 okay if this thing goes off let me know it's gone off twice I don't know why what's the last thing we studied what well that sucks yeah I don't know it just keep on having to select the source doc you got a phone what the number eight you got it eight four five oh eight oh seven as long as I keep selecting the source I don't know why it drops the source makes no sense ask it tell them it's in room 118 if they got a chance they welcome just come on in the class see if they can figure out why it's I got to keep hitting doc cam because it goes off civil engineering 118 I'll be done yeah but I got a student worker in here I'll get him if you push a button this is really strange but better than not having class I'm gonna grab a chair if you want to yeah when it goes off you just select source document camera and it turns back on okay I don't get it okay no no no go right here all right we were talking about columns sorry for the delay columns fail by having so much load on them that they buckle we have equations for the loads that it takes to buckle them we have mr. Euler's opinion which is accurate up to some breakpoint from which we find some of the fibers will go into the plastic region and of course when they all go to f sub y his opinions aren't valid mainly because the fibers are no longer in the straight line portion of the stress strain diagram e well the same problem happens locally but we've done so far as what they call global buckling for the whole column buckles but a second possibility is that these little stick out pieces here when you put a uniform stress across them there's so much stress that they will personally buckle if they're too thin so you have to check for local buckling as well as global buckling the phenomena is very similar up to some point these things won't buckle they're just too short and they're too squatty for instance if you make me a wide flange that looks like that then this piece just not gonna buckle locally it's too thick and doesn't stick out far enough now if that happens the real reason the whole column fails is not that it's buckled it may still be straight come on in yeah and they'll probably figure we just have to keep on pushing the button that says what a dock cam and it comes right back up and you have to sit here how long a minute two minutes okay this is my entourage incidentally we travel together there's two types of these things one of these elements like an element of a flange is called an unstiffened element means it is supported only on one edge a stiffened element is one that's harder to buckle because it is attached at two edges so they'll have different numbers whether or not it's a unstiffened or a stiffened element your personal column will be classified as either a slender or a non slender column if these little stick-out pieces have a tendency to buckle then you have got what we call a non slender column the limit state will be caused when the local piece locally buckles and the equations you've been using up to now won't apply now here's kind of what they look like in at some breakpoint on these flanges and webs they'll tell you what that break point is it depends on what it is and what it's attached to if you are to the left of that point you don't have to fiddle with it your equations that we worked out so far work perfectly on the other hand if you exceed this breakpoint then you will have to reduce the load you will get local buckling there is a symbol that they use just generic and it's lambda and that lamb does just something we've got to call the thing something so I'll say are you above or below the breakpoint are you above or below the lambda value for your wide flange or for your channel or whatever you're working with they give that the name lambda your personal value for your personal wide flange is just going to be listed as lambda if you're want to know where the break point is it's subscripted with an R like the radius of gyration of the little piece that's sticking out is so small but that's the that's the breakpoint if you remember previously we had a curve looked very much like this one for the column strength that came in at f sub y and it had a breakpoint above which mr. Euler's equation with a point eight seven seven attached to take care of things like how straight the columns are when you buy them and an equation to the left we have the same kind of a deal you're going to have a breakpoint your lambda the way you calculate lambda will be how far does the little piece stick out divided by how thick it is and how far it sticks out and how thick it is is dependent on are you talking about a channel are you talking about an angle are you talking about a wide flange but there'll be a b over t ratio for a wide flange or a t this is what you and I have been calling b sub f so far it sticks out in two directions how far the flange sticks out is b sub f over two b sub f is out of the book and then your t will be the t of the flange and that's a measure of its susceptibility to local buckling so you go get your wide flange and you calculate b sub f over two divided by its flange thickness and that'll be your value your value is to be compared with the number that we have found below which don't care above which you have problems this number just like the number we found before if you remember Mr. Euler came in and was doing great right about this point he wasn't doing so great we had a break point above that break point you used Euler's equation for the critical buckling stress f sub e