[SOUND] Hi and welcome back. In today's module, we're going to quickly review transverse shear stress. And so the learning outcomes from today is to understand how to calculate transverse shear stress in an object with a fairly simple cross section. This is intended to be a review assuming you've all ready taken mechanics of materials. If you've never seen transverse shear stress before, I ask that you go back into Dr. Whiteman's modules on transverse sheer stress and bending stress. And you can see the links here on the page. So a quick review, the assumptions that we've been making so far that we have isotropic material with a homogeneous composition, unless specified we're operating at room temperature. It's going to conform to Hooke's law in the linear elastic region that we're dealing with relatively small deflections and we're also, specifically in this example, assuming that we have uniform shear stresses across the width of the cross section. So beams have a transverse shear stress. And that transverse shear stress, the equation is VQ / Ib. So let's talk about what all these terms mean. V is the shear force throughout the beam. So you'll recall if we have a beam in bending, that you'll see a bending moment and a shear force throughout the beam and that our shear force at any point in the beam can be found by drawing a shear force diagram which we have here. So then, I is the moment of inertia of the beam, based off of the cross section. So here is our cross section and so in this case, our moment of inertia would be one-twelfth base times height cubed. And then, here is our neutral axis of the beam. So our neutral axis goes through the centroidal axis. In this case, our neutral axis is going to be in the x-z plane, so we see our neutral axis right here. b is the width of the cross section at the point of interest. So if my point of interest here is point P, then b is simply going to be the width of the beam at that point. And since the width of the beam is constant throughout this entire rectangle, the width of the beam is we're going to call b, for base. If it was an I beam, then it would vary, right? And so, it could be that if your point of interest here, this would be your b. Okay, and then Q is perhaps the most confusing term. So again, we have this point of interest P, that's where we're interested in figuring out what the transverse shear stress is. And so Q has an A prime term and a y prime term. The A prime term is the cross sectional area above the level at the point of interest. So here's our point of interest P and here's our cross sectional area right above P. So this entire area would be our A prime. And then our y prime is the distance between the neutral axis, so here's our neutral axis. It's going to be the distance between the neutral axis to the centroid of A prime. So you'd have to calculate the centroid of this area and figure out that distance, y prime. All right, so that is all the components that go into transverse shear. A couple of things to notice about transverse shear. So in bending stress, what you guys are used to seeing is that your stress is zero at the neutral axis and maximum at the top and the bottom of the beam. It's the opposite for transverse shear. So here's our neutral axis. Our transverse shear will actually be the highest right at the neutral axis, because it's going to have the most area above the neutral axis. And it's going to decrease until it hits zero at the top and the bottom of the beam. Also, to keep in mind, transverse shear stress tends to be much lower than the bending stress. And so, typically, people start to worry about transverse shear when you have odd cross-sections such as I-beams or T-beams. So let's take a look at an example. So here what we have is the same example we worked through for axial, torsional, and bending loads. We have this rod OA, it's attached to a rod AB, and we have this load P, pushing down here at point B and an axial centric load pushing in here along the X axis load F. And so, it says find the transverse shear stress at point O? And just a reminder, point O is at the very top of the beam right here, and we've determined that our neutral axis is in the X-Z plane at the very middle of the beam. And so, if we just start to write out our equation, our transverse shear stress is VQ / Ib, okay? So, so far pretty easy, we'll be able to figure out our shear force from this load P we talked about, and when we drew out the bending and shear diagrams in the lecture where we went through the bending stress. So we’d be able to draw a shear force diagram for beam OA and figure out the shear force at this point O. So I, that's just going to be the moment of inertia of this rod OA. And B, since we're at the very top, life gets a little confusing. B is infinitely small. And then Q, Q is equal to A prime y prime. So if we draw this circle, we're looking at point O, right here. Here's our neutral axis, right, x is coming out of the page, y is going up this way. And so, our A prime would be the area above the point of interest which is nothing. And our y prime would be the distance between the neutral axis and the centroid of nothing, so this is equal to 0. And so, our shear stress at point O is equal to 0, because B essentially goes to 0, and Q goes to 0. And that makes sense because again it's at the top of the beam far away from the neutral axis. Now, let's look at another example. Now, it wants us to find the transverse shear at point C. Now, the transverse shear is not going to be 0, because we're right at the neutral axis and I'm actually going to let you guys attempt to work through this on your own, and then we'll go through the solution in the next module. All right, I'll see you then. [SOUND]