[MUSIC] Hi, this is module 15 of Mechanics Materials part III on Beam Bending. Today’s learning outcome is to solve another elastic beam bending problem. And for this one were going to model this situation. So I have a crane type truck, I have a beam here that's coming out from the truck, and it's holding up this portion of the crane. And so the first thing I'd like you to do is try to take this real-world situation and model it on your own. And so, the way I've modeled it is I've said okay, this truck is going to act like a thick support over here and then I have my i-beam, that's going to be out here as a cantilever beam and it's going to be holding up some amount of weight on the right-hand side. And I did some calculations for a standard crane, and I came up with about 30 kilonewtons, and I came up with this beam being about 1.5 meters long. So that was my model, we'll proceed forward with that, and yours should be hopefully somewhat close to that. And so, now that we have the model of the beam, we have to choose what that beam is going to be. And so, we're going to analyze this situation using a what's called a steel S type I-beam. And so, we'll need the structural properties to complete this analysis for that type of I-beam. And so, I'd like you to do research on your own. Look on the internet, look on the resources that are available to you and try to find out for an S 305 by 74 I-beam what's the area moment of inertia, what's the section modulus and what's the depth of the beam. And when you've got that, come on back and see how you did. And so if you look those figures up this is my area moment of inertia, my section modules, and the depth of the beam. And so you'll also note that the cross-section, when you look at the cross-section for an I 305 by 74, it's symmetrical and so therefore, the neutral axis is through the center. And so, we have all the information we need, we want to go ahead now, and at a point, 0.15 meters to the right of the left fixed end, I want to find the normal stress due to bending and a point 55 millimeters below the top of the beam. And I also want to find the maximum normal stress experience that would be at that location in the cross-section, or that cross-section at that location in the beam. So what should we do first? And, what we've done in almost all of my courses is to first draw a three body diagram. And saw for the moment experienced at that point 0.5 meters to the right of the left fixed end. And so, here is my free body diagram. I've made my cut here. And so, I went ahead and I summed moments about the cut and I found the moment experience at the cut is 40.5 kilonewton meters. So we now have the moment experienced at the cut. What should we do next? Let's go ahead and use the elastic flexural formula to find the normal stress at a 0.50 millimeters below the top of the beam. And so here's my flexural formula. I had my M, I know that I is given. I found it, researched it and found what I is for this 305 by 74 I-beam. And, I need Y. Well, Y is the distance from the neutral axis up to the point of interest. In this case, the point of interest is 50 millimeters below the top of the beam. So that's going to be 102.4 milimeters from the neutral axis. And so I've got all the data I need in my elastic flexural formula. I can substitute it in. And I end up with the stress beam and this is at the top, so it's a beaming experience in compression in this case, 32.7 Newtons per millimeter squared but Newtons per millimeter square is the same as megapascals and so, it's in compression. And so that's my first answer, what should we do next? And now we want to find the maximum normal stress to find that? I'm going to use this formula which says take the moment it's being experienced divide by the section modules, we have the moment that was been experienced. We have the section modulus from the I-beam data. And so I can substitute those values in. And I find that my maximum value is 48.7 megapascals. Because of the loading situation, we're going to have compression at the top and tension on the bottom. So that's our other answer. And so, there is one last thing I need to do, and what is that? Well, I need to make sure since we used the elastic flexural formula that my beam remained in the elastic region. And if you look up the yield stress for steel in SI units, international system of units, you'll find it's 250 megapascals, so that's greater than the stresses that we're experiencing. So we're okay, and we've got the correct answers. And with that, we'll finish up the module. Thanks. [SOUND]