Current Attempt in Progress

In the gear system shown, the motor applies a $210$ lb $-$ft torque to the gear at $A.$ A torque of $T_C=230lb-$ft is removed from the shaft at gear C $,$ and the remaining torque is removed at gear $D.$

Assume that $D_A=6-$in$.-$diameter, $D_B=10-$in$.$diameter, $L_1=52in.,$ and $L_2=27in.$ Segments $(1)$ and $(2)$ are solid $1\mathrm{.}63-$in$.-$diameter steel $[$G $=14100$ ksi $]$ shafts, and the bearings shown allow free rotation of the shaft. Determine:

$($a$)$ the maximum shear stresses ${}_1,{}_2$ in segments $(1)$ and $(2)$ of the shaft.

$($b$)$ the rotation angle ${}_{\frac{D}{B}}$ of gear $D$ relative to gear $B.$