 All right, apples begin. Wait a minute, wrong vegetable. Lettuce begin. We were trying to find the strength of a column, which had an effective length of nine feet by being braced in the center of an 18-foot real column. It had a buckling length of 18 feet about the strong axis, half that about the weak axis. We were using these tables. We had worked out 1.2 dead plus 1.6 live or 1.4 dead I don't remember who won that fight. We need 560 kips of carrying capacity. We have found that these tables are only good with respect to the weak axis of gyration. That's not true if you're willing to get a phony K. In effect, take that r sub y out and put r sub x in. You can still use these tables. But starting always with weak axis, you've got to start with one and check the other one no matter what. It is a nine-foot long column, looking only under the LRFD numbers at a 10 by 33, not 560, not not. There's a 560 that might work. Now we need to check it about the strong axis. It's an 18-foot long column divided by rx over ry. Would you take your k sub xL divided it by r sub x over, where is that thing down there? r sub y. Here it is. Column you propose. It's a big old x. This may not work. It's got an rx over ry. It's equal to 1.71. We divide 18 feet divided by 1.71. We get a KL phony. And you can enter that into the table, even though it's not made for that. And you will get exactly the answer that is appropriate. Or you can work it out yourself longhand. And most everybody does a couple of them until they say, OK, it works. Enough of that. You need a 10.53-foot column. Since the 10.53-foot effective column is longer than the one you checked, 9 feet. That means you've got a lesser load, because you have a longer effective length. I'm not going to enter 10.53. I'm just going to go ahead and enter 11. Uh, nope. Didn't make it. Doesn't come up with the required 560 kips. So you can't use a 10 by 49. We'll next check 10 by 54. So I've got some more room to write here. Here's the information for a 10 by 54. Again, they came in for a 9-foot. Of course, they knew this was, this one already wasn't going to work. So they went to a 624 kips carrying capacity on a 10 by 54, buckling about the weak axis for which the tables were made. Then rather than going through the f-critical table and getting f-critical and finding out how much it's going to buckle about the strong axis, they cheated. They said 18-foot is the real strong axis length divided by, get the r sub y back out, get the r sub x in, 1.71, divide the real true kxl by 1.71, you get a kl phony. 10.53, I'm not going to bother with that. I'm just going to go ahead with an 11. You know, and I don't care if it's 10.53. If it's even 10, if it's even 11, it only drops to 585. If you only need 560, there's a good shape. Quick and easy, works beautifully. So we had an 8 by, I don't remember what we got. A 10 by is a 10 by 54. See if we can get a better column. Now we're in the 12 bys. I don't know how many pages I already went through on a 9-foot length, but by now I'm on this page. 9-foot length, 420, no. 560, no. 560, no. 611, yes. Now then I'm going to go find my k phony. My k phony. These used to all be 1.7. Where did this come from? This is the proposed shape. Wow, they're not all 1.7, are they? Look at these 2.64s. 2.11, 2.1. Anyway, they're divided by the appropriate r x over r y, r x over r y for the shape under consideration. So they divided 18 divided by 2.11, and they get an 8-foot, 8.5-foot effective length about the strong axis, and you don't even have to go back to the table. You already checked weak axis at 9 feet, and you know that if somebody says you need to check my phony column at an 8.53, that's a shorter column. So if you come up to 8.53, it's going to be higher than the number you've already got. It's going to be between 611 and 620. You should never interpolate, unless your number falls right in there, and you say, you know, I might make that. Don't bother interpolating. You know the number falls between 611 and 620. You know you only need 560. You can go home. Write it down. Put a box around it. Put a dollar sign next to it. Attach a bill. 12 buys. Now we checked the 14 buys. 14 buys. 9 foot. No, no. What is this? 560. No, no, no. Be sure you skip every other column. These are a lot of stress design. Yes. Wow, man. 699. I don't think there's much doubt that one's going to be okay. Well, I'm not going to bother with it anyway. It gives me that much strength about the weak axis. It's already heavier than the last one I got, so I'm not going to choose it. If you say, well, you haven't yet checked it about the strong axis, and I never will. I don't care. I mean, I'm checking about the weak axis, and it's, if it, and it looks like it would work nicely, but it's already heavier, so it's not subject to my picking it out of the set we already have chosen. I'm sorry. You don't have a use for a phony number. What's easy enough to get, you would take 18 feet. You would divide by the proposed KL over R. It would be 2.44. And you would get some kind