 Howdy. Well, y'all made it back. That's good. Got an interview. Who you going with? All right. Last time we had done beam base plates. Is that right? Is that what those were called? Beam base plates? Beam bearing plates. Column base plates. That's correct. Because a column has a base, so it needs a base plate underneath it so that it won't overstress the concrete. A beam got ends on it. It's got reactions. It does need to bear against the concrete. Also, this is not a base plate. They're done differently. The main difference is when you have a column pushing down on a steel plate sitting on a piece of concrete, the bending, I'll show you in a minute, occurs. These corners tend to wrap up in one direction, and these corners or these sides tend to wrap up. In the other direction, that's two-way bending. Whereas if you have a beam with a bearing plate underneath it on a piece of concrete, I really should have shown you an end view. They don't sit that way. End view. They tend to wrap up. These little sides of the plate tend to curl up just in one direction. One-way bending instead of two-way bending. So it gets a little more complicated. This is the equation that we derived. It's in your manual on page 4-16. So in one of the pages that you and I just did, it's used for a plate bending of any kind. If you got a plate that hangs out a dimension L, you'd have to decide what you think L is. If you think L starts right about here at a distance k, then how much it hangs out? That was L, two times the load carried by the plate through the column or through the beam, divided by there was our phi in the equation, nine-tenths. B times N, that was the area of the plate in yield stress. So go back and check the derivation. It's actually good for any plate that's got a little cantilever hangout on one or two or one or more sides. The piece of view in the equation is merely your request for load coming in. The stress that would be underneath the plates we're working on now would be the total load divided by the size of the plate, base times N. If you remember, a lot of my notes had N in the beam bearing plate stuff, because in the older codes, here's the concrete, the older codes, they call this N in a beam bearing plate, and they called this N in a column base plate. And people were getting confused and so they said, okay, let's just change the name of how far this goes back from N. We'll change you to the length of the bearing plate. That's what caused the change in the notes. The equation is the same. Sometimes you'll see this stick-out cantilever length brought outside just as L. As long as your plate's thicker than that, it will be acceptable. You know, I did say that was not in the manual, and that was true about five additions ago, and it is in the manual. Thank you. So write it down anyway. I remember that now, yeah. Page 4-16. Is that right? Did I get the wrong page number? Probably off an old manual, too. Let me see what somebody got. Let me see a book a minute. It's in the bearing plate stuff. Well, I'll fix that. I thought it was 4-16, but you ought to see, you know, have this equation right here somewhere around there. All right, so check that. Old book, but not so old they don't have it. At least I know I saw it in there. I know it's in there. All right, now then, first off, you've got to know how long these little cantilevers are. How long these little cantilevers are, you probably would think, well, the little plate underneath this wide flange hangs out this much. What we really find is there's so much moment right in there that it actually bends a little further back than that. So they make you say that the thing hangs out M. But to get M, you take the total dimension N of the plate, you subtract the depth of the beam, you divide both of them by two so that you have this dimension here, and then you back off a little back into the flange of the wide flange. 0.95 D is how far it backs up on for both sides. So we'll see an equation for M in a minute. We would say that N cut in half divided by D cut in half, minus D cut in half, but you only want this dimension so that you're back into the flange a little bit. As far as the width is concerned, you might think, well, the little cantilevers pretty much come out from the tip of the web. But even then, there's so much moment that it actually pries underneath that a little bit. And in this region, in here, the little cantilevers are probably even longer than that to some extent. So they make you bring the back of the cantilever, the fixed point of the cantilever back, so that this dimension is 0.F times the flange width. That would be B over 2 minus eight tenths, four tenths of the wide flange. That puts it back in here somewhere. It makes it a little longer, makes it a little thicker. Now back to where I've got all my pictures and things. Here's your concrete footing. Here is your column base plate. Here are your little pieces hanging out. There's your steel wide flange as seen from the top. There was one last note on this page. You have it on a different page. Back when we were doing the reactions and getting those reactions into the web, sometimes you have concentrated loads on the top of the column. It can get to be a problem once you put a concentrated load, I'm sorry, of your beam. You can put a concentrated load on there and this thing sometimes is so tall and so thin that it will buckle. And in which case J10.4, J10.5 tells you how to analyze that. If they say, okay, that's not a good design, you fall within the region of you got to do some more stuff, then you'll have to brace that top flange. Here are the little curls up on these things. Here it is seen in elevation. Here's the web. There's your flange. There's the cantilever starting back under the flange somewhat. Your job to take D times .95. And then what's left is how much it hangs out on both sides. And so you're going to be looking for that cantilever length. That's in minus .95D. And