Eccentric axial loading refers to the application of an axial load that is not aligned with the centroidal axis of the member.

Consider a member having a plane of symmetry with a load applied along the plane of symmetry.

The internal forces within the cross-section are represented as a force acting at the centroid of the cross-section and a couple acting in the member's plane.

The cross-section is in equilibrium when the internal force is equal to the applied load, and the couple moment is equal and opposite to the moment generated due to the applied load.

The stress distribution due to the eccentric loading can be written as the sum of the stress due to centric loads and the linear stress distribution due to the eccentric bending couples.

This expression shows that the stress distribution across the cross-section is linear but non-uniform.

This analysis is valid when the stresses are within the proportional limit, the deformation due to bending does not vary the moment arm, and the cross-section is considered at straight parts of the member.