 Okay, if you remember, I'm sure you do, because you're all right, we were looking at the design of prismatic beams, where we were specifically now choosing a particular beam for its characteristics, not just the usual stuff we've done in the past where we might say, well, maybe a B of a rectangular process should be such and such, but actually picking a commercially available beam of some kind. So we'll review that with a problem here and then we're gonna take a step beyond it. So we've got a 16 foot beam here with a slight overhang and some kind of uniform blow, 1300 pounds per foot. Perhaps a snow load or something like a uniform load like that. And you're given two things that the allowable normal stress is 24 KSI, so by that, I guess it implies that the material has already been chosen, the beam itself has not, so you're gonna have to specify a particular beam that will satisfy these two constraints. So I'm also gonna put on an allowable shear stress. So by means of those two, I'm gonna move them over here because as you can remember, what we need is the location of, not the location, the maximum moment to look at the normal stress and the maximum shear to look at the allowable shear stress. So both of those, some students do very well without a, so they should actually go fairly quick to form a load like this or just a single point load. Those shear diagrams at least tend to go fairly quick. If there are any actions, then you can almost draw the shear diagram in a few seconds. And then once you see that, you should be able to pick out at least the points of concern, the maximum moment for what we're looking for is a normal stress when you do a certain, what we call the section modulus. For the supports, maybe check with each other just to make sure you got those right before moving on. I know all the moments should be able to come up with these. You can plot two points, of course, to start a slope in between realizing there's gonna be a big jump in the reaction there. So remember, slope's 1.3 kip. So just to put it to scale, it's gonna look something like this, and then remember these two lines fairly quickly, basically that. And then you can use those two slopes to figure out what's going on with the moment. You don't need to actually calculate the moment. Just look at it a little bit to figure out what's going on, that's not Fj. You know what, start zero moment. Do you not? Because there's nothing at those ends to withstand any moment. You know the moment will be zero, that the slope of the moment will be zero along that line. It darts out pretty steeply, drops to zero. The slope is gonna be something like that. Then it continues from zero down to some big maximum. Maximum slope, it's like it might do something like that. And then it jumps instantly up very steeply and drops to zero again, which would be something like that. And so you've got two spots to check for the maximum because you're just not sure what your scale is here. You've got to check that spot and you've got to check that spot, which is pretty easy to do because you can just do it from either end. Shape, you're just not sure of the scale. Column those makes sense, now you see them? Just take the left end, go back to the support. Reaction here, 16,000, 16 kip, there you know that. There must be then some moment back like that. We do expect negative here, I'm not sure what we are. It would be positive, 23, 4 is what I got. The moment at this point here, kip, t, it's a moment. So you can protect with a maximum section modulus the allowable shear stress. You will now that you know the maximum moment and you know the allowable shear stress of a minimum section modulus is the maximum moment we now know over the allowable normal stress. It'll be the only 6.7 over here. By the flange, I mean these things, they come in, the tables come in two sets, an SI set and an English unit set. Make sure you're on the right one. Five beams, you're not going to get that, it just divides straight away there. So you have to check that, the very end of the class on Friday. As soon as you do that, have to check to make sure the weight of the beam you choose doesn't put you in trouble here. Once you get a beam that exceeds this S, then you want to look for a beam that has the lightest, linear weight. Other factors that are maybe size limits or something, but we're not actually designing buildings we're just working towards it. You have a beam in front of you, just above the S you've got there on the calculation. A couple percent above, 20 percent above maybe. Bobby, any look better yet? I don't know. God, that's a great one to be in, isn't it? It's huge. And to have a special on this week, we've got a 16 flitters over here in just a few minutes. Girls standing by, operators are standing by. I think most everybody, Colin, you got a beam? Got a couple good for a couple others to see if you can come up with a lighter second number. Most of us are zero and I'm a 12, 14, right? With a linear weight of 14 pounds per foot, but our load is 1,300 pounds per foot. So it's unlikely that's gonna be a big concern for increased normal stress. So then what about this year? There's a couple others, but they all have bigger numbers here at the second part. For the 14, there's a couple of 15s that look good. What then do you do about this year's stress? Just to get that, they