Question: The shaft shown below has a solid round cross-section & is supported by bearing at A & B. The nominal forces on the gears at C, D & E are also shown. The force on the gear at C varies± 5% from its nominal value. The shaft material is made of cold drawn steel with tensile yield strength of 36 ksi & an ultimate tensile strength of 58 ksi.

Determine following:

1. The location of maximum bending stress in the shaft
2. The diameter of the shaft for a 2.0 factor of safety for yielding using the maximum shear stress theory and the distortion energy theory at the location of maximum bending stress
3. FBD and bending moment diagrams
4. The deflection of the shaft at D in the z-direction and the x-direction
5. The factor of safety for fatigue (infinite life) with 95% reliability for the diameter determined above and at the location of maximum bending stress