of a phony KL over R. And it would, it might come down here where it won't work, or it may come up here where it will work. And I don't care, because I ain't going to make it work. It's too heavy. I was asked to pick the lightest wide flange. So those tables do, they work pretty nice. If you have kind of forgotten the forest for the trees, here's what we're going to do. Procedure for using table 4-1 on page 4-12. Those are your allowed load tables. For a 50 KSI steel only, the shape's listed only. In other words, those are all those tables are good for. If you got an 18 by, you're out of luck. If you got a 56 KSI steel, you're out of luck. The tables won't work, and you'll have to go back to the ways we've done before. First, you assume it will buckle about the weak axis. You get the effective weak axis length. Select the shape which will support the loads you need at that weak axis effective length. Then you check the strong axis buckling by getting a KL phony. You get that by taking the effective x-axis length, the true effective x-axis length, divided by the rx over ry for whatever you think might work. Probably already something that's been selected at this stage, but you don't know if the strong axis is going to control. Then you enter that KL phony to see the shape's capacity. You make sure everybody there is greater than the ultimate request. It is that shape will work. The tables, they have tables for angles. They're going to be 36 KSI steel. They have rectangular hollow structural sections, 46. They have round hollow structural sections, 42. That's what the tables will be based on, because that's normally what is used for those sections. Now, it makes perfect sense to me, but you know I'd done a couple of them. I wouldn't even tell you how many I did before it ever made any sense at all. I would suggest if you say I understand perfectly and you don't go try one of these, you'll find out that it's harder than you think. Practice with these things. Now, whenever possible, a good idea to provide extra lateral support about the weak axis of a column, because you obviously strengthen it the whole thing up quite a bit. If you can, that's good. If you say, look, I can't do it, then you just can't do it. You'll have to just let it buckle about the long, weak axis. Now, here is where I still didn't believe it. So I was checking the W10 by 54. You can go through what work I did and I did it using these tables and then I did it using the table 4-1, the load tables, and it checks. It worked. If you still don't believe it, like I still didn't believe it, I don't. You know, it just seems too simple. Then here's one for a 12 by 58. It's example 4-9 on page 140 for Segui. Here's where I tried just pulling the loads right out of the table with some phony things. Here's where I went ahead and actually used the tables, the equations, the tables, and it still works. Your choice. How many of these do you take a look at? There's no good examples of using both tables anyway. Here was, now this one you don't have a table for, an 18 by 58. Do we have 18? No, no, it's an 8 by 58. I thought it was an 18 by 58. So I got to say you're going to have to do that one just by hand. And once you did it by hand, if this wasn't 18 by 58 and you did it by hand using those F-critical tables, then you have one last check after that. What is that? You pick a shape using, not that table. Using that table, what do you still have to check? Once you pick a shape. Local buckling, that's correct. You have to check and see if there are any slender elements on the shape. You can quickly tell if there are any slender elements on the shape because any table that's in here will put a little C. Well, this one won't because this one has no shapes. Put a little C right next to the number. So you can go to the very first place where all of the shapes are listed and if there's no little C listed there, then it has no slender elements and you do not have to, well, you have checked it by seeing it. If it has that C superscript on it. This was an 8 by, this was a 10 by. It's a 10 by 54. This is just my solution of his example. His examples always get kind of tight. I kind of have a hard time realizing when he's moving from one thing to the next. So this is spelled out a little bigger, I think. Who controls weaker strong axis? I don't know. I just check the weak and then I'll check the strong. He says, how many things did you do? I say, one, two. I did two things. I checked the weak and I checked the strong. He says, what if I can tell you whether the weak or the strong axis is controlled right on the front end? Don't see how you could do that. And I probably would check them both anyway. He says, it's your time. He says, however, would you agree that if your K sub x L over R sub x, once you worked it out, you said, this controls. This is larger than the y numbers. In other words, the effective slenderness ratio about the strong axis is longer, meaning the column is longer than the y numbers. Well, it could be. He says, well, make that