[SOUND] This is module 21 of Mechanic of Materials III. And today's learning outcome is to solve an inelastic beam bending problem now for unsymmetrical beams. We've done it for symmetrical beams, now we're going to do it for unsymmetrical beams. And so here's our worksheet. We have a T-beam, so it's going to be unsymmetrical about the axis of bending. And it's made of structural steel, which is a mild steel. And it models well as an perfectly elastic plastic material, and so we're going to use this as our stress strain diagram. And we're going to do two parts. Today we're going to do part A, which is to determine the maximum elastic moment that the beam can support. So, this module will just look at the elastic action. And so, the first thing I want you to do is to locate the neutral axis, and by now you should be pretty good at this, because we've done some examples. And so go ahead and do it on your own, and then come back and see how you did. And, so I've used this axis as my datum. I know that i can find the neutral axis from the bottom, or the centroid, which is the summation of composite areas, the y to the neutral axis for each of the composite areas, times the area divided by the total area. And, so I'm going to break this into two parts. [COUGH] One is this rectangular composite part, and then two is this other rectangular portion. And here is the neutral axis, right in the center for this rectangle. So y1 is going to be 150 plus half of 50. And y2 will be 125. And, so I've got 150 times 50 for the area of the top piece. And then 50 times 150 for the area of the bottom rectangle, so that's the total area. And y neutral axis is y1, which is 150 again + 50 divided by 2 to this neutral axis. Times the area, 150 times 50 + the y2, which is 150 divided by 2 for this rectangle. Times its area which is 50 times 150. Divide that by the total area, and I get my neutral axis up from the bottom of being 125 mm. Okay, now that we know that, I want you to find the area moment of inertia, I, for this T section. And again, I'll break it into two parts. There's my neutral axis. Here's my formula using standard shapes for the total neutral axis. And so, this will be my first standard shape, the rectangle at the top. The distance from the neutral axis, I'll call d1. The distance to the neutral axis of the other composite, or standard shape Is d2. And, so I've got I neutral axis is the standard shapes ones I about its neutral axis, which is one-twelfth base times height cubed, or one-twelfth 150 times 50 cubed. Plus the area 150 times 50 times d1 squared. So d1, what I've done here is, I've taken the total distance up to this line, which is 150 + 50 divided by 2. And then I've subtracted the distance to the neutral axis. And then I do the same thing for the other standard shape. I've got one-twelfth base times height cubed plus area times d, in this case, d2 is 125 minus the distance to the center of this neutral axis to this rectangle, which is 150 divided by 2. And I square all that. And so, when you do that math, this is the area moment of inertia you arrive at. And so we’ve got all of the information now that we need to determine the maximum elastic moment. And I’d like you to try to do that on your own. And so we’re in the fully elastic condition. We know that the maximum stress is going to be experienced at the furthest fiber, in this case, it's going to be down to the bottom. And, so I can solve for M max. And M max is the sigma max that we get, which is 250 for the elastic region times I divided by c, which is again 125 down to the bottom section. And so if you multiply that out, this is the maximum elastic moment that you can achieve. And so that's how this problem is done, and we'll come back next module and solve part b. [SOUND]