didn't actually do the calculation off on your weekend by then. This stuff happened Friday classes for a while for people's Saturday weekend, Wednesday noon. Okay, then you gotta check the shear stress to make sure we're not over that allowable limit. We know where the maximum shear is or what it is. We're not so much concerned with where. We're concerned with what. We use here, Pat, remember that? Are you on that part yet? No, why not? Who's the flanges? Flanges carry almost no shear. Remember, the shear is a maximum in the center of the tapers to, well, tapers to nothing in the end. So, conservatively, we take the flanges out of that, just use the area of the web, which is right there in the table. There's the web thickness, T w. I d minus twice the flange thickness. So that went all the way back to a new S value, because it was, I forget, what was it? 1240. S on the 1240 was, or 1214. What came from that? Yeah, you've got a pretty good margin there. That's almost 30%. Well, the last one is 13.7. 13.7. Is it? Okay. 13.7. With just the 14 pounds per foot? Yeah. Had it on? It's only 1%. I can even draw that. 224 pounds. Do I have to do it in the end? Good. What did you say? How quickly do you want to be down to the principal's office? My goodness. The microphone didn't pick that up. Never, in my face of truth, never even going up against Bob's hard enough, but now you just made it work. Because that number you have there is this jump. Right? But that's the maximum shear we have to worry about. And to protect against the 8.8 per square inch, so if we have the area in square inches, we're okay. Something like what, 3.5 is the expected shear stress. 3.85. Yes. 3.8, okay, that's what I, that's 3.8. So it's okay, I'm sure it's the maximum expected shear is this point right here. Just just before the last support, and then provided by the area of the web. If you're doing a real quick calculation, you can just do a TW times D. But this is a little more conservative because we get less area, greater expected shear stress. And we want to make sure that we're under the allowable, which we are by quite a bit. Bob, that okay now? Are we using the D-share example? Yes. As long as the units are okay, which it is. They're in inches, right? Yeah. Everything's in inches, so we get kips per square inch, KSI, which is what our allowable stress is in so we can compare them. All right? Okay? You walk in this building, you send your loved ones out, your little brother will pay because it's a stolen truck. That little brother, you're not in the truck. Did you have a truck? Toy truck? Maybe that explains you think you don't have any toy trucks. All right, any questions before we go into the next phase of this beam design? Okay, here's the next thing we've done. These have all been prismatic beams. Do you remember the definition of prismatic beams? Same material throughout, though we can handle if they're not with our non-similar material techniques we were using a month or two ago. What else is part of the definition of prismatic beams? There's three parts to it. We've got ones, all the same material throughout. Isotropic, same material throughout. Something to do with the y-axis. What was that? Y-axis symmetry. Symmetry about the y-axis. This part may not have been as obvious because it's always been the case. So it just really may not even come up. What's the cross-section all the way down the length of the beam? It's certainly to our advantage to at least consider now if that's something that's important. The most obvious example that you've seen is imagine you have bookshelf. You've all seen those type of bookshelves where you put a track against the wall and then you clip the bracket into that track and then you put the shelf on those brackets and then you lay the book just along the bookshelf. What do those brackets look like? They're not uniform cross-section beams. And they are beams. They're loaded beams just like any other beam we've been looking at in this class. What do they look like? Aren't they much more? With this kind of load, there's a lot of moment back here so you need a lot of material. But as you go farther out on the shelf away from the wall, the moment decreases so decrease the material too. There's not as much to carry. In fact, as you get to the end of the bracket, there's no moment there. Might as well have no material and that's where the bracket ends. So the brackets are essentially long-gated triangles. They might have a little more shape to them. The type of you've probably seen are the ones that have a little hook like that. That helps hold the shelf in so it doesn't slip off. And then there's a little bit of design to them like that. But these, and even though it was to some degree, are very easy to make. They're made out of a constant thickness plate and they're just stamped out. And it's really economical to stamp two out of those out of a little section. All you have to do is have those hooks that go into the track. Usually looks something like that. And then you get two out of a single piece and you're not wasting any material by selectively designing the cross-section to best meet the load at those points. So we're gonna take another problem, very, very straightforward one. We'll keep this one kind of simple so we're not bogged down into details. Let's start with a very simply supported beam