A transmission shaft supporting a spur gears B and the pulley D is shown in the Figure below. The shaft is mounted on two bearings A and C. The diameter of the pulley and the pitch circle diameter of the gear are 450 mm and 300 mm respectively. The pulley transmits 20 kW power at 500 rpm to the gear. P₁ and P₂ are belt tensions in the tight and loose sides, while P₁ and P, are tangential and radial components of gear tooth force. Assume, P₁= 3P₂ and P, = P, tan (20°). The gear and pulley are keyed to the shaft. The material of the shaft is steel AISI 1144 OQT 1000. Determine the shaft diameter on strength basis. Use K₁ = 1.5 and design factor of 4. Design for reliability of 0.99 and you may assume size factor of 0.75 for the start. In doing so, follow the following steps: (a) Compute the torque delivered to the shaft at B. (b) Compute the belt tensions P₁ and P₂ at pulley D. (c) Compute the reactions at the bearings A and C. (d) Draw the complete free-body diagrams and bending moment diagrams of the shaft in horizontal and vertical planes (e) Determine the modified endurance strength of the shaft. (f) Determine the minimum acceptable diameter of the shaft.

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A transmission shaft supporting a spur gears B and the pulley D is shown in the Figure below. The shaft is mounted on two bearings A and C. The diameter of the pulley and the pitch circle diameter of the gear are 450 mm and 300 mm respectively. The pulley transmits 20 kW power at 500 rpm to the gear. P₁ and P₂ are bel