A special$-$purpose eye bolt with a shank diameter $d=12\mathrm{.}5mm.,$ passes through a hole in a steel plate of

thickness $t_p=18mm.($see figure$)$ and is secured by a nut with thickness $t=6\mathrm{.}25mm.$ The hexagonal nut

bears directly against the steel plate. The radius of the circumscribed circle for the hexagon is $r=10mm.,$ so

each side of the hexagon has a length $10$ mm $.$ The tensile forces in three cables attached to the eye bolt are

$T_1=3500N,T_2=2800N,$ and $T_3=5658N.$

a$.$ Calculate the resultant force acting on the eye bolt.

b$.$ Determine the average bearing stress ${}_b$ between the hexagonal nut on the eye bolt and the plate.

c$.$ The average shear stress ${}_{\text{a}\text{v}\text{e}\text{r}}$ in the nut.

d$.$ The average shear stress ${}_{\text{a}\text{v}\text{e}\text{r}}$ in the steel plate.