[MUSIC] Welcome back to Mechanics of Materials part III. We're moving right along in the course. We did a review of shear force and bending moment diagrams. We did the elastic flexural stresses and strains and now today we're going to come up with the all important Elastic Flexural Formula. And so our learning outcome is to derive the elastic flexural formula. And so here's where we left off. Well we found sigma sub x for linear elastic material was proportional to curvature and the distance y form the neutral axis. And we derived last module the moment-curvature relationship, where curvature was proportional to moment. Okay, so here are those relationships again. Let's go ahead and substitute in for kappa, which is now m over ei. And that will give us the elastic flexural formula, which is sigma x e= the e's cancel, so I get -My over I, very important relationship. There it is again, the Elastic Flexural Formula. And it says that stress now is directly proportional to the bending moment, M. It's inversely proportional to the area moment of inertia I, and it's also varies linearly with the distance y from the neutral axis. And this is all predicated on the fact that we're working with a linear elastic material. And if you recall back if you did my mechanics materials part two course on torsion, this has a direct analogy here to the shear stress that we found for a circular bar and torsion. Shear stress is analogous to, in the case of flexural formula, normal stress T is analogous to M, the moment. The distance y from the neutral axis is analogous to the distance rho from the center of our circular bar. And I, the area moment of inertia, is analogous to the the polar moment inertia. And so you can see that it's a different application but there's a lot of similarities between those two problems. And so here is the flexural formula once again. The maximum stress occurs where y is the greatest distance from the neutral axis, and you can see in my picture here, that would be down at this bottom fiber here on my cross section. And so we call distance c, and that's the furthest distance on the cross section from the neutral axis. That's where the maximum stress will occur, is down here and it's shown there as c. And so we now have the Elastic Flexural Formula, we know how to find the maximal stress on the cross section. And that's a good point to take a break and come back next module. [MUSIC]