then there's one on both sides. That's M. And looking at it the other direction rather than bending about the flange, which is this line right here, bending about this line, they ask you to take B minus .8 times B sub F with the flange. And then make that your cantilever length. So N would be equal to B minus .8. There's two of those things, one on each side divided by two. That's how long that cantilever hangs out. The equation we discussed for how thick the plate has to be with a given yield stress, piece of B over B times N is nothing but the stress on the bottom of the plate due to the concrete pushing against the bottom of the plate. And L will be taken as the larger of the two cantilever beams. However big this one is. And however long you don't really have that one. This is M. The other one is B or L, whichever is the longer of the two. That's the one that you'll use. Now when they do tests on these things they find out, geez man this really is kind of a mess. When you lightly load the column the whole plate does a pretty good job of being able to stay in compression. But when you really heavily load it the concrete has a little bit of defamation in it. And this center part of the plate will have a tendency to bend up because of the stresses in here. And you could probably fit a piece of paper under there for some short distance. So there's a difference between lightly loaded plates and heavily loaded plates. There's also a difference if you have what they call a small column, a small plate. This is a small plate. It doesn't stick out very far past the column itself. Or a big plate. Well here's a big plate where there's a whole lot of. In this one most of the bending is just because this piece right in here is unsupported and you get little short columns in there. But in this one here the effect of this long column coming here far overpowers it. So there's a difference in your answers for small plates and large plates. And it can get to be a mess. Nobody's really very well defined what the real break point is between small plates and big plates. So what they've really done is they've taken a couple of different analyses and they just kind of bunched them up all into a unified theory and based on the speed of light or something like that so that you can get the job done and still have reasonable, perfectly safe stresses at a reasonable cost. One of these things was a guy named Murray in 83 and he had the idea that we would take areas similar to what the wide flange itself looks like and then say that those little cantilevers didn't touch out in here and they were so long. Then a later proposal was Thornton and he proposed an analysis based on two-way bending of the plate between the web and the flanges. Basically he said look theory of elasticity has a solution for the bending stress in this plate. It's a plate that has uniform pressure under it. It is fixed at this line and ours is because due to symmetry there's one on both sides so if you push this down the plate shouldn't rotate underneath the web because the pressure on this side should be the same as pressure on this side and pinned along this edge. That makes sense because if you load this plate under pressure on this side and there isn't much on that side then it would tend to roll like it was unsupported but by a pin and then this in here is free. I said okay where in the world do you get an answer like that? He says well it's like I say it's theory of elasticity and they tabulate the results so you can get answers for what the stresses are in this plate. There'll be some bending stresses in here because the plate's being raised up. There'll be some bending stresses in here because it's the wall of a cantilever beam. So you go looking around and sure enough there's a bunch of books that tabulate this stuff. This is one of the most famous ones called Work and Young. Here they have the plate we're looking for. That's his case seven but the whole book is full of things like this. Here the edge of the plate is free. Here the edges of the plate are simply supported. That would be where it is underneath the flanges and here's where it is fixed and that's because there's another one on the other side due to symmetry this edge can't roll and the plate is loaded all the way across from the web towards the free edge. And you get these equations and you get these constants that go in there so it's pretty much right on the money. If on the other hand this thing does pop up a little bit and not any longer touch the concrete then you wouldn't want to load it. Maybe you only want to load it two-thirds of the distance from the web to the end of the load which case here are your numbers or maybe you load it heavily so bad that this plate you can see under there see things living under there small bugs well then you probably ought to only load it a third or maybe you say well why don't we just use a triangular distribution. They have all these answers and they have many more so if you run into a case like this for some reason these are good numbers to use for a specific design but in our case I know what they're going to do they're going to take all those things and they're going to draw a curve through the middle on the safe side and say use this because we just need to get this job done and fortunately these are not the most expensive items in town because they're relatively small. So what they've done back on this previous page they have put this isn't any different here to 60 cd my next page okay it'll be interesting we'll see what we can do okay it really does it start here they had something on the pre oh this is from the previous the previous theory says now these three approaches were combined by fourth gentleman and a summary of the results and procedures as followed the required thickness is same old equation what did you find out what page that was on it ought to be way back in looking in chapter four way back in the beginning