Welcome back to Mechanics of Materials Part III. Again, looking back where we're at in the course, we've been doing a lot of theory, but I want you to hang in there, we're going to soon be doing some real world examples and problems. But today, I want to look at the properties of sections. So we're going to determine, I told you a couple of modules ago, we will learn how to find this area moment of inertia, I, we're going to determine that today. And so, here's the elastic flexural formula we came up with last time, we said that the area moment of inertia we found was the integral of over the area of r squared dA. And it was a cross section's resistance to the bending about a certain axis. And so, how we find the area moment of inertia? Well you can integrate it directly but many textbooks and websites have tables for the standard shapes of cross sections that we will work with. And so, we can then take those standard shapes and we can combine them in a composite shape by using the parallel axis there, and which is shown here, and so, let's go ahead and do an example. Let's look at a standard shape that we'll be using a lot, which is a rectangular. If you looked that up in a reference, you'll find that I about the x axis is going to be one-twelfth base times height cube, and so I, the area moment of inertia, again about the x axis, is bh cubed over 12. And so let's use that standard shape for an example of the cross section we been working with, and so we're going to divide this cross section into three standard shapes. I'll have a rectangle at the top, a rectangle here in the middle, and rectangle at the bottom, and I want to find the I about the neutral axis for the composite cross section. And so we'll take this first rectangle here and that's going to be its I about its neutral axis is going to be one-twelfth, so it's going to be one-twelfth, base, the base for this top shape is a, times the height, is b cubed. And then I've got to add in, that's the I for the standard shape, the rectangle, about its neutral axis. But then I got to take and add the area of that shape, which is (ab) times the distance from our over all composite neutral access to the neutral access of that standard shape, which is d1 squared. And then we'll do the same thing for the next standard shape which is this rectangle in the center. Its standard shape I about its neutral axis is one-twelfth base. And in this case the base is d, the height is c cubed and plus the area which is (cd), times the distance from the neutral, the overall neutral axis to the neutral axis of that standard shape which is d2 squared. And then finally for the last shape which is the rectangle at the bottom, we have plus one-twelfth, base is f, height is e cubed, [COUGH] excuse me, plus the area which is ef (d3) squared. And so that's the total I for the composite shape. As we go forward with actual examples, we'll actually put numbers in and calculate a value for a moment of inertia. But you now know how to do it, and so we'll get started with some problems soon. [SOUND]