 Okay, I'm going to, just like I'll do with the homework, I'll hand you back an envelope that's empty, and you'll put your homework in there, and I'll give it to you. You give it to him, give it to him, give it to him, give it to him, give it to him, give it to her, him, him, her, him, him, him. If you wouldn't mind taking it over to him, across, across, across, across, you'll end up with it. If you would, just throw it back on the table, or you know, so over there I'll trip over it, and I'll pick it up, something like that. There'll be two envelopes. First one that comes by, stick your homework in there. Second one that comes by will be the homework that I'm returning to you. This one here, Larry's already decided where he's going to sit. He's going to sit right, you have to move that. I'm kidding, I'm kidding, oh my goodness, Larry's going to sit there, see how he neatly printed his name so I can read it. Tell me where you plan on sitting, that way I'll be able to figure out who you are. That's right, now there'll be a big ol' in alphabetics so that you don't, sometimes you know the prop just gives you back a stack. And if your number, if your name is Jones, there's no telling where you at. You buy ready to start. Get his telephone number so that I can go and get going here. Give her your telephone number, one or the other, I don't care how y'all get together, but if we're crying out loud, let's get started here. I'll be doing that to the same thing to two guys, there you go, get his telephone number so y'all can, mm-hmm, yeah. All right, we got down through about page eight on this stuff. This kind of page number, if I add pages in between here for a commentary or something like that, see if I've got some in here, usually do, here's one, oh great, doesn't have a page number. So it'll be 11a, I'll try and remember to use that kind of a parenthesis, it's like an extension to the text. Here's something that is my page 19a, when I'm referring to the book where you can get it, I'll say you'll find it on 2-48, I use those kind of symbols. So you know, when I tell you to go look on 16.1 or something like that, if it's got these around it, I'm talking about page 16.1-122 and the specifications and if it's like this, I'm referring you to some of our notes where you can find the information on that material. One of the main problems with this whole class is none of it's hard, makes a lot of sense, but the amount of information is massive. I mean when it goes clonk, you know there's a lot of stuff in there. So when you look in the specifications, the specifications on page 16.1-7 and he tells you, you'll find some information on in appendix C, something, finding the darn thing can get to be a major problem. So you really will have to know your way around the book. Putting tabs on it of course helps, but it doesn't really lead you to the table that you're looking for. A lot of times it just says it's on a 6.16-105 part something. That plus they divide it up into chapters and parts and sections and appendices and it really can get confusing. Now once you get used to it, it's not bad at all, but until then you need to kind of get a guide through this wilderness. We may have already mentioned structural steel. I wouldn't bore you with knowing how structural steel behaves. Yield stress, ultimate stress. Stress is equal to P over A. You and I will be using a new symbol. It won't be fun. You're so used to sigma, but the whole manual and the rest of the world has moved to that symbol, a little less theoretical. So if you want to know the real stress and the structure from your 305 class, it'll be listed like that in the manual. Yield stress instead of sigma Y and sigma U. Real stress in the section, a little f, special values of the stress like yield and ultimate will be capitalized. I think we already mentioned how you get the yield stress on a high strength material that doesn't have a really nicely defined flat portion to it where it yielded. They have selected these points using about .02 inches per inch of strain. Then plug those numbers back into the equations that they're using on materials that behave a little more nicely and are more ductile, and the equations still give good results compared to testing. So that's where they're getting this f sub y when you don't have a really nice easy way to look at it. A36 steel, one of the better ones. Yield plateau plastic range, if you don't remember your 306 materials work, a lot of that is in here. Modulus elasticity is the same for all the steels that you and I use. I think the only one I know that's not 29 is stainless steel. I forget. I think it is softer, but it's too expensive to use for most of our work. So for all practical purposes, 29,000 KSI, 29 million PSI. This picture looks like mine. I probably stole it from him for finding f sub y, tells you how, .2% offset method, what steel's got in it, go to your materials class, whatever it's got in it, that's what it's got in it. It has to have that in it to be that kind of steel. American Society of Testing Materials, the people that set up the rules, they say if your steel doesn't have this in it, you can't call it A36, or you can't call it A992 steel. Here's some others. Our most common ones that you and I use would be A36, A992. These are usually for channels, angles, American standard shapes. Oops, that's a dollar sign, isn't it? I never can help that. I mean, it's not like I'm greedy, but, well, that's not true. Wide flanges made at A992, usually now, it's a higher strength steel. It is not as ductile, but it's ductile enough to get the job done. F sub u, F sub y, 36 KSI on A36 steel. What is this number? Got me again. Well, yeah, it's ultimate strength. What is the number? 