 Howdy Look at this Well these people asking are we gonna hold class Friday? I don't want to come to class Friday heck. You don't come to class Wednesday Well you guys do but you're the good guys All right, I don't know how far we got on talking about holes in beams. I remember we had something started on them we mentioned that when you put a bending moment on a Wide flange and you have had to drill some holes in the flanges That you don't care about the compression side because the compression stresses will yield The steel around the holes and then the holes are just fetch up against the bolts and the forces will go right through Only if you have holes on the tension side do you possibly have to account for them If you don't drill too many holes, and they're not too big they find out It really doesn't change anything But they do insist that This flange on the tension side had been planned to carry some load the load that that flange had been care planned on carrying was F sub y The F sub u is okay in a minute F sub y Times the area of the flange The flange with no holes in it. That's what you told me you were going to give me Now when you drill the holes you say, but I don't have the area of the flange anymore. It's no longer area flange gross With the flange time thickness of the flange It's going to be a little smaller because I drill some holes in it and We find well, that's not too bad We can go ahead and let the stresses around those holes build up to the ultimate Without hurting anything that's exactly what you and I did on tension members when you were studying around the holes You ran the stress from f sub y up to f sub u and it was acceptable. You had to make some corrections sometimes So I say What I need you to do is I need you to go tell me how much you told me you were going to give me F sub y times the area of the flange gross and If the force that you are going to give me Which is going to be f sub ultimate times the area of the flange including the holes net If that force has come up to what you told me you were going to give me then that's okay We will not worry about holes However You do have to consider the holes you will have to drop the strength if you can't tell me that the net area When under the full f sub u if that force is smaller than you planned on giving me Then you're going to have to reduce the strength of the beam due to the holes. Otherwise you can walk on and ignore it Not actually it's a little different from that if it was that simple more people would do this for a living But we're saying that the flange force in the flange in other words the strength available at f sub u including the holes If it's smaller than how much full strength was desired And you told me you were going to give me at the yield stress without any holes Then you will have to reduce the strength and we'll talk about that shortly All the terms are defined area flange net. That's without the holes That's with the holes area flange gross is without the holes here the page numbers in the Specs that give you these same equations and it's on page 244 d also Now we've run into another problem used to be when a 36 was about the best we had A36 would come up here and it would just yield like crazy And then it would build up here from 36 maybe to about 58 and then it would pop And that was really good steel all of that ability to distort deform really helped us in a lot of ways Now then we got this high-strength stuff a 992 where f sub y is up to 50 and f sub u maybe is up to 65 and The distance between when the thing yields and when it is reached f sub u That doesn't have near the range that I'm used to seeing when we first set out this criteria for holes and So if you got a bad steel One where you're running the stress up to maybe I don't know about ten percent of the ultimate Rather than running it up to about maybe 20 or 25 percent of the ultimate Then the fibers just don't get to stretch like I had planned So if you have a steel where the ratio of the yield to the ultimate is Higher than 0.8. That's a not a very ductile steel and it's really ductile, but it's not like we had planned Then rather than having you check what did you tell me you were going to give me and Are you going to give me less than that you have to consider the holes? I'm going to tell you for those kind of steels. I want you to tell me what you were going to give me and Because the steel we're discussing is not as Ductile I want another ten percent tacked on to what you told me you were going to give me if You can't bring your f sub u times the area of the net flange with the holes At least up to what you told me you were going to give me times one point one Then you're gonna have to consider the holes just because of the steel you're using nothing wrong with it It's just not as ductile So what they do is they write the equation all in one swoop and they say if this is less than this You must consider the holes where this factor y Intention is a one if you got a really great steel where f sub y is down pretty much below f sub u About 80 percent But if it's higher than 80 percent Then you have to give me another 10 percent on this strength side and If you can't do that, then you must consider the holes. That's a completely different process Is it just telling you whether you must or must not consider the holes? Now if you look at a 992 steel and you look at the numbers you would say well, okay The yield is 50 and that's 65 There's a 992 6550 you'll find that that 6550 is down below the point eight So you say hey, I should be okay on a 992 steel Well, it's kind of in what you get in the a 992 steel And an a 992 steel you can have 50 to 65 and it still has a 65 a 992 name and this is a guaranteed minimum of 