[MUSIC] Welcome back to Mechanics of Materials part three. Today's learning outcomes are to define the qualifications for a structure to be treated as a beam, and to give some examples of beam bending. Mechanics of materials, as I stated in our last module, is the foundation for all structural and machine design. We start with an engineering structure, such as this bridge, which contains beam elements. Those beams are subjected to external loads. And in this course, we'll be looking specifically at transverse or flexural or bending loads. And that's going to generate internal forces and moments. Which in turn will be able to calculate stresses and strains and to finally look at the structural performance. Whether the design succeeds or fails. So, for beam bending, a beam is defined as a member that's loaded perpendicular to its longitudinal axis. And so let's look at some examples. The first example we'll look at is what's called a simply supported beam, which has a pin and a roller at the ends. And so, here's a model of that, and let's go ahead and look at a demo of this same structure. This is a demonstration of a simply supported beam where we have a pin connection to your left and a roller connection to your right. And even thought I'm a rather strong individual, I'll have a lot hard time as we go through the course in bending this beam enough so that you can see the flexure. And so, I'll be using this pool noodle to go ahead and show you the flexure and go through the theory of beam bending. So this beam now is going to be loaded for simply supported and pure bending, we're going to load it with moments at the end to cause it to bend, or flex. And this shows the beam in its flexed position. And I've exaggerated that shape when loaded. And so, we'll further classify this simply supported beam as being again subjected to what we call pure bending, it's flexure under constant bending moment, and there's no shear forces involved in this situation. Some real world engineering examples with simply supported beams again are bridge type structures and what I'm showing you here is on the right side of the bridge. When you've went across bridges or looked at bridges, you've seen these seems. And those seems, are where underneath the roller type support is located. And so here, I'm looking underneath the structure and you can see down here where the roller connections are. This would be one set of beams on the left, and another set of beams on the right. Here's just another view of that roller type support that you can see in beams. The next example of beam bending would be a cantilever beam. And here's a model of a cantilever beam. And, again, let's look at an actual demo. This is a demonstration of a cantilever beam, the yellow portion being the beam itself. Which is model to be supported with the fix support over here on your left. And once again, when I go through the theory we'll go ahead and assume that my beam is attach fixed to the left hand here. And then will be able to see the bending with this pool noddle structure where I can more easily bend it than the steel itself. And with a cantilever beam we're going to apply again a moment to bend that beam and here's the beam bent in its exaggerated shape when loaded. And we again will further classify, this is pure bending and no sheer force. So here's some real world engineering examples of cantilever beam structures. This is a crane type structure. We have the beam up here. We'll call this a fixed and over here attached to the truck and we've got a force pushing up. So we could model that situation like this. Okay, so you have the left hand side which is fixed, the right hand side is the force being pushed up against this end of the beam. Here's another example of a cantilever beam, this is a structure holding some wires on a train track, right next to a train track. So you can see this is the cantilever portion that we can treat as a cantilever. Some other examples of beam bending are non-uniform beam bending, or continuous beams. And so, here's a model of that situation and again let's look at a demo of this situation as well. This is an example of a continuous beam, where we have a pin connection on your left, and several roller supports. We have some forces acting down at particular places on the beam. And if we wanted to, we can also moel it with moments being generated at any points in the beam. So, in this situation we have beam bending with flexure, and now we also have shear forces present, and we'll analyze that situation in this course as well. So, some other real world engineering examples. Here's a bridge deck where the surface has been uncovered so you can see the beams underneath, and so you see the bridge deck chord structure. Here's another example. Here's a machine workshop, and you can see high beams in the ceiling that are supporting loads. And again, you may have wooden beams, the beams can be made out of different materials. Here's a structure with wooden beams included. And finally, another type of beam might be concrete beams. And this is concrete beams that are used in a barn type structure. And so, lots of different examples of different types of beams that can be used. So again, we'll start in this course looking at the case of pure bending. We'll do the theory development based on pure bending with no sheer forces. But then later on, we'll use this same theory, even when sheer forces are present. This is called classical beam theory, or often referred to as Euler Bernoulli beam theory, but if you look at the history of the theory for beam bending, there was many more than just these two individuals involved. And so starting next module, we'll go ahead and get started with the theory and learn how to solve some real world engineering problems. See you then. [SOUND]
