March 1, 2011

It won't if it doesn't

How can you prevent a column from buckling when it's compressed? Making it stiffer (that is, bigger and "fatter") is a possible solution. However, what if you wanted a really slim column?

Stop. Think on it, and keep on reading afterwards.



There's another possible solution: it won't buckle if it doesn't buckle. Yes, I know, it may sound like a trick. In fact, it is: the solution is not to compress the column. But... how can you avoid compression if it must be compressed (so that it is an actual column)? Easy: you just have to stretch it before. Never wondered why the thin spokes of your bike's wheels don't buckle? Because in fact, they're never compressed, they're always tensioned by means of the nipples.

That's a way to design a slim column: apply as much tension as it does not get compressed. There's a downside, of course: forces don't dissapear. A mean to stand the additionally developed forces has to be provided. To make that particular column slenderer, other columns will get more compressed and, consequently, thicker. The drawings below will help you to understand it.
Our three friends are standing over the columns. The three columns stand exactly the same load, the weight of one person.  In the drawing, one arrow represents the weight of a single person, from now on, 1W.

Suppose that, for some reason, it is decided that the central column should be thinner. We need to make use of the previous trick: instead of the central column we're going to put a string, and we're going to pull from it exactly the weight of two people, 2W (that's two arrows). The lateral columns become compressed 1W, while the central is tensioned 2W -the drawn deformed shape is exaggerated to emphasize that things do deform-.

Our three friends stand over the roof again. Each column is additionally compressed with their weight, 1W. But this time the final loads on each column are quite different from the first drawing: the central column stands 1W (like in the previous situation), but conversely, it is still tensioned (previously it was compressed). Additionally, the lateral columns are twice as compressed! Consequently, they have to be thicker. Result: thinner central column, bigger lateral columns. Two sides of the same coin.

Why have I explained this peculiar design concept? The answer, in the next post.

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