Hello. In this video, I will talk to you about the typology of trusses with a constant and a K-shaped truss configuration, as you can see it on this picture. Let's first find out if this structure is statically determinate or not. We have a fixed support on the left, so we have two support reactions. On the right, a mobile support, so three support reactions in total. We have one, two, three, four, five, six, seven, eight, nine, ten eleven, twelve, thirteen, fourteen, fifteen, sixteen and seventeen bars. And we have one, two, three, four, five, six, seven, eight, nine, ten nodes. Two times ten. That is to say three plus seventeen equal to twenty, equal to two times ten, thus this structure is a statically determinate. We can calculate it with the methods for trusses we have used so far. In this video, you can see this structure which I am loading with three loads on the upper part. You can notice that I have also placed weights on the supports to stabilize it because the structure is very deep so it is not very stable, it tends a bit to move transversally. Here is what we see when we look at the internal forces in a truss with K-shaped diagonals. We could already see it before since I had put timber elements, obviously, to resist compression. We can see that the upper part is similar to a truss with N-shaped diagonals in compression, then the lower part is similar to a truss with N-shaped diagonals in tension, the posts being half tensioned in the upper part, and half compressed in the lower part. Why would we want to create such a configuration? We will look at it again a bit later. This is a large structure which must carry a tall building over several stories. Here, we will have a story slab and the layout of diagonals would thus enable us to have a door here or else at this level there, a door here. Thus, it can be quite interesting from an architectural point of view to have this configuration. From a statical point of view, we will talk about it a bit later, this is not a solution which is particularly inefficient. Here, I have a K-shaped truss configuration in which the part of the K goes inwards the structure. And here, likewise, we can notice that the upper part of the truss has now diagonals in tension and posts in compression. The lower part has diagonals in compression, and posts in tension. The use of either one of these configurations with K-shaped diagonals will really depend on the structure. I am going to show you an example soon in the lecture about towers. We are now arrived at the end of this typology of trusses with a constant depth. Not that I pretend that we have seen everything in terms of configuration. We can see for example here, that adding intermediate bars, we can obtain variants. We could also add additional posts, these structures would remain statically determinate. Likewise, it is absolutely possible to have the half of a truss which has diagonals in tension, and the other half diagonals in compression. But with this, we have seen a wide variety of constructions. In the next video, you will see an assessment of their relative efficiency. Are there solutions which are better than others? We have seen in this video about the typology of trusses with a constant depth that the diagonals can have V-shaped, N-shaped, X-shaped, or K-shaped configurations. Some of the solutions we have looked at are not statically determinate but a lot of them are. We have seen that the sign of the internal forces still respect what we have seen about the arch-cable, that is to say that chords in compression are on the side of the arch, chords in tension on the side of the cable, and that the inclination of the diagonals compared to the one of the arch indicates us if they are in tension or in compression. We have also seen that the amplitude of the internal forces is relatively similar between these various solutions.
