GOAL: Shaft Fatigue Analysis

A make-shift temporary derrick is erected over a deep water well in a rural community that has lost access to electric as a result of storm damage. A rope-and-pulley system is attached to the derrick and used to lift a barrel (160 liters) of water from the well. Due to the limited supplies, the system can only provide a 2:1 mechanical advantage. The final pulley is simply supported at the midpoint of a support shaft that is made from a 24" piece of 1018CD 1" diameter round bar. The pulley is connected to the shaft using a shear pin joint made from a 3mm dowel pin inserted into a transverse hole through the shaft. Consider 80% of the life of the shaft as the maximum safe life. The shaft rotates 45 times per each lift.

Make a recommendation on the number of times the system can be used before risking the failure of the shaft.