Braced Frames: Toys Cbf Ebf 2pin 3 Pin

Okay, so the tension-only bracing cannot handle any compression, and so if the load, the lateral load, puts the diagonal into compression, it buckles, and we said one of the remedies is to make a brace that can handle tension and or compression or whatever comes its way. Another option is to, instead of a single brace tension only, the other option is to put a pair of braces. In both of them tension only, still not connected. So if you have a gravity load, neither diagonal is doing anything. The post and beam in white in this model is doing the work. But if you have a lateral load coming this way, then this diagonal is going to go into compression, this one is going to go into tension. So the one in compression is absolutely doing nothing. The force in that one is zero. This one's taking the load. But if I pull on it, then this one goes into tension and this one goes into compression. So it does nothing. Or if the load comes from this direction and pulls, then this one is doing nothing. That one is doing the work. But if it pushes, then this one is in compression, the other one is in tension. So there's two diagonals, but actually it's one at a time, depending on the direction of the load. Again, tension-only bracing is pretty flimsy, because you have a tie rod, or a cable, or a strap in light gauge metal framing. So not very capable, and in an earthquake, not a good situation to have tension-only bracing. Very good. So for brace frames, we have concentric bracing, and it could be only compression or tension member, compression and/or tension, or it could be tension only, and we need a pair instead of just a single. Tension only single is not a good situation. So that's it for concentric bracing. Now there's something called eccentric bracing, where the brace does not go from corner to corner, but goes from the foundation or the support to some point on the beam. It could have gone to here, but not to the diagonal. So now what happens here is this triangle is pretty rigid and braced nicely, and so is this one, but then there's a segment in the middle of the beam that is not braced that is called a link beam. So this one, compared to this one, this one has more ductility because the segment of the beam that is not braced is there to bend. Versus this one, it doesn't have as much ductility. It's much more rigid. It has more rigidity. So this one is more rigid, less ductile, but an eccentric -- this is a concentrically braced frame from corner to corner -- but an eccentrically braced frame leaves a segment of the beam called a link beam that is there to bend in an earthquake or something like that because bending gives ductility and the frame itself will not fail. So in a lateral load, you see this middle segment is doing that S number or ductility versus the triangulated piece is not. So eccentric bracing comes in a variety of shapes. It could be on a frame, on a tall building, or something like that. Here's the link beam, a triangle that is rigid, and then a beam that is there to bend. Or it could be eccentrically braced on one side and not the other. And there's the link beam. But one point to make here is the longer, sorry, the longer the link beam, this is much longer than this one, the longer the link beam, then the more ductile the frame. The shorter the link beam, the more rigid the frame. The triangle is bigger over here than it is over here. Triangle is rigidity. Unbraced piece of the beam is ductility. And the longer the link beam, the more ductile an eccentrically braced frame is. And therefore, the frame is going to dance with the earthquake. But then the secondary damage will be greater. Secondary damage meaning ceiling tiles, ducts, pipes, etc. So depending on the contents of the building, you might decide on the lateral bracing strategy. Be it just a moment frame, the building is going to dance a lot. or an eccentrically braced frame so that the unbraced segment or the link beam is small, or concentric bracing where it's more rigid and less ductile. And the last strategy, of course, is a shear wall. You can put a shear wall in there and then you get a lot of rigidity but hardly any ductility. Okay, before finishing the segment on bracing and moment frames, I would like to bring up these two toys that I have. They're like metal buildings. That's typically the structure. And we got to compare these two. Both of them are pinned to the ground, but the difference is not at the haunch. The haunch, they look the same. This is the haunch where the load is coming at an angle, making a detour and going down to the vertical is called a haunch. And usually that's a great area, so it has to be a moment connection. But then looking at the crown of this, we see a lot of material, very little material. So this is a pin, this is a rigid connection. So for the two-pin arch or two-pin frame versus the three-pin, pin number one, number two, number three, The two pin, it's like this is all one piece. It's one frame and sitting on two pins. The pin has two reactions, a vertical and a horizontal. The other pin has two reactions, a vertical and a horizontal. That's a total of four. Four is more than three, and therefore, this is indeterminate. There's one extra unknown. So when the load comes down, I'm not sure which horizontal is taking that load, but the frame wants to kick out because it's rigid. It's like a rigid frame wanting to thrust. So a two-pin frame is indeterminate. Versus a three-pin frame, pin number one, pin number two, number three, this one is less rigid than the previous, therefore the members will be smaller. The member sizes will be smaller than a two-pin frame. In a three pin frame, the building can wobble a little bit because the pin allows that movement. So it's like saying you have that structure leaning against that structure. And so each half is statically determinate because I have a pin down here, one, two reactions. And over here, it's just one leaning on the other, so these two are equal and opposite, and they cancel each other. So looking at this three-pin frame or three-pin arch, there's a uniform load, let's say, coming down on this guy. So there's a vertical reaction equal to whatever that half of a load is. The other half is -- we don't look at the entire frame. We look at one half, and we see half the load. That's the vertical reaction, but this half load also wants to make rotation. So, there needs to be a counter reaction here. Therefore, this horizontal is going to keep the frame from thrusting out. And then, if this wants to rotate clockwise, this horizontal reaction is going to be equal to the thrust that is up there. If the frame wants to rotate clockwise, this guy leaning against this one is going to make a counter moment and keep this guy from rotating clockwise or counter. And whatever happens in this pin, the same but in the opposite direction happens in the other pin. So we have a gravitational load here, a uniform load, let's say. Therefore, the vertical reaction is equal to that much. But this vertical load also wants to rotate the frame this way. But the lateral support of this other half, so as the uniform load wants to do this, this other half wants to keep it from rotating. And whatever thrust you have is balanced, whatever this load is, this load is equal and opposite. So these two are equal and opposite, these two are equal and opposite. If you want to, if this half wants to rotate this way, this other half is going to keep it from rotating. And whatever load you have at the top is resisted with these two. Whether you consider two halves or you consider the thing, it's the same. Whatever load is up here is going to two points. And then this reaction is equal to that reaction, and they're equal to the thrust at the base of this arch. So this one is statically determinate. This one, the two-pin arch, is statically indeterminate, whereas the three-pin arch is stable and statically determinate and cheaper than this one. Therefore, most of the metal buildings look like this. Okay, we'll go to paper.