A pin pinned beam column $($W$530$x$85)$ Grade $350W$ located in an unbalanced frame. The member is laterally supported by horizontal beams $4m$ at $3$ and $4m$ about the weak and strong axes. Total factored axial force $P=550kN.$

A$)$ Evaluate the applied factored axial load $($Cf$)$ and the flexural bending moments Mfx$,$ Mfy$,$ and identify the class of the section under combined compression and flexural moment.

B$)$Check the adequacy of the member to resist the applied loads with respect to lateral torsional buckling strength

C$)$ If the same section was subjected to a pure shear force, evaluate the maximum factored shear force $Vf$ that can be applied to this section.

Question $1$