65 now this guy happens to run this 65 up to 80 and you know it and This happens to come out 50 then 50 85. You don't have to do the a 992 steel. It doesn't have the 1.1 problem with it But what happens is this 50 can go up to 65 and it's still got the name a 992 steel And so it's very possible you get a steel where this number is actually when you get it 60 And the 65 is what he gave you to and the 60s down there right on top of the 65 And I I can't live with that I mean I can live with it, but it has an impact on whether or not you have to consider the holes and Since they don't tell you You always have to put the 1.1 on an a 992 steel if you call them up and you say I know you got 800 tons of steel out there for me You got tests on all of it says well it came out in about six batches. We've got tests on all of them What is the f sub? Why and what is the f sub u if the f sub y over f sub u is eight tenths or less Then and you can come up with this right here You don't have to consider the holes even for an a 992 steel But if you don't know and you won't know on a quiz because I won't know I won't have the test specimens You'll have to include a 992 in this 1.1 problem area now the reason for it is this And I hate to take time to show you Reasons for things. I think it's the only reason that you really learn anything is if you see why these things are happening Here's an a 36 steel in 305 you learned it around a hole you have a stress concentration factor which raises the stress Quite a bit maybe a factor 1.6. Maybe 2 Above the average stress across the section. So when you put in a load on this plate This stress runs right on up to yield There's your yield and these are down around 18 and this is down around who knows 22 When you put some more load on it then this fiber yields and it stays at this yield and it stays at this Yield and it stays at this yield and then this one comes on up and it gets to yield and then this is down to 25 Then when you put some more strain on it with this little fiber here. He's he's going on up the curve He's getting on up to around 50 Before this fiber finally gets to the 36 we're counting on But that's okay because he's well under this peak this break point and Therefore a 36 steel is behaving like I need to because of your holes Now here's a piece of a 992 steel one where we don't have the ductility as we do in the a 36 Same idea first off the stress goes up K times p over a Because of a stress concentration factor and it reaches the yield of 50 while this is still 25 Then when you strain it some more This fiber does stay yielded stay yielded a few of them are getting above yield because they're starting to climb on up this different-looking curve and Then when you finally get this one to 50 this guy's out here to 70 And that's not gonna cut it. I can't I can't stand that you're out there past the breaking point and That's why for some steels I'm gonna have to ask you to give me 10 10 percent more on the front end Just to see whether or not holes have to be considered On a piece a 36 steel it's very easy to come up with a case even though it's nice and ductile where the holes have to be considered Here's a case where the holes have to be considered There you go Yeah holes gotta be considered In other words, there's no way you get enough f sub u out of those little pieces To take care of all the f sub y that you lost So here's now if you have the bad news that you have to consider the holes First you have to cut your elastic section modulus down to account for the holes First off the whole equation is really kind of changed you used to say that the nominal moment was f sub y times Z Now then we're gonna make you we're gonna let you run it on up to f sub u The first thing you're gonna have to do is you're gonna have to drop it back to the elastic section modulus from the plastic section modulus So Basically, here's the bad news number one you don't get to use z sub x You have to go back to s sub x and that number will have to be reduced by the Small area divided by the large area That's basically your bending strength The good news is you get to run the f sub y all the way up to f sub u So rather than the old case where m sub nominal was equal to f sub y times z sub x Number one you get to run the f sub y up to f sub u But you got to drop the z sub x down to s sub x It's shown that it works best and not only that you don't even really get the s sub x because of the holes The only reason you even here is because you haven't to consider the holes You have to reduce the elastic section modulus by the ratio of the net area of the flange With the holes divided by the gross area of the flange without the holes That's your nominal strength Now there are many more nominal strengths that you got to also check You got to check the nominal strength due to lateral torsional buckling You got to check the nominal strength to the web local buckling. I guess not Flange local buckling. I mean all those other things still have to be checked. This is just at that point Wherever you probably are trying to find the maximum moment at a given point in the beam You're gonna have to see if the beam Will handle that moment. So basically he summarizes it as follows Does your ultimate force available in the tension flange under ultimate load ultimate stress Area truly there. Is it smaller than the? One or one point one factor depending on your steel Multiplied times the yield stress of your steel times the area you told me was going to be there before the guy with the drill showed up If that is true Then you must account for the holes and the way you do it is this the nominal moment is equal to f sub u Area the flange with the holes area the flange without the holes elastic