 Well, this is not too bad seen as how all the a lot of the people at Ten o'clock figured sure is too icy for me to make it All right, we were working on tension members We had mostly done plates up till now We had discussed oops a few would Put your homework in there and if you would give him that when he's finished and And then pass it up and down the rows one of them says submit one of them says return to students As of now the submit Bucket is light The other one's heavy It's over to you. It'll be reversed Okay, we were talking about yield stress and ultimate stress for various steels I don't remember. It's been a couple of days since we were There, but if you look on the previous page in Segui page 43 that must have been what we were talking about He's discussing it more. I think we've discussed it at length. So I think you'll be okay Lecture one flip class goes through using that table in detail with you if you still got questions about it three-quarter inch bolt Just to show you here's six holes in a plate. There's your three-quarter inch bolt The true hole size is one sixteenth inch bigger That's so you can get it together. That's for fitting it up And because you drill it or punch it in a rather unsophisticated way you leave marks all over it Which kind of hurts about another 16th inch of steel around the hole So whenever you do the following calculations, which we're going to work on you will assume a hole size Diameter of the bolt plus a sixteenth for fit plus a sixteenth for damage You will see a hole diameter of the bolt plus a sixteenth inch See the guy pick up a drill bit of that size to drill the hole that specification is in page 16.1-18 and It's on page 2-48. I guess the 248 is for f2y and f2u. I try and put my little notes pretty close to What he's talking about to account for possible roughness Around the edges of the hole Here is that spec and some other specs that we were Talking about here's how you find the gross area Gross areas total cross-sectional area right out of a table How you turn that into a net area that includes the fact that you drilled holes in it Net areas and some of the products of the thickness of the net width computed as follows Net area for tension and shear the width of the bolt holes So it'll be taken as a 16th inch greater than the dimension of the hole So you'll notice that the specifications require you to Pretend you've destroyed an extra sixteenth due to damage How much bigger you want the hole to be so it'll fit he doesn't care that's your problem But it is conventionally one sixteenth. That's why you only see him adding one one sixteenth here. He says go look at the hole They how big should the hole be he says I don't know that's your problem Practically you should take the bolt diameter plus a sixteenth of an inch He says now I don't care how you got that if you've got a quarter inch bolt in a two inch hole That's your problem. No problem, but because you drill that hole you make whatever that number is 116th inch bigger due to damage Sometimes you'll read Segui and he'll say bolt size plus a 16th plus a 16th you look in here And he just says plus a 16th you get confused Because Segui starts from the bolt size tells you practical added size plus damage This guy doesn't know about practical. He doesn't care that your problem Well, he's worried about is the damage part plus a single sixteenth above the drill size Which is of course a sixteenth bigger than the bolt size There's sometimes these things will zigzag around we'll get into that but we'll be coming back to this page I'll try and refer to the page number sixteen point one dash eighteen in AISC This is where I've stuck it in our notes pretty close to Segui's page 44 now he's going to start talking about an effective area and We've already done a little bit with plates plates are very effective. They're very efficient The load P comes through here and it slides down one two three bolts about a third of it very nicely through shear between the top plate in the bottom plate and comes out through the bottom plate and About two-thirds of its left and it comes down in here a third Comes through here. There's three-thirds here. A third is taken out There's two-thirds left about half of that comes out. There's one third left and it comes out and Those believe it or not. They're reasonably close like that Not because the bolts are so accurately put in the holes But more than anything if you put one of the bolts and it bangs up against both sides in a hurry Then you put another bolt and these holes don't line up very good first thing this boat will yield and it'll reach a peak number Then this boat will get a little bit of load and say oh, I didn't know you guys were even loading thing this guy says Oh, yeah, I've already just because I was where I was located I've already taken my share and I'm through the rest is yours And so all of these bolts will pick up loads evenly. That's pretty efficient It's a little inefficient because the load P in the bottom plate and the load P in the top plate don't line up perfectly By this number here T if this is T and that's T that'd be T over 2 they're two different size plates I don't know what this will be, but it's a little bit of moment in that joint Not enough that we worry about it not enough that we see it hurts our load carrying capacity. We ignore it you Is how we will take care of