A 40m long power shaft is positioned horizontally and delive

A 40m long power shaft is positioned horizontally, and delivers a constant (ignorable) torque as it rotates. Find the minimum diameter for the shaft such that it will last at least 5*10^8 cycles under its own weight if it’s made from a) 1050 CD steel (table A-20), b)2024-T3 aluminum (table A-24). Treat the shaft as a simply supported beam holding up a uniform distributed load (representing its own weight). Since the shaft is rotating, the fatigue loading can be considered fully reversed. Densities and other key material properties can be found in table A-5.

Solution

A 40m long power shaft is positioned horizontally, and delivers a constant (ignorable) torque as it rotates. Find the minimum diameter for the shaft such that it will last at least 5*10^8 cycles under its own weight if it’s made from a) 1050 CD steel (table A-20), b)2024-T3 aluminum (table A-24). Treat the shaft as a simply supported beam holding up a uniform distributed load (representing its own weight). Since the shaft is rotating, the fatigue loading can be considered fully reversed. Densities and other key material properties can be found in table A-5.