and very simply loaded. Proudly kill Newton on an eight meter beam. Not as simple as we can get. In fact, I think we started the first week with just that type of thing. Now here's the deal. Imagine that we've already got beams in stock. We don't wanna order new ones if we can use up these ones. Have a whole bunch of eight meter beams sitting around. Earl gave us a big special. I took a chance. I bought them all. Now we've gotta see if they can do the job for us. So here's the beam. Oh, I gotta make sure. I can't remember if this beam's in the book. If not, I'll just give you the numbers. Yeah, this beam, our book doesn't go quite up to what this beam is. So we've got a couple W690. By 125 beams in stock. Now don't bother looking it up. I'll have to give you those numbers. The cross sectional area is 16,000 square millimeters. Section modulus is 3510 times 10 to the third. Here's cubed. And the moment of inertia. Let's see what the expected moment is. Oh, by the way, the allowable normal stress is 160. Let's see what the shear is real quick. Shear diagram, because from that, we can almost instantly pick up the moment diagram. Obviously with a nice symmetric loading like this, single point loading will have 250 kilonewtons. And then since the load curve is zero, then the slope of the shear curve is zero down to minus 250. So real easy to come up with the shear diagram, which makes it then real easy to come up with the moment diagram. And I want to pay attention this time to where the maximum moment occurs. Let's see, the area of that 250 times four meters constant slope. So we know the moment diagram and that this maximum moment is 1,000 kilonewtons of meters. And it happens at the center. Make sure it's okay. We've got about 10,000 moments stock. They're down by the stocking fields. We've got the allowable normal stress. This beam is already in stock. So the section modulus is already chosen. And you know what the maximum moment is. What do you get for the stress limit for that beam? 285, it comes out to be 285. 1250 times 10 to the third. So the S we need is much greater than what we have. That's right. So why doesn't then this come out to be, are you sure your units are okay? Easiest one to do is change the meters to millimeters. Yeah, we've got megapascals times 10 to the third. And that will be, because this battle give us the, that will give us the millimeter squared on the bottom, which we don't want. 1,000 per meter cube per square meter, which is a kilopascal. Now we make it a megapascal. So what's that come out to? Times 1,000 squared, what, a billion? Well, as long as it matches, as long as it's megapascals. Why, I just need the actual problem. Dude, you checked yours and your S is still coming out low, but this is coming out, okay. So where's the problem? Who's up the whole problem? All the units, right? So you said you'd give me 508. Huh? Yeah, it's not. Okay, I'm sorry. We had what we wanted. I don't know, you were acting like it was okay. And so I was paying attention to the details and missing the ideas here. Yes, so that's too big for this, so it's gonna fail. However, so what it turns out is that this beam is okay for part of this load. Somewhere, maybe in here, the beam's okay for the ends, but not okay for the middle. So what we can do, our I-beam felt bad about this. So what Earl's done is made available some steel plate that we can weld on just for this center part portion against that so we can use the beams we've got, bolster them up a little bit where we're worried about them and come up with a beam that has enough of a section modulus because this will increase the section modulus by quite a bit, a lot of area away from the neutral axis. And then we can do, we can increase that significantly. So here's what I'll do for you. I know most of you are a little disappointed about that test score. So do this as an extra credit problem for Friday. Just throw 10 points on the test. Up to 10 points. So what you need to come up with is two things. How long should these plates be? How wide? Our 16 millimeter plates, 16 millimeter plates deal. So if you're watching the video, you weren't here, deal's not opening. Once we add those plates, that will increase the protection. Still a little bit more than we need, ideal would be if we had plates that actually tapered at the edges. But that's too much work. We just want to throw in some steel plates there, weld them on, you need the length and this width of the plate. The length you can determine just from this diagram. Where is it that the beam no longer can support the load that's increasing as you go towards the center of the beam? The moment's increasing from the ends, the beam's okay for a while, but then sooner or later it's not good enough. So you need to find that point, that'll give you L. And then you need to find B such that the section modulus increases to this new value here. But this was insufficient for this. So we're going to increase the section modulus until now it's enough to withstand that load. And that will determine B because that will be part of the section modulus over C. So C is increased, but I is going to increase by a lot more. Is that a deal? A little outside of the test, but I know you wanted some help here and this isn't that far removed from it anyway. Yeah, Freddie? You look nice, you have plenty of time to do it. On.