Hi and welcome to module three of Applications in Engineering Mechanics. In today's module, we're going to define multi-force members, we're going to review 2-force members from my earlier course, Introduction to engineering mechanics. And we're going to start to apply the 2D equil, quil, equilibrium equations that we reviewed in the previous module, to solve structures that have 2-force members and multi-force members. So those structures that have 2-force members and at least one multi-force member are, basically divided it up into two categories. One is a, a frame, we call it a frame, it's a stationary structure to support loads. As an example, a frame might be something like this step ladder again. This is a, a 3D structure, but we're going to model it as 2D and, and look at the loads that are applied on that step ladder. Other examples of structures that, that include at least one multi-force member, are called machines. These are structures that contain moving parts. as the example I showed earlier, a pair of pliers can be referred to, as a machine. They're designed to transmit and alter the effect of force, forces and they have the purpose of doing mechanical work. So, structures that contain at least one multi-force member, also can contain 2-force members. The multi-force members are defined, as members that are subjected to two, more than two forces. And I'm going to show some pictures of those later on in the module. And they also contain 2-force members, and you should already know about two-force members, because we covered that in my introduction to engineering mechanics course, and let's go look, go back and, and look at that that earlier course. So, a 2-force member is a, is a weightless member again, two frictionless pins, it can only be in tension in or compression. And so, in this case, it's going to be in compression. It's acting down at the top and up at the bottom 2-force members could also be in tension, but that's all they can be. Those equilibrium required that the forces had to be equal to each other. They have to be in opposite direction and they have to be co-linear, they have to be along the same line of action. And so, we found that BY was equal to DY, they were equal, they were in opposite directions for equilibrium and they're co-linear. And shape is not a factor and so, I've got several examples. This could be a, an example of the hydraulic arm BD, and so if I have a compression at the top and a compression at the bottom, they can only act opposite each other. And no matter what way I turn, the line of action between those forces always stays the same. Even if it was in tension, you can see that the force at the top and the force at the bottom are equal, opposite and along the same line of action. And so, that's what a 2-force member is all about. Shape's not a factor. So even if I take a curved 2-force member like this, it can either be in compression at the ends or in tension. Okay, along the same line of action. And just to show that shape doesn't, isn't a factor, I've even, took a weird S shape and again, either in tension or compression. So if I, if I drew that S shape Member, could be any shape at all. If I have two frictionless pins, one on this side, and one on this side, the only thing this can be, is in tension, like this, along the line of action. with the line of action being the same for both of those forces or it would be in compression. Here's the two points and the forces could be in compression, equal, opposite and co-linear. Okay, so that should give you a good understanding of 2-force members. When you can identify 2-force members, you can get rid of all but two reactions. So that was a review of 2-force members, from my earlier courses. Now let's talk about multi-force members. Multi-force members are members subjected to more than two forces. So here's, couple of examples. Perhaps I have, like a 2-force member. Two forces on the on the ends, but maybe I have another force here, acting in the middle. Or perhaps, instead of forces, I may actually have a moment or a couple, acting on the member as well. So those would be multi-force members. They don't have to be straight. in fact, with the 2-force members I, I, I showed some s-shapes, so maybe we'll take an s-shape here, again. It can be any shape you'd like. And let's say, we have several types of forces acting, and different moments, couples. And you'll see examples of these in, in real world structures. you'll even get a worksheet to do some of these, later in this, this module. Okay, now we're going to apply the 2D equilibrium equations, to solve these frame and machine structures and we're going to apply this principle. If a body is in equilibrium, the entire body itself, each of its parts are also in equilibrium, in their own right. So, for my stepladder for example, the entire stepladder and each part of the stepladder, has to be in static equilibrium. And you'll see how this works, as we go through problems. Now this principle is actually quoted from a book by McGill and King. Dave McGill and Wilton King are actually colleagues of mine, they're professor Emeritus from Georgia Tech. And this is the textbook I'll use several figures and examples from. Doctors, King and, and and McGill were kind enough to give me permission to use this text for examples as I mentioned in my introduction to this course and in the syllabus. There is no required text book for the course, but it's good to have an engineering statics book to use, as a reference and for additional practice problems. And this is, this is a good course that you, excuse me, this is a good text book that you might want to look at. So, thanks again to Doctors, Mcgill and King. Okay, let's conclude the module by doing a worksheet, where we identify multi-force members and 2-force members in the structures, that are, are shown here. First of all, let's look at this structure on the left. You can see up here at point B, that we have what we'll idealize, as a frictionless pin. here's an example of a frictionless pin. It allows rotation, but it doesn't allow any movement in, in two orthogonal directions, for instance, the X or Y direction. So that's a frictionless pin at B. You'll see that at point A down here, we have a, a, a rough surface or a friction surface, so A can't slide back and forth, to the left or right. And so, that also serves the same purpose as a frictionless pin because it allows rotation, but it doesn't allow movement in other orthogonal directions. And so, we're going to say that point A serves like a frictionless pin. And knowing that, we now have AB, with two frictionless pins as being a 2-force member. But body BC now has, will have forces from the pin at B, forces from the pin at C, and a force here in the mintal, so this will be a multi-force member. So let's do one more example together and then, I'm going to let you do the last two examples by yourself. In this structure, here's a bar with two frictionless pins only. So that is going to be a 2-force member. [SOUND] This also will be a 2-force member, BC. Are there any other ones? Yes, I see one down here. EF also has forces applied, at just two frictionless pins and that leaves two bars left. We have A, D, F, H, that's obviously going to be a multi-force member because it has forces at A, D, F and H and B, C, D, E, G, all. Er not, not B, C, but C, D, E, G also has forces at several places. So those are both multi-force members. [SOUND] And I would like you to do the same sort of analysis on these other two structures. And I've included a solution to this worksheet in the module, so you can check yourself out. So, that's it for today's module and we'll see you next time.