of the book 14-6 page 14 I thought it was in chapter four somewhere somewhere back in way back in chapter one chapter two it's not in chapter 16 at all it'd be in chapter four maybe four dash 16 no okay well I'll find it we'll find it 14 dash six okay well I got that's correct now they still got to be in an end because now then they're applying that to everything you do plates beams you name it if it sticks out on a plate that's it so what page is that is that page 14 dash 6 it is on that page okay maybe the one I showed you before I wrote that down wrong I don't know now it's too late I wouldn't I wouldn't doubt it thank you all right now here's what you do you do in effect the same thing your l squared now is brought outside l will be however long you think the cantilever beam is in our case l is equal to n minus point nine five d over two if it sticks out in one direction this is out from under the flange and n is equal to b dimension minus eight tenths of b sub f this is if it's bending about the web and you take the longer of the two and then it's possible that the little plate theory we were talking about may control the situation and you have to check and see if it is there are two count three calculations you have to do number one in and it's going in the same direction but in prime is equal to d b sub f right out of your column table dimensions square root divided by four you're going to take the longest of these numbers except in prime isn't just this really n is uh where does it go here I'll find in a minute here we go you got to look everywhere for these things lambda in prime so here's your in prime that goes right in there now then you correct it with a lambda now the lambda correction is all of this other stuff that we showed you before and and drawn a few curves through things first lambda is equal to two times square of x divided by one plus square to one minus x less than one where x is now then we're back on solid ground for depth of the beam width of the flange depth of the beam width of the flange parentheses squared times piece of you you know what piece of you is that's how much request you really will put on the column that isn't how much it will hold that's how much is really going to be on there it buckles it half of what it would hold because it's long and slender you put what you've requested here not fee times it but the real full blast load take a look on page 260 and then fee of the concrete piece of p remember they have a different symbol that piece of B is how much the concrete will hold the concrete will probably really hold 85 percent of the 28 day compressive strength times the area of the plate or the area of the concrete that's assuming they're both the same size except to be safe there's a lot of variation in concrete times 0.65 or if your plate is bigger than if your that wouldn't work if your plate is smaller than your concrete area if your concrete area is bigger than the plate area that's a better way to say it then you get a square root of a2 over a1 more load it's got to be careful because this is limited when a2 reaches four times a1 this effect stops working so tell me the area of the plate tell me the area of the concrete that is sitting on square root of area of the concrete over area of the plate times a1 again times the strength of the concrete again times fee for concrete and that's how much strength you can have out of the concrete with a limit of four over one that'll be when a2 is 4 a1 square root of 4 square root of 4 is 2 2 times 0.85 1.7 it's limited to this number don't go beyond that number that's where you get this term right here this is due to your column request this is due to your actual concrete strength so having all these numbers we get x who knows what that is what do you do with x you put it in here who knows what that is i can do it and where did it come from came from some of the things like out of the roark book and some other theory now what do you do with it well number one they find that lambda is really closely given by this equation and it goes like this plot of lambda versus x and it comes up and it comes up and it goes like that the truth is the limit is one it's it's actually a correction it's like c sub b in other words this thing is getting ready to be multiplied times lambda and it's a correction to how long that cantilever beam really sticks out so they tell you that the limit on this is a one and so they have you do not that they have you do this now if you say well i'm a weenie and i don't understand raise your hand if that's your case okay one then you can just take lambda as one i mean the best thing you're going to get out of this thing is so that in certain instances this thing won't make you use a thicker plate than you really need to that would help that would not the lambda n prime length down by lambda so he says it's pretty nice it works it's reasonably economical there's no need to determine where the plate's large small lightly loaded or heavily loaded and you can always just take lambda as one if you don't want the correction but if i come up with a problem where in lambda if that's a six and that's an eight and n prime is a ten you better go looking for a lambda if you get this as a six and that's an eight and n prime comes out eight you just write down don't need a lambda it's already no worse than anything i already have to take care of couldn't resist i plugged in x and lambda just an equation in excel and sure enough it looks like that and in the real world they really find it looks more like this so they just let you stop at one here's what the plate looks here is the flange pinned here's the flange pinned here is in this region the plate is unsupported in the middle so it bends like a uniformly loaded beam back in here it is jammed tight underneath the web and therefore it doesn't move up here's a top view of where these points are here if you look underneath the plate this is what you