Trusses: 1. Truss Concepts

So let's talk about trusses a bit. They span longer than beams do, and typically they're a lot lighter than beams because they don't have a solid web. They have a triangulated web, and the triangulated web allows ducts, pipes, electrical, etc. to pass through, which a solid web doesn't allow. Anyway, looking at trusses and trying to get to the concept, first of all, unlike a beam, a truss is axially loaded. So all the members are in tension or compression only, pure tension, pure compression, no shear, no bending. Shear and bending are for beams, not for truss. Now, as a collective, these bunch of members called the truss, They do a span, and they do shear and bending on the collective, but individually, each member of the truss is either in tension or in compression. Very good. So, I have to use colors here, and red is compression, and blue, let's use a better blue, this one, okay. Blue is tension. So, to avoid bending, all joints must be pinned to allow a little bit of rotation. Otherwise, if it's a moment connection, then it'll transfer bending to the next member. We don't want bending. The next thing is all panels must be triangles. And there is a relationship between the number of members and the number of joints. and that relationship is basically M plus 3 equal J times 2. The number of members plus 3 will always equal to the number of joints times 2. If the truss is properly triangulated, this relationship will hold. Never been on the ARE, not important. So, to avoid bending, all joints must be pinned, and all loads must be on joints only because if you put this load here, that member will bend. We don't want bending. We want pure axial tension or compression. So all loads must be on the joints only. Very good. So let's look at these images and let's try to identify the violations of trussness in these images. So, first of all, this is a uniform load from the bicycles, and they didn't put it only on panel points, they put it on the bottom cord. There's bending, theoretically, so this is a violation. This one here at the dry cleaners, also there is a concentrated load, and this concentrated load is right here, due to this heavy load. and where's the joint or the panel point is over here. That member could bend. So that's another violation. In this truss, very ugly truss that is upside down, but anyway, in this truss, what is the violation? It's the joint. It's a moment-resisting joint, and this is when you have moment connections, it's called a frame, not a truss. A truss has simple joints. Very good. Now, let's transition to understanding how a truss works. Very much like a beam simply spanning, the top of the beam goes into compression, the bottom of the beam goes into tension. So, just like a beam that is simply supported, a truss that is simply supported will be doing exactly that. Tension on the bottom, compression on the top. So let me draw these. There is tension on the bottom because it's simply supported. The supports are at the very end. So there is tension on the bottom. And there is compression on the top. The top chord is in compression. The bottom chord is in tension. Regardless, if the load is gravity and downward and the truss is simply supported, the top is in compression, the bottom is in tension. And it doesn't matter what the truss looks like. So in this truss here, the top is in compression. And the top is in compression. And in the bowstring truss, the top is in compression also. Oops, it doesn't like that. Let me kill this. So this member is in compression. And likewise, the bottom is in tension. So here we have a bottom cord. It's in tension on a simply supported truss. Very good. So that's the first rule I'd like to discuss with you. It's just like a simply supported beam. And when you have an overhanging beam, an overhanging truss behaves the same. So what's going to happen here is something like this. So it's going to do that. Oops, sorry about that. It's going to do that. And so repeating the same business as with a beam, Over here, the top is in compression. Over here, the bottom is in compression. And likewise, it reverses with the tension. So this point here is in tension, the top of the beam. And the bottom of the beam is in tension. And the top of the beam is in compression. Well, the same thing happens in a truss. So here's the overhang. The top is in tension. Between the supports, the bottom is in tension. And then the rest is in compression. So what happens here, the bottom is in compression, the top is in compression, and then the bottom again is in compression. Looking at the hanging cross, the top is in compression, and the bottom is in tension. Very good. Now when it comes to a cantilever, the top is in tension, and the bottom is in compression. Oops. Sorry, I forget to remove this thing. So the top is in tension and the bottom is in compression. So that's a cantilevered beam. Well, the same in a cantilevered truss that is hanging off of a wall. The top is in tension, the bottom is in compression. So that's our first lesson. What happens to the top and bottom chord? By the way, I didn't define it, but this is a top chord, this one. This is a bottom chord, and these are web members. And the joints are also called panel points. Panel point or joint. Very good. So, let's take the second concept I would like to explain. So, the top is in compression, bottom is in tension. In addition, over the support, if you have a vertical member, that vertical will be in compression. So look for a vertical over the support, that will be in compression. So over here I have a support and another support. If there is a vertical above them, it is in compression. So this one here is in compression, this one here is in compression. In the fink truss, there is no vertical, so that lot does not apply. The same with the how, the same with the bowstring. But looking at the overhanging truss, there is a vertical over the support. Well, then that one is compression. Same over the roller, that one is in compression. Doesn't apply in the hanging truss. Okay. Now, another rule I would like to discuss with you is if you have a load, a vertical load for example, and there is only one member underneath this load. Now if we look at the second load, this one, this is the second load, there's