Hello. In this lecture, I am going to talk to you about wall-beams and shear walls. In this context, I will discuss the thickness to give to these walls, I will define what is a wall-beam and what is a shear wall, they are two concepts which are very close to one another. We will look at how to create openings and especially where to create openings in deep beams, and then I will give you some examples of configurations where these elements are particularly efficient. Here we have the photo of a private residential building which is quite interesting: there are very large openings above the entrance, with essentially no load-bearing elements, these small elements here probably have the main function to carry the facade. How does this work? This works because above this very open space, we have, by all appearances, a very large concrete wall, actually, that is the wall of the room which is upstairs. We have here a beam with a very large depth, about more than 2.50 m. We can also see that it has a small slenderness ratio, that means that it is quite efficient to carry internal forces. When we can use the walls of a structure as load-bearing elements, that is very interesting because we will always have a large depth and a good efficiency. So we are going to have the possibility to create a large concrete beam (in the present case, that is concrete), with, for example, a fixed support on the left and a mobile support on the right. What are the loads which can act on this structure? Well, on each floor, there will be loads which are, in all likelihood, quite uniformly distributed and which come from the slabs, and then loads which act in each of the rooms of the housing. And then on the roof, likewise, we are going to have uniformly distributed loads which, going down, will give rise to some slightly more concentrated loads, here on the right, that is not even very important, because that is going to go almost directly into the support. So, how can this beam carry loads? We can imagine that it works as a beam with a very large depth, with the possibility to develop an arch-cable inside this zone here. Of course some diagonals will also be necessary, so we can imagine a shape, I am going to schematically draw it below, roughly a truss shape with this configuration. What simply matters is to place the openings in a suitable way, because here, you can see, my drawing is not exact, obviously the internal force cannot pass through this opening, so we will have to deviate it a bit, but overall, that passes in a quite easy way. And then, I remind it to you, since we are dealing with a beam with a large depth, the internal forces will be relatively small in this beam and then we do not need large zones to carry these internal forces. One of the things on which this principle of the wall-beams is based, is: how can we know the thickness of a wall? The answer is not obvious, if you are in a building, try to find the thickness of a wall on which you are leaning. We can see it a bit here, this thickness, and we can see that it is not that small in the case of this structure, probably because this structure does not only have the function to seperate you from outside, here maybe only ten centimeters would be necessary, plus, obviously, thermal insulation; but it also have the function to carry. But that is true that we are not really sensitive to the thickness of the wall, and it is thus possible to use wall-beams, which are load-bearing walls, and to give them a sufficient thickness to resist the internal forces which act. A shear wall is simply a wall-beam over several stories. Here I have an example of a building where, at the base, the idea was to have a very large open space at the level of the groundfloor. So here, it corresponds to a free space, that is to say that we will be able to place something there, but there will not be any load-bearing elements to respect, columns or walls, And here that will be a second configuration at which we will look afterwards, also with a large open space. We are going to assume that these structures are subjected to uniformly distributed loads. I am going to make them act only on the roof for it to be simpler, but actually they clearly act at the level of the roof and at the level of each of the story's slabs. How can this structure carry loads? We can imagine very well that a very large arch will develop, not over one story but over several stories. This arch can have a certain thickness, although, again, since it has a large depth, the internal forces are relatively small. And then we can very easily place the cable in the lower slab. So here we have a load-bearing system. You could ask me the question: "oh, but this entire structure is a concrete wall, but how can I pass from one part of my building to another?" I need to be able to move, if I have several shear walls, that is annoying." Of course in the example which we have seen before, the shear wall was used as an external wall, so we did not need to pass through it. We have put some windows though. But if it is inside, we would like to be able to pass through it. It should be noted that in all the zones where the arch and the cable do not pass, we could make holes. We cannot make holes everywhere, but we can make some. So, in all the zones which I have indicated here in yellow, we can create openings. So, of course, maybe this configuration is not suitable for what you imagined for the use of space. You should know however that we will choose how we are going to distribute the internal forces, for example, we will do it choosing where we place the reinforcement in the concrete. If there is reinforcement, the internal forces will come, if there is not, they will not come. So I can absolutely choose, instead of an arch-cable as I had proposed before, to have a structure which is rather constituted of trusses. For example, a truss like this, with here diagonals in compression. The possible arrangement of the openings is in this way slightly different: There are places where suddenly, we can create openings, while it was less easy to do so in the upper part. Here for example, I can create an opening which I could not make before. And then the advantage is that I maybe have a bit more regularity, the spacings between the yellow zones where we can create openings are more regular. This picture shows an example of building which has used this principle. I ask you to look at the facade for a little while, and to find what is particular. That is not a type of facade we are used to in Switzerland. Why is it special? Well, you can notice that the windows are