assumption with me just to see where we go. I said, okay. He says, do you agree that if you put your K x L, this right here last time was 18 times a half, I guess. It was braced in the middle. It was nine feet. This one was nine feet long about the weak axis. This one was a full 18 feet over the R radius of gyration axis. You find that this number is bigger than that number. Which one controls? Well, obviously the big one. I don't care which one's the bigger. The larger controls. Then all I'm going to do is some math. If you see me lie, you let me know. K sub x times L divided by K sub y L. That goes in the denominator. Yeah. Thing points the same direction. R x over R y. He says, do you agree that the strong axis buckling still controls? I said, well, I don't know. You tinkered with my numbers here. He said, that was the large number. Then, yeah, then I'll agree. If this happens, this, of course, is dependent on how you built it. This is dependent upon the proposed shape. There's nothing to do with how you built it. These are just the properties of the shape. If that happens, it's going to buckle about the strong axis. Thank you. He says, then would you agree this? Well, all you did was the little ends towards the R's, little ends towards the R's. Yeah, I would agree. Why did you turn it around? He says, well, because the book lists it like this. Okay. If this is true, this column will buckle about the strong axis. It says, all right, so I'm going to tell you that if you ever find a shape, if you ever propose a shape whose R sub x over R sub y is less than the way you built it, this is the effective length about the strong axis. This is the effective length about the y axis. If you ever find that ratio is less than that ratio, then what? I say, well, then it's going to buckle about the strong axis. He says, and if it's not, well, then it'll buckle about the weak axis. It has to. It's guaranteed. So what? He says, huh, hang in there. Remember, if the column you're considering has a listed Rx over Ry, less than your constructed values of kxl over kyl, cancel the L's if you want to for your column, then strong axis buckling will occur. If not, weak axis buckling will occur. He says, remember that. I said, okay, I'll remember it. Let's see him use it. First, got a column shown in 413. It's a 20-foot column. About the strong axis, there is no support. It's pen-pen. And about the weak axis, they have put two braces in here. They need a little more space, so they have a 6-8-6. The longest distance between nodes is 8-foot, so we would use the 8-foot length as the buckling length. I don't know what k is for that. I guess k is 8 out of 20 times L to give me a 8-foot length between nodes. He says, subjected to 140 surfaces, so-and-so, a992, select a w shape. Kxl is 20 feet, yeah. kyl is 8 feet, yeah. He says, the effective length kxl will control if this is true. Hang on a second. I'm not sure. Well, okay, he didn't really use this. He says, R this. This is what you and I derived. R sub x over R sub y. R sub x over R sub y. Less than kx over ky. That I agree with. He says, incidentally, you'll notice this kxl divided by rx over ry is the kl phony. Yeah, I didn't like that either. So in this example, do you agree that you have constructed your building such that kxl is 20 feet and kyl is 8 feet? I say, yeah, I did. He says, do you agree that that is 20 over 8? Is it equal to 2.5? He says, yeah, I can't help but admit it. He says, then if you go pick a column, that proposed column, if it has an rx over ry less than that number, now, wait, wait, wait, wait, let me go back here and check. If this over this is 2.5, if the column under proposal has an rx over ry less than 2.5, it will buckle about the strong axis. It has no choice. He's got me in a box. I agree. He says, do you know that this is true for almost every shape in the lobe tables? I've never looked. I saw a few. Saw a bunch of 1.7s. I actually saw 2.4 in there. He says, go back and look. Just thumb through the whole book. You'll find very few of them, almost all, less than 2.5. So he says, therefore, your column, the way you propose to build it is going to do what? Buckle about the strong axis. He says, I don't think you ought to bother with the weak axis numbers at all. Guarantee it's going to buckle about the strong axis. Now he says, not if you look down at the bottom of the table and it has an r sub x over r sub y is equal to 2.9. That one won't work. Actually, it will then. If it has a 2.9, you'll know that it's greater, so it'll be buckling about the weak axis. So he says, all I'm trying to do is save you half the work. If you don't want to try it, not a problem. You don't even have to use the KL phony. You should plan for an extra hour on quiz A, though, he says, because you're not going to get through as fast as everybody else. All right, well, let me see. You still asked me to pick the lightest wide flanks that would do this job. And it had a total load. I hadn't figured the total load yet. 1.2 dead, 1.6 live. So here we go. Piece of beauty. 