Hello. In this video, I am going to introduce floorings. We will first see why we need to make floorings, then, and this is the main question, how to make a flooring; and then I will show you which materials can be used - let's say, preferably - to make such structural elements. If we look at our progress in the Art of Structures, we are finished with the 2D part of the lecture about beams, and we are starting to deal with the 3D part, so we will talk about beam grids and slabs, but all this, within the general topic about floorings, since a flooring can directly be constituted by a slab, or else by a beams grid, which support a slab. How to make a flooring, that is good, but first, why do we need to floorings? Well, in human history, the first constructions have been directly placed at ground level, and the only structure which we used was a structure which aimed at protecting what there was at ground level. That is what we have, for example, in the case of a tent, or of a simple structure, in the form of a branches truss, for example. However, as soon as we wish to rise from the ground, for example to store at a higher level goods which we would like to protect from floods, well, we need to create a flooring, that is to say a surface which looks like the one of the ground: which is flat, for humans to be able to move on it, and then which is at a certain height. We easily mention, in our country, at least in French-speaking Switzerland, the lakeside civilisation, which settled in villages composed of huts laying on stilts; clearly, on to of these stilts, it was necessary to create a flooring, because otherwise, no life would have been possible above water. So, how to do a flooring? We can find the solution here, in this picture, or in these pictures of some old floorings. We use, of course, beams. Here, I have a beam, it can be seen in perspective, that is why I draw three lines: there is a beams which goes from there to there, and then here, the perspective does not really exists anymore, so I only draw two lines; and here, that is what I call a beam, we could say, a main beam. This beam, we will get back to it later, it spans from this wall, on the left, to this wall on the right. Then, we have, on this beam, and carried by it, other beams which are smaller. Again, three lines because of the perspective, here. Here, the perspective does not really exist anymore... still a little bit. We are going to draw a third line; here, again, and so forth. So we have beams which, instead of carrying between two main walls, are supported by the yellow beams. So here, I have a secondary beam. Then, on these beams, perpendicularly -- it should be noted that the secondary beams are perpendicular to the beams of the first level -- Here, I have elements which are boards, which are directly positioned on the secondary beams, and which cover the entire surface. So, once we have these boards, we have reached the objective -- I am going to add the line which was missing here, that is a bit disturbing -- once we have placed these boards, here - for example here, or here, these are boards; once we have place all these boards, well, we have covered the whole surface, thus we have reached our goal. We have of course covered the story underneath, but we have also offered a planar surface to the upper floor and we expect that it will be able to resist loads, for example, to put there a wheat stock, or else to get a living room. On the right, we have a similar picture, probably from the same period, with a slightly more complex construction -- by the way, the beams which we can see are quite elaborated, in terms of carpentry. So we have large beams, like in the previous structure; so these are the main beams. Perpendicularly, we have a series of secondary beams, here, or else here. And then, on these secondary beams, we can observe a set of additional beams -- so I cannot entirely draw them because of the text, but we can see them well here -- there are tertiary beams. And then, on these tertiary beams, we cannot really see them on this picture, but I draw them with dashed lines, we will again have boards. So a flooring, that is a serie of beams, on which, maybe, other beams lean, and on which, finally, we are going to place boards, which are going to be contiguous, to touch each other, and as a result, we will have a surface on the upper floor, which will be planar and will be able to resist loads. This method to rest timber beams on masonry walls is very old; here, we can see a photo of a wall of a house in Herculanum, that is the twin city of Pompei; where we can recognize rectangular shaped and closely spaced holes, which were clearly designed to place beams inside. So, if we imagine the beams which were placed at this level, we had a series of beams like this which were shaping a horizontal story. And then, on these beams, there were... well, these ones did not leave any traces, because it is not necessary to make holes in the wall to place them, but there was certainly a series of boards which created a contiguous flooring in such a way that, on the upper floor -- we can see that this floor was not very high; there was no lighting and it was not possible to live up there, so it was rather, in all likelihood, a storey to store goods, maybe precious goods, supplies, or things like that. So this technique, we can see, was already used 2000 years ago. Let's look at this other picture of the Pompei Forum which is slightly more detailed; this city has also been distroyed by a volcanic explosion in 79. We can notice here, on these marble elements which have been replaced according to their original layout, of course, the position to place beams. Well, you maybe wonder: "why is it much lower than the final level?" Well, you should realize that we really had quite sophisticated constructions. That is the Pompei Forum, so we can absolutely imagine that we had placed a certain number of boards on top of these beams... I am going to quickly draw them. You have boards which, for example, span between two beams, and so forth. And then, on these boards, we have placed a layer of sand: that was often used to level out the thickness -- I forgot to indicate here that these are boards, that is to say the flooring itself -- and then, on this element, finally, we can place the definitive paving, which is made of stone. So this, that is a solution which can be found in any kinds of constructions, until, let's say, the end of the 19th century. Depending on the luxury of the construction, we have or we have not an upper stone paving. Another interesting thing: since I am showing you these structural elements in Pompei, that is interesting to