Concrete: 2 Way Concrete Spanning Systems

So we saw in one-way systems that the concrete institute, ACI, the American Concrete Institute, specifies a ratio of greater than 2 to 1 is one-way and less than 2 to 1 is a two-way system. So in a one-way system, the main reinforcing is in the short direction, and then there's temperature reinforcing to prevent cracking, and that's in the perpendicular to the primary reinforcing. So much like wood and steel, there is primary, secondary, and tertiary systems. In concrete, though, they're all in the same plane and are poured at the same time. In two-way concrete systems, the aspect ratio is less than two to one, and the reinforcing is the same in both directions. So there is no temperature steel. It's the same size rebar at the same spacing in both directions. So there is something very peculiar for two-way systems that we need to address, and that is when you do not have any beams. There are two-way structural systems in concrete that do not have beams. They are called a flat plate and a flat slab. Flat meaning no beams or anything below the plate. So there is the issue of punching shear. When you don't have beams, the load could be high enough or the column dimensions are very small that it could punch through just like a pencil through a sheet of paper. So punching shear is a real concern and we see that regardless whether it's concrete or not. We can see it in the National Portrait Gallery here by Norman Foster in Washington, D.C. You can see very clearly that the size of the member over here is quite different than over here. It's getting a lot thicker where we're afraid of punching shear right over the column. So you can tell right away. The same with the Seattle Public Library by OMA and Rem Koolhaas, you can see it's a little bit darker around the column, and that's because there's two layers of this diagrid on top of the column to prevent punching shear. So punching shear is not specific for concrete. It's whenever the area of the column is small and the thickness of the slab is too thin, we need to increase the depth or the area over the column to prevent punching shear. So another thing that I need to define is the difference between a plate and a slab. When the bottom is smooth, there is no beam, there is no joist, there's no rib, there's no column capital, there's no drop panel, there's nothing except the column going into the plate. We call this one a plate. Versus if anything drops down, it's called a slab. So a flat slab has got to have something over the column versus a flat plate, it's just the column going into the plate itself. So flat plate is used for lighter loads versus flat slab is used for heavier loads. A flat plate is typically used for residential construction and for high rise. Also, we're trying to minimize, there's nothing dropping down here, so we're trying to minimize the floor-to-floor height. So every nine floors, you can get a 10th floor for free. So it's very economical, especially in high-rise construction. Sorry, in high-rise residential, because the load needs to be, the live load needs to be light. And so therefore, it's most efficient for residential high-rise. So, of course, we can't have too thin of a slab or too small of a column, then it'll punch through. So what they do here is there is no beam, there is no drop panel. So they put these studded rails, there's studs sitting on a rail, and they try to reinforce in two directions right around the column to prevent punching shear. By the way, punching shear is what happened at Surfside with the collapse of the towers there, the Champlain Towers. It was because of punching shear. There was additional load from the pools and the flower beds, and therefore it punched right through the columns. Of course, there is an advantage to not having beams or a drop panel or anything. The mechanical systems are free to go any which way, and the coordination is a lot easier to do between structure and mechanical electrical. Versus a two-way slab system. First of all, the reinforcing is the same in both directions. Here we can see in the formwork a drop panel that looks like this, that looks like this in the formwork. So that is to acknowledge that the load on this floor is a little bit heavier than residential. So we're going to need a drop panel right over the column. Okay, so these are examples of flat slabs and these are examples of flat plates. What else do I need to say on this one? I think I've said everything I need to say. We're just minimizing the floor-to-floor height, and it is for light loads, which means, light live loads, which means less than 100 pounds per square foot. And that's the largest in a hallway or an egress route or assembly space is 100 pounds per square foot. So probably these guys are for storage, for warehouse, for heavier, for parking, for something like that versus just residential. Okay, so let's get into these systems then, two-way systems. We're looking here at a flat plate. I can see very clearly from the formwork that there is absolutely no beams. There's nothing except the column rebar sticking out of the formwork. There's no beams, there's no ribs, there's no joist, there's no column capital, there's no drop panel, it's just a column running into the plate. That is the Aqua Tower for example, Jeanne Gang in Chicago uses a flat plate system, the Domino House Le Corbusier also uses a flat plate system, 1111 Lincoln Boulevard in Miami Beach by Herzog de Miron. Also you can tell the column is just running into the plate. There's a flat plate system. The same with the Ando Museum, the modern in Fort Worth. We can see the columns just coming into that plate. It's a roof system, I understand. But then here are all the stud rails and the reinforcing against punching shear. This is very critical and I need to emphasize this. Punching shear is basically shear but in two directions. So it's a two-way shear. Two-way shear where part