staggered from one each other. Here I have a window, and the one of the story below is here. Respectively, there is one here, and the one of story above is here. And that is systematically the case for the entire building. We are going to see that it is not really insignificant. We can also notice that the thickness of this wall here is not insignificant. And actually the thickness of the slabs which we can also see is not small. All this, we will see it soon, plays a part in the load-bearing system. Here we have an elevation, a side view of this structure such as it has been developed by its deisgner, the engineer Conzett in Chur. And the first thing to notice on this building is that we have here, like previously, a very large free zone. Here, this free zone is 28 m wide. In this zone, there is nothing, no post, nothing mandataory for the structure. How does this structure work? We can see on the drawing of the engineer that he has designed a system with diagonals: these diagonals here which are under compression. We can see that the internal force is not constant in these diagonals. It can be explained by the fact that there are loads which come from above which do not act in a constant way from the top, as I have supposed it for my previous drawing. And then here, we have many diagonals in compression with a maximal compression in the central part. Well, all these elements are compressed. There are also vertical elements in compression. And then, in the other direction, we have elements which are under tension. They have been made with prestressing cables, they are reinforcing elements which furthermore, are tensioned, which prevents the concrete to crack, and then they have a very large strength by cable. It enables to use the least possible space. So, I draw all these cables. Finally, to carry the tensile internal forces in the lower part, there are also obviously prestressing cables which go over the whole length of the building. To get the equilibrium, that is not drawn, but there is also compression here, in the upper part. I draw it anyway. In the upper parts, we can find compression in the slabs. Now we can understand why the windows had to be staggered. Look at here for example. I take this window. This is a window. And then I take the window which is just underneath, on the right. Well, we can notice that the space between these windows, here, you can see, is constituted by, on the one hand, the gap between the windows, which gives us a certain amount of material, and on the other hand, by the thickness of the slabs. That just leaves us enough space to make these elements in compression pass. You can see, for example, here too, that is very sensitive we just have enough material, enough space, to make the internal force in this diagonal pass, as well as the internal force in the prestressing system, and then sometimes the cables in the other direction too, but these cables are quite compact. So it would be impossible to create this structure if we wanted to make very thin walls, because we would have much larger internal forces and we could not manage to pass, and then if we had thinner slabs too. Here, I have made a photomontage of the internal forces, superimposing them on the structure. One more time, we can notice this zone, which is now used for commercial premises. That is a free zone, in which we could do something else in the future. A free zone of 28 m. In the right part, we can also see a free zone which is in this case clogged by the ramp descending into the parking. We can also have shear walls over several stories to make large cantilevers. That can be quite interesting, for example, if we are close to a road. We can have here a road or a sidewalk which passes under the building without having big complications. We thus have the possibility to create a building with larger dimensions. So, I am going to represent, here, the loads which only act on the cantilever, of course, when we will proceed to the complete dimensioning, we will take into account the other loads, but it enables me to concentrate on this component now. So here, because of the loads which act on the cantilever, I am going to have an arch which is going to form in my structure, and then to get the equilibrium, I must have inclined tension in the shear wall. And to have equilibrium on the right, I necessarily have compression in the lower slab. In this configuration, I have something which is quite interesting, I have a large free zone under the cantilever, like I had before. I also have it here, but we could have not wished it, maybe that is not useful. So now, I have these two large free spaces. I already also indicate them in the lower part. And I have the possibility to create openings in a large part of this shear wall, here, which will enable to open doors or, if necessary, windows. If however this geometry is not considered as sufficiently flexible, we can use another geometry. Well, we will not escape from the development of the arch around there, however we can decide to bring tension till the end of the building, and then to only make it go down at this moment. To have equilibrium, we have an element in compression here, and another element in compression in the lower slab. It enables us to have a different distribution of the potential openings in this shear wall. Of course, we could also choose a truss with V-shaped diagonals as we did before, or something else. There is a wide range of solutions to use depending on the requirements of the project. Finally, some examples of structures with concrete shear walls. We can recognize them here. I indicate the free zone in sky blue, the zone under which we are free. We have large cantilevers which, at once, provide shadow underneath, and create a dynamic: here we have a conference room which is completely outside the rest of the building, and this part here protrudes. Here that is a building near Lausanne with a very large cantilever. Since it is a school, it enables to have a covered playground below. In this video, we have seen what are wall-beams and shear walls. We have seen the importance of thicknesses, that of the shear wall itself and that, if necessary, of the slabs which take support on this shear wall to have a configuration allowing to judiciously place openings in these shear walls for example to create windows or doors enabling passage. I have given you some examples of configurations, particularly to create a large central opening, or else to have the possibility to create a large cantilever. And then, I have given you some examples of realizations using these properties.