inefficiencies in a joint you is equal to one for a plate bolted to a plate The true behavior of the load when you pull on this side The load comes down through the plate the stress comes down pretty nicely and uniformly And then first thing you know these little pieces of load these little stresses notice There's nothing there, but air and say so they start bumping shoulders with these people And they say look you're gonna have to move a little bit because I got to get around this hole They go around to the backside of the hole and they press they bear against the bolt That pushes the bolt to the left Until it contacts the plate underneath you see the see that plate underneath there and Then the load goes through that side of the bolt in bearing then it goes down in the bottom plate In other words, it's really coming around here around the hole and it's pressing against the bolt and Then this bolt being pulled that way is also really coming through here and Pressing against that bolt and those two loads are shearing that bolt bolted plates the affected the effective area is well, this is not the Area effective is always equal to you times the net area the net area is the area with the holes in it But for bolted plates you as a one hundred percent efficient Why there are no outstanding unconnected elements In other words all of the elements mainly both plates are connected to something The times you really have problems with this efficiency of the joint is when you have an angle bolted to something And the top piece of angle is hanging out in the air and the load is running down the 30-foot length Very nicely until you get towards the connection and all of a sudden all the little stresses and loads in the Top piece of the angle that's not bolted anything it starts saying move over move over get out of the way I got to get down there to that plate it becomes inefficient But with a little bitty moment on like that not a problem Yes, sir That is true, but they will not let you put too few because as you're probably thinking right now And I think I got a picture of it somewhere If you only had one bolt Then the fact that that those two points don't line up very well that caused a heck of a moment on there As long as you got a lot of bolts in here that moment is resisted Acceptably and they were so they just coded out or they just speck it out They just say can't do that gotta have at least so many bolts All right, and now we'll in here somebody who did that very thing Here he has a Five by three by half inch angle the five inch leg is laying down on the plate The three inch dimension is sticking up in the air the loads are coming down kind of trying to get through this bolt The loads that come down this piece of steel this top piece find that their element is unconnected They say gee I shouldn't have got in that train I should have got in this train coming in through here now I got to figure out how to get all the way down here and get through this boat down into the plate Basically this piece of the entire Angle isn't even loaded So you know these guys are sliding down in there that causes higher stresses around this point in the Angle and it causes it to hold less load You say well what we can we do about that? Well not really anything You just have to suck it up and you have to admit that the angle around the connections are not as strong as You were planning on it You'll help matters a lot if you'll make the the connection longer The length of the connection is considered to be end to end of the bolts So that would be L This case you don't have to worry too much about it because here L is zero and When you divide by zero in the equation we tell you you should be using you quickly say okay. I don't think I like that So you can't just use one bolt The eight and a quarter plate eight by a half inch plate The loads have much more time to get down in there Because you have a longer connection. There's still an unstressed part of the Flame of an angle up there that's still true in this case right here You see the person laid the five inch leg down Stuck the three inch leg up in the air the centroid the number that we're going to use well Actually, the real moment arm is a distance from the center of the plate to the centroid of the angle But we just the equations in the specs just call for you to Use the number from where the shear surface is to the centroid of the outstanding or the the angles Centroid towards the outstanding leg They say this part here We didn't count it a minute ago and we find we don't have to count that little extra moment in this case either But we've got to count something This is on page 1-44 and I've got some stuff on the next page This was much better. He still took the three inch leg and stuck it up And it is now unconnected and the distance from here to here Best I remember now Betcha I Think I looked that up You'll have to check and see if I'm making a mistake now or if I made it this morning at three o'clock I think that number is how far of that centroid is from the back of the angle If you really wanted this extra thing you'd have to add a half of a half inch plate Here's a guy who thought he was doing great has the same number of bolts has a nice long connection But he didn't know what he's doing. He stuck the five inch leg in the air So now then the moment arm is Well, it is the one that is the moment arm