The member shown is supported by two bearings $($simple supports$)$ at O and D $($note: take O as a pin support and $\backslash ($ D $\backslash )$ as a roller support$).$ The dimensions are $\backslash ($ O C$=60\backslash$mathrm$\{$~cm$\},$ C D$=40\backslash$mathrm$\{$~cm$\},$ B C$=50\backslash$mathrm$\{$~cm$\}\backslash ),\backslash (\backslash$mathrm$\{$AB$\}=30\backslash$mathrm$\{$~cm$\}\backslash ),$ and the diameter is $2$ cm $.$ Two$-$equal torques are acting near O and D $,$ in addition to the forces at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ as shown.

a$)$ Draw the axial force, torque, shear force and bending moment diagrams for OCD and find the most critical point.

b$)$ Determine the stress state at the most critical point

c$)$ Determine the principal stresses and the maximum shear stresses at the most critical point