# Eccentric Axial Loading in a Plane of Symmetry

JoVE Core
Mechanical Engineering
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JoVE Core Mechanical Engineering
Eccentric Axial Loading in a Plane of Symmetry

### Nächstes Video20.14: Unsymmetric Bending

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.

## Eccentric Axial Loading in a Plane of Symmetry

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.