notice these structural joints; Romans, on the one hand, did not have machines able to lift up infinitely large loads and, on the other hand, we know that it is not possible to obtain an infinitely large marble block in a quarry; so what has been done here? They have simply created marble blocks with inclined joints; if you remember well what we have seen in this course, here, an arch and cable will be able to interesect, just here, at the level of joint, and so on for the following spans. So, we have actually a system which works like a Gerber beam, since these jointshave been placed in a proper manner: they enable the internal force to be transmitted to the following element by friction, and then into the column. Let's get back to the construction of floorings. Here, we are in the citadel of Baux-de-Provence, in France, which has been built around the 12th century. We can see on the remaining facade -- it is made by natural stones, the rest did not survive -- but we can find in a very characteristic way, some cavities which can probably be considered as evidences that a flooring was spanning there, at that time, above the meeting room which was downstairs. One more time, that is likely that there were simply zones to store supplies, in this upper part. It should be noted that there are other holes which are probably there for the covering structure, which was used as roofing in this place, in Baux-de-Provence. On the right, that is the palace of the Popes in Avignon, where we can notice a large number of very closely spaced beams, so we cannot see the boards between them, in the upper part, we would clearly put them, we have this kind of boards. This picture is there to show you that a flooring can lean on a wall, but it can also lean on a wall with openings, or more exactly, a series of gothic arches, as you can see in this picture. Still inside the palace of the Popes in Avignon, we have another interesting structure, that is the one of the Chapel of the palace, that is the chapel of the pope; when we are walking around in the palace, we start by going up for quite a long time, and then we figure out, when we arrive in this chapel which is very big - you can see the group of people downs there which shows that it is not a small construction at all -- we have a very beautiful floor made of stone, and then a very large elevation, and when we look out the window, we figure out that we are quite high above the ground. How did they manage to do that? Is there a flooring like that of the Pompei Forum? No; if we look at the lower part of the structure, we can see that there is something which is much more sophisticated: the lower part of the structure is constituted by these crossing gothic vaults -- I am just going to draw this part here -- and then here, above, somewhere -- well, I am first going to draw it in white, for the moment -- here, above, we have the chapel. How can we make this? Well, it was made by creating... -- if I draw imagining that this is a cross-section of this part here -- we have this relatively thin zone made of stone, which is here to carry the loads; and then, above, we have a filler, probably constituted of stone shards, as we got them during the construction process. Above, we probably have added a thin layer of sand to level out the surface. And then finally, to reach the white level, we have placed a paving; which is made of stone, maybe of marble. And, in this way, we can reach the level of the chapel, and we do not perceive that we are not at ground level because we are walking on a stone floor; and if we look at the cross-section of the whole structure, we can see that, indeed, that is not a classic flooring, since there are no boards, but that is really something which is only constituted, or mainly constituted, of mineral elements. That is not a very usual type of structure; we can also find this kind of structure in some cathedral's crypt. In this case, that is a structure which is lower than the main flooring of the cathedral, even though in this case, the spans between the posts are often very small. Here, we really have a large span between the posts, in this room, which is under the chapel of the palace of the popes. What has changed since that time? Well, not a lot of things, we could say. Look, here, that is a building in Europe, a few years ago: what can we see? We can see large concrete beams, on which we have placed, transversally, large boards, also made by concrete. We can wonder why we have made the beam and the board separately; here, the answer is very simple: these elements have been precast -- we can notice that the columns is also separated from the remainder of the structure -- that is not necessarily the only way to proceed. I indeed have here a yellow beam, here a second beam, and then above these beams, in the other direction, I have placed boards. This is what we have just seen, we can do that with any kind of materials, clearly, that is almost the only solution if we use timber. But if we use concrete, the best solution is to make everything monolithic, that is to say to have a contiguous T-shaped cross-section -- you can see, I have an element which is precast, and then the following element -- I draw it with another color, it is also precast; it has a load-bearing function, mainly insured by the part which goes down towards the bottom of the beam in the central part, and then it touches the other element, which makes it very easy to create a flooring, simply juxtaposing several of these elements in this direction. So here, of course, I have the orange element. Here, I have the pink element. And then, at the beginning, I had the green element. So this is a solution with what we call a T-shaped beam, here, which we have already seen when we have learned to dimension beams. We know that it is a particularly efficient beam, since it can carry well the compression in the upper part. In this first lecture about floorings, we have seen that they are important elements for human society, since they enable human beeings to store supplies or precious goods in a safe place, at a certain height from the ground, or else to reuse the same surface than the one of the ground floor to have human activities, upright. We have seen how to make a flooring. This solution which dates from the Roman era, or even probably from before, with simply a series of beams which intersect, on which we place timber boards enable us to get a flooring. We have also seen that the basic material for floorings is certainly timber, but a material like stone can also be used, and then, more recently, that is concrete which is certainly the most used material for the creation of floorings.