Eppur si muove! (and yet it moves!)

Sometimes, when the behavior of buildings during earthquakes is explained, something simlar to "it's like if you put the building horizontal, it behaves like a cantilever" is said. Yes... but no.

As you could see in the drawing from the previous post, it's the ground  the one that moves (actually, pretty fast). The building is the one who wants to stay calm and still, but the soil insists so much that, at the end, the house accepts to follow its motion. That's why you see its upper part arriving always "late". The earth moves left, while the building wishes to stay right, and it's not until later that the building moves (deforms, to be precise) to the left.

But then, when the building gets to the left, the ground is already returning to the right, something that the building will (later again, of course) do as well.

So the building moves. Later, but it moves. If you were the man standing under the tree you would see it completely different:

You would say that it was only the house the one that moved, and for you, its movement would be quite similar to a cantilevered beam. But, remember this?

Because you step on the earth, you see the building moving, though it intends, in fact, not to move at all. If there was another house close to it, you would even see how they pound on each other.

But remember: I feel the earth move under my feet!

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.

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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.

Walking on a rope

And so... how many invisible men were you able to count on our last visual test? The answer, below:

Congratulations! I guess you were for sure able to tell that there were three invisible men walking on the rope. But perhaps it wasn't that clear for the plank.

What's the difference? It's on the way they stand the loads applied to them, and on the way they deform. While the rope clearly changes its shape according  to the people walking on it, the plank doesn't do it in such a clear manner. That's why you could count three invisible men, but perhaps were not so sure about the plank.

Cables (like the rope) are so flexible that they must deform in order to carry loads. They can only resist tension, and those pulls straighten them. So, in the end, they become straight segments between the hanging loads. If a new load is added, the cable changes its shape accordingly.

Structures based on principles similar to cables are called form-active. Because they shape themselves in harmony with the loads, they're very efficient when it comes to the amount of required material. Consequently, they can be incredibly slender. But you should realize that because of that, they ask for more depth than equivalent beams, and for a deep understanding of their structural behavior. There are several beautiful and remarkable built examples based on form-active structures, like arches, and membranes (we will see some of them in future posts).

Beams (that's what the plank is) are more rigid than a cable. They're usually so rigid that you don't even notice they deform. But of course, they deform (remember this?) though in a rather different way: they curve. That's because a beam does not only stand tension, but also compression and bending moments, as well.

Most of our everyday structures are made of beams, which are section-active. Somehow, they're the opposite to form-active structures. Instead of shaping themselves according to the loads they're submitted to, they rigidly force the forces to follow their shape: there's no way out of them. There's a clear advantage to that: the same shape is able to stand a diversity of loads.

Two different points of view, two ways of achieving the same mean.

Visual perception test #04

One, two... buckle!

Do not buckle, it's the law

OK, if you have followed the blog during its not so long history, the answer to this last visual perception test was quite obvious. Of course, the deformed one. One of the balloons weighted more than it should, and consequently, the stick to which it was stuck buckled.
That's the kind of deformation I want to explain you briefly today.
And what's buckling, then? It's a kind of deformation, so to say. Nothing new, just told you that.
Let's go a little further: it happens to things under compression. And still one step further: you'd rather it wouldn't happen.
Why so?
Make a little experiment. Take a cane (a stick, a ruler, anything that's thin will do), and press it lightly against the floor. That way, you're applying compression to it. Now, increase slowly the pressure you apply. While you press, it will remain straight. Until...all of a sudden, you will notice that the stick bends out!
That's buckling. It happens so unexpectedly. All at once, it buckles, and it no longer stands any load.
And that's why it is a very dangerous problem. When it happens, there's no way to keep it under control.
Imagine that one of the columns of your house disappeared. It could be a disaster. If one of the columns of your house buckled, you'd face a quite similar problem. It would be almost the same as it wasn't there.
Therefore, structures have to be designed not to buckle. Conversely to the traffic sign, "do not buckle, it's the law!".

Center of falling

So, in place of who you'd rather not to be? Because one of them, for sure, is going to fall down cliff (unless they can fly, and I wouldn't bet for it!).
To answer this question, our only concern is what happens to the whole group, about whether the balance pole inclines towards the cliff or it doesn't. To fall down or not to fall down, that's the question.
Only their relative weight and position matters, since the leaning of the pole (that's to say, its equilibrium, and the possibility of falling down) is only related to where they place themselves.
So let's simplify things:  let's ask each of the  groups to stand together at a single point on each plank. The only condition for this point is: the response of the balance board should be exactly the same as before. Since they are three, and if their weight is approximately the same, it would be quite similar if the three of them were in the same point as the one in the middle. So, let's ask them to put themselves that way. Maybe now it's quite clear which one of them are falling down, isn't it?

I guess you can see it clearly now.

The key concept we have played with is called center of gravity. This is a point where if all the existing forces were applied in it, the object would move (or stay) exactly in the same way as when the forces are applied in their actual locations: we shouldn't be able to tell the difference. Although it may sound hard, we're quite used to deal intuitively with this center of gravity.
As a rule of thumb, buildings should be designed so that their center of gravity is located in the right place, between the supports, so that the building doesn't wish to fall. They usually are. But sometimes, they just don't seem so. Then, there are two main possibilities: either big dead weights, hidden somewhere; or hidden supports to prevent them from falling. Both tend to be expensive. It's much better (and cheaper!) just to design with this simple concept in mind: center on the center!

Deforming or falling down

Let's answer the previously made question. Or... let's do it in a different way: instead of giving the answer, I'll give you a clue.