Concrete: 1 Way Concrete Spanning Systems

So now I will talk in this video about one-way and two-way but for cast-in-place concrete unlike wood and steel there's plenty of two-way systems in concrete for floors of course for roofs there is also in wood steel and concrete two-way systems first thing I need to say is that Concrete Institute, the ACI code specifies an aspect ratio of two to one for one-way versus two-way. Anything less than two to one is considered two-way. Anything more than two to one aspect ratio is probably functioning as a one-way system. One-way meaning it bends and deflects in one direction versus two-way bends and deflects in both directions. Also of note is that post tensioning, of course, allows a slab, a beam, or whatever it is to span farther or else to carry heavier loads. So that's one thing to say, and now I'm going to get into each one of these systems, but probably the first video will be about one-way systems in concrete versus the second video will be about two-way systems. So we'll start with a one-way slab beam system where we have a span range of 6 foot to 20 foot on the slab. And I hesitate with that 20 foot. All the books say 20 foot for a one-way slab. I think that's excessive because it starts to weigh too much. Because if you look at the span to depth ratio, it's L over 20. So for a 20 foot span, you need a one foot slab thickness. And let's remember that concrete weighs 150 pounds per cubic foot. Therefore, a one-foot slab is going to weigh 150 pounds per every square versus a six-inch slab is going to weigh 75 pounds per every square. And a six-inch is the minimum for a one-way slab. So we have to keep this in perspective, this number here, 75 pounds per square foot. Let's keep in mind that a metal deck plus three inches of concrete plus ceiling tile plus ducts plus carpet plus everything you want in a steel frame is probably 50 pounds per square foot. Here we have 75 pounds per square foot and we still haven't put the ceiling tile, the ducts, etc. So concrete basically is very heavy and we're trying to minimize the thickness in order to minimize the weight. Very good. So here is an example of a one-way slab, and it will not deflect as this dashed line shows. That's for a simply supported. In cast-in-place concrete, there is no such thing, except if it's precast. But if it's cast-in-place, then it's continuous, and it will not deflect like this. That's for a simply supported. Instead, it's going to stay put and square and 90 degrees over here. And then it'll deflect a little bit and come back to 90 degree-ness on the other side. So it deflects less. Very good. And then if you have a continuous, which is probably what it would be, instead of one bay, it would be continuous over multiple bays. Then again, it's going to do... I thought I drew this somewhere else. It looks like I haven't, but basically that's what's going to happen with the deflected shape. Oops, that's incorrect. It's going to do that. So there is a positive and a negative moment, and that's critical to understand with the reinforcing of the slab and the beams. There is, let's just recap shear bending moment diagrams very briefly. When you have a positive bending moment versus a negative bending moment, in a positive bending moment, the tension is on the bottom. In a negative, it's on the top, and the compression is on the top in a positive moment. In a negative moment, the compression is on the bottom. It's important to recognize where the tension is because we need to place rebar accordingly. It looks like on the bottom over here, so we're going to have some kind of rebar on the bottom here, but then it flips to the top over here, so we're going to need some rebar on top of the beam, and we're going to see that quite often. The top is in negative moment, and so it's going to get reinforcing on the top, but between the two supports, the bottom of the beam is in tension, or we have a positive bending moment, therefore the bottom is in tension, and it carries the rebar. So over here, it's on the bottom between the supports, but then at the support, there is a negative moment, and so it goes to the top. I would like to do that on this picture here, and I have written here that the slab trying to span between beams. Here's a beam, here's another beam, and it's trying to span between these two, so the rebar for the slab must go from beam to beam, and it'll probably be continuous across all bays, and we're going to put this blue rebar continuous from beam to beam. That's the slab reinforcing, and it's probably, I don't know, six inches, eight inches on center, something like that. So I'm increasing the spacing a little bit. But this rebar is to carry the slab from beam to beam. But if we zoom in here a little bit, this one piece of concrete, once we pour, it could be eight inches wide, but it's very long, six foot, eight foot, something like that between beams. So we're going to need, in a one-way system, we're always going to need reinforcing perpendicular to the structural reinforcing. The blue rebar is the structural reinforcing and I'm just putting mesh or number three the green rebars just to make the one cell smaller so it doesn't crack. So this is temperature reinforcing or welded wire mesh but the blue steel is structural steel structural steel to carry the slab from beam to beam, structural reinforcing. Okay, so that's a one-way slab, and then there's beams, and the beams are happy in the 20-foot to 40-foot range, with 30-foot as being the most economical. Please note that I said in previous videos for glue lamp wood beams, 30 foot is the most economical range. For steel white flanges, 30 foot is the most economical range. And the same for cast-in-place concrete. 