$07-$Mec$-$B$12013$

Part II

Problem $3.$ A common shaft with two gears on it is shown in the following figure. Two constant radial forces of $250$ lb and $750$ lb are applied at the left and right gear, respectively. The shaft is subjected to a time$-$varying torque from the minimum of $-200$ lb $-$ in to the maximum of $400$ lb $-$in$.$ Find the diameter of shaft required to obtain a safety factor of $2$ in fatigue loading if the shaft is steel of ultimate strength $S_{ut}=108$ksi and yield strength $S_y=62$ksi. What would be the maximum deflection in bending of the shaft?

$(20$ marks$)$

bearings are self$-$aligning so act as simple supports