Monthly Mechanics: Trusses

Previously, we discussed the opposing forces of tension and compression. We also explored structures that work in pure tension (cables) and in pure compression (arches). You might have noticed the limitations of these structures: it takes a lot of additional materials to build up an arch into a bridge, or a cable into a roof. Curves are impractical. But you can use straight lines if you combine tension and compression in the same structure. This powerful concept is the basis of a truss.

A truss is an assembly of long skinny pieces, called members, connected only at their endpoints. Each point where two or more members meet is called a node. When you put some weight on the nodes, each member has an axial force (a force along its axis), either tension or compression. But here’s the thing: the nodes are the ONLY place you can add weight. Any other place puts a member in bending and weakens the truss considerably.

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A pirate ship ride is supported by a truss.

The simplest truss is a triangle, loaded at the top node and supported at the bottom two nodes. A real-life example is the support structure for a Ferris wheel or pirate ship ride. We can figure out the support reactions exactly the way we’ve done it before: if the ride weighs 20,000 pounds and it’s divided equally, then both support reactions are 10,000 pounds.

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Look at the left diagonal member. Is it in tension or compression? The answer is compression, because the 20,000-pound load and the 10,000-pound reaction both push on the ends.

Here’s a trickier question: how much compression? It’s tempting to say 10,000 pounds, but notice that the 10,000-pound forces are vertical whereas the member is on a 45-degree diagonal. That means there must also be a 10,000-pound horizontal force. Take the vector sum of these loads (that’s a fancy way of saying you connect the arrows) and the result is a 14,000-pound load along the diagonal. Ditto for the right diagonal member.

There’s no horizontal reaction at the supports, though. The bottom member ties the two diagonal members together. For the forces to balance, that bottom member must be in 10,000 pounds tension.

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Most real-life trusses are bigger than our triangle, with dozens of members. Since all the forces are axial, they can span long distances with a minimum amount of material. And since the members are straight, they provide a flat surface for, say, a roadway or a ceiling.

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