Moments & Couples: Couples Definition

So we saw with moments that a force P at a certain distance creates a moment which could be clockwise or counterclockwise, depending on where the pivot is. Anyway, we also saw that this force P caused rotation at the pin and at the roller, and the beam ended up deflecting like so. So now if we have two forces of equal magnitude, and the forces are not head-to-head like this, otherwise they would cancel each other out. The sum of horizontal forces equals zero. But if these forces are separated by a certain distance, then they also make rotation. In this case, they would make counterclockwise, and in this case, they would make clockwise. Two equal and opposite forces, separated by a certain distance, are called a couple. We see that in everyday life. For example, a flat screwdriver, when you push on it this way, then you're tightening, and then if you were to push on it this way, then you're loosening. And then with Phillips, what happens here is we have one couple, and then we have another couple. And this other couple is also creating tightening. So there's two couples here, one created by these two, and another created by these two. Okay, so we see couples in everyday life. Here's another example, which is not quite kosher, but still. We have this crazy woman who is on this escalator rail, and we have one force going this way and another one going this way, and they're making a couple. They're separated by a certain distance, and she is rotating counterclockwise. Whatever. Okay. So back here, let's see how couples occur in structures and their value and their use. So, the moment created by a couple of forces is equal to one of the forces times the distance in between them. So, we have a moment here of 8 kip foot. And in this example, it is counterclockwise. Versus in the next example, it's two 4 kippers separated by 2 feet, therefore making 8 kip foot again. and this time it's clockwise. You can think of it as four kips at one foot plus another four kips also at one foot. So, together they create eight kip foot of clockwise moment. Whereas a moment is external force times distance, A couple is an internal force, it's an internal reaction to a moment, to an externally applied moment, or 4 times distance. Now if we look at this example, this one is not quite a couple because the two forces are not equal. But we can pretend that this is 4 kips and that this one is an equal 4 kip, and in addition there is a 2 kip because the top one used to be 6 kips. So this one is making a moment of four kips, let's say the distance is two feet, a moment of eight kip foot, and in addition, there is a push to the right of two kips. So this one is moving also and rotating. So the value of couple is to understand what is happening in structures. So, when you have an external load that is making a moment about this support, for example, that moment is clockwise, well, internally, the top flange and the bottom flange of this wide flange, the top is going into compression, the bottom is pulling out into tension. and together they cause a couple. And whereas the rotation, external rotation, is clockwise, this couple is counterclockwise, and it's resisting the effect of the moment. It's canceling it internally. So the depth of the beam is critical because that's the distance between the compression zone and the tension zone, which is the moment arm, or the couple arm, rather, of this internal couple. The same with the truss, the top chord is going into compression, the bottom chord is pulling out, and this external force is making a moment about this point. That moment is clockwise, while the internal couple is counterclockwise and resisting the effects of that external moment. So one last time, this is an external force P that is creating a moment equal to 4 stein's distance, And internally, the molecules of this beam, the material, is creating a counterclockwise moment due to the couple between the compression and the tension. And this one is counterclockwise because it has to resist the clockwise attack. And the value of that couple is either the compression times the distance between the compression zone and the tension zone. And that is also equal to the tension times the compression, sorry, times the distance between the compression and tension zones. Because we expect the amount of compression in the top to be equal to the amount of tension in the bottom. And that's the definition of a couple. So with an external moment here in this example, we see that the moment is created when the force at a certain distance from a pivot causes this beam to go into compression on the top, tension on the bottom, and therefore to rotate a little bit about the pivot. A couple, on the other hand, does not matter. There is no pivot. There is always a couple between compression and tension zones in a beam, separated by a certain distance d, which is essentially the depth of the beam, and it has no pivot. And clearly, the deeper the beam, the greater the distance between compression and tension, the greater the depth of the beam, the more the moment capacity, because the internal couple is getting greater, therefore you can handle more force times distance on the outside or moment.