Line of Action of the Axial Forces for a Uniform Stress Distribution

Line of action of axial force for a uniform stress distribution should pass through the centroid of the cross sectional area.

Explanation:

If the line of action of the force is along the centroidal axis of the cross sectional area there is no eccentricity in the line of application of force hence no moment is generated in the cross sectional area hence we get a uniform stress distribution as theorized by hookes law.

In case of eccentric force there is an additional moment in addition of the force. This induced moment induces bending in the section thus giving a non uniform stress distribution in the section.