TGV Bridge at Avignon by John is available under CC 3.0
Recently in beginner’s swing dancing classes I’ve described the connection between lead and follow when dancing side-by-side Charleston as being a bit like how pre-stressed concrete works. I promised a longer explanation. Here it is.
Starting with reinforced concrete
To begin we need to understand how reinforced concrete works.
When you build a beam in a building and you stand in the middle of it, the beam sags, albeit ever so slightly. To understand what is happening, you can simulate a simple beam by interlacing your fingers in front of you, palms down. Now imagine what were to happen if someone were to balance a bag of sugar on your knuckles: your hands would sink down, the skin on the underside of your fingers would stretch, and the skin on the top would pucker up. That’s because the skin underneath is going into tension, and the skin that is on top is going into compression. This tension-compression couple is what supports the load resting on the back of your hands.
For a video illiustration of this deomonstration, see this video I helped to script a few years ago at Think Up.
Now let’s imagine what happens if we were to build that beam out of pure concrete instead. Concrete is strong in compression, and so would have no difficulty in resisting the compressive force in the top side of a bending beam. But it has virtually no tensile strength, and so as soon as the underside of that beam starts to stretch it would suddenly crack and catastrophically fail.
So for about 130 years now, engineers have been embedding reinforcing steel in the bottom of concrete beams to carry that tension which arises when a beam bends. Steel is strong in tension (think of the steel cables in a suspension bridge). In a beam reinforced with steel, the steel rods act like stiff elastic bands which resist the tensile loads that are generated when the beam bends.
The importance of depth
Reinforced concrete is a popular building material. To work, the beams need to have a certain depth to them. To illustrate we can think what happens when we bend a 30cm ruler. If you hold the ruler out in front of you flat side facing down, and try to bend it downwards, it bends easily. But if you hold the ruler out in front of you edge-downwards, and try to bend it downwards, it is almost impossible. What’s the difference? It’s the difference in distance between the top and bottom fibre that determines the stiffness.
So, deeper beams are stiffer, and can span further between supports.
Pre-stressed concrete
The problem with deeper beams is that they require a deeper floor void between the ceiling of one level and the floor the level above. Building designers usually want to minimise the floor depth so that they can fit in as many levels as possible within a given height. More levels means more rent.
Pre-stressed concrete is an evolution of reinforced concrete which enables shallower beams and slabs to be used in buildings. In pre-stressed concrete, the steel bars of reinforced concrete are replaced with steel cables which run through the middle of the beam and are attached to a plate at either end. When the concrete is set, this steel cable up is tensioned up squeezing either end of the beam, putting the entire thing into compression.
The effect is similar to when you pick up a row of books simply by squeezing from either end. If you squeeze hard enough, you can pick up say 15 paper backs without any of the middle ones slipping out.
For an illustration of this principle, see another video that I helped to make a few years back at Think Up:
Now imagine you were picking up a row of books in this way, squeezing from either end, and someone were to put a bag of sugar on top in the middle, as long as you were squeezing hard enough, you could probably support the weight of the bag of sugar.
So what is happening here? In fact, the same thing is happening here as when the sugar was placed on our interlaced hands. The top of the books are squashed together, and the bottom split apart a bit. The difference is that because these bending forces are applied to a set of books that is already being compressed together from either end, the bottom edge never goes into tension: it is just a little less compressed. Similarly the top of the books are more compressed because of the sugar they are supporting.
Putting pre-stressing cables into a concrete beam puts the whole thing into constant compression, making the whole thing stiffer.
What’s that got to do with swing dancing?
In teaching beginner swing dancing classes there often seems to come a point where we have to move learners from simply dancing a choreography to leaders leading and followers following. The key to that is the connection between them, which works in different ways depending on the dance.
When dancing side-by-side Charleston, the leader has their arm around their follower’s waist. The follower needs to sit back into this arm slightly, and the lead needs to push against their follower’s back. This creates a slight compressive force between them, which is equal and opposite.
To signal to the follower that the leader wants to move forwards, the leader moves forwards themselves, and in doing so, increase the compression in the connection, which causes the follower to accelerate forwards.
To signal to the follower that the leader wants to move backwards again, the leader moves backwards themselves, and in theory, this reduction in compression should cause the follower to accelerate backwards.
In practice, what we see is leaders moving backwards, and become disconnected from the followers. This disconnection reveals that they never had that matched compressive force in the first place: the pre-stress was missing.
If that compression is there to start with, if one person reduces the compression by pulling away, the other starts moving towards them. If there is no compression, and one person reduces the compression by pulling way, the two simply separate from each other.
So, to get the connection right, get the pre-stress right.
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