Truss Bridge Laboratory

Bridges are essential to our nation's infrastructure. A simple bridge can be made by spanning a gap with planks. As the gap becomes wider, however, the planks will begin to sag excessively even under the weight of a person. If the bridge is longer still, the planks may break. When one of the planks, called a beam, is loaded, it bends as shown below. Lines are drawn on the beam for illustration.

A close-up view of a short segment of the beam is shown below. The top part of the beam is being squeezed (in compression) and the bottom part of the beam is being stretched (in tension). The force in the beam actually changes continuously from the top of the beam to the bottom. That means that in the middle (top to bottom), it is neither in compression nor tension. These forces act in a bending manner on the beam. This bending force is referred to as moment, as shown in the diagram.

If a plank bridge breaks, it is likely to splinter in the middle leaving the rest of the plank undamaged. This is because the center of the plank experiences much more moment than the ends, which experience none, because they are free to rotate without resistance. So the moment, or twisting force, varies continuously from zero at the left end to its highest value in the middle and back to zero again at the right end. The result is that although it is simple to build, a plank bridge does not make very efficient use of material.

One way of making more efficient use of wooden beams is to stand them on edge. If you have ever been in an unfinished attic, you may have noticed that the floor beams (and the rafters) are in this configuration. The beams don't bend as much in the upright orientation. This is because of a property called moment of inertia. The basic principle of moment of inertia follows. As we saw before, the highest compression and tension occur in the very top and the very bottom of the beam, respectively. We also found out that the middle of the beam (top to bottom) isn't working very hard at all. So what we want is to have as much material at the outer edges as possible and have as little material in the middle as possible. The pictures below show some beams to illustrate moment of inertia.

The two beams above are called I-beams or wide flanges because of their shape (when looked at on end). The left beam would be made of steel and the right of concrete. These show how material is concentrated at the top and bottom of the beam. The more material and the farther away from the center it is, the higher the moment of inertia, and hence the stronger the beam. As nature would have it, achieving greater distance from the center is more beneficial than adding more material, because the moment of inertia increases as the square of that distance.

Obviously, we cannot remove all the material from the middle of the beam, because the top and bottom must be connected. The material in the middle also keeps the top and bottom from sliding with respect to each other in what is called shear. Yet there is a more efficient way to focus material at the top and bottom and provide resistance to shear. The middle part of the beam does not need to be solid and continuous, but can instead be made up of thin rods. This is shown in the figure below.

This configuration establishes the basis for what is known as a truss. A truss is the oldest and most often used method of making more efficient bridges, and you will be building one today. A truss is a structure made from straight links connected at joints. The joints are always at the ends of the links, never in the middle. The links are called members, and in your case, they are craft sticks with drilled holes. The joints are assembled with small bolts in your case. If the term members makes you think of a team, you are on the right track. When a load is applied to any joint, the members will share the load, although not equally.