I was hoping someone might be able to help clarify where I might be going wrong with this question. I am being asked to essentially determine the maximum normal and shear stresses at the rigid support C due to load $F$ at the static weights.
I considered there would be a torsional shear stress induced by the torque, calculated by $$ \tau_{xy} = \frac{Tr}{J} $$ where $T = Fb$, $r$ is the radius of the shaft (the point of maximum torsional shear), and $J$ is the polar moment of area. There would also be vertical shear, maximised at the vertical centre of the beam, calculated using: $$\tau = \frac{FQ}{Id} $$ where $Q$ is the first moment of area for a semicircle, and $d$ is the diameter.
Where I'm having the most trouble is the bending moment at C. I chose to model the beam as a straight beam (which it clearly is not), supported (cantilever) at both ends with a load in the middle, giving a maximum bending moment of $$M_{C} = \frac{FL}{8} $$ from a table in my text, where $L = 2ac$. I am almost certain this is incorrect, so I was hoping someone might be able to provide some insight into where I am going wrong. I am assuming that the points that will experience the greatest stresses are most likely the top and bottom edges of the beam, where both bending and torsional stresses are maximised (and vertical shear stresses are zero). I know once I have the correct stress components I can use Mohr's circle to determine the principal stresses and maximum shear stresses that I would use in further analysis.
Full disclosure, this is a homework question, but it is a multiple choice quiz that allows multiple attempts and tells you the number correct, so I already have the "answer" to the question (which relates to material choices after determining the maximum stresses), so this is really only for my own understanding. Appreciate any help :)