50 what? 58 is a very good number, can also range on up to every now and then if you ask some part and they can find some for you and guarantee it. I think it was 80. Correct. Just somewhere around in there, but you'll be using the 58 number unless you have a piece of paper that says all the steel we mailed you that has a little red mark on the end of it is good and you can use the 80 number in your calculations. Here's his shorthand, Segui's shorthand for the AISC table 2-4. I will email you that. I thought I gave it to you last time, but I remember now. I remember I gave it to somebody. I took the other steel class because the prof couldn't come and I had those there and I thought I'd need to hand those out so I gave it to them. But I'll send you one. Table 2.4 for three steels. These are usually American standard. Used to be called I-beams because they looked a lot like the letter I. Channels, angles. These are HPs are common. I think they make it make them out of that. They're used a lot of time for piles. They're rolled especially to give you strength that is common for that purpose. And A992 for wide flanges. These two are very similar in composition and other properties as you see. How much carbon, how much phosphorus, how much sulfur. I don't know. It gets the job done. It's all I care. Standard cross-sectional shapes. Hopefully you know. Hopefully you know where they came from. They started off like this, standard American. American standard shapes also called an I-beam. They would have big old rollers. They'd be round. They look like this. They have a flat piece and they come back down. They've got a matching side and they roll about that axis. This starts out a bar or a big old chunk of steel. They force it through. They roll it and they move the rollers in. They move the rollers in, move the rollers in. They've got rollers on top. I think on syllabus, if you look down in there, it's got a video that you can click on. It goes to YouTube and they're rolling steel shapes. There's not one on there go to YouTube and say rolling hot roll steel shapes. It's really interesting how they do it. But they couldn't get any more than that flange width right there because these little corners would break off. These things, they didn't have that quality of steel. Now then they can stick a thing that's got a pretty sharp corner in there because it has stronger steels and they can roll that flange wider and thinner. Therefore, about this axis, there's how much meat you've got that far out. Now then you've got a lot more meat out there, so it's much stronger in bending. These are still good. They work nicely because of this extra thickness. They have more torsion resistance. These are pretty bad in torsion. And if you're going to put one on a roof, here's a roof girder. They are the top of a truss and of course it'll be bolted to the truss. Then you have your roofing material on the top and it's bolted to this. The roof has a tendency to slide down, putting a bending torsional moment around that axis and a wide flange doesn't really do a very good job of resisting that torque. These are still useful, that's why they still make them. There's an angle. There's an equal leg angle. There's an unequal leg angle. There's a channel. This thing here, he says, is an 18 by 50. You can also look in the book, you find a bunch of 18 by's. They just make the flanges a little thicker. They may make the web a little thicker also. So because after a while you need a thicker web to hold these two pieces together. So this is an 18 by and then it'll be plus or minus. You may find one of them is exactly 18 inches deep. Some will be less, some will be more. There's a W18 by 60, W18 by 82. What's the 60? Pounds per foot, weight in pounds per foot. That's correct. What is it in the metric system? What would you think? Tell me again. KSI? Well no, because that would again be an American unit. What are those people always dealing in? You don't go get a pound of Rice Krispies, kilograms, that's right. So it's kilograms per what? Per meter. And then I think the depth, they usually list it in millimeters as opposed to meters. You can look in the book, they have a bunch of them. This particular angle right here is started out as a plate. You'll notice you can determine its cross-sectional area without a book. And I've done that before, I've given somebody a five and a quarter by six and seven eighths inch angle that is a half inch thick and ask them how much area it had. And the reason you can