30 foot is a very nice and handsome base size for beams to span. Now, a rule of thumb is the depth is the span divided by 25. So if we want to go 25 feet, then we're going to need a beam that is one foot deep. And the width is, as a rule of thumb, a half the depth. So six inch by 12 inch, I'm hesitating with what I'm saying because six inch is too narrow for concrete. The minimum in concrete is eight inches. So I didn't like what I said because 12 inches, half of that is 6 inches. That's too small. So I'm going to make it 8 inches by 12 inches at least. Okay. So, and then we have a big girder. This is the primary structure. It's carrying the secondary. This is the secondary, which is the beams. And then the tertiary is the slab. Very good. So it's stacking systems perpendicular to each other. And here's the reinforcing in three dimensions. It looks like it goes over the top. Let me see if I can copy this quickly. I haven't done this before. Let's hope it works. Okay, let's copy, duplicate, put it over here. Yeah, something like that. Okay, what happens here is the rebar goes on top over here and on the bottom. On the bottom here, positive bending moment, negative bending moment over the beam, positive moment between the beams, and then negative over the beam again. So that's what that slab is doing. And we have temperature reinforcing, this one, temperature reinforcing, or just mesh, It doesn't matter. It could be in two directions or a simple smooth rebar number, a grade 40 or whatever in that direction. That's not the important one. The important one is the blue one that is going from beam to beam. This is the structural reinforcing of the slab. Okay, what else do we have? So then to span a little bit more, we can go 10 foot to 40 foot. And if you post tension, of course, it's going to be more than that. The ability to span is going to be more than that. And so we'd go from 30 to 80 feet. And this is a one-way ribbed slab or a joist. And the idea is to make the slab lighter in order to span more. Remember earlier we said a one foot thick slab is just too much weight. So this way we're making it a lot lighter. Very good. So here what we have is we have these, where are they here? these pans. In this case, there's either steel or plexiglass, sorry, or yeah, not plexiglass, but fiberglass rather, pans. And in between them is a joist. Right here is a joist and another joist and another joist. And these guys are either 30 inches or 20 inches, somewhere in that neighborhood, because anything more than 30 inches spacing is considered a beam. Anything less than 30 inches is considered a joist. Very good. So we're going to reinforce this way from joist to joist so that the slab can span between these ribs or joists. It's called a ribbed slab. And that's what the pans look like. In this case, they're steel. Sometimes they will taper the tip of the joist in order to give it more area to be able to handle more sheer and bending moment. So here we can see a massive bore with pans that are humongous, very large pans. And again, the idea is there is a joist, another joist, another joist, and the slab has to span from joist to joist. So we'll put reinforcing accordingly. And this is a one-way system, and therefore it's going to need temperature reinforcing in the perpendicular direction, just to make each piece of concrete small enough that it does not crack. Here we can see the underside of these pans. Now with a one-way pan joist system, it could be either layout A or layout B. And the difference is, of course, in the formwork and in the span of the primary. This is the primary structure. And this is the secondary. So there's a lot more secondary members in layout A and much fewer in layout B, but the beams are shorter. Shorter beams. Oftentimes, layout B is preferred. So the joist span in the long direction, the beams are shorter. We have to keep in mind that the beams and the joists have to have the same depth, otherwise it's not efficient. If I'm going to have to work on the formwork to make beams deeper than joists, then forget it. It's not worth it anymore. It's no more efficient or practical. So oftentimes layout B is preferred just for simplicity and simplifying the formwork versus in this case I'm spanning a lot. In case A, spanning a lot, the beam is going to have to be deeper than the joist. Therefore, it's no longer efficient. So this is for the 20 foot to 60 foot range. Again, 30 foot is the most economical. And the depth of the joist is the span divided by 20, roughly, rule of thumb. Very good. So here's what this looks like. And we can see an imprint of the formwork of the pan here. Here's one pan. It's from here to here. There's the pan. And these things are tapered so they can be pulled out easily. after the pore is completed. These things are tapered like this so that the joist is trapezoidal, if you wish, and reinforced accordingly. Very good. So that's what a section through this might look like. Again, we're going to need to have steel on the top here to counter any negative moment. Very good. So again, the primary beam is happy in the 20 to 40 foot range with 30 foot being the most economical. And the joists are in the 10 foot to 40 foot typical. Unless you post tension, then you can go much farther than that. Very good. That's a pan joist or a joist system or a ribbed slab. All of these mean the same thing. we're making the slab lighter so it can span farther. Now, I didn't say this on the previous page, but basically, if the spacing here is 30 inches or less, we're calling it a joist. If it's more than 30 inches, it becomes a beam. So if I take out this guy and take out this guy, that's it. Now, all of a sudden, the span is much larger of the slab, and we're going to call it a one-way slab beam system. So this one is a one-way slab beam system. And of course, this spacing is much more than that of a joist. But otherwise, it's the same. Again, the primary members are spanning 20 to 40 feet. The secondary members or beams are spanning 10 foot to 40 foot. And pretty much, that's what we were looking at earlier. Here's a live picture and here's the slab reinforcing going from beam to beam. And in a one-way system, that is too big a piece of concrete. It'll crack. So we're going to need temperature reinforcing in the perpendicular direction. And we can see here that this is the girder. And it's spanning from column to column. There's a column here. There's a column here. And it's carrying a bunch of these beams. So in this case, the beams are going the long direction. The girder is going the short direction. Okay. Same thing over here. I have these smaller, they're not joists because that dimension looks like it's more than 30 inches. So I'm going to call these beams. Stop. Oh, geez. Okay. Quit it. Very good. Cancel. How do I cancel? I can't cancel. Geez. Okay. Now we can cancel. Okay. So here again, we can see the primary reinforcing is going to go perpendicular to beams. The primary slab reinforcing, I keep saying that. And perpendicular to that, there is temperature steel against cracking. Very good. Here we can see there is some additional rebars here because that's the negative moment and they're adding a few rebars to take care of that negative moment that happens over the support. Very good. We're not ready for two-way. Okay, I'm going to stop this here and then I'll start the two-way in a short while.