put times point eight seven seven then you had a different equation something raised to the power raised to the something times f sub y below this break point we got break points in this kind of work all over the place the break point for a wide flange is point five six times square root of e over f sub y and that may be the number for something else we just have to see but it costs a lot of money and they can tell you that this is what it's a factor a function of it's all steel so this will always be 29,000 if you have a wide flange made out of 50 ksi yield steel then that's just a number you crunch that number out turns out to be 113 if you have a wide flange made out of a 36 steel I'm not sure you know why you would do that because it's not gonna be as strong you don't have to be a lot more steel involved but you take e over 36 ksi time square root time point five six and that would be the break point above which you have problems with the local buckling below which you do not here's another thing that can buckle this is the flange of a wide flange it's also the flange of a tea because teas are cut from wide flanges here is the web of a wide flange and the supported length is right down here a little bit below where this radius comes out and right above right there where that radius comes out and the tendency to buckle is what they call H you can get H by measuring the depth of the wide flange you subtract a thing called K there are two of them in the book one of them is K sub DES for design and one of them is K for sub DET for detailing detailing as you might imagine they tell you that number usually in sixteenths of an inch so you can tell whether or not you can get a wrench in there and tighten up bolts and stuff like that you want the design number it's not hard to tell the difference because one of them is I don't know point 106 and one of them will be plus the flange and one of them is a sixteenth number we don't use anything that are sixteenths those sixteenths are used to see whether or not you can fit things together depending on how long this is if it's very long you see how it has a very high lambda and if it is very thick it'll have a lower lambda telling you whether or not has a high susceptibility or a low susceptibility the break point for the web yeah break point for the web is one point four nine this is the break point for the flange now I don't care for it but everybody says it but me they call that the upper limit and what they're really saying is the upper limit below which you're okay with the upper limit where you're getting ready to not be okay I really like to think of them a lot more like their break points between bad and good and it's going to even be more important I think when you start getting more than one break point down here because it won't be too long before we're going to have some things that go like this go like this and go like this you're gonna have a break point you can have break points so I think rather than trying to remember which region you're in figure the break point and then go get your number whatever it is for and see which region you're in there your break points base 16.1-16 table be 4.1 a here's what we said there's that number we just discussed point 56 that is for flanges of rolled eye-shaped sections did you guys fix it okay well I got my backup are these are those your keys oh okay thank you I don't get that that happened how many times five six okay flanges here are your flanges there's your b over t your b stick out is b sub f over 2 that's where you get your b over t is your measurement your b sub f over 2 of course is b and thickness here are for webs of doubly symmetric eye-shaped sections and channels that include an s shape or wide flange here is your break point on that one one point four nine here's a break point on an angle b over t here the break point on crosses here the break point on rectangular tubes here's the break point on a tube a tube as a tendency to locally buckle also your measurement your criteria for what do you have in the shape you're requesting is it's outside diameter divided by the thickness and this is no square root on this one there's a break point below which you're good above which you'll have to include the effect of local buckling yes sir it's on page sixteen point one dash sixteen sure typical there's somebody who wrinkled up the flange that is local buckling of the flange here's one that's more flange here's one local buckling of the web now in truth you'll notice rather than actually go buckle something in the flange only and then buckle something else in the web only they just went and took something made a little short column out of it and squashed it so hard everything in sight buckled but basically you see what's happening this is the problem you can tell it's not real also because generally speaking if you put too much compression across here one side will tend to go up while the other side will tend to go down in other words the whole thing will roll when it is but local buckling like this this one is pretty is typical of what you really would see if web itself buckled they wanted to get two and one on that demonstration here are typical values this is in the front of your book page 1 dash 24 for a 14 by 132 cross sectional area depth you would need the depth you would need to subtract 2 times k design it's not quite true because anything for convenience these people are going to give you they're going to give you depth minus k design over to and they're