do that is because you take plus six and you back off half of the three quarter inch plate thickness from which it was made. And you add six inches and you back off half of the three quarter inch thickness of which it is made. So in other words, you basically say six plus six minus t, that's what they buy to make this out of. And they shove it through the rollers and they turn it into a six by six by three quarter inch angle. Here's an unequal leg angle. It's a six by four, the large number is given first in the designation, six by four by five eighths inch thick angle. That identifies it so that you can go find it in a table. When you want to know how much bending strength it has, you've got to go look, six by four by five eighths inch angle. Here's a channel. The channels, I believe they are, they're really that depth. I don't think they come in plus or minus numbers. The American standards are usually, if it's an 18 by 70, they're usually right on the money, 18. I think there's two or three of them that somebody said, look, we really need a little more meat on the top and the bottom so they move the rollers out and maybe it's 18 and a half. So you can't say for sure how deep they are. These are nine. These are pretty close to the number. These are all over the place. There's some wide flanges in there that I think they're maybe in the 24 inch range. They range probably all the way from 24 up to 30 as people just keep wanting, give me more, give me more. So they would get to be deeper. Those are real dimensions. Well, I mean, that's nominal because it's plus or minus. But when you go look in the book, those are real. And so when it says 18.36, it means that's really how deep it is. There are tolerances, of course, but basically speaking, if you bring a thousand of them out here, they'll average out right at 18 or 18.36 or whatever's listed. This is a T, didn't used to be a T, used to be a wide flange. It's the only way they make them. They roll a wide flange half as long. You know, if they need two of them, they roll one that's however long you want it, actually, then they cut it in half. So if you tell me that you need a WT 18 by 105, I'll tell you what they made. They made a WT 18.36 by 210, that's what they made, then they cut it in half. They made a 18 by 105 T. You need to know that because a lot of times there'll be properties that you need that are not listed under the T's. Go find the property for the wide flange from which it was cut, and you'll be able to get the dimensions. It's just they didn't want to bother listing some of those things twice. There are also other kinds of shapes, bars and plates. For some reason, I have no idea why it was eight, but anything eight inches or smaller, smaller than eight inches, they're called bars, just so you know. When you get somewhere you won't look ignorant, wider than eight, they call them plates. Give you steel pipes, they can give you HSS, Holla Structural Sections. Some people say Holla Structural Shapes, that's probably okay too, but it is not stand for high strength steel. It doesn't do that. I was thinking, well, maybe I got some more pictures of them later on. More good information, round HSS, designated by Outer Diameter and Wall Thickness. Pipes are identified in a different fashion, usually by an OD and a Wall Thickness. If you need something bigger than you can buy commercially, have a beam looks like this, supported on the ends, there's the flange, there's the flange, the web is in the middle, but unfortunately your bending moment looks like this and you just can't get a shape big enough to do that. You can weld some plates on the top, weld a plate on the bottom. You've got to really want it because welding something like that's very expensive. Doubler plates are reinforcing plates. If you get just out of hand where nobody rolls anything close to what you need, you can make it up out of plates. If you don't need a lot of torsional strength, this is a quick and easy way to do it. If you need something that's got torsional strength, you close in this box and you get a lot of torsional strength out of a closed section like that. Double angles are listed, double channels are listed. I don't know if double channels are listed or not, but a lot of times you'll have two angles back to back. Sometimes they'll be jammed up against each other and bolted, sometimes they'll put a washer in between the two to make them stand off from each other to give you a little more bending moment about some axis and then put the bolt through there. What material is used, I think we already mentioned, angles, plates, American Standard, miscellaneous, wide flanges, channels, miscellaneous channels, A36 steel, piles, HPs, A572, wide flanges, A992, these are preferred. You can get them in other materials. If the guy says, I've got a lot of this and I want you to use it, that's okay. It's just that if you're looking for it, it's not always easy to find and the guy is not really geared up to send out a lot of it. Pipes made out of A53, you have no choice, that's all they make them out of. HSS shapes, A500, grade B for round hollow