 Hi, so in this video I want to talk about internal forces. Now internal forces are those kind of imaginary forces that we look at that are inside of a rigid body, and they're really the forces that create stress, so we can use them to analyze stress in a situation. So when we talk about free body diagrams and internal forces, you know, I might take and say, okay, let's have a free body diagram, which looks something like this generic angle bracket, and I'm going to say it's a two force member, and if you recall two force members are basically not like that, but basically members that have forces applied at only two points, and for it to be in equilibrium, those forces have to lie on the same line of action, so this dotted line that connects the two points where the forces are applied means that, you know, for equal and opposite forces to be true, the direction has to be specifically specified as along that line of action that connects those two points. So if I have a free body diagram that looks like this, and I want to know what the internal forces look like, so say I'm going to cut across this free body diagram on one side, and then separate it out, I'm going to have two members, one on each side of the cut, so if I pick the one to the left, or kind of bottom down left here, and say that's the free body diagram I want to look at, I still have my externally applied force, F in the same direction that it was originally applied, and now I have something going on up here, right, that has to balance this force. Now, typically how we would represent this is we would say, well, we have an axial force, right, let's just call it A, but the problem that we would quickly see is that A doesn't balance F, right, they're in different directions, so they aren't equal and opposite, so we can go ahead and say, well, we need something else to balance this, and we need another component, for example, let's draw perpendicular to A, and typically we would call that V for the shear force, and these are great, that helps balance another portion of F. The only thing we're missing now is that this can still rotate, and it's not in rotational equilibrium, so we need something to balance that rotation, so F would tend to cause this body to rotate clockwise around the point here, so we need a balancing force for that, which we will call M for bending moment, and my arrow's kind of hidden here, but you get the idea, so these are the three internal forces that we care about for this planar situation. Now, again, as I just mentioned, it's planar, so we have three degrees of freedom, which means three internal forces, if it's a 3D object, which of course all real objects are, and if we can't approximate it as a planar system, then we have to draw all six possible reactions, and I'll show that in a minute, but let's take a look at an example of what this might look like with something more relatable. So, suppose I have a screw or a bolt threaded, embedded in something rigid, like a piece of wood, and I want to turn this bolt, so I have a wrench, my rudimentary wrench shown here, which is on there, and I apply a force to this wrench in order to turn it. Now, let's say this is at some distance B from the center line of that bolt to the place where I'm applying the force, and I'm going to say there's a distance A between where that force is applied in that direction and where the bolt enters my fixed material. Now, I need to identify a location of interest where I think there's stress that I want to know about, so if I'm analyzing this bolt, I can pick somewhere in here that's going to be this internal location that I'm interested in, and because we know something about what the stresses will look like, I'm going to pick a location that's near the base of my part. Let's see if we can do this without right-clicking. No, apparently I can't. I don't know why. Okay, so I'm going to pick a location that gives me more information about what's going on, and that is right at the base of that bolt. So now I have to start thinking about, okay, well, what forces are present at that location? Do I have axial? Well, axial would be in the vertical direction on this bolt, and my force is pointing into and out of the screen, so I don't have any axial forces at that location. Do I have shear? Axial, sometimes we might call P. Do I have shear V? Well, shear is into and out of the board, which is perpendicular to A, or excuse me, P, so therefore I do have a shear force, because it has to balance that force F. Next question, do I have moment M? Well, because the force is applied up here on the wrench, and my location of interest is down here, and there's a distance between those two things, A in this case, yes, I do have a bending moment. So what's the last thing I need to consider? Well, because this is being turned around its vertical axis, or its longitudinal axis, I have to realize that I have torque also, T. And now I've got to start thinking about what these are. Well, moment is F times A, because the distance, perpendicular distance between the line of action of the force and that point is A, and for torque I have F times B, because the perpendicular distance between the vertical axis and that rotational point is in the distance of B, or in the direction of B, and therefore I need to use that moment arm when I'm determining that force. So these internal things that may or may not exist, P, V, M, and the new one I just added, T, which for torque, all need to be considered as I do this. So I've got those, and my next step then would be to take this into stress, which I'll do later in a different video. One quick note on the fact that we do have three dimensions of stuff going on. So if I have some arbitrary object, which I can very poorly draw in three dimensions, and I apply forces, maybe I apply a vertical force, a horizontal force there, horizontal force there, maybe I apply another force here, doesn't really matter, any combination of forces, and then I want to look at some internal location and see what's going on. Well, it's important to realize that when I do that, I have all these externally applied forces, I have possible forces balancing these in a number of different directions. So it's important to be careful about what I have going on. And when I do this, I can also see that, well, I might have rotational directions. So I take my three cartesian axes, I can rotate about each of those axes as well. So that's three directions of force balance, three directions of moment balance, that all need to be considered. And they all may produce normal stresses and shear stresses, which we'll get into later. So those six possible combinations of things all need to be considered. And we'll go into that deeper in a later video.