going to divide it by the thickness of the web somewhere where's the thickness there's the thickness of the web but you know you could be asked to check it on an exam check the number there's probably one or two wrong in the book and say go see what the h over t sub w is or h over to b sub f over t sub w whatever and pull the numbers out and the number in the book could be wrong but there's your depth there's your k design this minus two of these for the web divided by the thickness of the web here's your b sub f right there divided by two to get the stick out of the wide flange on one side only divided by the thickness of the web that number there is going to give you a measure of susceptibility to local buckling but in truth on the next page here they are for that same shape there's b sub f over two divided by the thickness of the flange for this shape that's your number this will have to be compared to a breakpoint here is the susceptibility to the web buckling says little h little h is actually d minus 2k designs is right there d minus 2k designs here the numbers calculated out 17.7 here's sugui's take I just put the whole table in there the same numbers there is your breakpoint for the flange there's your breakpoint for the web here's for t this is for the t sticking out the same as this one doesn't have to be it is here for the web 1.49 versus 0.75 now they don't make any sense why is d over t 0.75 and this is h over t sub w what do you think the difference is between a wide flange and a and a t they're both made from the same thing well this is a stiffened element somebody's holding both ends of it down and this is a non stiffened element this one is more subject to buckling local buckling I don't know here's two angles pair angles they're exactly the same except they got different numbers wonder why that is the gap that's exactly right these two have to be bolted together and then this part here will support each other and they make a pretty stiff little element so these things aren't as likely to fail then these here where they are they're going to be still bolted together but they probably have a washer in there like that and that washer may only occur every you know five feet or something like that these are more susceptible to buckling so you see here you have a lower number and the lower number means that further down to the left you're going to be more susceptible to buckling if you exceed that number you'll have to take local buckling into account an example I like that that's a nice ringtone man it's better than some I've heard I hate my dad and I hate my mom and I killed the cat and a blender bomb and a geez man don't go to an interview with that on your cell phone wow for a w-14 by 74 he would like you to investigate local stability this is lambda you this is the lambda of the flange this is the criteria that you were told that you must follow when you look at the table for wide flanges b over t where b is the stick out is b flange over two and then t is the thickness there's b sub f over two thickness of the flange you can check these numbers out there on these pages and you get six point 41 out of the book and this says you get 6.43 numbers change every now and then every now and then all of a sudden a wide flange will have this much cross section area and the next book they come out it's got a little bit different those things happen not exactly sure why it could I guess really be that they go out and buy a bunch of them and this major made by different people and they have slight differences and so they say okay well this year it's this number I mean you don't care not gonna change anything but if you get something like that's a little off shouldn't bother you you still know what you're doing it's just to change the numbers the break point for case one for the flange is point five six square review over f sub y there's e there's f sub y he says investigate the column of example four two that must have been a 50 ksi steel thirteen point five you are to the left of the break point otherwise if you were to plot this look something like this and here was your break point thirteen point five you are at six point four one then this is you therefore it is not subject to local buckling for this shape as far as the flange is concerned here's the web lambda for you is the lambda of the web as opposed to the flange here it's calculated you could have looked it up in the book is twenty five point four break point it's subscripted instead of by you as when the radius of gyration pretty well gives this thing problems lambda subar there's your break point number and it turns out to be thirty five point four again you are to the left of this number and since you're to the left it is not subject to local buckling so local instability is not a problem now here he tells you how to correct it if you have local buckling of these elements you have to even in this class know how to tell if it's subjected if it is subject to local buckling because what we're going to do is if we find it we're probably going to avoid that shape because we don't really have time to cover everything in the book than this is one of them we don't it's not straightforward they will do it if you go to graduate school we just don't do it in here so if you come up and you find that one of these shapes has is non slender in other words has elements which are subjected possibly not possibly but they will be subjected to local buckling then we're going to avoid them we don't have to avoid