[MUSIC] Hi and welcome back. In today's module we're going to talk about axial and torsional stresses. And we're going to work through an example problem. This is continuing unit two static failure. The learning outcomes for today are to understand how to calculate both axial and torsional stresses in an object. And again, this is intended as a review. So, if you've never seen these stresses before, please check out Dr. Whiteman's videos at the link below. Last time we left off at working through the example problem on Worksheet 3, where we had rod OA which was attached to another rod AB. And rod AB was assumed to be strong enough and therefore no analysis was necessary on it. The analysis we were attempting to do was to calculate the stresses here at point O and we were calculating the axial stress and the torsional stress. And if we look at the loads that we have on this rod, we have a load P which is acting in the negative Y direction on point B. And a load F which is acting in the negative X direction at the end of the rod. So, if we continue to go forward, here on the right hand side of the screen, you can see a diagram and it's showing the top down view of this rod. And I've actually developed a small model of the system that we're looking at, where here is point O, at the end of the rod, and our force F would be coming in along the X axis here. And our force P would be coming down along the Y axis here and actually causing the rod to twist. So let's think through what assumptions we need to make. So let's see, our assumptions are going to be that our rod is isotropic and homogeneous And we're also going to assume that this load f is an axial centric load. So we're going to break these out by the types of loads that the rod is experiencing. And we can see load F is going to cause a compressive axial force that will be felt at point O. So if we go through we can say the stress is due to F divided by A and it is going to be negative as it's compressive. Where F is equal to 1000 Newtons and A is going to be the cross section of the rod at point O. So it would be this cross section here, which will be Pi times D, which is 0.04 divided by 2, so Pi R squared. And what this gives you is roughly 0.8 megapascals. So you can see that point O, here and here is experiencing a stress of 0.8 MPa. That's pretty straightforward where students tend to get confused is the torsional stress calculation at point O. So if we look at our equation for torsional stresses we see tau. which is shear stress, equal to T the torque times r over J. And in this case it's r because O is at the surface of the rod so we are looking at the radius of the rod. So the first step is to think about what is the torque. And if we look back at this example you can see point P is pushing down on rod A, B and it's causing rod O-A to twist, right? It's feeling this torque. So a torque is a force times a distance and here's our force. And it's acting at this distance between the force and the centric axis of this rod, which is 0.1 meters, we can see right here on the screen. So tau is equal to our torque which is going to be (500N x 0.1m) and then our radius is going to be d over 2. Now here's another place where students get confused. Just a reminder that your radius is not this distance. Your radius is from the central axis of the rod to the point that you're looking at. So your Point O is on the very top here. And your radius would be something like this right here. So your radius or your diameter divided by two. Okay, so d over 2 and then we're going to multiply that times our polar moment of inertia which is J. So for a cylinder J is going to be 32 divided by pi d to the fourth. I've actually used the reciprocal because it's one over J. And so then when I calculate that what I'm going to get is my d's are going to cancel here I'm going to end up with 16 times 50 Newton meters divided by pi x d which is 0.04 meters cubed. And that gives you a torque of right around four megapascals. Okay, so the key things here are to understand what is the torque, and what is the radius. That's where students typically get confused on this problem, okay? So that's the end of the worksheet three example problem. Next time we're going to start reviewing bending stresses. I'll see you next module.