a diagonal and a vertical. This rule doesn't apply. But for load number one, there's only one vertical, it's in green. Now, this is like a column underneath load number one must be that load number one, sorry, that that member is in compression. It's being pushed. It's like a column that load number one is going into that member. I cannot say the same over here because there's one, two, three members. I don't know where that load goes. But this one looks like the rule applies. There's only one load and one member under it. The same applies here, the same applies here, and the same over here. So let's look for this rule one more time. That's not the case for this one because this one, I'm not sure where the load goes, but it's not going into that vertical. Here in the fink truss, everything looks like it's diagonal. Looking at the overhanging truss, I see this member. That one looks like it's the only vertical member underneath a vertical load. So that one is in compression. Not the case over here because, let me take this off, because there's two members. Excellent. I don't see any more of that. I see it in the hanging truss in the middle. This load has only one outlet. Got to go in here and push down on that member, sending it into compression. With the cantilever truss, I see it in this member. Whatever this load is, that member, vertical member underneath that load, has to pick up that load. Even if it's 2.46, then the red member I just drew, the vertical, will have 2.46 of compression. Very good. So we've covered two rules so far. Sorry, three rules. The vertical over the support is zero. And if there's only one vertical load and one vertical member, that member takes that load. And then the third concept we covered was the top and compression, the bottom and tension, if it's simply supported, or else it's like an overhanging beam or a cantilever beam. Excuse me. So let's get to the next one. The next rule says that in an arch, when you have an arch, it is capable of carrying these loads. And what the arch does is it sends them this way. Down and out. But you don't put a column underneath an arch because it doesn't need that column. the load is going this way, axially. And we see that in the work of Gaudi, where he studied things with hanging chains, as in tension, and then flipped them and built them in compression. The arch and the cable are structural conjugates. Whatever happens in a cable, if you have the same form and you flip it in compression, the same thing happens as far as load trajectory. but of course an arch needs more mass than a cable. So compression requires more cross-sectional area than tension. So now to determine the force, whether it's tension or compression, in the web members or the diagonals, I'm going to look at the center of the truss and I'm going to see if I have... Oh, come on. if I have I'm going to see if I have a cable or if I have an arch. So looking at this spread truss and zooming into load number 1, I see a cable. I see a cable here hanging. And load number 1 goes down that red column in the middle and ends up down here. And the two cables pick it up and send it up to there. Triangulation. Very good. Looking at the HAL truss in the middle, underneath that load in the middle, I see an arch. Now, this load is going to go down the legs of the arch, and it's going to end up here, unlike the Pratt truss. It's split up, it's a mirror of it. Let's look at the Warren truss. Here's the center line, and it looks like underneath that center load, I have an arch. So an arch is in compression, a cable is in tension. We look at the diagonals, we start in the middle of the span and we see if we have a cable or an arch. This is assuming that the loads are equal. If the loads are unequal, then something different happens. I don't know what happens. We'll have to look at the loads individually. Very good. Now I see in the Pratt truss, I see another cable, which is this one. So that member is also in tension. And if you notice, I'm doing them in pairs. there's cable A and there's cable B if the loads are equal and symmetrical. Likewise, in the HAU truss, there is arch A and then there's arch B, this one. And arch A is in charge for load A. Arch B is in charge for loads A and B. There's two more loads here, B. So as you go out from the center, you're picking up loads, and the arch is being loaded more. The same with the cable down there. Cable A is in charge of one load in the middle. Cable B is in charge of one, two, three loads. Likewise, the arch in the Houtras is in charge of one, two, three. The middle arch is in charge of only one load in the middle. Very good. Now, let's track, let's do the Warren Trust next. I have an arch in the middle. It's Arch A. And then I have a cable, this cable. And this cable, B, is in charge of all the loads between its two ends. Sorry, not including these two loads. So it's in charge of one, two, three loads. This load here, this green load, finds an arch here. So there's an arch here, this one. So there's an arch here, and then there's another cable. See, the orientation is important of that diagonal member. So that's what's happening in the Warren versus the Pratt truss. So let me summarize very quickly here. If you have that on your parallel chord truss, if you have that, I don't care how many you have, but they're in pairs, then you have all cables. And then if you have this situation, which is the mirror of that one, And if you have an arch, and another arch, and another arch, yes, these are like that. Then you have compression. Compression versus tension. And then in the Warren truss, what we have here is we have an arch, and then there's another arch but it's farther away, and between them there's a cable. So, that's how we look at diagonal members in a flat cord truss. Now, I would like to look at the Pratt truss. I'm going to erase a little bit. I would like to look at this load in the middle. This load here. Where did it go? This one. It traveled down that vertical member underneath and ended up down here. And then it was picked up by the cable, and now it's here. Where does the next load go, the purple load? It's not going to go into the cable and compress it. It has a column underneath it. It'll go into that column and send it into compression. So