structural shapes, and grade C for rectangular shapes. So obviously there's your round shape and here's your rectangular shapes. Then they make a bunch of weird things, they can roll them out of relatively thin stuff for car parts and they become very efficient, they're made just for a very particular purpose. Weirdest one I ever saw, they actually extruded it out of aluminum and they use them in windows. They have all these little connector things and they snap together and the glass goes in there and they glaze it and it's really interesting why all the little pieces are there. A few homework problems are on eLearning. I doubt that the eLearning doesn't even exist anymore and homework problems. All right, here's that table. So I'll post it right along with everything else. And it's got the stuff at the bottom that you say I cut off. Now when you see what I've posted out there, you will just say jeez, what happened to this big old piece of the book? Well, that's because it's the book and I don't mind showing it to you here, but I really don't want to post it online and have them fuss about it. So you'll find big old pieces of it that I didn't do anything with, just redacted. But I got a whole bunch of notes in the middle of their stuff, well that's just too bad. They shouldn't have put their stuff so close together. So I left their stuff with my notes. Things like this, you've got to have this book anyway, so I know you're going to get it. This is a typical sheet and what page is it on? In the AISC manual, what page is it on? 1-26, and where is it in my notes? 19B, right. And you will, you'll get confused by that every now and then, because I really, the first time I got shown how to do this by Terry Cahoodic, I taught him how to do a loud and stress design. He taught me how to do LRFD. And I was, there was notes everywhere. I couldn't figure out where the things were. On one page it would refer to 15 different places in the manual. And so I try in all the notes, you know, I'll say, okay, here's this equation, you can find it on this page. And if you want to know where that equation is, it's not in the AISC manual, we derived it on our page. So that's what those refer to. Typical, here's a 12 by 58, 12 inches deep, no, no, not really, 12.2 inches deep. Architectural dimensions, engineering dimensions, anytime you see quarters and halves and things, they're just trying to see if something will fit. Here's the web thickness, there's your web, here's your flange, thickness of the flange. These are a whole bunch of dimensions that we use in our equations. We derive an equation that's got 83 terms in it. We group a bunch of the terms together, pull the numbers out of the dimensions on the wide flange and stick them in. That's K for design purposes. This is K for detailing purposes. This is the one you'll use. And anytime it says inch and a half, that's not usually something you use. Sometimes it is, but basically you're into design. K1 is used for something in our equations, but I doubt I'm going to ever see it because it's not in decimal form. T, T is the distance that you can get a plate in between these two things without banging into this radius, and it's probably used for some other calculation. And in that case, again, it's kind of a detailing thing. See if you can get a plate in there to bolt this thing to a girder or to a column. Workable gauge means it's got a flange on it. Somebody wants to put a plate on top of it, bolt it down, or they want a girder to go across the top and they want to bolt it down. You want to know about how far apart should you drill the holes. For W12 by 58, five and a half inches is pretty much standard. Coming two pages wide, left hand page gives you all of this, right hand page gives you bending strengths, gives you a bunch of other quantities that you need to calculate buckling limits on this shape. Here's your x-axis strength, here's your y-axis strength. That's R, some tough stuff. H, some zero, polar moment of inertia, warping constants. They're all grouping of terms out of a set of very complex equations that you don't want to have to calculate it. And so they have it in here for the designer to just pull it out as a single number. I'm sure you know, I hope, sigma is equal to mc over i. That's equal to m divided by i over c. i over c is known for these shapes, so it is listed for your convenience as the section modulus. That's this number here, yes. There's your channels. This particular channel is 10 inches deep. See how all the channels are all right on the money? There's the other side of that page. All right, turn it off. We know it's a very throaty machine, yeah, yeah. Thank you. Here's an angle. This is an equal leg angle, 8 by 8 by 1 1 1 1 8. Here's the bending strength about the x-axis. Here are some torsional properties. There's your warping constant. There's your polar moment of inertia. R bar sub zero for use in something. There's the other side of that page. There's the x-axis strength on the previous page. Here's the y-axis strength. Since one of the major axes is the minimum axis, that's the z-z axis, if you just