1.2 dead, 1.6 live. He's got to have 840 kip column. He has KXL is 20 and KYL is 8. He says, I guarantee you it's going to buckle about the strong axis. As long as when you look at the bottom, the shape gives you an rx over ry less than your 2.5 that you got because of your way you constructed it. He's got the column load tables with a KL phony of 12 feet. Now let me see where that came from. Where did he calculate that? Where do you see that? Yeah, but okay, so the... Okay, let me go back over here because I got a bunch of stuff over here, too. Here's the KXL over ry. There's your K phony. I got ahead of myself. He knows he's going to be below 2.5 he thinks. Here he assumes it's 1.7. I don't know why he's going to assume it's 1.7. I've seen a 2.4. He says, well, you do, I admit. He says, you know what? You see, a bunch of 1.7s. Well, what if I get over there and there's not a 1.7? What does the word assume mean to you? Assume means let's pretend for a little while unless it's wrong. Then we'll fix it. So, okay, we're going to assume that we're going to run across a bunch of 1.7 columns. And therefore, we're going to use the true k over r divided by rx over ry of 1.7. We're going to use a k phony of 11.76. And if that number is not the number you're proposing for your proposed column, well, then you fix it on the spot. I say, okay, so in other words, you're saying that I can use a 12-foot column in the tables as k phony. Actually, for most of the 8 bytes, it's 1.73. So here I went ahead and did it again. Over 1.73 could still come about 11.56. I'd still probably go ahead and use a 12-foot column to study it. Even if it was 11.2, I'd probably use a 12-foot column. That's a little on the safe side. So now we go to the tables. Here's an 8-by. I'm down on the 12-foot length. I'm looking for 840 kips with a k phony of 12. No, no, no, no, no, no. Okay, there's nothing in there going to work. Here's none of the 8-bys work. That was the last page on the 8s. Here are the 10-bys. Why didn't he try 12-foot column here? Ooh, looky here. See, the guess that it was probably going to be around 1.73 didn't turn out. So I've immediately got to go ahead and fix that problem. I'm going to get the k phony as kxls 20 feet divided by rx over ry 2.16. It's a 9.3-foot column. And I'll use one a little longer just so I don't have to mess with it too much. 10-foot column. Come in at a 10-foot column. I don't get my needed 840. Is this one about the same? It's about the same. It's about the same, yeah? Okay, so I'll stick with that 10. No, no, no. See, is that about the same? No, now we're back down to the 1.71s. And that turned out to be what? A 12-foot effective length on the column. So I switch over to 12. See, switched over now to a 12. 12-foot column. Doesn't matter, it's not working anyway. 840, nope. Okay, I'm going all the way to a 10-by-54 column. Here I'm on up to a 10-by-60 column. I'm still, look at all those 1.7s, he was right. That's not a bad number just to guess. 840, 840, no, 940. Okay, so that column works about the strong axis. Now then I'm going to take about five minutes to check and see if it works about the weak axis, right? Yeah, there's a guy in the back who says, I'm not, I'm going to take a nap. Tell me when you're through. No, I'm not going to check the weak axis and the reason being is your ratio of whatever over, whatever was two and a half, and as long as this number right here turned out less than two and a half, it's guaranteed to buckle about the strong axis. So you're welcome to check about the weak axis. If you want to, you can sing and dance if you want to, but that's a waste of time. That's it, you're through. So knowing that the thing doesn't buckle, or which axis it buckles about, certainly saves you some time. But incidentally, you want to see it. It didn't take that long. How long was it truly? A weak axis? Eight feet? Well, okay, that's pretty obvious. Eight feet, you know, is sure enough is buckling about the strong axis. You say, well, I just don't want to bother, you know, to go up and check it. There it is, 1060. So you've got 940, you need it 840, there's nothing lighter that's going to work. So you write that down as a choice, a W10 by 88. Get over in the 12 buys. First off, oh, lord. So just new game. Rx over Ry, in this case, is greater than 20 over 8, greater than 2 1⁄2. So weak axis buckling will control. You don't need any phony stuff. You know that if this one's going to work, check it about the weak axis and you're finished. For this case only, that 2 1⁄2, some students on an exam, they say, okay, that 2 1⁄2 is like a magic number. It's not a magic number. Because you had a strong axis thing that was 20 feet long and a weak axis thing with a couple of braces in the middle was 8. That's where the 2 1⁄2 came from. On the exam, when this is a 24 and that's 12, you got a new number to compare greater than or less than with your Rx over Ry values. Since this is greater than 2 1⁄2, weak axis buckling will occur. I go straight up here and I find me somebody who has, I need 840 kips. Weak axis is going to control. So there's your 8 foot. Weak axis can know. Weak axis know. Weak axis know. Now, of course, you've got to be down here checking these numbers. Now all of a sudden you have a new number that's less than 2 1⁄2. Now then strong axis buckling is starting to control. So now I'll be putting in the kx phony. The kx phony. Here it is over here on the side. Kx phony is 20 over 2.1. 