section modulus for the shape under discussion where this is either a One or a one point one Then he kind of forgets to tell you whereas if F sub u area flange net is greater than or equal to this then you get the full plastic moment Even though you got the holes there you do not have to account for them I mean in effect you have accounted for them because of the studies that you've done and we find that You can that the moment developed will be the full Im plastic of course the fees got to go on everybody before they really get out in use But we're talking about nominal moments nominal moments just like the specs do Yeah, that's that's the only ones that probably are going to be connected like this Angles, you know probably just going to be connected on one leg and we've already found out how to take care of them All right, so he has a problem. It's a w 18 by 71 You can find the information on it on this page and I got a page here with 18 by 71 information That flange wide flange has a seven point six four b sub f and has a point eight one thickness It is made out of a 992 and since I don't have tensile coupon tests on it I'll have to consider the one point one as a requirement He says use cease to be as equal to one Well, I can tell you whatever he he hadn't shown me his moment diagram, but I bet his moment diagram doesn't look like that That's not this case because if it was he'd be telling me use a cease to be as one point one four This case here must either be this one where it's ten feet long That's the ten feet unbraced length with constant moments on either end are possibly a beam Brace brace brace brace equal loads where the moment in the region of study is m sub a m sub b m sub c m max and C Cb is one if he tells me that must be one of these cases now just to Divert a minute and see where this stuff is in the specs Proportions of beams and girders sixteen point one sixty four Here's where this is greater than this the limit for tension rupture does not apply all that saying is You're cool. You don't have to study any whole information Whereas if it's less than that then you must account for the holes and this is how you account for the holes And then of course all the terms are defined Continuing with our 18 by 71 First off he wants to know if it's going to flick fail by lateral torsional buckling. I'll leave it for you This is old stuff The curve looks like this There are tables that tell you L sub plastic and L sub R. We're at 10 feet So we're on here if you remember there's that equation for that straight line You got to go dig out in plastic f sub y s sub x your brace length is 10 feet L Plastic is six L radius of gyration is 19.6 blah blah blah blah and that's how strong it is if it's Laterally torsionally buckling if that controls but since it's got holes in it I don't know whether this will control our web local buckling will control or Not web flange local buckling or if those holes are going to cause the problem. So now this is new Incidentally when this person was calculating this stuff he calculated the plastic moment as f sub y z sub x That is not permitted if this was a w14 by 99 with an F on it Remember the z sub x is true and that's true But that number right there may not be true if the flange see this flange if the flange has problems in inventing About the best way you could get the number that goes right here would be go to your Z tables where it gives you fee in plastic and divide the fee back out so you could get the real web flange local buckling plastic moment and use it in this equation The other possibility would be to go dig this Rascal out and track it down until you got to ten feet From those charts So here's our new stuff first we're going to see if the flange holes need to be accounted for gross area of one flange is 7.64 inches wide point eight one oh inches thick That's how much area you told me you were going to give me and then I see this guy with a drill walking over here Active hole diameter one inch plus a sixteenth fit plus a sixteenth damage one and an eighth Therefore the gross area of six point one eight eight You took off the thickness of the flange twice Times the diameter of the hole Geez man. That's a that's a lot of lost steel. You brought the steel area down to four point three Question is what did you tell me you were gonna? What are you gonna give me you're gonna give me 65 ksi? Times this teeny area left over after the drill guy left That's two hundred and thirty eight kips Whereas you told me you were gonna give me fifty ksi times six point one eight eight Which is something else and not only that because you're using this crummy non ductile steel Even though it's wonderful stuff You got to give me a ten percent increase of that before I compare You told me you were gonna give me less than this times one point one. That's what I got to have You didn't do it Came nowhere near what you promised me you must account for the holes You simply account for the holes By give me the ultimate strength 65 ksi Give me the flange area with the holes four point three six six Give me the flange area without the holes six point one eight eight go dig out the elastic section modulus 127 and that's how much moment you can have That's M sub in that's how much you can't have it you've got to give me a point nine on top of it This value is less than we found 64 60 was lateral torsional buckling this controls It's a value is less than that it controls Here he's divided it by 12 and then he didn't complete it really because before anybody can really Hand it out. You got to put the point nine on it before it goes out the door 436 Kip feet Here is The information used in that went to the z-tables went to a w18 by 71 There's your l sub r. There's