Moments & Couples: Moments Definition

Okay, so in this video I'm going to talk about moments, couples, and rotations about a certain pivot point. And for the ARE, the Architect Registration Exam, I can tell you that for the past 30 years I have seen a lot of questions involving moments, rotations, couples, and typically they are asked with math. So I need to hunker down and do a little bit of understanding first, and then we have to do some math. Very good. So looking at a typical beam that is loaded in this example with 10 pounds that is coming in at 4 feet from the left, 12 feet from the right, And if the right support were to settle or were to move or were to be removed, then the 10-pound load will cause rotation about point A. And what will happen is this member will rotate if that roller support settles or gets out of the way. So, there is a rotation here in the clockwise direction. And the amount of moment that caused that rotation is the force times the distance. Force times distance. The perpendicular distance between the force. Here's the force. And we're looking for the perpendicular distance to the pivot. So, we're looking at 4 feet. So, the force is 10 pounds times 4 feet, or 40 foot-pounds. So, the units of moment are pound-foot, or kilopound times foot, or pound times inch, or kilopound times inch. Very good. So, force times distance. Excellent. Now, if the pin on the left were to rotate or to drop out of the picture, then the pivot shifts to point B. And this beam now will make a moment and will rotate in the counterclockwise direction. And again, the moment is the force times the distance to the pivot. Now, the pivot is point B instead of point A. and the perpendicular distance from the line of action of the 10-pound force to the pivot B is 12 feet. So we're looking at 10 pounds times 12 feet or 120 pound foot. Now in the previous example, it was clockwise. In this example, it's counterclockwise. So let's establish a convention. If clockwise is positive and counterclockwise is negative, And so this moment here, the first one was clockwise. So let's call that positive. And the second one was counterclockwise. So we're going to call this one a negative moment of 120 pound foot. The convention doesn't matter as long as you don't add clockwise and counterclockwise. Those are opposite. So which is positive, which is negative, doesn't really matter. Very good. So now if the supports remain in place, then the beam is not going to rotate as a unit, but it'll still, this 10-pound force is going to cause the beam to rotate about point A, and also to rotate about point B. So what ends up happening is that, and it rotated here, and it also rotated in a counterclockwise dimension, in a counterclockwise direction at B, and in a clockwise manner at A. So let's look at this beautiful picture here. There's a trailer here that was filled with boxes, and when the boxes were removed, it rotated, because, let me see if I can do this, paste, there it is. So here it is. there was boxes here that were removed and here's the supports, the two tires or maybe there's a hitch here. So when these boxes were removed and these boxes were still in place, they made a counterclockwise moment about this pivot and caused the trailer to rotate upward. Looking at this simple door here, it looks like it came unhinged. It looks like it's rotating a little bit in that direction. This is getting wider. This is getting narrower. Looking at this partition, if we lose the lower hinge, what's going to happen is the partition wears its dead load, and its center of gravity is over here, and its dead load is so much. So, it's going to, if you lose that bottom hinge, it's going to rotate in that direction until it bumps into the wall. Once it bumps into the wall, it stops. But the rotation here is counterclockwise. Very good. Now, if we lose the upper hinge, if we lose the upper hinge, then nothing's going to stop this. This is still going to rotate counterclockwise, but it's going to come totally unhinged. and fall off the wall. So force times distance is my moment. In this case, give me this dimension and tell me the weight of the partition and the weight in pounds times half the dimension of the partition because the weight is centered at the centroid. So let's say this is 20 inches. Well, then 10 inches times the weight of the partition is the tendency to make it rotate. That's what a moment is. It's a tendency to rotate a body, in this case the partition, clockwise or counterclockwise by a certain amount, force times distance. Very good. So let's put in some math with this now. Let me erase a little bit just so that things are a little bit cleaner. Very good. So looking at this system that I have right now, I have a 10-pound force that is right here. And this, sorry, a 10-kip force. And there are several pivots because a moment is force times distance to a certain point. So, looking at this moment, equal force times perpendicular distance to the pivot. So, if my force is 10 kips, now I need to know where you want your moment. About point A, here's the force. I can move it anywhere on its line of action without affecting the problem. Here's the 10 kip load. How far is it from point A? 1 foot. So, times 1 foot equals 10 kip times foot. Is that rotation clockwise or counter? It looks like it's doing counterclockwise. So, counterclockwise. Similarly, if I were to think of that 10 pound force, or sorry, 10 kip load, about moment, about point C, This was the moment at point A. Now the moment at C is 10 kips times the distance between the line of action, this one, of the force of 10 kips to point C. So times 4 feet, and this is 40 kip times foot. And it looks like the rotation this time, if this is the force, it looks like the rotation is clockwise about C. Okay, whether positive or negative, I really don't care. I just need to know if it's clockwise or counter. Now, the moment of the force about point D is the force times the perpendicular distance. 