Combined Loadings

If a loading results in more than one type of stress, the total stress in a cross-section can be calculated by adding the individual stresses together (superposition). A review of the stresses covered in this course is below:

Axial Force Axial loading leads to uniform normal stress.
Torsional Moment (circular shafts) Torsional moments lead to varying shear stress in the cross-section.
Shear Force Shear forces lead to varying shear stress in the cross-section.
Bending Moment Bending moments lead to varying normal stress in the cross-section.
Pressure Pressure leads to uniform normal stress.

Stresses under Combined Loadings

The goal in combined loading is to determine the stresses at a point in a slender structural member subjected to arbitrary loadings. A cross-section is cut through the point of interest and the internal loading/moments are evaluated at the centroid of the section to maintain equilibrium. This internal system of loading will consist of three force components and three couple vectors (moments). To sdetermine the stress distribution at the point, the principle of superposition is applied.

Combined Loading Summary:

Axial force and in-plane couple vectors (moments) contribute to the normal stress distribution in the section.

Shear forces and the twisting couple vector (moment) contribute to the shear stress distribution in the section.