Hello, With this lesson about frames, we will broach the last topic of sructures of the course "The Art of Structures". What is a frame? Well, we can see that in this structure. Here, that is an electric pole in a suburb. And, what can we see? The usual system in the upper part is a truss with X-shaped diagonals, pretensioned in all likelihood, since they are only cables. It enables this post to transversally resist to some internal forces. In the lower part, it would have been logical to also use diagonals. But in this case, straightaway, we can see that there is a small path which passes there, underneath. We can see that it would have been dangerous for the people who are walking around, especially if there was someone riding bicycle, he would really have risked to hurt himself against these cables. So, it was decided, just for this level, not for the rest, to change the type of structure, into a structure which has the same function, so it is able to carry vertical and horizontal loads, but which gives more space; this type of structure is called a frame. What we can already see well in this picture is that there is considerably more material in the frame than in the simple lines, I mean, the filigrane diagonals which we had in the upper part. That is a property of frames; they are not extremely economical structures. We are going to look at what is the position of the frames in the path of structures and then to look at what is a frame in more detail. That is really something which is midway between an arch and a beam or several beams. Within the path of structures, this is the complete version which thus includes the courses "The Art of Structures I" and "The Art of Structures II", we can see that the frame is the penultimate lesson and actually, that is the last type of structure, since the last lesson will deal with compressed elements and stability which are not properly types of structures. Frames include all the types of structures which are almost arches, but not exactly. If we look at this concrete bridge, which is essentially subjected to uniformly distributed loads over its whole length, the logical shape induced by these loads would be a parabolic arch, a second-order parabola. But, actually, we can see that the shape which has been given to it is slightly different, since, here, the arch is a bit higher that it would be in the case of the funicular arch. Why do we do this? For a very very good reason: because this bridge crosses a river. And if we have water which reaches this level, for example, you can see that here, the blue arch would be a large obstacle to water. Here, we gain maybe one meter of width on each side, where water can pass and then, it can be very important during a flood. So, the shape of an arch is not the appropriate shape and then, we choose a frame instead of an arch, so we have a shape which wanders a little bit from that of the arch. That is also what we have seen in the initial example where we had a truss with X-shaped diagonals and then we replaced it by a frame, to have a solution which was more favorable to the use. In this lecture, we have seen what is a frame. In the example of the bridge, we have seen that it is an intermediate solution between an arch and a beam, actually, a modification of the shape of the arch. In the first example, we have seen that it is the modification of the shape of a truss. In frames, there are compressive and tensile internal forces which coexist within structural elements, just as in the case of the beams.
