[MUSIC] Hi, this is Module 29 of Mechanics of Materials part III. We're continuing on with the design of a beam for a real world engineering design problem, and we're going to review now what's called the maximum normal stress failure theory. And so here is our worksheet. We said that our beam would be experiencing elastic flexural stress and transverse shear stress. We're going to check several different critical points. We're going to use for the design what's called the maximum normal stress theory. We've been using this before although we didn't label it as the maximum normal stress theory. This is when the failure, we say that the failure occurs when the sigma actual is greater than the sigma experienced the normal stress experienced is greater than whatever normal stress we just define as being the failure stress and as I said we've used it for some of the examples. You'll recall these examples from my course mechanics and materials part one. Here was a design of a wooden trust member subjected to an axial load. You can go back and review that if you'd like. Another design that we went through, using the maximum normal stress theory was shown here. So we have a situation where we have pure bending. We said that the section modulus was the moment over the distance to the extreme fiber. And so sigma max was the moment experienced over the section modulus. And so for design we want the section modulus of our actual beam to be greater than or equal to the maximum moment that's going to be experienced in our beam. Over what we're going to determine is being our actual or allowed stress. And again, maximum beam moment expected. We can insert in our design and we do insert in our design as an engineer, a factor of safety. We want that factor of safety to be greater than one, so we don't experience failure. And the factors safety is defined as the failure stress and we as the engineered defined what were going to use this failure. Often times it's the yield stress over the actual stress that's experienced. And so, we have sigma failure over the actual or allowed stress that we're going to design for. We take that actual allowed stress. Substitute in here and we know what the maximum bending moment or we can determine what the maximum bending moment is expected from our shear and force of bending moment diagrams. And we can design or find a cross section that has a section module that's large enough to accept that load. And so this section modules as I had mentioned earlier. Can be found at a number of sources. They're listed in tables in the manual for steel construction which is put out by the American Institute of Steel Construction. And, most of these resources are free to the public for various cross sections. And so, as a conclusion for the maximum normal stress theory failure occurs when the sigma experienced is greater than the sigma failure. By experience we generally use this theory of failure and design for brittle materials so it's not good for ductile materials like steel or aluminum or plastics because they have a tendency to fail and sheer but for brittle materials this is a good failure theory to use, and so we'll pickup from this point next time. [MUSIC]