Moment Frames: Toys Multi Story

So this segment is about lateral resistance on a multi-story frame. The post and beam with the pin connections, as you see here, is perfectly fine with gravity loads. It can handle gravity loads. With lateral loads, it just racks totally. So it cannot handle lateral loads. So what can we do to reinforce laterally this post and beam? Strategy number one is to have rigid connections unlike the previous frame that had pin connections here. You can see the reduction in area of this model. So instead of that, we keep the joint monolithic. now the beam when it's loaded with gravity, it bends and it affects the columns around it because it's a rigid frame. But for lateral loads, there's a lot of bending and it's more resistant to lateral loads than a post-in beam. Post-in beam is totally incapable of resisting lateral load, but a moment frame can resist lateral loads by bending. see the beams and the columns, everybody's bending here, and that bending brings ductility. So in an earthquake, this frame would be doing that, bending, reverse bending, bending, reverse bending, absorbing the energy from the earthquake. The other strategy, of course, is to have bracing. So we can brace this bay. Now if you put a gravity load at this floor, the diagonals do nothing. course over here they're doing nothing, but when a lateral load is applied, then some of the members go into compression, you can see they have buckled, whereas the other members are in tension. But if the load reverses, as is the case with lateral loads, then one set of diagonals compresses and goes and buckles versus the other set is in tension. There's two diagonals but one is working at one time and these are of course not connected. So in an earthquake, a brace frame has less ductility because it's triangulated and it has therefore more rigidity so it won't sway as much as a moment frame. Therefore, it's a little bit better for the interiors, the secondary damage. the ceiling tile, the ducts, the pipes. They're going to be a little bit more secure with a brace frame because it's more rigid, but the structure itself has less ductility, therefore will attract more force, more base shear from the earthquake. And of course, the third strategy to resist lateral loads is a shear wall. And now this is extremely rigid and has very, very little ductility depending on what it's made of, but typically it's made of concrete or masonry or maybe on lower structures. It could be plywood or OSB. So now we can have pin joints everywhere, but it's not going anywhere laterally because it goes into the shear wall. So we have three strategies for lateral resistance: a shear wall, a brace frame, and then of course a moment frame. but the post and beam is useless when it comes to resisting lateral loads. Okay, another thing to consider is where and how often do we brace. In the case of brace frames, it is typical to have 25% of the base, a quarter of the base, laterally enabled, be that moment frame, brace frame, or shear wall. So in this example I have one, two, three, four, five bays. A quarter of five is one and a quarter, so a little bit more than one bay. We need to brace two bays. So here's an example, two of the five bays are braced. Here's another example where I brace the end bays and leave three bays unbraced and pin connected. Now, this bay here is vulnerable because the next brace bay is pretty far from it. So, still, five bays, I need to brace a quarter of them, that's one and a quarter, two bays, so I braced the end bays in this example. But in this one, I went one bay in. Now, this bay is surrounded by braces. this bay here has a brace bay next to it, and this bay has a brace bay next to it. Anyway, so with lateral loads, the load comes in here, and one set of braces goes into compression, the other set is in tension. But if the load reverses, then the reverse happens. The other set goes into compression, the first set is in tension. Please just keep in mind the direction of the load. In this case, the load is pulling on these diagonals, and in this case, the load is pushing on this diagonal. Therefore, we see that they buckle. Now, if the load reverses from this direction, we see that it's pulling on this diagonal and pushing on this one. So this one is going to buckle, this one is going to stay. This one is going to be in compression, this one is going to be in tension, and here we go. The braces in compression, if the load is excessive, will buckle. And this one is in tension. Of course, we're in steel for this framing. So that's the lesson from bracing. And I'd like to repeat that when this member, this beam is loaded with gravity, the diagonals do nothing. So the diagonals are there for lateral load. So if the load is coming this way, this one is in tension, this one is in compression, if it's coming this way. Very good. But at the same -- with the same token, it's going from right to left. Well, if I pull on this corner, that is also going from right to left. So if I pull on it, well, the same thing happens, and this is hard to maneuver. But basically, the left set of cables or daggles goes into tension, whether it's on this corner or on this corner, it's really the direction of the load towards the diagonal or pulling on the diagonal. Versus if it's on this side, then the right set of diagonals goes into tension because I'm going left to right. Likewise, if I pull on this corner going from left to right, this set of diagonals goes into compression. This one goes into stretching. So here we go with this one. The right side buckled. Okay, that's enough for lateral bracing. and moment frame for lateral resistance, be it moment frame or brace frame or shear wall. Those are all strategies that are employed to reinforce the frame laterally for wind or earthquake. Okay, we'll see you on paper.