Trusses: 2b. Truss Chord And Web Forces

Let's look at trusses through pictures. Let's try to observe some properties, and then we will articulate them on the drawings. So starting here in the middle with the Cistercian Chapel outside of Dallas, it looks like there's a rafter and another rafter. They're carrying the roof, and they want to spread. So there's a very thin cable between them that goes into tension and keeps them from spreading. You can see here there's a very thin wire. So the top is in compression, the bottom is in tension. It's simply supported on the two stone walls. In this example, compression, wood is very good in compression, so they use glulam. Steel is outstanding in tension, so they didn't put wood on the bottom, they put a steel cable. Same with this example here where the top is in compression and a glue lamp member, and the bottom is another tie rod or something very thin but very capable in tension. And then when there's a lot of mass, we can read the compression. When it's thin, we can read the tension. Same with this example of a pedestrian bridge in Atlanta at the airport. The top is in compression. The bottom is in tension. And looking at the web members, I see a cable here like we did in the previous video. I see another cable. I see a third cable. And a last one. So, looking at this truss, we should be able to tell from the area if it's a thin cable, it's tension. Compression buckles, so it's going to need a lot more mass than tension would. Tension is small, compression is huge in steel. Okay, looking at this pedestrian bridge, we see that it bows up, and therefore it's deeper in the middle because for the assembly of members that are in tension compression, for the assembly, there is bending moment. It's very high in the middle. Let's give it depth. And it gets less towards the support. We can get by with less depth at the support. Then looking a little bit closer at the web members, we see a web member here, and then we see a thicker member as we approach the support. So the shear is increasing towards the support. The web members are in charge of shear. The bending moment is increasing towards mid-span. The top and bottom cord are in charge of bending. Together they make a couple and they take care of bending moment. So what else do I have here? I have a highway sign. again we notice that the top and bottom are much thicker than any web members because the top and bottom are having to do the moment they're having to span versus the web members, the verticals and diagonals, are basically tying the compression zone to the tension zone. That's their function. And they do shear and you need less area than what you need to span. the span makes the couple and we need thicker members on the top and bottom cord always in a truss the force in the top and bottom cord is much more than any of the web members looking at this image here the first thing we notice is there is moment connections the second thing we notice is there's no diagonals not one way, not another way, there's no diagonals. This is a virundile truss is what it's called. It's a whole story typically, a whole floor. Here's a scale figure. And it has moment connections, not like a truss that has pin connections. And it's very rigid and it's doing shear and bending and transferring moment from one member to another. It's a frame. It's not a truss, but it's called a Verandeele truss. There's the moment connections. We see them very clearly. And a Verandeele truss does shear and bending, not tension and compression only. Okay, so let's summarize in these diagrams. We said earlier, in an earlier video, that in the middle, if you have a cable, you're going to have tension. And in the middle, if you have an arch, you're going to have compression. So now trying to understand the function of the top chord and the bottom chord, the area there is much more than the web members. So looking a little bit closely at the pen weights I have in this diagram, we start to see a few things. First, there is compression in this member, but the next member, this is BC, the next member CD will have that much compression and a little bit more. And then the member DE will have that much compression and a little bit more until we reach mid-span. At mid-span, DE and its symmetrical EF are doing a lot more compression, oh, sorry, a lot more compression at mid-span than at the support. Likewise, it diminishes as we go back. So, let me fix this and say, okay, there's that much compression. There's more in the middle than there is on either end. The same with tension. So, there is a little bit of tension here. There's more tension in the next member towards the center. And then, the most tension is in the one nearest to the center. And it mirrors. Now, when it comes to the webs, we saw in this image that the web is increasing as you go towards the support because it's picking up load. So, this first cable A carries a certain amount of load. Well, cable B is doing more than cable A. It has more loads to pick up. Cable A has one load. Cable B has three loads to deal with, and so it's going to need more area. And finally, cable C carries the most weight because it's the biggest cable, and it carries one, two, three, four, five loads. So cable A has one load, cable B has three loads between its ends, and cable C has five loads. Very good. The same with the arches in the HAU truss. There is an arch, let me color this very quickly. I'm in blue, so I'll use blue. The bottom chord is doing a lot more than the web, and it does more as it approaches mid-span. In mid-span, it's doing the most. The same with the compression on the top. There's compression, and there's more compression in the middle. Oops. The same with the Warren truss. It has compression on the top, and that compression increases as you approach mid-span. And the same with the tension on the bottom. There's tension here. there's more tension in the next panel and the most tension at mid-span. Likewise, the webbing in the Warren truss and in the How truss is going to be more as you go from the center or mid-span to the end. So I'm trying to represent that with line weights. It looks like there's a lot more on the arch as it nears the support, the same as it was with cables APC in the previous example. So now there's an arch here, and there's a larger arch here. And there is a cable between those, And that cable is carrying more than the arch in the middle. So here's two strikes for this one and two strikes for this cable. So that's the progression. A, B, C, A is in the middle and it carries a certain load. C is on the end and it carries a certain load. B in the middle carries more than A, although it's in tension. But it, magnitude wise, it's carrying more than A. With a cantilever, the top is in tension, but the logic applies here. There is tension on the top, but that tension increases as you near the support. And likewise, in compression on the bottom, there is compression, there is more compression, there is the most compression near the support, and the diagonals are doing the same. Good enough!