Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.

In such cases, the internal forces within the member's cross-section can be analyzed by considering both an axial force at the centroid and a bending moment caused by the load's displacement. This displacement generates a moment, creating a couple that must be counterbalanced to maintain equilibrium. The resultant stress across the cross-section is a combination of uniform stress due to the direct axial load and varying stress from the bending moment.

The stress distribution across the cross-section is linear, resulting in different stresses on either side of the centroid—one side experiences compression and the opposite side tension. This analysis assumes that the material remains within its elastic limits and that the deformations do not significantly alter the load's displacement. It is primarily applicable to the straight, unwarped segments of a member. Such considerations are crucial for ensuring the structural integrity and stability of engineering designs, especially when components may be subject to unusual loading configurations.