The beam with a solid circular section supports at point B an axial load of $25$ kN and at end C a vertical load perpendicular to the axis of the beam with a magnitude of $1$ kN$,$ the material used has a modulus of elasticity of $200$ GPa and a Poisson's ratio of $0\mathrm{.}29,$ determine the minimum radius required for the beam if the material has a yield stress of $350$ MPa, and an FS of $2\mathrm{.}5$ should be considered, use the Von Mises and Tresca criteria.

Find the axial forces

Find the torques.

Find the shear stresses

Find the numerical solution for the two criteria