stick this thing out in the air by itself and don't connect it to another angle or support it somehow, it'll buckle about this axis. So you also need z-z axis properties, including moment of inertia, section modulus. You'd use that in your critical buckling stress equation. Now, knowing all those properties, we're going to design some things. You did. You did some design in 305 because they told you that it was a simply supported beam. And they said it had a load across the top. You had to draw a share in a moment diagram. Knowing the maximum moment in that beam, you found the required section modulus. And then you went to a table like this. And let's say, for example, the required section modulus was, I'll get into some reasonable numbers here, the required section modulus was 70. Came down here about the strong axis, and you said section modulus, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, wait, wait, wait, OK. W, have to look on the previous page, a W, 10 by 68 would do the job. How much does it weigh? The 8 pounds per foot. And you went on up out of the 10s, on up into the 12s. We were looking for 70, no, no, no, no, no, no, no, no, no, no, beep. Now then that one is a 12 by 53. Well, by 53 is lighter than a 10 by 68. It saves you seven pounds per foot. You say, well, at $1 a pound, I'm not sure it was worth the trouble. Costing more than that. Costing more than $7 just to find it. That's $7 a foot. And the beam is 80 feet long. And there are 10 of them in this room. And there are 40 rooms on this floor. And there are 60 floors in the building. And all of a sudden you realize you just save those people $1.2 million. That's why they pay you the big bucks. You're the cheapest thing they got. But the way you designed it was, you said, here's a typical beam, I'll just say a rectangle. It's got a bending moment on it. You put a little bending moment on it. And the stresses went to here in tension. Now that's compression, in compression and in tension. You put a little more moment on it. And it went a little bigger. You put a little more moment on it. And it went to here. And that was F sub y. And we told you it was time to stop. Because at that point, one of the fibers failed. It yielded. That's a loud stress design. Since it failed at that given moment, then we don't want it to fail, so we're going to make you put a factor of safety on that number and back off to stay away from this fiber failing. And I don't know what, maybe 1.6 is probably appropriate or some number that is set by your peers. And so you came back down here. Basically, you took the F sub y. You cut it down by 1.6. You used that as the allowed stress. And then you designed the beam. Your criteria was when the stress in the beam, at any point, reached the yield stress, failures occurred since we don't want anywhere near failure. We divided the stress yield by a factor of safety and told you don't let it exceed this number. Would have been the same thing as taking the moment that you then applied and cutting it by 1.6. So you could find the allowed moment on a given shape by multiplying F sub y divided by a factor of safety times a section modulus. Or you can reverse this equation and solve for a section modulus is equal to the moment you need times a factor of safety where basically you're raising the moment divided by F sub y. That's either design or analysis. M is the moment caused by your American Society of Civil Engineering mandated working loads. What was the working load for this classroom? 40 pound per square foot. What is it on the second floor? Hallway, 80, some of you got minds that boggle my mind. And on the first floor, what was the loading? 100, right on the money. You say, I don't know how he knows that. I don't either, have no idea. But it's impressive, it really is. Of course, if he just said 120, I'd have said, yeah, yeah, yeah, yeah. Because I don't remember, but I know where to get them. I go to the ASCE and I ask them, I say, are you the load guys? And they say, yes, we are. We've got a lot of ladies in here too. I say, OK, are you the load people? They say, yep. I say, what is the loading on us so and so, so and so, under so and so conditions? Bingo, they gave me the number. Those are the working loads. Or they're called service loads. That's one method of design. Now, mostly a gentleman called Beatle decided that that was nonsense. And we said, OK, what is your idea? He says, the thing hasn't failed. I said, well, they said it failed. It got outside of the allowed stress. So many things got a tremendous capacity left in it to handle load. They were, OK, show me where this excess load is at. He says, OK, well, put a little load on there and tell me what you get. And for a uniform loaded beam fixed on each end, it turns out the moment on the ends is twice as big as the moment in the middle. So at some point, this thing reaches f sub y. About that time, the allowed stress guy is jumping up and down. Nope, nope, that's it. No more, no more. Don't put any more load on it. He says, ignore him. Get f sub y on both ends. Get f sub y over 2 in the middle, because of the