2.1, 2.11, who cares? That's about 9 1⁄2. It's a 10-foot length. Still not 840. Still not 840. I'm already to a 12 by 58. I'll move on over. 12 by 58. There's a 12 by 65. These numbers are all about the same again. So I'm okay just using the number I had before 12 feet. This is again less than 2 1⁄2. That's why strong axis will control. Well, feet, no. We need 840, no. Here we go. Got 887. Do I now need to check weak axis? You can if you want to. The thing was 8 feet long. It's just that quick to check it. But even that little bit, it's not necessary because strong axis buckling will control because your X over our Y is less than 2 1⁄8. Pick it, put a box around it. 12 by 79. If it's lighter than the previous one, that's our choice so far. 14 bys. 14 bys. Golly. Who controls stronger weak axis? Who controls who controls very good. That's exactly right for this particular configuration. So here's your weak axis controls at the 8 foot true length. 840, no, no, no. Strong axis starts to control. We've got to calculate a KL phony. Somebody scratched out the KL phony here. Not needed. Weak axis controls. Okay, well that's in this region. Somebody was calculating K phony divided by 3.07. 3.08, something like that. It wasn't necessary because the weak axis controlled. Then we get into the strong axis controls. 2.44, let's calculate the KL phony. 20 over 2.44 is 8.2. Go ahead and round it longer to 9.840, 840, 840. Yes. And that's the end of it. If you want to know what an 8 foot column would do about the weak axis, it'll go to 8.79. But that's a waste of time. There's a W14 by 74. I don't remember the numbers of those. We should have been writing them down. Take the lightest one. That's the one we use. If they're the same weight, then you ask the architect. Would you rather have a 16 or an 18 by in there? Well, I guess they'd rather have the 16 by. A little more room on the floor. If I say it'll cost another dollar a foot. He says, how can it be? It's the same weight. I said, well, one of them comes out of Houston. One of them comes out of Chicago. He says, go away, man. Give me the lightest. I mean the cheapest one. Now, for isolated columns that aren't part of a continuous frame, isolated columns like this. This is a frame, but it's just a one-story frame. Things either are fixed and fixed, or they're pinned and fixed, or they're rollered and fixed or whatever. Not something like this. Not a multi-story frame. Then the cases they give you in this table are probably plenty good. They work nicely. That's because we pretty well adjusted the numbers on the top and the bottom to fit just a single-story frame. If, on the other hand, you get into something like this that is either braced or unbraced, then the true stiffness to rotation of this top is very dependent upon the girder that it is welded to. And the tendency for this piece to roll is very subject to what it's welded to. Down in here, this was very subject to what it was welded to, and they almost wouldn't let you say it's fixed. They really wanted that number changed to a practical number. If it was a real pin, they didn't mind that. They said, you can come up with a real pin. Oh, there he went. There he went. Oh, dang it hurts. What's wrong with your neck? I was in Lowry's class today. Could be worse. You're going to hit your head. I had one guy fell on the floor, man. He got up bleeding, Mama sued me for boring lectures. Okay. And I've done the same thing, so don't feel bad. But it's fun to get everybody else half awake again. So what I'm going to show you here is, if you're in a multi-story frame like this where these things are pretty hard to determine whether this should be fixed or pinned or something, it's not so hard down here. Should it be fixed? No, not really. You remember we had a couple of drawings, one where it was big old thick plates welded to monstrously big footings and things. But in these, they're nicely welded. The problem is, is they are subject to rolling depending on how stiff these girders are. Now, how stiff a girder is to rolling, let me put this over to the side. This came out of our years in my 345 book. And we did a thing called slope deflection to solve for moments inside of statically indeterminate structures. And the equations were that the moment on end A looking towards end B was a function of how much the joint rolled. Depending on how much the joint rolled, the moment would be given by the radians of rolling times 4EI over L. That was how much moment would be generated in each pounds on that end. And when you look at a column and you say, are you going to buckle on me? He says, well, I'm