So what did you find this time with the beam simulator? The first time we used the beam simulator, we found that the cross-sectional shape and the material and the height of the cross-section did not change the moment in the beam, so it did not was not a factor. But hopefully you found that the cross-sectional shape and the height were a factor in the bending stress. So cross-section is not a factor in bending moment, the actual force or moment, but it is a factor in the bending stress. And this is actually helpful to engineers when we try to design beams. So how will we predict when it's going to fail? The first thing we have to figure out is what the moment is going to be along the length of the beam. In this class you can use the beam simulator to help you calculate those moments. But what an engineer will usually know, they'll have some idea of the length that they need to span. They'll have some idea of the loads that are going to be applied depending on how it's going to be used. And they'll have some idea what the supports are going to look like. So with that information they can then figure out what the moment is along the length. And once they know that maximum moment they can start to make some estimations on what material will work and what height of cross-section and what shape they want to use. Makes it a little more straightforward though if I can calculate that moment without the shape affecting it, I can get that moment and then I'll be able to experiment with different shapes and heights. So where is this beam likely to fail horizontally or along the length it will fail where the moment is maximum. And then where along the height, that's the other thing the engineer has to figure out, is where on the height do they expect failure. So they can calculate the stress at that location and make sure it's okay. What typically happens is we'll have it on the top or bottom edge and I brought my flexible beam again so we could take a look at this grid again. So as I flex this beam, I'm going to exaggerate it, but the bottom is intention again and the top is in compression. So the bottom will be in, the bottom is getting longer, top is getting shorter. We have tension and compression. Some were along that height, we'll have a zero line. It's called the neutral line where there's zero stress. If we go from tension to compression, we have to go through a place where there's no stress. The other thing you can look at when I bend this grid is when the grid starts with vertical lines and then as I bend it, those lines stay linear, they're still lines but now they're off at an angle. This is important because it shows that the deformation and the stress will have a linear distribution so we'll go from tension to compression along a line and stress and deformation will be mirrored in that sense. But that will also tell us that we're going to get our maximum deformation at the bottom or the top surface. So an engineer will typically look for where is the maximum tension or where is the maximum compression. And again, materials often behave differently in tension or compression and beams are included in that. Wood is one example that has one allowable stress in tension and one in compression. It's not unlike a truss except for now everything is happening in one single beam. So beams versus trusses, it's one of the questions an engineer will try to answer when they're designing a system. It's a better use of beam or a truss and that will depend on different factors. Truss tends to be more efficient because the tension and compression are in those separate members but it also tends to be a deeper system. So if you don't have the space for a truss, you might go to a beam. The equation we use to calculate the bending stress in this beam is MC over I again and I will go through and calculate those bending stresses for a couple examples including the Eiffel Tower which we can model as a beam. It's a vertical beam but it's got an excellent parabolic shape.