the truth is they just don't make you go all the way to the center of the plate They make you go to there. I Think as much as anything We're not even sure what plate we're going to use yet And we need to go on to get on the design and the guy said look it really doesn't make that much difference the real problem is this piece here and so the specs call you to Find the number from there to there and it's in the tables There may be some reason for doing that the guy says look, I don't have any choice. It won't fit the other way It's just he's going to take a hit on strength Here's where you find those Distances from the back of the angle here. I can check that right now I have written here from the back of the five inch leg to the centroid is point seven four six for Five by three by half inch angle Here's a five by three by half inch angle. That's why bar I Want X bar? See I want to know how far it is From here along the three inch leg and that's X bar and X bar that's why boy. There's X bar for that angle is point seven four six. That is I did have the wrong I Was showing a moment arm and they don't really use a moment arm. They use how far it is From the back to the centroid now. There are two Y's and X is shown here One is the distance to the elastic one is the distance? Yeah to the elastic Centroid and one is the distance to the plastic centroid Not interested in the plastic centroid in a connection. It's you need the elastic centroid So you'll see a Y bar, which is what you use and a Y P They're both shown almost the same. I could barely see there's a little difference there Here you pull the right number from the tables What is the P and a have no idea? Don't don't don't just look in the book and find something. What is the J and X or? Raise to E and expect an answer go go talk to somebody who does steel man. I don't steal. I do water resources He and a plastic neutral axis I don't know that's right, but he's not gonna yeah He's not gonna rebut it because I don't know tell you how you find out you go look in the glossary And he's got everything big you sheer lag factor a little Y bar plastic neutral axis Look there he goes. Look the base back in the glossary already It's in the front of chapter 16 not in the back. There may be another one there where you're at Okay Now we're going to design or analyze a plate Could be asked to do either one It's a half by five inch plate a 36 steel uses attention members. So this is an analysis problem once You to assume that the effective area is the true area because he says you weren't supposed to have told him yet about that you the Reduction in strength because the centroids don't line up so so badly Assume it's a one. That's not a problem. This is gonna be a one What is the design strength for LRF D and then what is the allowed strength for ASD? We don't do any of that and when he asked for the design strength He's asking you to go find out with the specifications say The 305 strength is going to be the average of a thousand tests And then he wants you to multiply it times a Resistance factor to turn it into a design strength That's the design number. That's how much load you can put on it Now here he drill the four holes like this He could have drilled them in a straight line the plate would have been stronger But the connection would have been longer the reason One of the problems with this plate is going to break across two holes So you're gonna have to subtract two holes from your cross-sectional area Here it is in three dimensions. It's five inches deep. It's a half inch wide This is a five eighths inch bolt plus one sixteenth due to fit plus one sixteenth due to damage It's a three-quarter inch hole effective hole size See something like that, you know holler He's something called P&A in a book. You don't know what it is. Don't ask Okay, first we're going to admit that the thing may yield across its gross section in other words Once the long thirty foot length of the member yields it may get so stretchy that it just can't Support the loads to our satisfaction. That's called gross section yielding For yielding of the gross section we calculate the gross area without the holes five by half two and a half square inches We apply the yield stress to the gross area that comes right out of the table for f sub y and f sub u Two and a half square inches times 36 ksi this thing will average out if you tested a thousand of them at 90 kips Some of them won't make it up to 90 kips and so you're not going to be able to use 90 kips And I don't know which one it is, but I know my luck. It would be mine So when nobody gets to use 90 kips, that's nominal Going on to fracturing through the holes the net section our net area is the gross area We already calculated two and a half square inches Minus the holes Well here the holes right here these holes are three-quarters inch tall and a half inch wide so three-quarters times a half and Fade your plane runs through two of them just because you drilled four holes doesn't mean it's four holes You drilled four holes with the load first found a plane of weakness at two holes So you have a half times three-quarter times two you subtract it from the gross It leaves you the net area Because it's a plate on a plate that is also the effective area 1.75 square inches This is true for this example, but a sub e doesn't always have to be a sub in so be careful And the