Monthy Mechanic: Cantilevers

Cantilever (CANT-uh-leave-er) sounds like a bad pun. If she has an aspirin allergy, you cantilever, but you can give her Advil. In fact, a cantilever is one of the two most common ways to span a distance.

When a beam is supported on both sides, it’s called a simple span. We’ve seen a bunch of simple spans before: a log over a stream, a flat roof held up by walls on either side. Simple spans are nice because any weight on top gets distributed to both ends. But sometimes you can only support your beam on one side: a diving board, for example, or a roof overhang to keep rain from dripping down your walls. That overhang is what’s called a cantilever.

Cantilevers really want to bend, which makes them weaker than simple spans. Why? If you put a weight on the very end of a cantilever, there’s only one support to provide a vertical reaction. What’s more, the load tries to rotate the beam around the same support. To prevent that rotation, the support sees a couple of horizontal reactions: inward at the top of the beam and outward at the bottom. (See how those two reactions pair to make a rotation in the opposite direction?)

Canti0

Sometimes engineers will combine a cantilever with a simple span to get the benefit of having two supports. In this case, the simple span is called a backspan. This is how a diving board is built.

Let’s put a 75-pound person at the end of our diving board. If the cantilever (the overhang) is 8 feet and the backspan is also 8 feet, then how big are the reactions? Well, think of the middle support as the pivot on a seesaw. For the seesaw to balance, we need an equal weight on both sides. The person pushes down the left side with 75 pounds, so the right support pushes down the right side by another 75 pounds.

Canti2

(IMPORTANT!! The 75-pound force from the right support is a REACTION, not an action, even though it points the same direction as the person’s action.)

Now we have 75+75=150 pounds pushing down. All the forces need to balance, so we need 150 pounds pushing back up. That reaction happens at the pivot point, the only support we haven’t determined yet.

Canti3

Look at that: we ended up with a reaction twice as big as the original load! Yikes. I hope the diving board exercise makes it clear why cantilevers are worse than simple spans, structurally speaking. But cantilevers are useful for tons of reasons, aesthetic and functional, so we’re stuck with them.

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