all of them because one of the things we use in here is we use tables and they'll tell us how strong something is for various shapes in the table well the guy who did the table he went to graduate school he knows how to do this and so local buckling is included in the table numbers the only thing is it's not included is if I pick a shape and ask you how strong it is and you get up to the point where you say this thing is gonna locally buckle that's gonna be the limit at that point you're gonna have to say I don't know yet that takes care of that's one of the reason we don't have time five pages ten pages of calculations and derivations good stuff as soon as they make this a four-hour class we'll cover that quick review this is global buckling and the reason I know it's global buckling is because I see that global buckling number I don't see those numbers that we were talking about a minute ago this is Oilers formula right here this is point eight seven seven Oilers formula it's listed in your manual E three dash three you'll find all this on page sixteen point one dash thirty three here's where oilers Oilers formula just went astray because he didn't take into account that the fibers were yielding F critical in this region is point eight seven seven Oiler F critical in this region point six five eight F yield F Oiler multiplied times F sub y if the yield is 50 and mr. Oilers says five million this is a zero anything raised to the zero power is one one times F sub y that makes a lot of sense that's the critical buckling stress on a one inch thick tall wide-blanch what you do with it once you get the critical buckling stress you multiply it times the gross area what does that give you that give you then across sectional strength okay what the nominal strength then and I was just looking for that particular technical term and then to turn it into the design strength which is okay for you to run the piece of you right up to is called the resistance factor okay what is that for a column buckling point nine that's correct point nine you saw why didn't remember all that well you're okay because I hadn't had a quiz yet pretty soon it's gonna matter you say well I don't think so because I'm gonna bring my big old thick hundred dollar book you can find it in the book you're good to go but there's a lot of fees in there if you just flip through you saw there's a fee point six oh six I'll try that one tables for compression members so that you don't have to do all this work all this work is good stuff a lot of useful things they'll tell you the global flexural buckling strength they're on page four dash three twenty two for example that may be in the middle of the table maybe the beginning I don't remember where they are referred to as column load tables that tell you the selected strength they always any of these design aids gonna always include the resistance factor so be careful with that if you work out the strength of your column and you've got the nominal strength there and then you go look in the table they won't be the same because you forgot to put the fee in there you so the tables illustrating the following example I'll take your word fart says he wants to compute the available strength of the compression member of example for two I was a 14 by 74 20 feet long we had already calculated for that 20 foot thing we went and got the minimum radius of gyration about the weak axis 20 foot times 12 divided by the radius of gyration about the yy axis it was a pen-pen column that was a one I'm just reminding you I'm sure you remember all that turn out to be 96.67 what are the units of this thing that's correct she's shaking her head the right direction her head's going like this no units because it's a ratio it's an inches over inches times a factor and the gross area is 21.8 so we page 120 here it's where he repeated all the numbers I wonder where I could grab them and see them he says we have tables for your pleasure for fees of CF critical table 422 don't that's my guess is this is the page that's my page that's his page I got got it coming up on the next page they're only given for integer values of slenderness ratio you can take your choice you can just go ahead and pick out the little bit more severe number or you can interpolate that's not my job to teach you teach you how to interpolate I think did y'all already put your homework problem in there yeah okay well you can give that to her and she can give you the homework problems to hand back here's what the table well this is the table for where I was getting the numbers from there's a 14 by 74 I got a couple of pages of that invariably here is your area here is your x-axis radius of gyration here's your y-axis radius of gyration we took the 2.48 and we calculated k l over r for it here's the table under discussion table 4-22 you must do your own slenderness ratio check just knowing how much stress you can put on a 50 ksi piece of steel doesn't include the fact if that 50 ksi piece of steel has slender elements so you're welcome to use this but the slender element check must be done after you use this to see how strong your column is this is not including the slender elements possibility if the k l over r we got page after page of this that was a 50 ksi piece of steel here's a k l over r is one and I think that's where we're going what was the k l over 96 or something like that so I'm looking for the k l over r of around 96 here we go here's another summary the k l over r was 96.77 I don't want this column that's