this is a compression member, and this is a compression member. And guess what? These two loads, the pink and the green, are down here now. And cable B picks them up and takes them to the upper left corner of the truss. So, we're going to go symmetrically. This one is a purple and a green and they went down this column, which is red. They came down to here and cable B picked them up and put them up here. So now we have a purple and half of a green. And they join with this brown member and they go down the red column and now they're down to the ground. Okay, so that's the load trajectory in the Pratt truss versus in the How truss. Let's see what happens here. In the How truss, what's going to happen is the green load is going to come down the middle and is going to end up here. It splits down the legs of the arch. And this member has to pick it up and take it to the top. So this member is going to stretch. It's going to get longer. It's going to go into tension with its mirror image. So now those two members are in tension. And where's the green load? It's here. Oops, that's green. So now it's up here at the top chord, and the purple load shows up. And the purple load and half of green are going to take this path to the support. So they're going to push on arch B. Very good. Now, what is this guy doing? Nothing. Because you don't put a column underneath an arch. If you put a column underneath an arch, it's a zero member. It's not going to do anything because the load is going this way. It's not going to come down here. So we can take this one out, and still the arch works perfectly fine. I can remove this member, and I still have a triangle. And the load is taken care of. I cannot remove this load, sorry, this member, because somebody's got to take the green load. So that's the function of that vertical member underneath the green load. It has to take the green load. That's different than the How truss. Likewise, in the Warren truss, here is a vertical member underneath an arch, does nothing. And then for this arch, there's three toothpicks. They're doing nothing. Those are doing nothing for that purple arch. So those are zero members, all of them. They're doing nothing. And they can be removed. You still have a triangle and the load is taken care of. Excellent. Now, when it comes to pitch trusses, there's really no telling what these members are doing. Because pitch members for a roof, and there's wind, and there's snow, and there's live load and dead load, and it just got ugly. I need to know which one is the larger one. But I think maybe these guys are compression. Because they look like an arch. And this one is probably like a cable. Very good. Let's go to this overhanging truss. And with an overhang, you always look between the supports. That's one condition. And then you look at the overhang as the second condition. So let's look between the supports. Well, just ignore the overhang. Assume it's not there. Then I'm going to see an arch in the middle, underneath the load in the middle. I'm going to see another arch, and I'm going to see two cables, or two tension members. NCARB used to like to ask the question, here's a cross, which members can be replaced with cables? Well, in the previous examples, anything blue, anything tension, can be replaced with cables. Also, in steel, it is always preferable to have the diagonals in tension, Because you save a lot of money because in tension you need a lot less cross-sectional area than you do in compression. With compression you could have buckling. You're going to need a chunkier member. It's heavier. It's more expensive. So preferably diagonals are in tension in steel construction, in steel trusses. Excellent. Now let's examine what happens to this member. Let me not use blue because I don't suggest that it is tension. Let me use a neutral color, purple. So what is this member doing? I don't know. Let me see. There's this brown load on the end. It went down the red column and ended up down here. It cannot take a detour to the support. It has to be pulled back by this member. So that member is in tension. Now looking at the overhang, it's not a mirror image, and I did that on purpose. It should be a mirror image. I did that on purpose just to illustrate that this other brown load has a direct path to the support. So it's not going to take any detours. This one on the left did not have a direct path so it had to make a detour. So this one just finds that strut underneath it and goes into compression and makes it straight to the support. Well, guess what? I didn't use this one. I didn't use this one. Those are zero. And over here, this member will end up being zero, as I will explain in the next video. Oh, this one is zero because it's a toothpick underneath an arch, so that's doing nothing. Let's look at the hanging truss. It looks like this one is a cable. It looks like this one is an inner cable. And let's track the green load. green load went down the red column ended up here the cable picked it up and split it in half to two points then the purple load came in and pushed on this member so that member has to be in compression it's like a column underneath the purple and half the green and the same on the other side so that's what's happening with the members in the hanging truss. As for the cantilever, where did this green load go? This one. It went straight into the red column, now it's here. Again, it cannot take a detour and go into the red member. It has to be picked up by this diagonal. So this diagonal picks it up, and now the green load is over here, and making its way back to the top support. The second load, the purple load, cannot take a detour, so it's going to find a red column underneath it, and it's going to go into that red column, and now purple is down here, and It needs a cable to pick it up and send it back up. Does that make sense? So these members are in tension. And had they been in the opposite direction, had they been triangulated like that, they would have been in compression. I will explain on the next page, but this one is doing nothing. Very good. I hope this helps a little bit. Understand the concept of trusses. Big picture, tension or compression, top chord, bottom chord, web member, over the support, zero member is coming up on the next video.