Harmonic Structures

Advice #1: Put a cloud in your structure!

2011-03-30T22:14:00.008+02:00

Eppur si muove! (and yet it moves!)

2011-03-23T23:51:00.000+01:00

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!

Jishin

2011-03-16T23:08:00.000+01:00

Snow on the roof

2011-03-08T22:53:00.002+01:00

Why did I tell you such a weird thing in the last post? The reason was the KAIT Kobo building you can see in the photos below.

External view. Photo from naoyafuji.

Internal view. Photo from brandon shigeta.

Is there anything remarkable in this building? Since the previous post had something to do with columns, you may make an educated guess...

There are many, many columns, exactly 305 steel columns in total. Careful, don't let them fool you. In fact, there are only 42 columns. But wait, didn't I write 305... where did the other 263 columns go?

They're still there, of course, they didn't disappear in the air. But they're not columns, they just look like columns. A column is not only a vertical constructive element. There's an additional feature it must fulfill: it has to be compressed. And these 263 ain't compressed at all. They're tensioned: the roof pulls them.

Such high number of supports was intended for architectural reasons. They limit the different spaces, and resemble a natural bamboo forest (which happen to be in Japan, like this building). Almost every single column (290 of them, to be accurate) has a different quadrangular shape, ranging from 16-by-145 mm, to 63-by-90 mm. If the thinnest of them (which is not even 2 cm thick!) was a real column, it would buckle. So, the question behind the structural concept was the one I asked you in the previous post: how to prevent such a thin column from buckling?

The "columns" would buckle when the roof is loaded...

And the answer is the same: it won't buckle if it doesn't buckle.

To achieve our slogan, the steel structure was built in two phases. First, the 42 real columns and the roof steel frame (made of 20 cm deep steel beams arranged in a 1.5 by 0.9 m grid). Then, the 263 fake columns were hanged from the girders, the roof was loaded with weights up to the snow load (the maximum vertical load the building has to stand), and then (and only then) the lower part of these 263 supports was fixed.

When the roof was unloaded afterwards, the roof structure went up (as you already know, with the previously applied "snow" load it was deformed), and consequently the 263 false "columns" were tensioned. By means of this peculiar strategy, these supports are supposed to be never ever compressed and consequently they will never ever buckle, they will always stand straight and resemble real columns to the profane eye, but no longer for you, right?

Details

Location: Kanagawa, Japan
Architect: Junya Ishigami + associates
Structural engineer: Konishi Structural Engineers
Year: 2008
Material: steel
Built area: 1898 m²
Height: 5 m
Weight (approximate)

columns: 47 ton
roof: 1432 ton
ratio: 1.35 ton/m²

It won't if it doesn't

2011-03-01T21:59:00.000+01:00

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.

Stairway to Viamala

2011-02-22T23:33:00.002+01:00

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

2011-02-15T22:14:00.008+01:00

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

2011-02-08T22:12:00.000+01:00

One, two... buckle!

2010-02-09T22:33:00.002+01:00

Do not buckle, it's the law

2010-01-22T14:27:00.003+01:00

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!".

Visual perception test 03

2010-01-12T23:05:00.002+01:00

Is it alluminium? No, it's...

2009-12-21T23:25:00.002+01:00

And the answer to the previous riddle is...
Wood.

Or, more exactly speaking, its cell wall, half of which is cellulose (the same fiber which paper is made of).

Consider this: the tensile strength of these wood cell walls is about 150 MPa (each square centimeter stands 1.5 tons!); the tensile strength of alluminium ranges from 25 to 125 MPa. Thus, if we had two rods of the same size, one made of alluminium and one made of pure and perfect wood, the wood one would break at a higher force!

Remember what I told you in a previous post: wood was developed to hold up the tree and to carry the sap from the roots to the branches. So the idea was to develop a very strong material. Not only to use less amount of it, but also because the more holes it has, the more sap that arrives to the right place. More with less.

Material properties are taken from Ashby and Jones. "Engineering Materials 2. An Introduction to Microstructures, Processing and Design" 3rd edition. Elsevier, 2006.

Riddle 01

2009-12-16T11:36:00.000+01:00

What's nearly as strong as alluminium,
has rings but it's not married,
and is old and young?

Center of falling

2009-12-08T23:19:00.004+01:00

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!

Visual perception test 02

2009-11-26T22:34:00.001+01:00

Good old wood

2009-11-18T21:52:00.002+01:00

Wood is a fascinating material. It's a natural "alive" material (which is not totally true, but we'll leave that for another post), and that makes it specially appealing.
The first wonderful thing, its designer: Mother Nature. It's been slowly designed, proved and redesigned for millenniums. Plenty of time to develop it!
And that's the point... if you really had time to make something, wouldn't that something be quite close to perfection?

Wood is thus perfect for its missions: aliment and support. Sap must reach every single cell, and the tree must stand up proud and strong as well (nothin' to do with the oak of the previous post!).
Wood fulfills both purposes up to grade. We'll have time to see how its structural mission is carried out But that's another story and shall be told another time.

The next time you rest under a tree, think: it's not only a shadow more. Wonder at the wonder wood.

Deforming or falling down

2009-11-13T22:07:00.001+01:00

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.

An old fable tells about a proud and enormous oak who made fun at a fragile and small reed. Then a strong wind blew. The tree tried to stand but was uprooted. The reed, instead of keeping still, moved with the wind, and... he wasn't pulled out! He was able to deform with the wind, and this guaranteed his survival.

We usually think that our houses and the structures which support them, are immovable. Luckily, it's not that way. Structures do move (and I don't mean because of earthquakes!). Actually, they stand up because they deform. What usually happens is that these deformations are so small that we usually don't see them.

Let's think on a spring or a rubber band: if we stretch it (we apply a force), it deforms (it's longer): the bigger the force, the bigger the deformation. It's not only that the spring (the structure) deforms itself when the force is applied. It is also that it necessarily must deform to stand the applied force.
So if it's deformed, a force is applied to it.

No force, no deformation. No deformation, no force.

Now, look again at the image of the previous post, Who would you say now that's really pulling?

Visual perception test 01

2009-11-10T23:29:00.001+01:00