Trusses: 2a. Truss Chord And Web Forces

So I'd like to go over this tension or compression business in trusses and in general, not just in trusses. So on this document, tension is expressed in blue. Anytime you see blue, the reference is to tension. Anytime you see red, the reference is to compression. So in a truss, the top cord in a simply supported truss, a truss supported at its ends, is in compression. Top cord in compression, bottom cord is in tension. Regardless of the configuration of the truss, it could be a bowstring truss, it could be an upside down triangular truss, it could be a parallel cord, it doesn't matter. As long as it's supported on its ends with two reactions, then the top chord is in compression, the bottom chord is in tension. So that is illustrated here. We can see I've colored on the left, the top chord is always red, the bottom chord is always blue if it is simply supported. Here's an example. In this church, the top chord is in compression. the two rafters basically, and the bottom is in tension. And we see this detail of a cable, very thin cable on the bottom, just keeping these two from spreading. They want to spread out and the cable on the bottom is keeping them from spreading and therefore goes into tension. And so that's what it looks like. But on the far left column, we have the simply supported truss. The top cord is in compression, bottom cord is in tension. In a cantilever, of course, it reverses. The top is in tension and the bottom is in compression. For an overhanging truss, what happens in between the supports, I'm sorry, just one second, what happens in between the supports from here to here, The top is in compression and the bottom is in tension, just like a simply supported truss or beam. But then once you pass the overhang, it reverses and it becomes like a cantilever. So the top goes into tension, the bottom is in compression. Very good. So what about the web members? Are the diagonal web members in compression or in tension? And there's a couple of easy ways to determine that. But what we've covered so far is the two cords in a simply supported, in an overhanging, and in a cantilever truss. So now let's look at the web members. If the web members form an arch about the center line, then those web members are in compression. Over here, I'm looking at the how truss, and I'm seeing this arch here. It's like an arch and the two members are in compression. And then there's another arch parallel to that first one, but it has a wider base. And very good. So there is an arch around the center line. Therefore, those two web members are in compression. However, if they form like a cable, then around the center line, then the members are in tension. So cable is like tension, arch is like compression. So we can see in the Warren truss that there's a pair of arches in the center line. I'm sorry, that should be red. In the center, there is an arch and then there's another arch. But then there is also a cable around the center line and another cable. So arch cable is the way of thinking of the whole truss as a unit. This, of course, assumes that all these loads are equal or symmetrical rather. And the truss is simply supported. Very good. Another way of doing this is you look at either the left or the right and you zoom into the support. If you see a diagonal at the support, then the member is in compression. If there is no diagonal at the support, then that diagonal is in tension. So that's a quick way of figuring things out. So looking at the support, if there is no diagonal, that means that the load went to the top and didn't come to the support, which means the diagonal at that last bay is in tension. Very good. You can look at either the left or the right. They'll give you the same result. So looking at this first support, I see a diagonal coming into the support. Looks like that would be compression versus the second case down in the Pratt truss. I see that there is no diagonal. Therefore, it must have gone to the top before coming down. That is a diagonal in tension. Very good. So those are two quick ways of looking at web members and determining if they're in compression or tension. Again, you can go either on the left or the right and zoom into the support and see if there is a diagonal, then it would be in compression. If there is no diagonal, then it would be in tension. Same thing with simply supported cantilevered or overhanging. We zoom into the support, either left or right, and we see if the member, sorry, if the diagonal member or the web member is coming into the support, then it's compression. If it's not coming into the support, then the member is in tension. So the overhang here is a good example. The left support has a diagonal coming in from the right, and on the left-hand side, on the overhang, there is no diagonal, therefore it'll be in tension, versus, I've done this on purpose, the truss is supposed to look symmetrical, but I've done this on purpose so we can see the difference. On the right support, the roller, we see two diagonals coming straight into the support, they must be both compression. Whether it's a cantilever, whether it's a simple support, or whether it is an overhanging truss, the rule is the same. Look at the support, see if there is a diagonal coming into it or not, and that will determine if it's compression or tension. So looking at this gate, for example, I see on the left-hand side, there's some hinges. On the right-hand side, there's the latch. So looking at the left, I see down here, this is the support side, and I see a diagonal coming into the support must be this member is in compression. Now, if you have determined the direction of compression, for example, then any parallel member to that compression member will also be in compression. If it's not parallel to it, then it would be in tension. Very good. So all parallels will be the same stress. And if it's not parallel, then it would be the other stress. So looking at this on the right-hand side, if this is the direction of compression, then this one is not parallel to them. Therefore, it must be not compression or tension. So that's this other rule that we can apply. Start at the support. Into the support is compression. If there's no diagonal into the support, then it's tension. And then go with parallels. All parallel members on that half of the truss, of the symmetrical truss, should be the same stress. If they're not parallel, then they're the different stress. So here's the outcome of our conversation with all the colors on there. Red is compression, blue is tension. And all three trusses, the Howe, the Pratt, the Warren. Looking at this example, for example, I see in the middle of this truss bridge, I see a cable. Oops, this is not enough color. Okay, let's try to increase the pen weight a little bit more. Maybe that's too much. We'll see. So there, there's a cable here. There's another cable here. There's another one over here. and then somehow they flipped at the very end, they flipped the diagonal. It's not parallel to the blue diagonals, therefore it must be red. So that's how we can read real-life situations. I have this gate here. If I look at this gate, again, I look at the left support or the right support, and I zoom into that support, and I see that there is a diagonal, in fact, coming into the support must be a compression member. Looking at this side, I see a diagonal coming in, must be compression. Very good. This is a trickier example, and I don't have a good picture. I need to go back and get a picture because this gate moves. So it is supported here and here. But then the gate, when they open it, it'll end up being in this location. So I don't have a good picture for you. I apologize. But we can talk about it right now the way it is. In this position, it looks like there's two diagonals coming into this support. Well, then it looks like that member, both diagonals are in compression. Okay, we see it here, a little detail. the two members coming into that support make it compression at this location when the gate is closed. When the gate is open, it's a totally different story. Now, another rule for you, other than trusses, if you have a diagonal member, and if the diagonal member is below where the load is to be, then the diagonal is in compression. I see over here, if there's going to be some kind of planter or something hanging from this bracket, well, the diagonal member is underneath the load. Therefore, this will be a compression member. This canopy here in the middle is sitting on that diagonal. The diagonal is under the load, therefore it's compression. Same with this mailbox. The load is over here and the diagonal is below, therefore that's a compression member. Versus if the diagonal member is above the load, then that diagonal is going to be in tension. We can see it clearly here with the pots hanging. The diagonal member is above. Had it been below like this it would have been a compression member but no in this case it is a tension member. Same over here I have a canopy or whatever this piece is and it's hanging and the diagonal is above the load and therefore it is a tension member. Here we have an example of both. In the upper case, the diagonal is below the load, therefore it's compression. But in the lower case, the diagonal is above that platform or that floor, and therefore it's in tension. We see the same here, where I have diagonals underneath the canopy. Those are going to be in compression. But in this case, they are hanging. They're above the load, and therefore, they are in tension. And that concludes this segment. I hope you're clear on diagonal members and whether they are in compression or tension. If they are above, then they are tension. If they are below, then they are compression. If there is a diagonal coming into the support, it's compression. If there is no diagonal coming into the support, then it's tension.