QUESTION $4.(10$ Marks$)$

A steel shaft is supported on smooth bearings that allow it to rotate freely. If the gears are subjected to the torques shown and the shaft is solid with a diameter of $40$ mm :

a$)$ Draw free body diagrams for AB and BC $(2$ Marks$)$

b$)$ Determine the maximum shear stress developed in the segments AB and BC $.(6$ Marks$)$

c$)$ How would the calculations change if the shaft was hollow $($write out the equations$)?(2$ Marks$)$