Moment Frames: Bent

In this video I'd like to talk about rigid frames or bends, rigid bends, that are these pieces here, these red pieces that are laid out at a certain spacing, a certain distance between each other, that are very strong in their own plane. They can carry dead load of the roof, they can take a wind load, and very strong in their own plane. But when it comes to between these pieces, they are unable to handle out-of-plane loads. They're going to need some kind of lateral stability. And that would come either from a moment frame, a brace frame, or a shear wall. So I need to tie these two purple pieces together, either by making moment connections here and elsewhere between the two purple pieces, or else by bracing. I can brace this, but I have to go all the way up and all the way down the other side to get a braced bay, also called a bent. The braced bay or the laterally enabled bay is called a bent as well. So, out of plane loads are dangerous and we need to take care of them. Very good. The origins of this system, I believe, is in bridges. And here we're looking at a bridge in Switzerland by Robert Maillard from 1930. And we notice a few things. One is this arch is pretty thick up here, but then it gets thin towards the support. And furthermore, it gets thin at the crown, thin at the support, thin at the other support. This is a three-pin arch. And this purple piece is as if leaning against this green piece, and they're supporting each other. So that's a three-pin arch. versus a two-pin arch that we see, for example, in the Cowboys Stadium in Texas. There's this rigid arch, but it's supported on pins at the ends. So that is a two-pin arch, and we can see here the pin under construction. Whenever that area comes down to a point, that's a pin connection versus the Sydney Harbor Bridge, for example, which is a fixed arch. It's one piece just like the Cowboy Stadium, but if you notice, this one is getting deeper and thicker and more mass at the support versus this one is getting smaller at the support. So this is a pin connection versus a fixed connection. When you get more area, you're making a fixed connection, But in both cases, the arch itself is one piece, unlike the previous example from Maillard. Okay, so two pin, three pin, and also the supports. Are they pinned or are they fixed? If we look at IIT in Chicago by Mies, we're going to see again these rigid frames. Let's pick a color that works here. These rigid frames. No, that's terrible color. Okay, let's just go with red. So I have this frame here. It's very rigid. It's capable of carrying the roof or hanging the roof from the bottom flange of this deep white flange. And the same on this other one. But between them, Mies would roll in his grave if there were bracing here. No way to accept the bracing. No way to put a sheer wall. So it must be this is a moment connection for lateral stability. Otherwise, these things topple like dominoes. So, there's probably moment connections for these horizontals that are keeping all the individual bents or rigid frames stable in the lateral direction. Okay, so the Industrial Revolution, the Second Industrial Revolution, was in full swing when these structures came about. And we're looking at the World's Fair in Paris of 1889 that gave Paris the Eiffel Tower. In addition, the Galerie des Machines by Ferdinand Duterte and Victor Cantamin. This one is these portal frames, or this arched frame, and let's see what's going on here. There's a reduction in area at the support. There's a reduction in area at the top versus over here. There's a lot of area. And then there's a pin at the other support. So this one is a three-pin arch. And the pin is very nicely articulated and detailed beautifully. And it allows for a little bit of thermal expansion and contraction. And if foundations were to settle, this frame accepts that reasonably well. So rigid frames or rigid bends are made of steel. They're also made of wood. Here we can see barn raising of sorts. That's the idea behind the portal frame. So, we see these 3-pin and 2-pin arch in steel, we see it in wood, and we see it in precast concrete. So, it's basically these planes that need to be attached to each other. And that's what this system is, the rigid bent. Very good. So, here we are in wood, and they're erecting these rigid bents, and then they'll brace between them. So some terminology, the crown is up here, the haunch is the transition of the load from an angled to a vertical surface or a member, and the support. And to determine if it's a 2-pin or a 3-pin, we need to look at the crown. If it's a continuous area like that, then it's going to be a 2-pin, versus if there is a reduction in area here, then that would be a 3-pin arch, assuming, of course, that the bases are pinned and not rigid. Very good. Crown, haunch, and support. The haunch is always rigid. So, this could