Hello. In this video, we are going to look in more detail at the properties of materials. In the previous video, we have seen that, at least for a moderate level of load, materials behave in a linear and elastic way, that is to say that the lengthenings or deformations are proportional to the loads or to the stresses. If now I look at what happens with a steel rod, I take it in my hands and I bend it, it deforms, it is very clearly visible, if I relax my effort, the rod gets its straight shape back, it behaved then in an elastic way, and if we did a more detailed test, we would see that it is also linear. I do the same thing with a timber rod which deforms and with a glass slab. Of course, the deformations of the glass slab are relatively small but we can see that it curves. If now I take the steel rod from before again and that I bend it in a more pronounced manner, obviously my effort increases but at a certain moment, I feel that the deformations increase in a much quicker way and if I relax my effort, the rod remains deformed. Schematically in the stress-strain diagram, we have an initial part with a slope equal to the modulus of elasticity of steel, Es, and then at a certain moment, we have a significant increase of the strains, epsilon, without the stress increasing. This level of stress is characterized by the value fs which is the yield limit of steel. The stage during which the strain increases without the stress increasing anymore, is characteristic of what we call a plastic behavior thus here we have plasticity of the material, while in the initial stage we had elasticity. Here we look at a tensile test of a steel piece in a testing machine of our laboratories. What we can see in this diagram on the right is that the internal force increases quickly, the stresses increase quickly until reaching the limit fs, after which we have an horizontal stage characteristic of plasticity then the stress increases again to reach a maximum value here which is characterized by the tensile strength, then the deformation keeps increasing, we can notice on the right, on the left, in the video, that on the middle of the test piece, there is a zone in which the strain concentrate and finally, we see the failure of our element for a stress which is, by the way, lower than the initial yield stress but importantly with very large strains, four hundred for one thousand, that is to say forty percent of lengthening of the element. That is very good, it is a very good behavior, however, indeed, for the dimensioning of the structures, we are not going to use these properties because the structure would deform too much to be usable. We can here sketch the properties of steel which are characterized by an initial stage, with a modulus of elasticity Es, a yield stage with the yield strength fs and a big stage of increase of deformations with the tensile strength ft and then finally the failure, characterized by very significant strains. For the dimensioning of the structures, we are generally going to stay in the extreme left part of the diagram, that is to say where the strains are essentially of an elastic nature with sometimes, a little bit of plasticity. The behavior of a material which behaves in this way, that is to say with an elastic stage and then a long plastic stage, is called a ductile behavior. Let's now look at the behavior of another building material less common, but that we know well, which is the glass. I take again the glass slab that I had before and I bend it, I increase my effort and, well, what has to happen happens and suddenly the glass breaks. The behavior can be sketched in a diagram in this way, with a linear elastic stage with a modulus of elasticity of glass and then immediately after, we have the failure, with a certain tensile strength. There is no yield stage of the material, we thus have a fragile behavior. This fragile behavior is not extremely desirable but that is not either impossible to accept it and we can build glass structures but we have to prevent these problems to occur. We are here interested in another common building material which is concrete. On the left, in the testing machine, we have a cylinder of concrete which is subjected to compression. The compression increases without enabling us to see anything of the behavior. If we look on the right of the diagram which comes from this test, we can see that there is an initial stage with a modulus of elasticity Ec of concrete, and then, this initial stage quickly makes way for a stage in which the strains increase in a quicker way than simply elastically but the material continues to show a satisfactory strength until we reach here the compressive strength of concrete, fc, and then a little bit after, if you look at the compressive test, we see the appearance of vertical cracks, parallel to the axis of the internal force which indicates the onset of concrete failure which happens a little bit later. The behavior of concrete is thus somewhat of a mix between the very ductile behavior of steel and the very fragile behavior of glass. Let's sketch in this diagram the behavior of concrete. In compression, we have seen it, it has a modulus of elasticity, Ec, a compressive strength, fc. In tension, concrete really behaves like glass, that is to say that with the same modulus, it will reach a very low tensile stress and then it will cease to resist. For practical reasons, we can always consider that concrete is completely fragile when it is subjected to tensile internal forces. The graph on the right sketches the behavior of timber. In compression, timber has a relatively low strength. Once it has reached its maximum strength, it crushes then, after a quite significant deformation, it reaches its failure, then we have a compressive strength. However, in tension, the strength is larger, however the behavior is more fragile, we have a tensile strength larger that the compressive strength and then, in the intermediate part, we have a modulus of elasticity of wood which is well identifiable. We have seen in the previous slides, various behaviors of the materials which can be sketched in this way, with a modulus of elasticity, a maximal strength and then something which decreases either directly or a little bit later. We want to idealize this behavior as an ideal elastic-plastic behavior, with a module of elasticity and a tensile strength. Obviously, this does not apply to glass but you will see that the principles of dimensioning will also enable us to dimension glass structures. In closing, I am going to give you some characteristic values of the quantities whose we have talked about for the classic building materials, which are steel, timber, concrete and glass. Steel has a very high modulus of elasticity which is equal to 205,000 Newtons per square millimeter, its tensile strength is very good, its compressive strength is good but unfortunately, because of the phenomenon of instability, it is a little bit worse than in tension. The specific weight of steel is 78.5 kiloNewtons per cubic meter. Concrete is a material which varies, but has typically a modulus of elasticity of 30,000 Newtons per square millimeter, its behavior in tension is very bad, however its behavior in compression is very good and its specific weight is 25 kiloNewtons per cubic metre. Timber has typically a modulus of elasticity which is also quite variable but let's say of around 12,000 Newtons per square millimeter, its behavior in tension is good, its behavior in compression is also good but with some limitations since it has some troubles regarding stability and its specific weight varies, but a good timber has a specific weight of around 8 kiloNewtons per cubic metre. Glass has typically a modulus of elasticity of 70,000 Newtons per square millimeter, a good behavior in tension but I do not give it three pluses precisely because it is a fragile behavior and it has also a quite good behavior in compression but it is also subjected to the effects of stability and finally it has also a volumetric weight of 25 kiloNewtons per cubic metre, like the concrete. We will see in the following videos more accurate values of the strength of these different materials but for the moment, you have already the modulus and the specific weight. We have seen in this lecture that in addition to the modulus of elasticity, the properties of the materials are characterized by the strength. We have seen that at the time when the failure occurs, there are two types of behavior which are quite fundamentally different, ductile behaviors that is to say when the strains increase without the stresses decreasing and fragile behaviors like the one of glass when all the strength disappears as soon as failure occurs. We have also seen that the common building materials are characterized in this way, that some of them are very close to a perfectly ductile behavior like steel, others like concrete or obviously glass are close to a fragile behavior.
