Hello. In this lecture, we change thematic in the course "The Art of Structures II" since we move to the subject of beams. We will see in this video, that there is a strong relationship in the way trusses and beams work. Just a few words to get our bearings; in the course "The Art of Structures II", we have already studied trusses and their extensions in 3D and we now start looking at the subject of beams. On the basis of what we have already seen for trusses, we can design the required width for each of the elements of the structure and afterwards, build a truss which would exactly have the required dimensions. Here, certain diagonals are very thin, while others are a bit wider, certain chords are also quite thin and others require more material. On the basis of the calculation of the structure, assuming that there are no other load combinations of course, which would need larger dimensions, we could very accurately create a truss which would perfectly resist the internal forces we have calculated under the loads which are imposed and this, with a minimal amount of material since we would just use the required amount of material. We could make this truss using timber, concrete or steel. Let's imagine for example, that we build it using a large board of timber. There is no problem to have these cuttings done but we can notice that we would have, in all likelihood, to throw away these triangular elements because they would be useless for us. Likewise, we could imagine that this truss is made by concrete in which case the formwork to make all these triangular openings, we can do it of course but it would constitute a non-negligible work. And, if we had to do this with steel, we would either do it with lots of small bars which would impose a very significant welding work, either we would do it in the same way than for timber, from a steel plate and then with important losses. A solution could be to say: "what if we kept the orange parts?" We do not strictly need them since they are not necessary for the strength. Only the grey part can carry all the loads, however, it would simplify our life. For example, if we make the concrete truss we could make a much simpler formwork only making the lower beam. That is to say, a beam which has a constant depth and which does not have any holes. Here, we have the whole beam which is here and it would be much easier to form it of course and we would use quite a lot of additional concrete but on the whole, it could be simpler. Let's define here the dimensions of this beam, so it has a span which is the distance between the supports, which is equal to L. It has a cross-section depth which is equal to h and a cross-section width which has a value of t. In this case here, we have a rectangular cross-section, we will see other types of cross-section later. So we have here a beam with a rectangular cross-section, knowing however that all the concrete, steel, timber, all the material is not necessary, the orange part is not needed, only the grey part is indispensable but for simplicity, we have decided to keep all the material. This enables us, according to the title of this slide, to move from a truss to a beam. What is a beam? As we just saw it, it is an element which carries loads but when we hit it, it does not reply to us. That is not an element which is transparent, which enables us to see what happens inside. Using the same amount of material, I have rotated my beam, I have kept the same loads. From the outside, nothing different happens. Actually, what we want to see in the following lectures among other things, is what is the influence of depth on the internal forces inside a beam. Since the beam does not tell us anything by itself, what we can do is to imagine what happens inside; so I have my beam that I had on the screen, one of both with either the large, or the small depth, both loads of ten Newtons and I can imagine a truss inside this structure and this truss, I can calculate it. A condition that I have to respect is that the depth of my truss cannot exceed the depth of the beam. So my truss is entirely included within the beam, that is not exactly what happens inside but that is a visualising which enables to understand what happens inside the beam and which, as we will see, is very efficient to design the beam itself. In this introductory lecture, we have seen what is a beam and we have seen that there is a strong link between a truss and a beam, either as we conmsider the beam as a truss in which we have filled the holes, or on the contrary, when we seee the the truss as a way to understand how the internal forces act inside a beam.