be a frame or an arch, a two-pin frame and a two-pin arch, or a three-pin frame and a three-pin arch. And again, we need to look at the support. Is it pinned or is it rigid? And then at the crown, do you have continuity? Is it the same size member or does it reduce an area? That's how we can tell if it's a two-pin or a three-pin or if the support is rigid or pinned. Very good. So those are the areas we need to look at. So examining these images, looking at the crown for this first image, I see a continuous area. I see one piece. And the haunch here, you can see this scale figure, it is huge. The intersection at the haunch is huge because the force has to make a detour and go downward. Now you notice that in this image it's getting a little bit smaller. Must be there's a pin at the top. Likewise with this image, it's very fat up here at the haunch, but then it's narrowing down. Must be that's a pin. Very good. At the Waterloo Station in London by Nicholas Grimshaw, we see a pin down here, we see a pin up here, and a pin on the other side, and we see the member getting larger here, and then at the pin it gets smaller. So this is a three-pin arch. Versus, so the first thing to look at is the crown. The second thing to look at is at the support. Do we have a pin or a rigid connection? In wood, it has to be pinned. We cannot make wood monolithic with its support, unless we cheat and pour it in the concrete, which is not nice and certainly not on the IRE. So, let's recap very quickly here about steel connections. If the anchor bolts are between the flanges, then you're going to have a pin connection. But if the anchor bolts are outside the flanges, then you're going to have a fixed connection. If we look at the second image here, we see that there's a large area at the haunch, and then we see it tapering down to a little area that must be a pin. Same with this image, it's tapering down to a pin at the base. If we look at this image also, we see that this member is not tapering, must be that one is rigidly connected. So the next thing to consider is components and cladding. These are the primary structural pieces. These here are the primary structure. And then these are considered components and cladding. We have two of them in a metal building or a rigid frame such as this one. The purlins are in charge of dead load, basically the weight of the structure, the weight of the roof, pardon, and also wind uplift or downward push depending on the slope of the rigid frame rafters, which are these pieces. The steeper they are, then the wind pressure is positive on the windward side, but the shallower they are, then it's uplift. The girths, which are on the vertical surface, we need to attach some kind of siding to them. So the girths are responsible for wind load. Back to the purlins, they are usually Z in profile. Here's a Z purlin. And then the metal roof comes on top of those. So purlins usually are Z profile. The same with, sorry, the purlins are going to get some kind of blanket insulation. And there it is. And then there's some kind of standing seam metal roof that gets on there. The girts, on the other hand, are also Z in profile. And wherever you need to put siding, we're going to put these girts on the ends of the building. So all of these are part of the girths, and they're all going to receive siding. Whether the siding is metal, whether it's brick, we need to put between the rigid bends, we need to put some kind of CMU in order to receive insulation, and then brick, for example, will have our control joints. Or whether we have cast stone, metal siding, the detailing has to keep the weather out. So as far as sequence of construction for these metal buildings or rigid bents, it starts with the verticals. Those are erected in place first. Those are items one and four down in this key drawing. And all of those are erected first, as we see in this picture and in this one. Again, this is a pin because it's tapering downward to a narrower area. Then the rigid frame rafters, 2 and 3, are attached on the ground and lifted into place on top of 1 and 4 that are already in place. Here, let's look at this animation quickly. One and four are going into place first, and they are pin connected because they're tapered and because the anchor bolts are between the flanges. And then two and three are attached on the ground and lifted into place, and moment connected at the haunch. Then the bracing goes into place, and the blanket insulation will follow once the purlins and girts are in place. Then the blanket insulation is coming in. Here my student took too long, so I trimmed it a little bit. Then the standing seam roof will come down on there. And the siding. We need to talk about the bracing of these members. They're usually a tension-only bracing because this is a cheap building type. And so tension-only bracing is basically cables. And