your l sub p in that equation Here's your 18 by 71. There's your flange width. There's your flange thickness Here's your 18 by 71. Here is your elastic section modulus How much did it change? See it changed You know pretty much because when the web yields it it picks up some numbers But they don't they don't let you have that You drop to the elastic section modulus. Good morning You know if you're gonna come in late, I mean it's not really but if you're gonna come in late You should and then I don't pick on you because I will pull guy ran all the way to get here Either that or limp, you know like a car ran over you. Yeah. Yeah, something okay, okay All right now this is out of the 13th edition just because I wanted these notes on the side didn't want to rewrite them It's the same information as yours How to find this is where I told you if you'll just track down a w18 by 71 You can get the nominal moment You just go to the z-tables and you find out where a w18 point seventy one comes in the z-tables would tell you immediately easy to find in the z-table 548 Then you simply track it down. You say it's not the lightest. That's not my problem and when it hits 10 Then that's how much plastic moment fees of the msp You get off of it a lot of off of it according to lateral torsional buckling. Sometimes that's well worth doing On the other hand if you're trying to track down this 18 by 76 You may be five pages back Came down here on the next page came down here in the next page came down here next page You're finally here and you're finally to the 10 foot mark You know sometimes it's more trouble than it's worth and his use of that equation is appropriate Because it tells you how to get it without going through those different pages This is the same one in the 14th edition Already did holes and beams already did that already did that example problem with my notes on them Open steel web joists will come back to if we have some time I see when the last time we had time 1982 all right base Bear beam bearing plates and column base plates on the exam you will invariably be asked to design a base plate or to design a Bearing plate you need to know the difference This is a column. This is the base of the column piece of steel of Reasonable thickness so that you don't just poke a hole in the steel along with a concrete that is a base plate and Usually it'll say in the column to be used on the problem They're also telling you it's a column base plate the design of this is quite different Here is a beam a beam has no base so you can this is not a base plate this is a Plate where the beam presses on the concrete and the plate bears on the concrete like a bearing stress Is there a bearing stress under here? Yes, there is but it's not called a bearing plate base plate and I don't do that to just mess you up But every now and then you give me a beautiful design for one of these Or you don't because it's so difficult, you know, this one was simple or vice versa So know the difference between a bearing plate and a base plate you can't hardly go wrong columns have a base beams don't Whole purpose is so that when you push on The concrete very weak with this high strength steel You don't just gouge a little H shaped hole in the concrete But I'll steal plate between the two Same way with this one here. This steel is quite strong You can have such high loads that the concrete's only got maybe 3000 5000 psi Where are this stuff in here? We're talking about 60,000 psi strength you can mash a hole right in the wall or right in the concrete footing with these things You need a plate underneath them to spread the load out so the concrete is happy Yes, it can be but generally speaking if the thing is always in compression They're gonna they're going to put some holes in it. Yeah Because invariably, you know, you get wind loads on the columns and things like that They'll put a bolt and they'll put they'll embed it down in the concrete now then on a bridge a lot of times The ones I see they don't do that because there aren't any loads sideways generally They just sit it on top of a bearing pad and it sits there forever But if you wear suspenders and a belt Bolt it down your friends may let you and then say Look what this guy spent $800 bolt in that plate to the ground. Ha ha All right now Just between you and me you see I have a little investment in pictures here And unfortunately in this book and this is a GUI they and in the code or in the specs They call this length of the bearing pad They called it in and they call the width of the bearing pad B So the area of the bearing pad was in times B the new Specs call it length of the bearing pad So you just have to bear with me any place you see oops, there's one right there any time you see an N Just think length of the bearing pad most of them. I think I've found and I've already marked them Use these notes Here's a top view. Here's a beam coming across. We're going to do bearing plates First Here's a concrete footing or it could be a part of a wall which extends out in both directions Here's the plate and the beam is set on top of it. There's your steel plate Here's your beam. Here's your concrete column or your concrete footing. It's top view Here's a kind of an end view in your book It's an end view because he doesn't show it the 3d stuff part to it. This is B This is the length of the bearing pad And then it sits on top of something that's weak like a concrete or masonry Here's a side view. This again is L sub B Here's the web. Here are the flanges of the beam That force under that plate actually feeds up into the beam So that the stresses go up nicely at about a two and a half to one they find that out just by putting string gauges on there And it goes up