Hello. In this video, we are going to talk about truss structural elements. To do so, we are going to revisit a certain number of structures, which we have seen together, at least those of you who have followed the course "The Art of Structures I". The first picture which we can see here is that of the Tower Bridge, in London, and we remember that we had represented it as a system with two types of cables: a cable which goes down more on the left, for the case in which the loads rather act on the left part of the structure, and then a cable which goes down a bit more on the right, for the case in which the loads rather act on the right part of the cable. And that is really how it works, but we can also notice that there are here, diagonals and posts, to stabilize the structure, and then we are actually dealing with a truss. So now, we could completely calculate the internal forces in this truss, simply supposing that it is statically determinate, that will not be the case, because of the X-shaped diagonals, but we could simplify it. But however, the way it works does not change, that is to say that both these cables which I have drawn in pink and in sky blue remain elements which are in tension, actually the diagonals do not carry much internal forces, only in the cases in which there are load eccentricities. For the Golden Gate Bridge, in San Francisco, you remember that the deck is used to stiffen the structure, in such a way that variable loads do not make the shape of the cable change too much, making the utilisation of the structure uncomfortable. What we can see now is that this deck, to be stiff, is constituted of a truss with V-shaped diagonals, with additional posts, here, vertical; this structure is statically determinate, we could thus calculate the internal forces in this truss. That is obvious that it is favorable to use a truss which, thanks to its large depth, will be stiff, having at the same time a large proportion of void, which thus does not use too much material. You probably remember this ice stadium in Stockholm, where we had a big load-bearing cable, which works together with a pretensioning cable which is used to prestress the red cable, in such a way that it does not deform too much: for example, when there is wind or snow. And then we obviosuly had columns in compression, here, and we can obviously see that we also have, now, a lot of diagonals, here, which are added to the structure, and which make it a truss. But fundamentally, the fact that we have a load-bearing cable does not change, so the upper element is in tension; a pretensioning cable, the lower element, it is also in tension, and then the diagonals are here to facilitate the support of assymetrical loads on the roof. For the olympic skating rink of Munich, that is the same thing. We have here a big arch; and you remember that in the arches, it is important that the pressure line can move inside the arch in such a way that we can have internal forces which essentially remain in compression. To create this volume in which the internal forces can move, three tubes have been placed at a certain distance, and to keep the structure stable, well, we have created a truss, here we can see it, with diagonals; this is thus a tridimensional structure, this is a truss, very clearly. The Austerlitz viaduct is a structure which is similar to the one of Tower Bridge, with two arches; if I take again the colors I used before, we are going to have a blue arch, which is first in the lower part, then in the upper part, then again in the lower part, and a second arch, and afterwards we move to the top again, and then a second arch, which is the pink arch, which is always on the other side of the section, with respect of the blue arch, it enables to carry internal forces which are assymetrical, for example, when the subway is only on the left part or on the right part of the structure, but we can also obviously see that there are additional elements, which are diagonals; so, both these arches are materialised as a truss. That is the same thing for the Maria Pia bridge in Porto. Here too, we have an arch with two hinges, but the space to enable the variation of the pressure line, this space, is essentially created with void, and then some diagonals, using the shape of a truss. So here, we clearly have a truss, with X-shaped diagonals, which is created to create the spacing between the upper arch and the lower arch, using very little material. Finally, we have seen this structure, this lenticular shape arch-cable, so we have a lower cable, we have seen the lower cable is actually materialised by two continuous elements: two cables, and then the upper arch; it is also materialised by two elements; we can see that these elements are repeated afterwards, this is a multiple structure. But we have two arches which work together with both cables on the bottom, and one more time, these structures are built with the shape of a truss with diagonals which enable to stabilize this structure. So we have this in the upper part... in the lower part, but also in the upper part. What we have seen in this video, is that the truss is a type of structure in its own right, and we have seen how to solve this type of structure, but it is also a way to build structural elements. So we can have arch structure, cable structures, arch-cable structures, or else cable-beam structures, which are elements that, indeed, are made with trusses. What must also be said, and it is probably the time to say it in this course, is that structures are not always pure; it is very easy to have several types of structure which act in the same structure. Obviously, in this course, I try to take structures which clearly belong to a type. They are cables, or arches, or else trusses, but actually, in reality, combinations are often chosen, because it is more efficient, because it is easier to build, or simply because that is the choice of the designer of the structure.