of the slab will remain on top of the column and the rest will go down. So punching shear. Very good. So this one is the same size rebar in two directions. Having an overhang in any of these two-way systems is very helpful because it reduces the deflection. And the negative moment takes away from the positive moment. So it's good to have an overhang. Also, the formwork is very simple. Therefore, it's cheap. And there is nothing dropping below the plate, so floor to floor is going to be less. And so the biggest advantage, I think, in a flat plate and a flat slab is that there are no beams. Therefore, there is no grid. Therefore, you can put the columns wherever you want within the limit. Typically, these flat plates go 12 feet to 25 feet. and unless you post tension, then it'll go a little bit more. The thickness of these flat plates is somewhere between 8 inches and 12 inches. So that's the entire structure. There's nothing dropping below that 8 inch to 12 inch. So we're going to need all the reinforcement we can handle right over the column to prevent punching shear. So with no beams, no grid, it's very easy to do the layout. but also floor-to-floor height benefits. And therefore, with less floor-to-floor height, the structure is lighter, there's less finish on the facades, there's shorter interior walls, shorter stairs and columns, less plumbing, mechanical equipment, everything is less, and so is the foundation to carry less weight. So those are some of the advantages, Some of the disadvantages, clearly in the absence of beams or a drop panel, your punching shear is a big issue. And it's the thinness of the plate. You might have to go to a thicker plate to reduce the deflection and reduce the likelihood of punching shear. But also in getting a thicker plate, it's better for noise transmission, fire separation, etc. So, in essence, this system is for light loads and residential high-rise, typically dorms, hotel, motel, multistory, something like that. So, that's the flat plate system versus the flat slab system. Basically, over the column, there is a drop panel, or this is a drop panel, or maybe just a column capital, such as this one. So it's the same as a flat plate, but this one is for heavier loads, and we're worried more about punching shear, and we're reinforcing locally over the column. So it's the thickened area around the column to mitigate punching shear and a drop panel, as I said earlier, a drop panel or a column capital to mitigate that punching shear. So the punching shear depends on the thickness of the slab, whatever concrete is going to come on top of this much. This is the drop panel that is to prevent the punching shear. So typical spans again from 20 to 40 feet, warehouses, industrial heavier loads are going to require a flat slab versus a flat plate. Please notice there is still no beams so it's just a little bit more depth over the column but just over the column so mechanical systems etc are still running around very nice and easy. So, a flat slab system versus a waffle slab. A waffle slab is a two-way. We looked earlier at a one-way pan joist. Well, this is a two-way pan joist. It's a coffered slab or a ribbed slab. There's ribs in two directions, and their reinforcing is identical. and again above the column we need to have solid concrete. We cannot have coffers there because we're worried about punching shear. So there's always a solid over the column and then depending on the magnitude of loads you can have a drop panel. This one is solid and then there is a capital on top of the column. All of this for punching shear. The span range for waffle slabs is between 20 to 60 feet. And please, for these systems, all of them, the flat plate, the flat slab, the waffle slab, the two-way slab, the one-way slab, the most economical range is 30 feet. And I'll repeat that 30 foot was the most economical range for glue lamp and for steel white flanges. So 30 foot is a very comfortable span for light to moderate loads. So like a one-way pan joist, there is domes this time. In a one-way pan joist, they were rectangular. Here they are square. They're called domes, and they're made of steel or fiberglass. And this is the rib, and it is reinforced in two directions. and the depth of the dome comes in different sizes. But typically these domes are 19 inches by 19 inches or 30 inches by 30 inches and they come in depth of 6 inch, 8 inch, 10 inch, 12 inch, etc. Plus there's at least 3 inches of concrete above the dome. So these ribs are usually six to eight inches. Therefore, they have rebar in them. Very good. So it's very stiff system with joists going in two directions. And therefore, it is better. It has less vibration. Maybe for hospitals, you want to attenuate that. So that would be a good application. And there's always a solid head over the column. Again, punching shear. I have to say that many times because that's critical in two-way systems that do not have beams. Very good. So a waffle slab is always something pleasant to look at. And so typically that would not be covered. It's a bank lobby or something very nice to leave exposed. Finally, a two-way slab beam system, again, is in the range of 20 to 50 feet with 30 foot being most economical. This is an example of an airport where you have beams in two directions, that way, that way. Same dimension, same reinforcing. And it's an increased stiffness with these beams and therefore less deflection. this one is pretty hard to run the mechanical systems electrical plumbing so that has to be tightly coordinated before anything is poured but this one is thinner the slab is pretty thin so it is lighter than a one-way slab because the slab itself is thinner than a one-way pan joist or a one-way slab beam. So the formwork, of course, is going to be much more expensive because you're doing twice the number of beams, etc. So that's it for two-way systems. It's critical to understand the issue of punching shear over the column.