How Trusses Work! (Structures 5-1)

hi i'm paul kasabian i'm a structural engineer and this is a piece of paper again and what we know about paper that is when it's flat it doesn't do well in compression but it does do well in tension right so if we put the two together on a piece of paper i drew on earlier and we have blue representing compression where it's going to represent tension i'm going to hold the piece of paper at one end only it's what we call a cantilever and then i'm going to put a force down at the other end using this other hat right and when i do that this happens right so you can see the red line that diagonal that's still in tension it's straight and it's taut in that diagonal direction from my nose corner to the opposite diagonal corner whereas where the blue lines are that's in compression you can see the paper has kind of buckled along that diagonal direction so using tension and compression if we wanted to we could make that diagonal stiffer to be able to take compression and or use the diagonal in the red direction to take tension whenever we're dealing with a cantilever and an end load and so this is the start of trusses because this is trust behavior tension and compression working together diagonally so let's look at this in more detail first a reminder of where we've come from remember we did cables that were only in tension flip that round to be arches only in compression columns as singular compression elements and today for the first time we're putting these things together we're putting them together to form a trust tension and compression working together and excitingly the first time we're dealing with spanning a distance greater than the length of the pieces that it's made from otherwise known as structures so as we go through here's a first example i'm going to be building up a cantilever for you and then making it a truss that spans a distance that's where we're going with these diagrams so the first diagram here we've got tension in red compression in blue and a weight at the end this is representing exactly what i showed you with the piece of paper when i pull down on one side and we saw the direction that the compression was going on on the diagonal and hear the tension and in this case we have a set up where both can exist now this is a structure may look a little weird so we can change it to sort of something that we're more familiar with seeing and this sort of makes more sense to most people there's a weight at the end we're pulling it um up using the hand that's in tension and because we're trying to have it as a cantilever the hand that's in compression is pushing it out so allowing it to be further away from the supports now if we go and expand this a bit and you'll see as i build these diagrams up the weight stays in the same place and we're going to expand the cantilever to one side we're dealing with more structure here by going a further distance we'll introduce this additional compression element and this additional tension element and we have again tension and compression on the diagonals they're balancing each other out and in terms of their horizontal load and they contribute to carrying this vertical load through to the back of the cantilever if we go again we end up in an interesting scenario where you have to trust me on this but this is physics the tension in this diagonal and in this diagonal are the same why because essentially the weight that vertical weight as it moves across the cantilever stays the same right but this blue compression here is darker than this blue here because as we go further back in the length and span of the cantilever the compression along this base is going to increase because something has to do more work as we do a greater distance and back further still these two red diagonals are the same these two blue compression diagonals are the same but as we pull back we're getting a darker red here than this red a darker blue than this blue because that that's where there's increasing force to manage what we're dealing with now um we normally don't want on the next image what i'm going to show you is is flipping to vertical impressions why because if i go back to this we don't always want longer compression members remember we dealt with this in the columns video i showed you where the length of a compression member matters quite a lot so we can shift some of this around in this way to make those compression elements as short as they can be basically going straight from top to bottom and leaving the diagonals in tension that's generally a good idea when you're dealing with any mix of tension and compression elements now what i'm going to do is flip this around i'm going to mirror this which is going to look a little odd but there we go this on on this side that i'm showing you was the same as i showed you before its mirror is over on the other side and we have here sort of weird seesaw structure right um but it's following the logic of what i showed you before we've got weights on either end and a support in the middle i'm showing this to you because now we're going to flip the weights to supports and the support to a weight so all tension and compression is going to reverse but all geometry otherwise is going to stay the same so watch this there we go right i'll go back see that the reds and the blues are going to switch now i've got supports at either end so we've got the weight in the middle now being carried back with compression diagonals because that's reversed from before and we've got the verticals in the middle between as carrying tension and remember this is what i showed once before we're now going to try and measure the weight of the structure itself it's a measure of material efficiency given how we're choosing to lay out our structural members that make our whole structure like that gets to be our choice if we understand the behavior so let's make that switch that we did before now that we have this spanning truss that's really what we have here right this this moment of a spanning truss so we're going to make those uh compression members vertical only so that they're shorter and we're going to have the diagonals in tension and now what we're seeing is something that it's we've got a more efficient structure it's lighter as a structural weight in terms of the usage of material and you may remember um this image from the very first sort of cables video i did so what i want you to see is that just we're building up these pieces because that's how they behave and they don't change their behavior just as we start adding them and making them work with other types of structural uh items so the v-shape that you're seeing in the truss makes sense essentially you could almost see this outer ones as being part of a broader v as well because that's how cables want to behave right so and we've got a series of kind of columns propping apart the top and the bottom we also have compression along the top and tension along the bottom so if we now look at a bridge example of this and i like this one because it's a very simple bridge but it clearly shows what's going on in terms of member sizes right we've got tensions on the tension on the two diagonals as i'm showing here and the vertical members which as short as they can be those are in compression which is why they're a little chunkier than the tension rods that you're seeing here we can see this again in a longer span bridge even though it's a photograph on the skew now that we know how things are behaving we're going right okay here's my tension diagonal as part of a border v and here's my compression vertical and that makes sense because the compression vertical is i will call it chunkier but it's chunky in terms remember how we distribute area it doesn't have to be solid just like i showed in the column video but it's broader there's a lot of members lacing it together to provide overall stability to the compression prevented buckling so back we go to our typically very efficient spanning truss right like we've saved material weight from what i i first showed you how about we try and make these compression members still by sort of bracing them off what's going to be called a k truss now that sort of did some things it's a little weird a bunch of the forces started to go in different directions and in fact if i go back and forth you'll see that didn't really help us as much as we might have hoped it would um given we we had a good thought and sort of wanted to implement it but as with many things and you have to try something new to get ahead so let's consider this one step forward before going two steps ahead which is that we're thinking about a better placement of some of these nodes to allow for reduction in the length of all the compression numbers and an increase in length for all the tension members if we could somehow maximize that for tension minimize for compression then then we would be getting to a more efficient structure and what that ends up being if you actually study that is this form this is an optimized truss right we've now moved some of these a little bit into different locations than they were before but you'll start to see not only does it sort of look quite beautiful but also quite natural which is maybe why we think it looks beautiful in terms of what we're used to seeing but what we've also got here you might start to appreciate is what looks like a series of arches right overall going compression and a series of hanging cables going through it right like we've we've essentially taken ourselves out of a more rectilinear land and way of thinking and expanded it i will counter this with the note that you see there's no more sort of triangles in this section this is a very optimized truss because it's optimized for this load in this location it would not be optimized if this load moved around or there were lots of different loads right so when you have a limited situation or something that you can control you're more able to optimize for it but even so this gives us the minimum weight truss in a way that is tension and compression working together with pieces that are smaller than the eventual span that they create to provide a very efficient and beautiful structure and that's trusses you

Channel: Paul Kassabian

Views: 10,851

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Id: KJdIbCn4NuE

Length: 11min 19sec (679 seconds)

Published: Sun Mar 14 2021