Hi and welcome back to Module 6 of Applications in Engineering Mechanics. We're moving right along in the course. This is the overview of all the topics we'll cover. You can see we've, we've reviewed my earlier course, Introduction to Engineering Mechanics, and we're into structural applications. We've studied frames and machines, and today we'll start playing trusses. So truss elements are used to support loads in many structures. And that's what we're going to start studying today. So we're going to define what a truss structure is, and the advantages of a truss structure. We're going to list common assumptions used in analyzing truss structures. And we're going to talk about a couple of methods that we will use to analyze truss structures. So as a definition, trusses are structures that are composed entirely of slender members joined at their end points. And so all the members of the body, or the truss, are 2-force members. Here are some examples of structures that contain, tr, truss elements. And, these are bridges. these happen to be bridges that were, pictures that were taken by my daughter during a summer when she was working as a co-op. you'll see trusses in many other applications, however. Maybe in the, the roof of your house you could see, the trusses that were used. Or if you're in a, in a sports stadium, if you look up at the roof, you can often see the, the truss elements that are used to support the structure. So what are the advantages of truss structures? Well, they have a lot of high strength, and they're useful in long spans with low material quantity and weight. And again that's the picture of this bridge that you can see, has very large spans carrying very heavy loads. So, there are some assumptions that we're going to use in analyzing truss structures. To simplify the, the modeling of them. One is that we're going to say that the loading is applied only at the joints, so that they're all 2-force members. We're not going to have any loads in the center of the members. The members are going to be connected by frictionless pins. We're going to idealize those as frictionless pins. And we're going to say that the weight of the members themselves, are negligible as compared to the forces applied to the truss. And, for my students that are outside the United States, I am sure that the, the kip measure of unit is a, is a little bit confusing. kips are used in the United States. It, it is an English system unit that is not used in the rest of the world, unfortunately. But I, I sometimes wish we would go to the International Systems of Units in the US. But a kip is 1000 pounds. And so we'll, I'll be using that system of units in this course, at times. Analyzing truss structures. Well, we're going to cut structures, and we're going to cut through the members that we're interested in finding what the forces are. And then we're not going to cut through the joints themselves. we're going to continue to cut the truss to isolate a portion. If you remember back a,a couple of Modules ago, I stated that the entire structure has to be in equilibrium. And if I isolate any portion of the, the structure it has to be in equilibrium as well. Once we isolate that portion of the truss, we're going to assume that we have ten, tension in the cut members. If the value comes out to be negative, we'll know that those members are in compression instead, instead. And if we isolate a portion of this structure, and it includes an external reaction like this pin or this roller, we'll need to solve for it. But if we, if we don't need to solve for the external reactions, we won't. There are two methods that we're going to use for analyzing trusses. First is the method of joints. That's going to isolate one of the joints and do an analysis. It'll be a concurrent force system because all of the forces will go through a single point. So all their lines of action will go sing, through a single point. We won't be able to use any moment equations, we'll only be able to solve for two unknowns. Because we'll have the sum of forces in two orthogonal directions. The other method we're going to use is the method of sections. That will be a section of the truss instead of just the single joint. And it will be a non-concurrent force system, so we will be able to use the moment equation as well, so we'll have three equations of equilibrium. And therefore we'll be able to solve for three unknowns. So that's it for today's module. And I'll see you next time, and we'll start applying these methods to solve for real world truss structures.
