Hello. In this video, I am going to give you an example of predimensioning of the slabs of a rather simple building. I will briefly talk about the configuration of the building, we will especially see that it is usual not to have the same configuration for the basement than for the upper floors. The purpose of this exercise is to obtain, for all the slabs of this building, the depth they should have. That is clear that in a later dimensioning, there will be some considerations to make, especially the determination of the amount of reinforcement. Here is the building, you have a more or less faithful picture on the right; so this is a building which is, for the usual stories, supported by columns, with a span between the columns of 7 meters in both directions. We have two particular zones in this building: a zone here, shaped like a horseshoe, with a hole -- that is the meaning of this symbol -- in which we will have space for the elevators and the stairs; and then, a concrete wall, simply, to insure the horizontal stability of the building. So that is a concrete wall... and then here, several concrete walls. This part, here, is called the core. The core is the hard part of the building which holds it horizontally; the concrete wall, on the right, also has a function in this context. We thus distinguish, in this building, on the one hand, the foundation slab, which is thicker; I am not going to talk about it, its dimensioning is an operation which is out of the scope of this course. Then, we are here under the ground, we are going to have concrete walls on the outside the building, and then inner walls or columns, we will get back to it later on. Here, we have the slab on top of the basement, which is a particular slab. And then afterwards, we are going to have a series of story slabs, which are roughly all similar: one, two, three, the roofing slab is slightly different, since its loads will be smaller. But we will not take it into account; we are going to deal with, on the one hand, the slab on top of the basement, and then the slabs of the usual stories. There are fundamentally two possible solutions for the basement: we always have this hole, since the elevator or the lift goes down till the basement, and we can also have either cellars, either technical rooms in the basement, for which we will have a lot of walls; I still assume -- that is an hypothesis which is not always verified, but that is reasonable in this case to have the same span of seven meters in both directions. And what we want to see is how to dimension the various elements. Let's first assume that these walls are masonry walls, except the core walls, and then the outlying walls, of course, which must be in concrete to protect us from the ingress of water, and so forth. What we can notice is that we have, as supports, for this slab, here, a clamped wall; here, that is a clamped wall; here, because of continuity, that is clamped, likewise in this direction. So if I get to this table, that is a square slab, with all the sides clamped, so the coefficient is here 0.56. And actually, all the slabs, whereever they are -- this one is clearly inside, it is clamped on all its sides -- but all the slabs of this building have the same properties: this one is also clamped on the left and on the right, such as this one. There is an exception: that is this slab, here, which is clamped on the left, clamped on the right, clamped on the bottom, and then here, on the top, it has a free edge. If we look at it, that is this configuration here; we would thus have a coefficient, here, of 0.67. It is going to have a significant influence on the dimensioning of our structure, and maybe that it is not desirable, because there is a big difference. A solution could be to add a beam here, a beam under the slab on the basement: in this way, we would have a simple support on this side, still the clamped supports of the three other sides; and at this moment, we would be here in the figure, with a value of 0.59 which would be very very close to the value of 0.56. That is something which is not decided yet, that must be discussed with the architect, to know if it is possible to create this beam, if it can be sufficient. Another solution would simply be to thicken the slab in this zone here. Another configuration for the slab on top of the basement is to assume that this basement is going to be used for other purposes, for example to park cars; and then, we would have, in this case, a slab supported on walls, outside and on the core, and on the other hand, on some columns. The configuration here is a bit complicated, since there are configurations which we have not necessarily in our table. Considering that, here, the corner of this slab, with this column, corresponds to the corner of this slab with this wall corner, we can consider, here, that we will have a coefficient of 0.90 for this span. Here, we have a slab with the same configuration, so a large part of the slab has this same configuration. Some particular cases still remain: here, in the middle, we are not absolutely sure, but that is clear, that it is less than 0.90. So if we choose the depth which corresponds to the coefficient of 0.90 for the span, we will be good; likewise, here, that is also less than 0.90, because of this wall, but that is probably quite close to this. Here, we probably have a slab which carries in two directions, so probably a value which is around 0.67, but clearly still under 0.90, so we can neglect it; here too, less than 0.90. However, here, we have a particular configuration, and we have more than 0.90. What is precisely the value? That is not easy to say, we could imagine that it is around 0.93; but that is something which should be dealt with in more details. For the dimensioning stage, we are going to keep in our memory that this zone here has a small problem, but we are not going to consider it any longer. Let's now move to a story slab: it first has, in the corners, a configuration which is the same, obviously, than the one we have in our figure; so the four zones in the corners have a span coefficient of 1.01. This zone looks like what we have seen in the previous case, with a wall on one side and two columns, around 0.90. Here, probably, we have a configuration a little bit like this, with 0.93. Here too. Here, in the middle, we are maybe not at 0.82 yet, but clearly at less than 0.90: likewise here, less than 0.90. And here, less than 0.90. However, here, we have a particular configuration, since we have the equivalent of a column: (counts the columns) We probably are... - but we only have one span, we have no continuity -- we probably are around 1.01, but in all likelihood, even, above 1.01. This is again going to be one of these particular zones, that it will be necessary to consider separately. We now want to take back the various factors which we have obtained in our configuration: as a reminder, the factors which we have obtained were 0.56 for the case of the slab supported by walls located in the basement, 0.93 for the case of the basement with columns, and 1.01 for the current storey. Multiplying them by the span of our slabs, it gives us equivalent spans of 3.92 m, 6.51 m and 7.07 m. The minimal width for this slab would thus be 3 920, divided by the factor which we are going to obtain entering in the table at the level of 3.92 m; we are going to use, for the whole building, an admissible vertical deflection of 1/300 and a live load of 2kN/m². Here, we reach slightly more than 22, so we are going to say 22.5; so 3 920 divided by 22.5, it will give us a minimal depth of 174 mm. Obviously, it will be a value which will have to be rounded, maybe to 180mm, or to another value, it will depend on the result of the final dimensioning. I remind you, that is a predimensioning, to obtain an idea of the width of these slabs. For the solution, in the basement, with columns, we have a minimal width which is equal to 6 510, divided by the factor which we obtain entering at the level of 6.50m in the graphic, here. So we obtain 19. 6 510 divided by 19 gives 343 mm as minimal depth. Finally, for the story slab, the minimal depth will be given by 7 070 divided by what we obtain entering at the level of 7.07 m; so approximately here, in the graphic, with a factor of roughly 18, which gives us a minimal depth of 392 mm. You should note that the slenderness ratios which we have for these slabs are thus around 20, sometimes slightly less than 20, in some other cases, a little more than 20 if there are lots of walls. In this video, we have carried out the predimensioning of the width of the slabs of a building, in a part with walls, and in another part, with only columns. Depending on the story, the depth was quite different; also, depending on the use that we want to do of the building. We have seen how to proceed to the choice of the depth, noting that there are often exceptions, for which we know less accurately the equivalent span, which means that it will maybe be occasionally necessary, in some places, to increase the depth of the slab, or else, during the final dimensioning, it will be necessary to put more reinforcement in this place. Finally, I remind you that it is only a predimensioning, so you obtain the width of the slabs; that is not enough, it will be necessary to proceed to the dimensioning, to know which amount of reinforcement it will be necessary to place inside these slabs.
