Advice #1: Put a cloud in your structure!

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.

Stairway to Viamala

In Switzerland, there's an old path, dating from roman times, which crosses the Viamala gorge. In 2005, after a previous wooden footbridge was destroyed by a landslide in 1999, a new bridge was built. It was placed in a new location, with  less posibility of falling rocks.

The bridge spans 56 meters, about 70 meter above the valley, and quite a peculiar feature: it connects places with a height difference of 22 meter. It's not only a bridge, but a staircase.

Photo from lixelle

Photo from Marco Zanoli

It's a cable stayed bridge. The wood plattform (the bridge deck) hangs from steel cables which, as you already know, deform accordingly. Its funicular (the shape the cable adopts when it deforms), together with the steep stair, give rise to a powerful structure.

General forces: the weight of the bridge is supported by the upper cables in tension.

The two main steel cables, of just 36 mm of diameter, carry the load by means of tension to the foundations located in both sides of the river. Hanging from them, smaller cables (10 mm of diameter) hold the glue-laminated larch beams. Well, not really. That wouldn't be a good idea: instead, the secondary cables (those hanging from the main cables) are attached to transversal steel beams (HEA 120), and the wood beams are layed above them. This is in order to prevent tension perpendicular to the grain to appear and... believe me, you'd rather not do that. Have a look at the technical drawing here, to see how it is built.

The bridge deck is inclined, and it pushes on its lower support (that's ok, business as usual), but it pulls from the upper support. That's a different story: the bridge's own weight is trying to drag the foundation into the river. How can you avoid that?

The forces you have to stand if you don't want everything to fall down cliff!

Moreover: the cables pull inward (that is, deep into the gorge as well!) thus, something has to be done to prevent the fall: an outward force is more than required. The foundation is responsible for that and, apart from its design (have a look at it here), it must be really heavy. Its own weight is its only tool. Actually (have a look below, at the details section), the foundation of this apparently light bridge weighs seven times more than the bridge itself. It's not what you see, but also what you don't see.

Details

• More information about the bridge, and pictures of the building process.
• Location:
• Traversiner Tobel, Graubünden, Switzerland
• Concept: Conzett Bronzini Gartmann AG
• Year: 2005 (built from May to August 2005)
• Span:
• 56 m (footbridge)
• 95 m (main cable)
• Materials:
• wood
• pine (heartwood) from Nesselboden,
• larch, glue-lam and roundwood (heartwood) from Rongellen
• steel cables and profiles
• concrete foundation
• Weight:
• 26 ton (bridge)
• 192 ton (concrete foundation)

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.

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!