through the flange and it goes up through the fillet Remember there is a flange here and you remember that fillet It goes up through that until it hits the really thin part of the web So there is an area of the web Where right about across here it could start to yield the web of your wide flange We'll have to make sure that doesn't happen way that could happen most obviously I Got a picture of one of them here Have to be ridiculous I don't know I may run across one but where you make this thing very very short just just about an inch long Well, then there's a good chance when that load feeds into the web the web will yield at that point Remember what you've already studied you've already studied that the web itself Will withstand The reaction due to shear Vq over it or in our case V over the area of the web But if you can't if it yields here before it gets into the web Then you still lost you still came out behind Here's how it yields. Here's an end view of a wide flange Here is your B Could be that B is the same as B sub F Usually it's a little longer than B sub F kind of so you can see them hanging out and Then it has some length which we will have to design for This is always going to be at least B sub F. You wouldn't want a little eight inch plate under there You want the stability of this thing sitting on it? Here's your K design. That's the distance to the through the web plus this radius Here this load is feeding up in here and cutting out at about a two and a half to one angle and That's a longer length And you find that when you put this reaction force that you've asked for over this thin Kind of long cross-sectional area in the web You can go up to f sub y If you go above f sub y, I'm not I'm not going there That'll be your limit Here is your nominal strength Let's look at this one will be as good as any your nominal strength will be he shows us like a 45 degree angle That's no fair. It's a lot flatter than that. It's two and a half to one Your length of this line right here will be L sub B plus two and a half times K design That's how long that will be. I think I surely I got a better here. We go. This is a better one right here Here's your plate your plate is L sub B long here that force is feeding up into your thin part of the web which starts Right about here at K design. So the length of that line where the stress has got problems Is L sub B plus two and a half times K sub design. They just call it K Here's your 2.5 K design plus L sub B. That's the length Here's your width thickness of the web You can see it right here, and then you get to multiply that times f sub y That's if you got a plate on the end of the beam I'm kind of using his figures Here we go. I Like that better There's your L sub B plus two and a half K design Here's a beam that's coming across the top. This is a girder This is a floor beam the floor beams got some pretty high loads in it They have decided they need to put a plate between the two to keep the stresses down and when they do This is L sub B For an interior beam this thing feeds off to the left At a two and a half to one rate and it feeds off to the right So now then the length of the yielded web at the thin part is L sub B plus five times K design So for exterior or close to the end plates The length of the line is that long for interior beams For interior loads on top of your girder L sub B plus five That's why this one has the two and a half plus L sub B things of the web f sub y this one has five times K Design plus L sub B. I don't see off hand where his Nominal strength is but it's obviously that length right here times f sub y thickness of the plate probably on a future page All this stuff is on section 16 1-134 page Interior plate Here's an interior plate Here is where it comes from in the specs 16.1-134 That yielding is so reliable and so tightly controlled You don't need any variation you get it all whatever you get. It's yours And here is the R sub in for an interior plate I know that because it says a five and here's one that's close to the end I know it because it's only got a two and a half on it Plus L sub B. There's your f yield. You'll notice he calls this f sub yield in the web Because it's a it's very common to make up your own beams You'd make this out of a 992 steel and you'd make that out of a 36 steel because a 36 is a lot less Expensive and you're not getting a lot of bending strength out of the web anyway And therefore he wants you to be sure that you're talking about yielding the weaker steel He wants you to put in the yield For the web not for whatever the other pieces are on there We don't usually talk about those but it's here. So you you should question where that came from in Hawaii Now not only can you just flat yield? This steel when the load gets up into your poor old thin web You can actually cripple it By that I mean When you put the load on here I've got a picture right quick This one the load was put on the top here the web just buckles to the side Here's a crippled web where the load coming up from the bottom There wasn't a load on the top on this one and it just it didn't yield the steel, but it was just too thin and so the web crippled or buckled Here's one where the top flange see they were pushing down to this compression side the top flange had Local buckling problems, and if you look you can see that the web is also having problems It's pooching out and bending in and out of the paper here Causing a buckling problem of the web This one's quite evident. You'll notice a Wing on a model airplane where they twist the thing and they've divided it up into little cells This is the compression direction for the way. He's twisting it and this is the tension direction That's what we're talking about that