see a b c d e f has moved up possibly no contact possibly still is in some contact regardless it's acceptable and back under there you see those points that's where the web is so as an example we've got a 10 by 49 uses a column supported by a concrete pier as shown it's a 18 by 18 i went ahead and showed 20 by 20 the reason they're only taking 18 by 18 is they got steel in there and they don't want me messing with this other dimensions in here they want that concrete not used for structural use they want it in there for fire protection they want it out there so in case of a fire when this concrete starts spalling off you still got the 18 by 18 in the core of the column kind of like this on the top we just he gives you all the stuff you need he tells you the strength of the concrete dead load live load a 36 base plate peers 18 by 18 so your load 1.2 dead plus 1.6 live this computer required bearing area here's what we did for any kind of plate whether it's a beam bearing plate or a column base plate we need to know how much area the concrete will say good enough any less area the concrete gets overstressed the load piece of nominal what you and I would call it they call it and we got to call it piece of p if we're going to work with their concrete 0.85 fc prime 28 day strength a1 squared a2 over a1 has to be less than this number it's under the plate nominal concrete strength we'll see those pages equation j82 bar v of concrete times p sub p namely how much it can take that's your design strength has to be greater than how much you request and I'd say that fee for the concrete times mr. concrete's opinion of how much load he can take his nominal strength it's 0.65 you see how the code changed or the specs changed 0.65 times 30 day strength for this particular concrete of 3000 psi times area one times area two over area one area two is the area of the concrete area one was the area of the plate got to be bigger than this number that's design being greater than the request now that tells me I need 137 square inches of concrete that's a lot less than last year so if I give him 137 square inches with a two inch wide by 50 inch long plate the concrete's happy he doesn't care but you know I'm not going to let things hang out like that make sure your upper limit's okay because 137 square inches of concrete may not be right you've taken the square root of a two over a one into account so you have been asked to carry 349 b 1.7 as a limit fc primary one would be 0.65 1.7 is your limit times three ksi times 137 square inches is what you propose that concrete would cough up 455 kips of load which means that this did not control had it controlled then you would find that the concrete could only cough up 300 kips and you'd have to go back and scratch this out and put the 1.7 in there and tell me how much concrete you need same thing could have happened to you back when we were doing the beams this is the first time we've really seen it checked well I guess we checked it every time now then the plate can't like look like this or somehow you're gonna have to make the plate at least as big as the column doesn't have to be much bigger could be perhaps only half inch all the way around half inch out that's acceptable if the concrete's happy with it then we're happy with it but that that wouldn't be happy even if the concrete only needs that much area concrete I mean the column has to touch the plate everywhere underneath the column otherwise the load and the flanges wouldn't have anywhere to go so he says you need 137 square inches of concrete the area the length times the width of the column that is a w10 by 49 you go check it it's got about a 10 inch width on the flanges and it's about 10 inches deep so he says the area b sub f times d would be a 10 times 10 just if it's just barely the size of the column and that's a hundred since that's smaller than how much you force to give me regardless then I'm happy with your plate your plate will be forced to be bigger than the size of the column you have a little squatty column like this you could hang these out you have a long tall column like this you could make the plate more in proportion to the size of the wide flange if you let this plate hang out another choice for this one could well be where you put a little more hang out here a little less hang out here so that these little cantilevers aren't quite so long and that would make the plate a little thinner and if you got 5 000 of these things running around then it might be worth you know optimizing the size of the plate so that the cantilever hanging out this way is about the same length as the cantilever hanging out that way within what you can ask the people to do you can't ask them for a 10.716 plate that way and an 8.032 plate that way they're going to tell you to go away yes sir you really don't do what you do you're going to have to make that stick out a little further we got we got room for that to happen in other words if you said that I really need for the concrete a 10 by 10 column and this 10 by 10 plate and this is a 10 by 10 column you're not going to put up with that you're going to go ahead and make it 11 by 11 or something so that you can so it sticks out a little bit they always do now that you don't have to weld this to the plate it's not that that thing sticks out so you can connect it because what they'll do is they'll just put a little angle right here and bolt it to the footing and then bolt it to the column and that'll keep the plate under the column all right so back to our calculations here are the dimensions of our little cantilever strips this in he has proposed since he needs 137 take the square to 137 get 11.99 by 11.99 or something like that so why he didn't pick a 12 by 12 column don't know doesn't matter whatever he picked that's what we're going to show you the analysis for but the 12 by 12 column was still hung out on both sides by an inch we're going to use a 13 inch wide plate