a loud stress there's phi sub c f critical for 50 ksi steel these are based on the equation 3 2 and 3 3 on this page he knows when you're above or below a break point you remember what the break point was for our for our 50 ksi steel global buckling I mean that's really getting down and dirty to ask you that was 113 in other words if you multiplied 4.71 times the square root of 29,000 ksi divided by 50 ksi you got 113 so that's the break point he knows when the break point occurs so he knows when to use one equation below the break point and he knows when to use one above he knows which one to use our slender this ratio is 96. something right in between 22.6 22.9 to interpolate you get 22.67 including the phi if you'd rather you can just take the lower permitted stress and not bother interpolating and in this class you most certainly can't because like I say not my job to teach you how to interpolate and I know you know how to do it so I don't care so if you just want to go to the nearest the next lighter one the next lesser permitted stress than that would be okay here are more pages where the Kaila raw is higher than 113 and more of them remember no slender element check is being done in these tables now let's see where he went ahead used that maybe it was back on the previous page that's local buckling slender element of web or a flange all right so here's what he got he got out of the table 22.67 interpolating then he says then my final answer for how much loads you can have is area gross remember seeing that 21.8 square inches out of the table times a critical buckling stress we got at the table 22.67 including the fees of C that includes the fee says a real tendency to put another fee on there ought to do that that multiplied together gives you 494 kips of load now we don't know what the load request was but whatever it is has to be less than 494 and I says there's a second set of tables which will include the shape itself rather than just talking about the steel because you still now have to see if the 494 is acceptable by checking slenderness ratios of the web and the flange of that shape this column load table was done by somebody who knows how to do that if they are slender elements he'll do that 18 pages of work for you before he goes into the table because this is not theory learn how to do it today that book you bought there that's do it real world let's get on with it column load tables are in part 4 they're on page 4-16 for example probably the one we're going to use and I got it back in 131e here is a typical well it's not typical it's the one he asked for it's a 14 by 74 again here's your 14 by the 16s are in the preceding pages the 10 buys are in the later pages here's a 14 by 74 this is a loud stress design it's easy to get in the wrong table this is your KL the R is already in there he knows how to calculate the R your length was 20 feet and your K was what one why was it one only one way it'd be a one because the column is what how's it supported and on both ends that's right look at everybody looking at you ugly they're not looking at you ugly because you're brilliant they're looking at you ugly say the longer we wait the less we have to memorize don't answer his questions KL was 20 feet and so all you do is you go across to you find a 14 by 74 and you get same number 495 yes sir the K values I can't know I'm sorry I told you in the last class if you look through there some way thank you I just really and you know I've got it but I don't think I've seen it in this set so we'd have to I'd have to go back to a previous set I will say that as you go through your notes or you go through these notes I've tried everywhere to mark you know where those pages appear all right so 495 is a done deal well wait a minute I don't know if it's a done deal it could be that that has slender elements don't care you said a minute ago you cared well a minute ago I wasn't dealing with the 14 by 74 shape I was just dealing by anybody was made out of 50 ksi steel which incidentally the problem with these tables and a good for anything but 50 ksi steel and when you go to the angles you'll find they don't have anything but 36 ksi steel because that's what we usually use for those kind of things so that's why I know where the breakpoint is and that's why he knows what this number is and that's why our value checked to also because he's obvious this must not have slender elements because if it did this number using that F critical table would give us the wrong answer which we would know that it was going to now you want to know who really does have column problems then elements there's a guy that's got column problems right there if that's made out of 50 ksi steel that little C superscript there means this guy's got slender elements therefore many of these numbers not the short fat ones but the long slender ones are going to be affected these numbers will be changed they'll be reduced because they have local buckling here's here's what he says see it's shaped this slender for compression with S of Y is 50 ksi heavy line indicates Caleb or R equal to a greater than 200 he's saying for heaven's sakes you really shouldn't be working in this region I'm not even going to tell you how much load there's going to carry because it's just not good to be able to carry 500 400 300 kips you're already down to 100 below that he suggests you don't go it's not against the law it's very uneconomical quick review analysis of columns here are your e3 equations e3 1 and e3 2 e3 3 e3 