WORLD FOR CIVIL

Topic 8.3: Special Topics I - Non-Axial Loads

We next look at the case where there is a non-axial loading on a structure or structural element.

In Diagram 1a, we have shown a structural element in tension with a load F acting at the edge of the element. The load force F is non-axial, it is not acting along the axis of the element, however we can represent the effect of this edge force, F, by an axial force, equal to F and acting at the centroid, and a moment (torque) about the centroid, as shown in Diagram 1b.
When we represent the structural element in this manner, we can determine the axial stress acting on the element by superposition of stresses, as shown in the following example.

Example: In Diagram 2a, we have shown a 2" by 2" structural element with a tensile force of 5000 lb. applied at the edge of the element as shown. In Diagram 2b, we have replaced the 5000 lb. edge force with a 5000 lb. force acting at the centroid of the element and a moment about the centroid of 5000 lb. * 1" = 5000 in-lb.

We next determine the normal axial stress and the bending stress on the top cross sectional area. The normal axial stress is given by:
= F/A = 5000 lb./(2"x 2") = 250 lb/in².
And the bending stress is given by:
= My/I = 5000 in-lb.* 1" /[(1/12)2"*2"³] = 3750 lb/in². Where for y we have used the maximum distance from the neutral axis to the outer edge of the area, giving us the maximum bending stress. In Diagram 3a we have shown the normal stress distribution on the area. In Diagram 3b we have shown the bending stress distribution along one edge (it is the same across rest of the area). From the direction of stresses we see that they add along the front side of the element face, and subtract along the back side the element. We can then find the maximum axial stress from:
Maximum Axial Stress = 250 lb/in² + 3750 lb/in² = 4000 lb/in².