Hello. In this video, I am going to introduce the topic of stability which is the last topic we are going to see within the course "The Art of Structures". I am going to present to you the phenomenon of stability or rather of instability of structures, and then I am going to remind you what we have already seen in the course "The Art of Structures I". Here you have the complete path of structures. For those who have joined us in the middle, I remind you that we have started here that is to say, with trusses, then we have treated beams and wall-beams, frames and then of courses beam grids and slabs. Today we reach the last topic : that of stability. The phenomenon is very simple. In this video, you can see me with a bar made of bamboo on which I lean. When I push on it, this bar gives way like the cane of a certain comedian. The result is that I cannot really lean on it. The load is limited. The structure takes a funny shape. This picture summarizes quite well the phenomenon of stability: at once the knowledge we have about it and also the technics we can use to prevent it. Of course, the fact that the cane bends does not mean that columns are always going to bend. On the left, we have a structure which is about 2000 years old, from the Roman era, with columns which have very significant dimensions and which are also extremely close to one another. And on the right, we have a modern structure from the 20th century, the end of the 20th century, designed by Norman Foster. We can see columns which are really distant from each other, which are very tall, because they are in the background, they are taller than the Roman columns and they are extremely thin. How can it be possible? We are going to look at this and we will get back to this subject later on. Fundamentally, we want to look at what happens with a bar either in tension, either in compression when it is subjected to a load Q. If I first start by the bar on the which is in tension, what happens when I place a load on it and when I give it a certain deformation to find out if it is stable or not - generally, we are going to deform the structure a little bit and look at what happens - well here, the structure returns in place, that is to say that the deformation decreases thus the structure is stable. Even if we bother it a little bit as I did at first, it is going to come back to its initial position. If however, I have a structure in the configuration that I have drawn on the right if I had made a model of this, you would have seen me trying to hold a bar up at the end of my fingers. That is already not easy when I do this, but if in addition, we apply a deformation then the structure keeps going further and further. That is to say that the deformation increases and thus the structure is unstable. Somewhere along the line, quite quickly, it is going to end on the ground. Remember: that is a video which is from "The Art of Structures I" when I introduced the topic of arches. When I add a second load on this arch on the right, we can see that it collapses and the structure falls. That is a relatively serious topic. Let's get back to this topic through two examples. I am first going to apply a load Q on the left and on the right on both my structures, so a cable structure and an arch structure. Well, in both cases, since the shape of the structure is identical to the shape of the pressure line or of the tension line if we want to talk about... or of the funicular polygon, if we want to talk about the cable. In both cases, we have a stable structure. The pressure line is identical to the shape of the structure. Therefore this structure is stable. Here too the structure is stable. Do not say that all structures in compression are unstable. They can absolutely be stable. However, if now we add a load on the right, that is what we had done in "The Art of Structures I", - I encourage you to watch this video if you have not - what is going to happen is quite different for the arch and for the cable. Indeed, in the case of the cable, the cable is going to change its shape but keeping the same property: the pressure line is going to remain identical to the shape of the cable. So we still have a stable structure. However, what happens on the right is quite different. I first drew, here, the grey shape, the shape that the structure tends to take - actually, that is the one it takes in my video - that is to say that where there are more loads on the right, the structure goes down. The bad news is that the shape of the funicular polygon - we have seen it in the course "The Art of Structures I" but you can understand too that it must be symmetrical to the one of the cable - this is the pressure line, so where the structure wants to go down, the pressure line, on the opposite, would like that the structure goes up. If we think about a mirror, it works with the cable but it does not work here. Here, the pressure line gets further from the arch therefore the structure is unstable. This is fundamentally what happens and which explains the difference between tension and compression and the phenomenon of stability. That is this distance, for example here, between the shape of the structure or the shape the structure would like to take and the pressure line. In this video, I introduced to you the basic principles of stability. We have seen that the behavior of elements in tension is fundamentally different from that of elements in compression, the elements in tension being always stable and the elements in compression being either potentially or really unstable. We have seen the importance of the position of the pressure line. In the following videos, we are going to see in more details how this stability phenomenon works, and how to prevent it.