wrinkling of the web When you load it called web crippling It is a buckling of the web caused by this compression force on the bottom there. You see the little buckle marks It's possible if you put a load here you'll cause little buckle marks in These directions down in the web and this is a mess There's nothing there's nothing else you can say about it But it's it's all the theory is there and it's been verified by test if you have an interior load The strength of the beam as measured in web crippling. This is the nominal strength 8 tenths of the thickness of the web squared plus Onto 1 plus 3 times the length of your bearing plate There's your length of your bearing plate There's your length of your bearing plate Divided by the depth of the beam times the thickness of the web by the thickness of the flange Raise the 1.5 bar square root of e f sub y thickness of the flange thickness the web Don't ask me who had time to do that somebody with a lot of money and a lot of time done a big research project and Found out how strong these things were Back when everything was a 36 steel and they were all fat webs probably never had to worry about it Stronger the steel gets the thinner the sections get the more we have to do this research find out Where we're gonna start getting into trouble This is for an interior load Where the loads are dropping off on both sides Or here where the loads are dropping off on both sides If you get near the support like this one as you can see you're unsupported out here So you have a much higher chance of this thing crippling and There's they find that you can't even have one equation to determine How much strength you have short plates have this equation and Long longer plates have this equation say it looks the same. Well kind of kind of pretty much Okay, well this number is different and that's the same and that's the same But it's it's actually got to have a different equation. What is a short plate? Here's a short plate right here if l sub b is Less than two-tenths of the depth That's a short plate if l sub b is Longer than two-tenths of the depth of the beam. That's a long plate. Here's a short plate Here's a long plate You can see where you get more strength out of this one because you you know You're back in here further before the thing might have a tendency to cripple How you get the answers? Well, I don't ever do that I just write a maple or EES to get in there and whenever I have to grade a quiz and you've got a bunch of weird numbers I just put the weird numbers in there and hit a button You probably do the same thing once you get out Yeah, yeah, yeah, and you're gonna tell me again, aren't you? Concrete bearing strength. We know how strong the beam is now. We can stop it from crippling We can stop it from just shearing. We can stop it from yielding Now then we got to talk to mr. Concrete What we'll do is we'll put that steel pad on top of the concrete and we'll make it big enough so that the pressure between the bearing plate or the Base plate whichever we're designing It's got a low enough stress in the concrete that the concrete is happy First there'll be an l sub b and then there'll be a dimension in the in and out of the paper This is out of the ACI specs the ACI people use a simple piece of P Found to be point eight five times the 28-day compressive strength times the area of the concrete that is being loaded You and I will immediately turn that into p sub nominal or r sub nominal or whatever we're gonna do because that's what we use for nominal strength Now then that's if the plate fully covers the column if it doesn't Turns out you get some more strength you get the strength you had before But you also get to raise it by the square root of the area of the concrete divided by the area of the plate You can't exceed this number here the specs here's the Information out of the steel out of the concrete people Similar to concrete test point eight five fc prime blah blah blah the curves Here's what we just said if your plate which is called area one Completely covers your concrete which is called area two in all of these equations then you get point eight five fc prime a one just like a concrete cylinder test and It starts breaking just like you saw your concrete cylinder breaking pieces start to fall off on the outside If on the other hand you have the same size plate But it's on a bigger piece of concrete Then as you see all of this concrete is kind of contained inside of this outer perimeter And so the load picks up dramatically If area two is bigger than area one if area two is equal to area one Well, there it is square root of one is one and there's your equation and there's your equation but if area one is Small compared to area two you get to add they've tested this to verify it Square root of the area to divided by area one So the first thing I did is I had a big old floor and I put a little old plate And I put a load on it and I found out the load could be two trillion tons And they said hey jerk You there's a limit to this, you know, I admit that it's you know, it's a lot stronger You know if you've got a lot of concrete outside of it But all you're gonna do is you just gonna push the plate and you're gonna just push a little square hole in the concrete So there's a limit to when this square root of a two over a one is permitted That is when area two Reaches four times area one When it reaches that limit, then you got a quit Here's your equation. Here's your square square root of area two when it reaches four area one over area one Area one cancels square root of four to two times point eighty five That's your limit. You can't go any bigger than that no matter how much concrete you provide And we'll get into that again next time