[MUSIC] Welcome to module three of Mechanics of Materials part one. Today's learning outcomes will be to discuss one of the concepts that I talked about at the beginning of the course stress, and we're gonna define and discuss normal stress and shear stress. So, heres where we left off last module with an axial centric load on an engineering structural member. So here's the axial centric load being applied to our structural member. And again, this structural member may have a circular cross section. It could have a rectangular or square cross section, or perhaps an I beam as long as the load is axial and going through the central of the cross section. We can then do cuts to look at the internal forces developed in the member. This is a transverse cut an when I do a transverse cut I can reveal a potential of up to two orthogonal forces on the cross section, an N force and a V force. In this case, if we look at equilibrium in the Y direction we see that for a transverse cut with axial loading, the V force is gonna go to zero, but then I can also do a non-transverse cut. And when I do a non-transverse cut, I end up with a normal force which we're going to label as N. And again a sheer force which we're going to label as V, and combined, they balance out the P force, the external force on the left. Let's look closer at this non transverse cut. On this cross section we're going to develop what's called normal stresses, or signal, which is the force per unit area perpendicular to the cut surface. Here's a graphic of that normal stress. And so sigma is going to be defined as the total normal force divided by the cross sectional area. And we're gonna assume that that force is uniformly distributed around the cross section, and so it's gonna also turn the average stress and because we're doing a non-transverse cut, we also talk about this being stresses on an inclined section or a plane. And, the sign convention would be that if the stresses are in tension and the forces in tension that's a positive normal stress. If we're in compression, then that's going to be a negative normal stress. In addition to the normal stress, we also develop something called Shear Stress and it's given the symbol tau, and it's the force per unit area parallel to the cut surface. Here again is a graphic of that. So the Shear Stress is equal to the force, V divided by the cross sectional area. And again, we're gonna assume that it's uniformly distributed across the section, and so, therefore, it'll be the average sheer stress. So now I want you to do a worksheet on your own to apply these principles that we've just discussed. We have a flat steel alloy bar. It's a rectangular cross section with the dimensions given. It has an axial load. It's a centric load 60 kN, and I'm asking you to determine the normal stress and the shear stress on the bar for both the transverse cut and the non-transverse cut or the inclined plane. And when you finish that up, I have the solution in the module material. [SOUND]