Moment Frames: 2a Toys Moment Frames

Now what happens if we rigidly attach the horizontal to the two verticals? This is called a frame when you have rigid connections between horizontal and vertical. So it's no more a post and beam. Unlike the post and beam, the connection between the horizontal and vertical is pinned. Here it's rigid. It's a moment-resisting connection. So if I have what is called a moment frame, and I load it with a gravity load, this angle shall remain 90 degrees no matter what happens. In a moment frame, this angle remains 90 degrees. So as I push down, the beam wants to bend, but the columns are monolithic with the beam, and so this angle shall remain 90 degrees. The legs want to kick out. So there is some thrust at the base because they're kicking out and there is a need for a reaction. Let's see if I can flip this the other way and make it work for me. What is needed at the base is we need some kind of reaction to bring back that leg into vertical. Now as we bring it back into vertical, that's -- sorry, that horizontal push with my finger is what the pin is supposed to do at the base of this moment frame. It's supposed to keep the leg in place. And so as it brings that leg back to vertical, notice what happens to this angle here. This part of the beam wants to go up. You see what's happening? It wants to go up to keep the 90-degree-ness but also stay in position at the base, and the load is still pushing downward, but this angle wants to remain 90 degrees, and so what's going to happen here is there will be a point of inflection over here. I will explain this a little bit better on the next toy, but I just wanted to show that what happens here is the legs are spreading, and there needs to be a reaction on this end to keep the leg from going and of course another one on this end to keep the column vertical. Okay, so let's look at a toy that I can manage a little bit better, which is this one. This is still the same model as before. It's pinned at the base, it's rigid at the top, but now I have something tying the legs together. So when given a gravity load, what happens here is that angle should remain 90 degrees. And this beam is in tension on the bottom, compression on the top. But then at the angle we saw to keep this leg in place, this angle has to go up a little bit, but the beam is going down. So there's a point of inflection here. And what's happening, frankly, is tension, tension, tension, tension, and then it switches. Tension goes to the top. There's compression on the top, it switches. Now it's compression on the bottom. It's really just like saying that is the column. The column takes part of the beam, and the beam is like from here to here, not the full length. It's between points of inflection because what's happening here with a gravity load is the beam is doing that. It's doing this S, sorry you can't see that, let me do it again. It's doing that. So it's doing that here and then the reverse over here. Now what about the column? The column, if it's pinned at the base, then it's bowing in one direction. It does not have a point of inflection. So actually, let's just backtrack a little bit. Compression on the top all the way to here, then compression on the bottom. This side or this face of the column is also in compression. And this face of the column is in tension based on the way it's bowing. Excuse me. So compression, compression, compression up to the point of inflection, then it flips all of those points are in compression. Versus tension, tension, tension, now the top is in tension and the outside of the column is in tension. So actually, there's two points of inflection. Here, let me draw the second one. It's right here. So the beam is as if spanning from here to here, and that's one of the columns, and that's the other column, but the columns are pinned at the base, so they can rotate here. That angle is no longer 90 degrees. It bows in a little bit. Very good. So for a moment frame, that angle shall remain 90 degrees, and the horizontal is going to to have two points of inflection, one and two. The column does not have any point of inflection because it has bowed in one direction, basically. If it reversed curvature like this one did, this one did an S, it reversed curvature over here, and that's the point of inflection. The column did not do that because it's just bowing in one direction. Okay, now what happens under a lateral load? A moment frame is more rigid, of course, than a post and beam. The post and beam racked when it got a lateral load. This one, of course, is going to maintain the 90-degreeness of the corner here, the connection between the beam and the column. But when it gets a lateral load, let's see what happens. This angle shall remain 90 degrees. The base is pinned, so that angle changed from 90 degrees. What did the horizontal do? It went down, then it went up. Looks like there might be a point of inflection here with a lateral load. So it goes down, it goes up. The column is just bowing one way. So let's recap. It looks like compression on the beam from here to here. It looks like compression on the beam from the point of inflection onward. it looks like tension on the top of the beam, it looks like tension on the bottom of the beam for the left half. Looking at the column, it looks like all of those components, all of those pieces of material are in compression, all of those are in tension. So recapping, tension on the outside, compression on the inside, versus the other side, let's see if we can do the other side. Oops, not strong enough to do that. Okay, you're not going to see it with the camera in that position. But basically, this face is in compression, this face is in tension, and the top is in compression, the bottom is in tension. Compression, compression, tension, tension. And