this is 10 inches so we're going to say that we want the little the little caliber beams will hang out 13 inches minus 95 percent of the distance from there to there that's the point 95 there's two of them on both sides going to hang out 1.75 inches in this direction and on the other hand is going to be this but a little deeper than that it's going to go back to about here that's 13 inches wide you're going to subtract a point eight it's also 10 and then put one cantilever on both sides 13 minus eight tenths of b sub f divided by two so this will be the one so far then in prime quarter of square root of 10 times 10 two and a half inches therefore there's no reason to calculate lambda because you already got to have a two and a half now then if this came out four inches hanging out four inches i probably would go for the lambda and see if i couldn't get that cut back down to back around the two and a half conservative just let it be a one then you take your max of all the numbers found so 1.75 2.5 or 2.5 take the longest one now we're ready to see how thick the plate ought to be thickness of the plate should be the length the cantilever hang out two times the 349 piece of you requested nine tenths is fee i thought fee for concrete was 0.65 oh we're not designing the concrete now are we we already made mr concrete happy what we're doing now is we are working with a steel plate the 13 by 13 plate 36 ksi 0.893 you're going to go ahead and make it an inch thick if you look on page one dash eight i hope that number is right and copy it down wrong you'll see plate thicknesses they tell you the proper dimensions for plates or what is expected up to i don't remember maybe three eighths of an inch you can specify them in sixteenths of an inch and they're on the shelf pass that there every i don't know who knows eighth of an inch pass that is every whatever couldn't resist for us here was x for baker v sub f for dog baker flange squared times our ultimate divided by the capacity of the concrete port of 10 to 10 over 10 to 10 squared times there was your request here was your capacity of the concrete i calculated that here by the time i wrote down p sub uh fee piece of p i realized i didn't know that yet here was how much the concrete would be happy with point six five factors uh resistance factor point eight five fc prime 28 day strength a one times square root of a two over every one area two is the concrete area one is the steel concrete is bigger than the steel 13 by 13 is the steel rank that out the concrete is good for 388 kits before it'll have problems now says 349.6 from earlier on page 260 h 8 h but the plate sizes change back when you got that 349 capacity of the concrete that's when you were working on a different plate since it's gone up to 13 by 13 that's a new capacity here's your x plugged in right here point 901 here's your lambda plug in the x and you get 1.44 times one well i wish i hadn't even asked he's gonna make me make the dang plate even thicker but i don't have to do that because i get to stop at one so it's still two and a half inches but there are the calculations if you're curious i mean there's nothing to them serious uh should you be able to do that because i'll give you a plate where due to n prime our rascal comes out longer than the other two old pop quiz his makeup pop quiz but it wouldn't be for today 36 deal what is required thickness of the plate if you put 600 pounds per square inch underneath the plate should be able to do that and this is where your text covered what we covered these various methods by Murray Thornton that stuff rork got on a solution for that one here's the problem we just worked all right uh range range from a 30 to 100 i don't think anybody's dead but you're gonna have to do less texting and more listening i got them alphabetic guess who gets up first i just saw him where's a car okay i'll call your name out acar well there he is you know i don't remember uh i just recorded him in there if you'll email me i'll be glad to return the email with that to everybody else so i'm looking for a's come on forward and pick up your quiz adjumaly not here if you don't say here or something berry should already be up here we're in the bees seas ought to be coming up bowman bowman not here bowman's here brute buchet brawn brawn not here cow's seas ought to be up here causado cantu cantu's not here cantu's here carrigan k k kerington kasey chung clark clark chung's not here chung's not here you jerk clark cook cook's not here okay i'm gonna call your name if you don't say here i'm gonna put it in the stack you'll have to wait curtis d's ought to be here where's the villa where's euless euless not here so now i know why i got all these 30s euless is not here but your forester falton forester falton i don't know i don't think so gram gram get get get get get off my stage get off my stage gram gamble dig uh mr who who's here hillbig nobody got two quizzes did they hardy i mean i may have mispronounced your name i can hardly read some of herty a hardy johnson right here not only here but right here coot's coot's not here leon not here lahog michael where are my other m's no none of the other m's are here come on up here mace where are the ends no ends are here navel these perkins reinhardt these reyman rots what comes after r s savoy steinhubble stevens suduki trisca trisca here tidwell to morga thompson vickers vickers not here vickers is here wiley and zapata here always last estus i had all the quizzes i called estus uh either that or i call jones by mistake but it looks like estus sorry quizzes that's a good way to get in trouble thank you grades are not cast in stone one quizzes posted go make sure that you know why you got counted off before you come and ask anything about it or you will really look dumb oh okay yeah i'm actually a pledge for oh sure yeah i was wondering if you would mind i'd love to congratulations thank you thank you sir you bet you too