[MUSIC] >> Welcome to Module six of Mechanics and Materials Part one. Today's learning outcome is to define what we're going to call two-dimensional, or plane stress. And so we left off last module with a 3D state of stress. And I've shown our stresses in the positive sign convention. And we said that we could express this tensor of stresses in a matrix as shown. Now, for two-dimensional stress, or plane stress, we're going to say that all of the out of plane stresses are 0. So we're going to say that all of the stresses on the z face, the normal stress on the z face, and the shear stresses on the z face, are going to be equal to 0. And so I'm just going to end up with a two dimensional state of stress. Okay? So I've zeroed out all my shear stresses, and normal stresses in the z direction. And I end up with just stresses on the x and y planes. And I've shown them again in a positive sign convention. And so, here's my sigma x in a positive x face, in the positive x direction. Here's a negative sigma sub x on the negative face, or a negative on negative is a positive. I've got tau sub xy. Tau on the positive x face in the positive y direction. Here's tau sub xy again. This is tau on the negative x face in the negative y direction. So a negative on negative is positive. Tau sub yx. Positive y face, positive x direction. Negative y face, negative x direction. And so, that's a two-dimensional, or plane stress situation. In real-world situations, real-world problems, that are three-dimensional, sometimes the plane stress assumption can really simplify the problem and without significantly affecting the results. And so, there's a number of real world engineering problems that you can use the plane stress assumption. And a common one is when we're analysing thin plates and maybe one application might be the skin panels on aircraft wings. And so here's an aircraft wing. If we look at the z face as being the surface of the thin panels, the stress is acting on that surface. Our order of magnitude's smaller than what would be in the x and y planes. And so, this is a real good application of plane stress. And so now we know what the plane stress assumption is. We know how we might use it. And so we'll continue on and analyze it some more. [MUSIC]