Problem $3(25$ points$).$ In the figure, shaft AB transmits power to shaft CD through a set of bevel gears

contacting at point E$.$ The contact force at E on the gear of shaft CD is determined to be $($FE$)$CD $=92\mathrm{.}8$i $$

$362\mathrm{.}8$j $+808\mathrm{.}0$k lbf$.$ A bearing life of $108$ revolutions is desired with a $90$ percent combined reliability for

the bearing set. Assume an application factor of one. $($a$)$ Determine the reactions at C and D assuming

simple supports assuming bearing C carries the axial thrust. $($b$)$ Should the bearings be oriented with

direct or indirect mounting so that the bearing C can carry the axial thrust? $($c$)$ Assuming bearings are

available with K $=1\mathrm{.}5,$ find the required radial rating for each bearing.