looking at the column, it went out of 90-degreeness, and it's bowing in one direction. This column is all compression on this side, all tension on this side. Okay, so that's what happens with a lateral load. Of course, the lateral load could come from any direction. It could do this where, wherever the load is, the beam goes down. And the column is going to bow in the direction of the load and the pin allows the rotation, but the rigid joint keeps the squareness of this angle. Okay, so another variant is where you have a rigid connection between the horizontal and the vertical, but then you change the support condition from a pin, which allows rotation, to a rigid monolithic, where the column and the base are one. So that's a rigid frame on pin supports versus a rigid frame on fixed supports. Both ends are fixed now. So when I load this one, let's see if we can do this right. So when I load this one, that corner shall remain 90 degrees. And it looks like the beam is doing what it did earlier, which is two points of inflection. There's one here, and there's another one here. and the column took part of the beam, the other column took the other part of the beam, and the beam is from here to here now. The difference between this one and the previous one is basically at the base. So if we look at the one that is pin connected at the base, we see the column bowing out in one direction. But if we look at this one, the one with the rigid base, we see that part of the column is straight because this connection is not going to allow rotation, whereas this one does. So the difference basically is in the column. So this one bows over the length of the column. This one, the base claims part of the column and the bowing begins from here up. They look the same, only the length of the column. got a lot shorter when you had a rigid support because that belongs to the base. And now it's like the columns from here to here only. Versus in this example, the column is the full height. Okay, what happens with a lateral load? With a lateral load, I think the beam is doing exactly what it did earlier. It has a point of inflection somewhere here where the beam is curved upward. Now it's curved downward. There's compression on this side, the compression flips to the bottom. There's tension on the bottom, the tension flips to the top. I think the big difference between these is in the column. Because again, we're talking about a rigid base condition versus a pin base condition. Here's a lateral load on a pin, on a pinned moment frame. You see that this angle changed from 90 degrees. and the column bowed in one direction. Versus when you have a rigid base, that portion of the column belongs to the base, and then the bending of the column starts at a certain height up. So when I think about this one, now the column is also doing this S business, and it has a point of inflection. So now the beam has two points of inflection and the column, each column, the other side also under my finger, you don't see it, but this one also has this S motion. So there's a point of inflection on the column. Let's recap very quickly. Compression on the top on the beam, tension on the bottom. It flips. Tension on the top, compression on the bottom. As far as the column goes, I think all of that is in tension. And it flips to this side. Now this side is in tension, this side is in compression versus compression all the way to here. This is all in compression and then the compression flips. I'm sorry, yeah, this becomes in compression on this side. Tension on the bottom, flipping to tension on the top all the way to here. Then there's tension on the other side. Compression on this side, compression on this side, compression here, compression here. Now the compression flips to over here. The tension is here. The tension is on the top all the way up to here. Then there's compression on the bottom. Okay, I hope this helps. This is a moment frame. We will draw this on paper and make sense of it and we'll look at the video. I'll freeze this frame and we'll try to draw what we see here. Now moment frames were created equal. Some of them look like this where the beam is significantly stronger or more rigid, stiffer, than the column. And what happens in this case is if you get a gravity load, that's fine, the column bends a little bit, the beam bends a little bit, but if you get a lateral load. You see what's happening? The column is totally freaking out and bending and doing point of inflection, but the beam is so strong that it's not bending. This condition is called strong beam, weak column, and it's not a healthy situation in a seismic zone. In a seismic zone, the beam is going to break the column in a heartbeat versus a regular moment frame where the beam and the column are relatively similar in stiffness. In an earthquake, this one is going to do that, and that bending, reverse bending, bending, reverse bending is dissipating the energy of the earthquake. So moment frame is very good for the structure in an earthquake because it absorbs the energy of the earthquake and translates it into bending and deforming the beam. And steel, of course, is a material that is very ductile, and so it goes and comes back very nicely with the earthquake. So in this toy, we have a strong column weak beam. Again, they're not similar in stiffness. And so when you get a lateral load, the beam is going to freak out way before the column. And so that is a structural irregularity. Again, in an earthquake, not a good situation because the beam will be too weak compared to the column. And they need to be more similar. Although this is a moment frame connected at the top and rigid at the base, still there's a disparity in stiffness between these two, which makes this a structural irregularity.