How Bending Moments, well, Bend?

A simple beam that works to carry the shear stress must also be designed for the bending moment. Think of a scaffold plank, a 2 x 10 piece of wood spanning 6’. As you step onto the middle of the scaffold plank, you notice some deflection downward. The scaffold plank is now experiencing a bending moment. If you think about the actual plank directly under your feet, the wood fibers on the bottom of the plank are in tension, they are being pulled apart as the plank bends downward. The wood fibers on top of the scaffolding plank are in compression, they are being pushed together.

You can visualize this effect by holding your right hand outstretched, palm facing upward. Take the index finger of your left hand and poke down into the middle of your right palm. Cup your right hand just a bit. Now you get a visual of a bending moment. The skin on the bottom of your hand (around your knuckles) is in tension…the skin is being stretched tight. The skin in your palm, right near the applied load of your index finger, is in compression…the skin is bunching together. Figure 1.4 illustrates.

This concept of bending is important to understand. The scaffold plank acts as a beam, which is under load and is resisting the bending moment. Consider the cross section of the beam (i.e. the scaffold plank) at the point of load (where you are standing). When a structural element is being loaded in bending, the deflection, even if only a small amount, causes tension in the lowest fibers of the beam and compression in the top fibers. The failure due to bending moment occurs as the beam deflects and either the bottom fibers pull apart and fail in tension or the top fibers crush and fail in compression. This is illustrated in Figure 1.3 Bending Moment.

The shape of a steel “I” beam follows from this understanding of bending moments. Since the extreme stress in tension is at the bottom of the member and the extreme stress in compression is at the top of the member, a regular rectangular shape would have most of its area under low stress. Only the very top and very bottom would be under maximum stress. Figure 1.5 shows how a rectangular shape and an “I” beam might be stressed. Obviously, since the steel rectangle beam weighs 97 lbs/foot and the W12x45 “I” beam weighs 45 lbs/foot, the steel “I” beam is much more efficient to use.