A beam-column is a structural part that can bend (as a beam) and compress (axially). The combination of bending and axial compression can result in complicated behavior, necessitating careful study and design to assure the structure’s stability and safety. Beam-columns are frequently used in building frames and other constructions that are subjected to both axial and bending stresses.
As a structural engineer you need to perform several set of checks at member and cross section level to design a beam column member.
Design of beam column at cross section level
AISC 360 gives an interaction equation that takes into account the reduction in axial load carrying capacity due to bending moments.