moment diagram. Moment diagrams here comes up half as big, comes down like that. He says, pour it on. Well, first thing is this fiber right here can't go above f sub y. So as he put from w1 to w2, this fiber yields, and this one yields, and this one yields. And first thing you know, this stress distribution looks like this. And of course, the allowed stress person is apoplectic by now. He's laying on the ground in a fetal position. And he says, my guy says, pour it on. And so this joint completely yields, and this point completely yields. Every fiber has yielded. I mean, those little fibers are here and here and here. And he looks at me and says, does anybody die? I says, no, no. He says, can we quit? Should we quit? I say, yeah, I think maybe you ought to quit. He says, bull, look at these fibers in the middle. They just now reach an f sub y in the middle. Pour it on. Bring it up from w2 to w3. And these stay the same. You keep on straining them, and they keep on moving out down this road. But what the heck? You know, we still got this we haven't even talked about. He says, pour it on. First thing you know, though, these fibers all go plastic. These fibers all go plastic. And then these two also go all plastic. And this thing becomes, it's got a moment. It's got a moment. It's got a moment. But any more load, it won't pick up any more moment. So it doesn't actually collapse because of this, but we call it a collapse mechanism. Have tremendous additional load carrying capability when you use plastic design. Kind of hard to talk people into because the thing, when you said the word collapse, everybody kind of backs off like, ah, I don't think I want to do that. But it works. And you're permitted to design by that. Then we have what we call load and resistance factor design. It's kind of a blend between the two. Number one, we're not going to drive it till we get three hinges and a collapse mechanism. But we are not going to worry about the fact that some place in the structure, we have completely yielded all the fibers, because we know there's more strength beyond that. Times this class over, 1220, OK. It's similar to plastic design. We don't use the collapse of the whole structure. We only allow one plastic hinge or one plastic point to form in the structure. The nice thing about the plastic design is when this load was failed here and failed here, the load found another path to go where there was still some strength. Namely, it was nothing more than a simply supported beam with some great big moments on the end. Simply supported beams, we use them all the time. So they'll start out with reaching some bending stress. At some point right here it looks like the fiber will reach f sub y. At the same time this fiber is here, at this time the fiber is half of f sub y. No stress at the neutral axis. You keep on putting moment on it. Then this fiber would like to move up above f sub y, but it can't. And so this one goes to f sub y. That one goes to f sub y. We're going to use that moment as our limit state where the entire section has reached yield. Now then another thing about this, kind of unlike a loud stress design, we added a factor of safety of maybe 1.6. Sometimes the people who did a loud stress design say, you know, because these loads don't happen very often because they don't last that long. And maybe when you have those kind of loads, we'll let you change that factor of safety to 1.4 under certain conditions. OK, well now I kind of got two factors of safety. These people take no prisoners. I mean they give everything a factor of safety. I got a dead load. They say, I don't believe it. I think it could be bigger than that. I say, yeah, you're going to have a factor of safety. How much you want? And they give me a number. Then I got a live load. And I say, and this is the live load. Comes right out of ASCE. They say, oh, we don't really believe that at all. Ooh, I get a feeling he's going to put a bigger factor of safety on the live load than he did on the dead load, which is certainly appropriate. Then we got the wind load. It gets a factor of safety. You don't have the earthquake load. It gets its own personal factor of safety. Then we have the snow load. It gets its factor of safety. Everybody's got his own factor of safety, pretty nifty. So there's nobody in there just gets a factor of safety just because he got in that box with somebody else. Then we start talking about how strong is the piece of steel? He says, what is it? I say, it's piece A-36. He says, what are you going to do with it? I'm going to make a tension member in our trust. He says, how are you going to connect it? Well, I don't know. It doesn't matter. But I need a factor of safety. No, no, no, no. You bolt it. You hurt it. And you're going to have one factor of safety. And if you weld it, you don't hurt it. And you get a different factor of safety. So not only do the loads have very personal factors of safety, but the materials themselves and the way they're used get very personal factors of safety. Some of those are called resistance factors. Some of them are called load factors. Load factors