[SOUND] Hi, this is Module 18 of Mechanics Materials part 3. Today's learning outcome is to now solve another problem. This time for inelastic beam bending. And so, here's the situation, I've got an I-beam made of cold-rolled red brass and we have the cross section, I-beam symmetric cross section that I've shown here. And we're going to say that the red brass can be treated in elasto-plastic material which is stretched, probably not a great material to say is perfectly elasto-plastic but the procedures remain the same. The elasto-plastic assumption really works best for something like mild steel but we're going to South park A in this module and parks B and C and subsequent modules and we want to start by finding the maximum elastic moment at the beam can support. And so, the first thing I want to do is find the neutral axis and determine the area moment of inertia, since it's a symmetric cross-section, we know that the neutral axis will be right through the centroid, right through the center here. This is my neutral axis, which means it's 150mm below the web flange intersection at the top, or 150mm above the web flange intersection at the bottom. To calculate, so here again, let's look at that. There we go. To calculate the area moment of inertia, what I'm going to do is I'm going to take an entire rectangular cross-section. And then, I'm going to subtract out these cutouts. To find the area [INAUDIBLE], that's one way of doing it, you can do it the way I've done it in the past, you will get the same answer. And so, I've got in this case, now I about the neutral axis is 1/12 base from my big rectangle is 200. And the height is 325 cubed. Then, I'm going to subtract out these two rectangle cut outs. And so, their base is 200 minus 12.5 divided by 2 because there's half on either side. So that's going to be 93.75. And the next, times their height which is 300 cube and if you do that math, you'll find that I about the neutral axis equals 150 times 10 to the 6th mm to the 4th. That's rounded off to three significant digits. And so, I have my I now. I know that the maximum stress is equal to this formula. I want to solve for the maximum moment, and so I've got M max = sigma max I over C. Sigma max, just before we get into the plastic we did for a fully elastic cross section is 410 mPa times I, which is (150 x 10 to the 6th mm to the 4th). And remember, megapascals is the same as Newtons per meter squared. And then, we're going to divide that by C, C is the distance to the top or bottom because of the symmetric cross-section, which is going to be 162.5 [BLANK AUDIO] mm. And if you calculate that out you get 379x10 to the 6th N mm. And so, that's our answer. And we'll come back, as I said, next time and do part B. And in the following module, part C. So well see you then. [SOUND]