holes. Each bolt can be assumed to transmit one$-$eighth of the applied force. In other words, there is negligible friction developed at the contact surfaces between the plates. Whereas high$-$strength bolts can be tensioned so as to develop very large frictional forces between the assembled elements, if ordinary bolts are used as in this case, then it is reasonable to neglect the interface friction. If this joint is subjected to a tensile force $P=160$ kips, determine:

a$)$ the average shearing stress in each bolt,

b$)$ the tensile stresses in the main plate at sections $1-1,2-2,3-3$ and $4-4,$ and

c$)$ the maximum tensile stress in the cover plates.

Draw free$-$body diagrams for the isolated elements in each part of the analysis..