A bull wheel is used to turn the cable for a ski lift (Fig. Q3.1). The...

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A bull wheel is used to turn the cable for a ski lift (Fig. Q3.1). The shaft and wheel are attached such that they rotate together within two bearings at each end of the shaft. It can be assumed that the shaft experiences three-point bending from contact with the cable, pulling the wheel against the mid-point of the shaft, and the two bearings at each end. The bearings can re-orient during bending so that the shaft can be considered as a simply supported rotating beam. Ski Lift Bullwheel T Shaft Bearing Cabic 4/8 Fig. Q3.1 - Perspective and side views of a ski lift bullwheel (a) Calculate the peak tensile stress at the shaft's mid-section if the tension in the cable is 20 kN, the shaft length between the bearings is 1 m, and the radius of the shaft is 0.05 m. [8 marks] (b) Calculate the number of years required to cause fatigue failure of the shaft if it rotates once every 10 seconds and is assumed to operate for 12 hours per day for 250 days per year. The following high cycle fatigue equation applies to the steel used in the shaft: % = 1000N-0.15 A bull wheel is used to turn the cable for a ski lift (Fig. Q3.1). The shaft and wheel are attached such that they rotate together within two bearings at each end of the shaft. It can be assumed that the shaft experiences three-point bending from contact with the cable, pulling the wheel against the mid-point of the shaft, and the two bearings at each end. The bearings can re-orient during bending so that the shaft can be considered as a simply supported rotating beam. Ski Lift Bullwheel T Shaft Bearing Cabic 4/8 Fig. Q3.1 - Perspective and side views of a ski lift bullwheel (a) Calculate the peak tensile stress at the shaft's mid-section if the tension in the cable is 20 kN, the shaft length between the bearings is 1 m, and the radius of the shaft is 0.05 m. [8 marks] (b) Calculate the number of years required to cause fatigue failure of the shaft if it rotates once every 10 seconds and is assumed to operate for 12 hours per day for 250 days per year. The following high cycle fatigue equation applies to the steel used in the shaft: % = 1000N-0.15

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