4 one of them gives you a fee one of them gives you this one of them gives you that one gives you below the break point one gives above the break point they're all right there and our notes there they are here are here's table 422 that's a great little table the only problem is it is not going to be able to cover the slenderness slenderness of the elements because you don't know which element you're working with you don't know which one covers all common F sub Y that's what's nice whereas the tables down there they only cover specific F sub Y for those kind of shapes normally used lambda sub R not checked for slender elements but all shapes are covered and this one only a few shapes are covered you go back to those tables you find out they run out of things in a hurry there aren't any 8-bias there aren't any 21 by 50 150 shapes and things like that because they're not commonly used for commons columns why his excuse for not putting another 200 pages and charging you another $50 and give you a dolly with the book the values in the table based on global buckling and these equations local stability is assumed and you must not exceed the slenderness ratios now this is I think badly written above this line he's talking about one thing he's talking about table 4-22 and he says well I told him I was doing that yeah but then you said all those some shapes and so on so you didn't really tell them we're talking a major change in thought here this is table 4-22 and these are out of the column load tables here he's warning you that you got a check for excessive width thickness ratios and here he's talking about the column load tables he says in here the tabulated strength has been computed according to the requirements of members with slender elements and no further checking is needed they're good to go they include that design design becomes quite easy with the tables that's not quite easy very few people on earth can do it but you and me to get an economical shape here's what you do you'll be using table 4-1 and it's on page 4-12 he would like you to design a compression member for a service load of 165 dead 535 live 26 feet long pinned on each end he wants a 992 I don't know is that 50k si steel it better be because I'm not gonna be able to use the tables otherwise I'm gonna find out if that's 50k si steel in the buck that's exactly right and he wants you to pick a 14 by shape so just play in the 14k shapes load 1.2 dead 1.6 live there's your piece of use 1054 kips you got to give me something stronger than that nominally times a resistance factor bigger than that number from the column load tables we go to the column load tables this is the 14 by page I'm gonna start with a ooh I don't like that one oh I don't mind that one what's wrong with this one got slender you don't have to check it's got slender elements you're in the tables where the check has been made and corrections have been made you have to go down to a 26 foot column you need 1054 nope nope nope nope see how they're getting fatter see how they're getting heavier stronger go the next page 26 feet I need 1054 no no no no 1054 that'll work a w14 by 132 look in your book it says a w14 by 145 what he forgot to do was a w14 by 145 used to be the right answer because this number was 1050 in the last in the 13th edition of the AISC manual call them up and ask them why they added a little bit you remember a little while ago where they changed the R design a little bit and they changed the H over 8 sub W a little bit you know I don't know if they got better numbers or what but it doesn't matter if they're gonna let me have the other 10 kips I'll take it if all of a sudden I get to drop a size from 145 to 132 legally and no it won't fall down I'll take it here incidentally is the old edition the old 13th edition look at that 1050 you need but you needed 1054 the addition you can live with a smaller shape now then if I ask you to design something without being stuck in the 14 inch region we just say that this one is 24 feet long and you need a load of 275 the same columns I'd go to 24 feet I'm looking for 275 no no no no no I turned to the next page those were eight buys look at that none of those eight buys worked they were all bummers 275 now I'm in the 10 buys no no no no yes 275 a W 10 by 54 is it does it have slender elements no none of these have slender elements that not that it matters that's still a good number so the lightest one I got so far as a W 10 by 54 remember that now let's go to the 12 buys here the 12 buys 275 no no no no 292 that weighs more I'll stick with the one I had a 10 by 58 let's look in the 14 buys 14 buys made 275 275 there we go 61 that doesn't look like I'm gonna win you know I'll check them all because you never know there's something else may show up but a 14 by that's all they got either that or I got tired of doing it and maybe hopefully check the other ones but they weren't they didn't work there's your lightest column shape right there why didn't you just show me that on the first day we got here in class I could have done that you could have but you wouldn't have any idea in the world what was going on that's why all right see you next time sorry Ben you can ask my guys the dang thing went off 20 times no don't no no I don't know what you're getting ready to turn off but it's it's still recording and if I don't get out gracefully I lose the lecture I'll get it thank you here real hold that back yeah back where we got it from somebody in another class is probably sitting in it