raise the load from the ASCE numbers in a very personal manner. Resistance factors lower the ability of the member to resist loads by very personal. How are you going to use them? And that's one of the real advantages of this method, not to mention, of course, the fact that this is permitted in the design. You really all know what LRFD stands for. It'll help in understanding what the dickens we're doing in here. You say, well, I know it stands for load and resistance factor design. Yeah, but what it really is, it is load factor design. And resistances also are factored in the design. Load and resistance factor design. The whole idea in a loud strength design is where you tell me how much strength you require. You go calculate how much strength is allowed. You make sure that your required strength is lower than how much is allowed. Usually by a single factor of safety, perhaps modified in some cases to some amount to try and take care of gross problems where the factor of safety just didn't apply. Unlike in LRFD, everything in his brother will have a factor of safety. These strengths we're talking about, axial force, bending moments, torsional moments, lateral torsional buckling, compressive strength due to buckling, shear strength in the web on the ends of the beams. I don't care what you're calculating, the idea is the same that the required that you should be able to calculate from statics or from 345 or from Mastan or a computer program, how much is necessary when you put the loads on there has to be less than the allowed strength. These loads would be this strength to be calculated on the basis of just flat right out of the AISC book. And then the allowed strength would have a factor of safety applied to it. I got the message. Thank you. He says, this is a loud stress design. We already talked about that. He says, we have loading. We have, where's our plastic design? Here's the plastic design. Here's how you do the plastic design. Load and resistance factor design. The same idea. You'll notice a little difference in the word. Unlike just saying the necessary load that I need to carry, it is now factored. It's AIS, it's A-S-C-E loads of service or working loads that are bumped up by personal factors of safety. That will be the factored load. Factored strength. This actually consists of 10 terms. You'll factor the dead load plus then you'll factor how much lab load that goes with it. Then plus you'll factor how much snow load goes with it. And all those personal things factored goes on this side. Then you only have one thing here, one strength. If this is a bending situation, you'll have a bending moment under different conditions. You will have different factors of safety. So there's only one term that goes on your strength side. This one here will consist of several terms. That's what he says here too. There's a sum of the service loads times their personal load factors, personal to the type of load under consideration. Has to be less than your theoretical value that you got out of 305. You'll have to bump that number down by personal resistance factor. There's only one of these because there's only whatever kind of resistance you're talking about. Shearing the web, that'll be a good one. Bending strength, that'll be a good one. I think we really already did that. The only difference is there's a few numbers on there. You'll stress over factor of safety. That must be a loud stress design. Design the lightest beam. Here's an example of you and me using plastic design all the time. In 305, if you remember, when you had a hole in a plate and you pulled on the plate, we had stress concentration factors. Sometimes these stress concentration factors got up to two or three. When you really pulled on the plate, the stresses were small away from the hole and very large around the hole. And if this is a piece of glass, I seriously need to know this number. But if it's a piece of steel, I don't much care. But if it's a piece of steel, as you keep adding load to this structure, first thing you know, this fiber will reach f sub y and it will stop picking up load. It'll go right on that flat part. Then this fiber will reach f sub y. And as you keep adding load, this one will reach f sub y. Probably when that one's reaching f sub y, this one really may be on up in here, you know, a little bit, it's possible. But just holding it down to f sub y, I can pretty safely tell you that the load that this thing can carry would equal to this cross-sectional area multiplied times f sub y, every little fiber. I don't want it to happen many times. I mean, if it even happens many times, we've got problems. However, my guess is enough deformation will occur that you'll know it happened. Somebody will come screaming out of the building. I say, it's gonna fall down, it's gonna fall down. It's not gonna fall down. I don't want to be in it either, but it's not gonna fall down. It is just yielded excessively. Say, Joe's still in room so-and-so and he can't get out. Yeah, well, that's because he's got too much deflection and the doors are jammed. But it's not gonna fall down. We'll beat the-