10 kips times there is no distance between D and the line of action. So then it's 10 times 0. There is no moment. There is no rotation. There's just the 10 kip load that's pulling up without any rotation. versus the moment at point B. It's equal to 10 kips times the distance to point B, which is 6 feet. And this 60 kip foot tendency to rotate the moment is, in this example, about B, is counterclockwise. Very good. So force times distance is moment, and it's kip times foot, or let's see, moment, the units are force times distance. So it could be pounds times feet. It could be pounds times inch. Or it could be kilopound times foot. Or kilopound times inch. These are the units of moment. Pound foot, pound inch. Kip foot, kip inch. Please do not confuse this with kip per inch. That's something else. This is kip times inch. Excellent. So let's put our information to the test here. This looks like one ugly truss. You're never going to have anything like this on the IRE. I'm not going to ask the question about solving the entire truss. I just want to ask a few questions about each of these forces and the moments they make. So please ignore all the forces on this truss except the 4 kip load. Assume that's the only load on the truss, nothing else. So here's the geometry of the truss. It has panels A, B, C, D, E, F, and they're 5 foot increments, and the base dimension is 12 foot. Very good. So how much is the moment of the 4 kip load about point Q? That should be zero, correct? Because the point Q is right on that axis of the load, so it's 4 times zero or zero kip foot. Very good. How much is the moment of the 4 kip load specifically about point A or pivot A. Now it's four kips times the distance between the four kip load and the pivot you're looking for. That looks like it's 24 feet. So four times 24, which is 96 kip times foot, 96 kip times foot, and it looks like the rotation is clockwise. Excellent. So how much is the moment of the 4 kip load specifically about point or pivot F? About pivot F, it looks like we need the distance from F to the 4 kip load. That looks like it's 36 feet. So 4 times 36 is 144. And it looks like it's doing counterclockwise of 4 kips times 36 feet equal 144 kip times foot. And it looks like in that direction, that's counterclockwise. Excellent. So, et cetera. That's how we find the moment of each force when we come to calculate reactions or to calculate torsion or whatever it is. Just keep in mind that it's force times distance. Very good. A few more questions about this one problem. Can we calculate the moment of this 11 kip load about point or about A as a pivot? So, we're going to need, assume this is 11 kips, and the moment at A for the 11 kip load, the moment of the 11 kip about A is force times distance. So, if the force is 11 kips, we need that perpendicular distance between the line of action of the 11 kip load and the pivot A. So I am looking for this dimension. And this dimension, let's see how much that is. Oops, I didn't quite hit that line, did I? Okay, so let me try again. I'm looking for this dimension. So it looks like 8.33 plus 8.33 is 16.66. You're not going to use this axis because this is a funky looking truss. I'm just trying to explain moment is force times distance. So in this case, I needed this dimension. That's the perpendicular distance between the line of action of the force and the pivot you're looking for. So the moment is 11 times 16.66, and whatever that gives is kip times foot. And how much is the moment of the 11 kip load about point P? Same thing, that distance is still the same, and the rotation is counterclockwise. Very good, about point M, same thing. about all these points on the bottom chord, the moment is 11 times 8.66. Versus the moment of the 11 kip, about f, that one is equal to this much. That's the perpendicular distance, 11 times 8.33, and the rotation is clockwise, about point f. Very good. So, before leaving this problem, delete. Let's just look at the moment of 5 kips about point L. Why point L? Just because I feel like it. It's the same about point J, it's the same about point A, it doesn't matter. So we're going to need this dimension, which is this dimension over here, which is 15 feet. So the moment of 5 kips at point, what is that, point L, is equal to the 5 kip load times the perpendicular distance from the 5 kip to point L. Looks like 15 feet. or 75 kip times foot, and it looks like that's a clockwise rotation. Okay.