A solid steel beam with a circular cross$-$section, fixed at its upper end, is subjected to a horizontal force P$,$ as shown in the figure.

Given that the yield stress of the steel is $560$ MPa, determine:

a$)$ The maximum value of P that can be applied to the beam, using a safety factor of $2$ and applying the von Mises criterion. $($Identify the critical sections and calculate the equivalent stress in these sections$).$

b$)$ Construct the internal force diagrams $($shear force, bending moment, and torsional moment$)$ along the beam, ensuring clarity in the representation of the critical points.