Hello. In this video and the ones which will follow, we are going to look at the typology of trussees with a constant. There are several videos, because the amount of matter is significant, but you will see, they are rather simple. There will be an introduction in this video, and a conclusion at the end of the last video, so there will not be any intermediate conclusions. Concerning the typology of trusses with a constant depth, we will see what are the possible configurations; since these trusses have a constant depth, the chords -- there are not a lot of variants, however, we will see that we can have diverse types of diagonals. We will check if these structures are statically determinate, -- most of them are, but not all -- we will look a the sign of the internal forces in the chords and in the diagonals, and then we will make some comments about the amplitude of the internal forces, where the internal forces are maximum, for example. We will start by the trusses with V-shaped diagonals, which we have already seen quite a long time before, let's check that this structure is statically determinate, I am not going to do it for all of them, but... here, we have two forces at the support, and here we have one, three in total, to which we are going to add the number of bars: (counts the bar till 31) Now, we are going to count the nodes: (counts the nodes till 17) 2 times 17 is equals to 34, which is equal to 3+31, therefore this structure is statically determinate. As we have seen it before, when the heigth of the arch above the cable is maximal, the internal forces in the upper and lower chords are maximal too. Likewise, when the inclination of the arch is the largest, that is to say near the supports for the loads which we have applied here, the internal force in the diagonals, both in compression and in tension, is maximal. Here is another layout of truss with V-shaped diagonals; the truss is lower because it is located underneath the supports. The observations which I have made before are still valid -- of course, the structure is statically determinate -- the maximum internal forces in the chords are in the middle of the span, and the maximum internal forces in the diagonals are near the supports. Please note that the sign convention remains valid, that is to say that the diagonals which have an inclination similar to the one of the arch are in compression, the others are in tension. Below, we have a variant of the layout of this truss, in which we have added additional vertical elements. The interest of these additional elements is to enable to introduce more loads. You can see that the loads are also smaller, but since there are twice more, it gives us the same total load, because otherwise, it is necessary to carry over the load till the adjacent nodes; -- in trusses, we cannot apply loads anywhere else than on the nodes -- and then it creates a complication, it requires secondary elements, about which we do not talk here, which are more significant. So this solution, here, to add vertical elements, is quite interesting. I am not going to do the calculation, but I can tell you because I did it not that long ago: we have three support conditions, plus 47 bars, which is equal to two times 25 nodes, therefore this structure is also statically determinate. In what we have already seen before, there are also trusses with N-shaped diagonals; we have two configurations, this one in which the diagonals are in tension, because they are systematically placed in the opposite direction to the shape of the arch thus all these diagonals are in tension, here. And then we have, here, this configuration, in which all the diagonals are in compression; these diagonals, here, are in compression since they follow the shape of the arch, while the posts are in tension. Maybe there is no internal force in the middle post. How do we choose between both configurations ? Well, if I quickly come back to this configuration... here, the posts are in compression, I am quickly going to draw them... In this case, the longest elements are in tension, this is a configuration which is suitable for the steel structures, since this material can accept strong tensile internal forces, however, there are some problems with compression; and shorter the elements are, the better they can resist compression. So here, this is an ideal solution, because the long elements are in tension, the shorter elements, the posts, are in compression. Conversely, here, especially if we look at this structure which is from the 17th century: we had not much steel, so we try to make the elements in tension as short as possible, however, the compression can be taken by timber elements, which resist well to this type of internal force. In the next videos, we will continue to explore the various possibilities of typology for trusse with a constant depth.
