Consider a rod subjected to an axial force; as a result, a resistive force is developed across the cross-sectional area, which is termed as stress. The SI unit of stress is Newton per square meter.
Now, consider a bridge truss member subjected to an axial force. It develops internal forces and stress normal to the cross-sectional plane, called the normal stress.
The resultant normal stress represents an average stress over the cross-section, rather than at a specific point.
According to the conditions for equilibrium, the internal forces equals the applied force, implying that stress distribution is uniform, except near the point of application.
However, this uniform distribution is only possible if the line of action of the loads passes through the centroid of the section, termed centric loading.
When axial loading is applied eccentrically, the distribution of forces and stresses cannot be uniform or symmetric due to the additional moment created.
So, the actual stress distribution in an axially loaded member is statically indeterminate and depends on the specific mode of load application.
17.1:
Normal Stress
Normal stress is a type of stress that occurs when forces act perpendicular, or normal, to a material's cross-sectional area. This stress often arises in structures when subjected to axial loading, which is the application of force along the axis of an object. A practical example of this can be found in bridge truss members.
When a rod is under axial loading, the internal forces and corresponding stress are normal to the plane of the section, so it is termed normal stress. It's important to note that stress represents the average stress value over the cross-section, not at a specific point. The average stress is calculated by dividing the magnitude of the resultant internal forces distributed over the cross-section by the area of the cross-section.
However, the stress at a given point may differ from the average stress, as it varies across the section. Especially in slender rods under axial loads, the variation can be significant near the load application points.
Equilibrium conditions suggest uniform stress distribution in axially loaded members, except near load application points, assuming centric loading. However, eccentric loading creates non-uniform stress due to additional moments, indicating statically indeterminate stress distribution.