let's go back to our presentation. As far as bracing goes, there are some rules and regulations. What we have here is tension-only bracing. And that means it cannot handle compression, which means it's a cable or a tie rod or something similar, a strap. That's what's used for tension-only. A very small cross-sectional area. once the cross-sectional area of the member becomes larger than maybe a tube or a pipe or a wide flange or a pair of angles, a pair of channels. Now that is no longer tension only. It becomes tension and or compression. But it costs money versus cables. Cables are cheap. So tension only bracing and must maintain symmetry of bracing. Otherwise, the building twists, and that becomes a problem if one side is stronger than the other. That's torsion. In addition to symmetry, taking the last bay is best for wind. So if we can brace the last bay, this one and this one, that would be awesome. Also, in addition to symmetry and getting the last bay, the minimum number of lateral bays, minimum number of bays, should be 25% of the bays. What that means is a quarter of the bays need to be either, need to be laterally enabled either by a moment frame, a brace frame, or a shear wall. So in this case, I have four bays, one, two, three, four. A quarter of that is one. So at least one bay needs to be braced. If you had eight bays, a quarter of that would be two. At least two of the bays need to be braced, shear-walled, or moment-framed. So let's take a look at some bracing schemes very quickly. Sorry, this is the tension-only bracing. It's just a pair of cables. One is working, the other is doing nothing. if the wind reverses, then the cables also reverse. So looking at this image here on the right, it's awesome. The cables are doing nothing. They haven't been tightened yet. But if the force of wind comes in this direction, then this cable here goes into tension, this one. And this one goes into compression, and it does nothing, which is what it's doing now. But should the wind load reverse and come from this direction, then this one would go into compression and slack off, whereas the other one would be pulled and would go into tension. This one would go into tension for the green load. Okay, so tension only bracing, and please note that the entire bay is braced all the way up and then down on the other side. that's also called a rigid bent. A bay that is braced is also called a rigid bent. So let's study this a little bit more. I have two situations. One is an odd number of bays. The other one is an even number of bays. And let's remember 25% of the bays minimum need to be braced. So it would be ideal to get the very last bay. If you do get the last bay, number one, for example, then you want symmetry. So I'd like to have bay number seven also to be braced. We have seven bays. Seven divided by four is one and a bit. So I need at least two bays. So there's two bays. But I think there's too many bays here that are not braced. I would like to get a little bit more stiffness. So let me put another bay and brace it called a bent. Now, if I look at my scheme, bay number 6 is near bay number 7. Bay number 7 is rigid, so bay number 6 is taken care of. Bay number 5 is near a braced bay. Bay number 3 is near a braced bay. And bay number 2 is near a braced bay. We're good. Versus if I have, if you won't give the last bay to bracing, you need it for openings or something like that, That was the best bay for wind bracing is 1 and 7. But if those are not available, I'll take bay number 2. That's the next best one. I want symmetry again, so I will take... Here's the center line. So I will take bay number 6. 2 and 6, that would be awesome. We said 7 bays divided by 4 is 1 and 3 quarters almost. We have enough bracing, but it might be prudent to add one more, this one in the middle, and keep everything symmetrical. Now each bay is either braced or adjacent to a braced bay. Keep the symmetry. Now in an even number of bays, the same discussion, I would like to have bay number one, and if I do have bay number one, I would like the other end bay also. So that's keeping the symmetry here. Here's the center line of this assembly. So, if I brace bay number four, then there's three bays on this side, and there's two bays on this side. This one is near a braced bay. This one is near a braced bay. But this one is, there's no bracing near it. So I might add one more. Then I'll add another bay and keep my symmetry. Now each bay is either braced or near a braced bay. If that end bay number 1 and number 8, if those two end bays are not available, well then I'll take the next one, bay number 2. And I want symmetry, so I'll take 2 and 7. And there's too many bays in the middle, although 8 divided by 4 is 2, and I have enough bracing, I feel that the middle here is just not stiff enough. So I'd like to add one more bay, and I might add it at bay number 4.