not sure yet. I haven't really tested it. I do kick out. I'm a little out of line. Just came that way in a box. And there's no way you can get that out of there perfectly. So when they start putting some load on me, I'll kick out just a tiny bit more. And I will put a moment on here. And if this is a weenie girder, a little slim guy, I'll just pop on out to the side. And I'll roll that joint and I'll roll that joint. Say, are. Which is, well, are. If I find out this is a monstrous girder on the top and a monstrous girder on the end, I won't be able to just kick out. I will be, the points of zero inflection will be moved away from the center lines down in the middle somewhere. And it could be fixed, fixed. It could get that bad. I'll say, OK, so in other words, whether or not you buckle is really a function of the girder's rotational strength. He says, well, that's about half of it. OK, you mean because there's two girders coming in? He says, well, no, I don't care, you know, two come in. I just take their total EI over L. He says, I got to say in the matter too, even if he's there and I am, if I'm a little weenie column, when I want to buckle to the side, I just don't have the strength to roll that thing. But if my EI over L coming into these joints is a beast, then I don't care if they're there or not. I'll just say roll, and they'll roll. They just won't have much choice. So it's kind of a relative size of the bad guys coming in wanting to buckle and the good guys coming in from the sides of the joint not wanting to roll. They're happy just staying straight. So what they find is they can get a ratio of the bad guys to the good guys and that ratio will tell them whether or not or how hard it is or how likely it is that that joint will be able to be made to roll. Here are your bad guys coming in. If you've got a real heavy, strong column, when it says roll, it's going to be tough to do much about it. There's a column that comes in from the top of the joint and there's a column that comes in from the bottom of the joint. And then of course every column has a top and a bottom. Then here are the good guys. These are the guys that are coming in from the side. They were built without any rolling in them and they don't want to roll. And if it's a really large girder, then you'll take this ratio and you'll find that the little tendency to roll divided by a lot of tendency not to roll will be a low number. Or the other thing can happen. You have a beast of a column in and you've got little weenie girders in there then you'll find this number is going to be a bad number. It's going to be a large number. There's one for the top and there's one for the bottom. Since E is the same for steel, we've got here E sub C over E sub G. Is that concrete and steel? No, no, no, that's for the column. When you do have concrete columns and steel girders and things like that, then you use two E's. We don't get into that. So these are the columns and these are the girders and the E is the same for both of them so he can knock that out if you want to. Now a short reminder of this. You had theoretical and you had recommended values. You'll notice that this thing is called a braced column and side sway has been inhibited by bracing or by putting a horizontal member up against the wall or a big old another building or against a rock embankment and putting a footing in there but somewhere another the top when it buckles stays right above the bottom. Here's one that is also braced. Side sway is inhibited. Here's one was unbraced. Side sway is uninhibited. I use these names now so when you see them in a curved layer on you won't be surprised. Braced is always side sway inhibited. Unbraced, see it, is side sway uninhibited and unbraced again, side sway uninhibited. So by braced we mean something made like this. A brace and a brace. You're going to have a few more. You can't go 40 of those without going ahead and putting some more braces. You'd have too much slack in it. Or you're going to have unbraced. If the guy says I don't like those braces I say well they sure do cut down on the weight of the columns. He says I don't really care. I've got to have a door, got to have windows. Make it like that. That's unbraced, that's braced. These things will buckle like this. Things will buckle like this. Braced. Now let me save this until later. This is where we get the numbers from. The sum of the columns, some of the stiffnesses of all the columns under consideration, some of the stiffnesses for all the girders trying to stop this thing from rolling and buckling. So here's a couple of them. Just told me. Here's an example. Beast of a girder. Pretty good size column. The column under study is column 2. Column 2 will have a top joint to it. It's going to have a E or column 1 tending to roll the joint. An I of column 1 tending to roll the joint. Plus an EI and an L. An L of this member. This is going to have his own personal EI over L. He won't have his own personal E. They're all the same. But he'll have his own I and he'll have