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## Main Question or Discussion Point

A shaft of diameter 10 inch is supported by 3 ball bearings. An external force (F, given) from pulley (diameter not given) also acts on the shaft. The supports are subjected to bending load (moment and transverse shear) and torsion load due to pulley. Yield Stress at Tension given. Assume no axial load. I need to calculate the reactions and moment equation for the shaft.

My approach:

- Statically Indeterminate

**(1)**∑Fy = 0 = Ra + Rb + Rc -F

**(2)**∑Mc (CCW +) = 0 = 5F-6Ra-3Rb

**Solve (2) for Rb and Plug it in (1)**

To write a moment equation, I make a cut between Rb and Rc

Summing the moment at the Cut (o)

∑Mo = 0 = -Ra(x) -Rb (x-2) + F(x-1) + M = 0

**(3) M = Ra(x) + Rb(x-2) - F(x-1)**

After this I can calculate the reactions using deflection method (singularity equation).

However, I am not sure that my moment equation is correct. Since the problem states that the shaft is subjected to bending load and torsion load at the ball bearings, do I have to account for these in my moment equation? If so, how?