his own probably a different length. That is the columns desired to buckle. The columns want to do that. They want to roll that joint. Opposed to girders. Here's this girder. He's going to roll and he's a big old thing. You'll have to take his EI over L coming into the top and his EI over L coming into the top joint on member 2. And that ratio will give you an idea of how difficult it is for this column to do his thing when the girder doesn't want to do his thing. Down here on the other hand this is going to be a lot closer to a pin. This is probably going to be pretty close to fixed. This is going to be pretty close to pinned because it's a beefy column coming into a really weenie girder. These numbers coming in will be on the top. These numbers coming in from the side will be small and they will be bad as far as money is concerned because this is almost pinned. You could make the top fixed and the bottom fixed. You'll have a K of 0.5. Well, 0.6 or 0.65 or something practical. But if you let this be pinned and let this be pinned I can tell you what K is. K is a 1. You have to design for the full length. Here's another one. 16 foot columns. Here if you have weenie girders and weenie girders it's just pinned. It's a full 16 foot length. If you put some strength in the girders you don't put it in there for this purpose but if you have to have it for the floor if you put a reasonable size girder then this column will not be able to roll the joint as easily. In other words there'll be some moment from the girders coming into the column and they'll move this point of inflection down from 16 feet down to maybe 15 feet or 14 feet apart. Then if you could really fix it and really fix it by having massive girders then it'll come down even more. Here's one where this is pinned pinned this is not so pinned this is fixed fixed. This is the bad guy he wants to roll these are the good guys. You'll see when you work on their numbers they'll be come out with the different K's and the different K's the bigger the K gets the worse it is for you. K is zero would be nice whoa I'd like a K is zero K of .5 probably is hardly obtainable cuts the true column length by half K is one is pinned pinned some of them are worse than that you remember the flag bowls they had a K that made the effective length like 2.1 or something wow there's braced these are braced you're going to have a set of numbers for braced situations and unbraced situations here's an example rigid frame shown has these girders coming in strengthening member AB member AB has a weakening problem because the column comes in and wants to roll the joint we'll work on that one next time did homework get passed out? where did the homework folder end up? oh there over there okay you'll got them I'm sorry I guess you were here there's here thank you have a steel bar no just go on the internet and say cross-sectional area steel bars concrete bars it's not in hours no if you're talking in the steel manual I don't think it's in there sure yes sir I'm just doing homeworks normally determining the view value for the welded sections let's say this is a plate and weld section we're going to put on and we're going to go this side this side but sometimes I see it as welding like a wedge side all connected use one okay use just straight one so you don't do like you equal one minus no see the only you don't do use you got a one minus X bar over L on a welded plate no matter what the only this one is a different end table 3.1 well I'm not sure what you just said but this is the situation okay if it's welded on the end only then you is a one but you only get to count whatever the area is on the on the end or something if you need more well than that to hold it you know then you can put some more weld on the sides you is still one for that case the case where it's not still equal to one is when you decide you're just going to weld across these two sides okay table 3.1 well yeah that's right I don't remember the table number but you in effect have an unconnected element even though it's part of that plate therefore and it depends it depends on the ratio of this to this they'll and they just like give you a number to use yes okay that's I was kind of trying how they come up with it experiment and test no all this stuff was going to be effective just explain to me okay my other thing my other question I'm sorry head load one point yeah how do we calculate the dead load is calculated it's under your feet right now how thick is the slab in other words let's just say it's six inches thick so you multiply six inches times one foot times the volume that's there it's take one foot wide one foot across and it's six inches deep that's so many cubic feet of concrete they're way so much that square foot you see them on the ground right there the little tiles right underneath there seven of those go to that beam and seven of them go to that beam and so you now know load per foot that's dead load you your lab load that was your last question I just remember one more thing alright you