nominal strength from your 305 work would be stress times area effective. It's a hundred and one kips One policeman says you can put 90 kips on it and then I'll shoot you One of them says you can put a hundred and five hundred one point five kips and then I'll shoot you I go for this number here the lower of the two. Yes, sir Yeah, that is indeed because see the bolt is going to be 5-8. It's back in Why do they multiply the three-quarters? Well, see this is the height of the hole That's the height the width of the hole of the steel that you lost was a half and Then there were two of them then the nominal strength your 305 strength for fracture across the net section area Stress times area you get a hundred and five kips Now you still don't know who controls here And so I really should have shouldn't have stopped there because the policeman doesn't get in the game at this stage Because this number is gonna have to take a little hit on strength Because it's just yielding and that's not too dangerous This thing here is fracturing and that's really a serious thought And so it's going to take point seven five hit Where this is only going to take a point nine hit so I still don't know who's going to win so going ahead and putting the Resistance factors on there point nine of the ninety and point seven five of the hundred and one Turns out that the limit is seventy six point one kips worth of strength design strength Now that still doesn't tell you if the thing is going to work or not because nobody yet has given you loads You still need this number to be compared against the one point four dead And against the one point two lap was one point six dead and so on and so on and so on Yes, sir. Well It talks on these pages that we're marking, you know This is where you're getting picking up the the strengths Let me see if I've got this right here Right, that's in the commentary somewhere, but it's all You just see here. No, but usually you know Here we go F sub y sub g on page two dash forty eight pretty close to it's going to be the same thing They're gonna have the fee factors right next to it So it's all in other words, so we hadn't done anything on his own here. It all came out of the out of the specs and Somewhere in here. I'll have those But you know, who knows when they'll finally show up there's effective area there's effective areas The only thing I know if I haven't written it down again We must have written it down some some on some earlier page that we worked on Give me that page number that you found it in the just in comments two dash twelve So it's on page two dash twelve But I'm telling you if it doesn't say sixteen point one cents point something. It's just a note to people Okay. All right All right, I got a go on here I don't want to not answer your questions, but I may have to put a note and then ask me after class If you can't find it here Probably right here. There we go. I don't know. I just didn't notice sixteen point one dash twenty six All right. Now then we got our f sub y and our s sub u. Here's where we got it got it on page two dash forty eight from our Material strength tables He says it looks like we've kind of forgotten stress concentrations on those holes So if you remember your 305 work these holes had very high stresses on the inside not so much on the outside The p over a you're using is down in here somewhere But he says we really have it because What happens is that the fiber that's highly stressed reaches yield and then first thing You know all these stresses reach yield. So the final stress distribution before the plate really breaks really is uniformly distributed He says if you remember from your 305 work, they would go up to about three times as much as more than twice the average Here's actually the thing come out of our 305 book. They can be three times as much We don't care if they're three times as much because once the plate starts to yield it hasn't broken But it just quit picking up load as you keep putting load on the plate then This fiber stops adding stress, but doesn't drop it like a piece of glass wood This fiber then reaches up there then this fiber reaches up there and then this fiber reaches up here And now then everybody's starting to move up towards the f sub u But you've already been told to stop at f yield Next example. We've got a single angle tension member It's a three and a half by three and a half by three eighths There it is three and a half by three and a half It doesn't matter which leg he sticks up, but I'd always lay the long leg on the bolted side By three eighths it's connected to a gusset plate Seven eighths inch diameter bolts are used. Therefore. They're going to use an effective hole as one inch Gonna use a 36 steel as usually expected on the out of the steel tables Service loads 35 now we're gonna get to compare with some loads 35 dead 15 live. He wants to know if it meets specs He says if you don't mind, I'm just gonna pretend that you know how to Use the number u Even though you don't just so we can Demonstrate how this problem works says once you get a little more sophisticated I'll show you how to pull this u out of a table Are calculated The load comes down and fails through only one hole. So be sure you only subtract one hole from the Gross area to get the net area Here are your dimensions where the holes are we don't really care where they are in this case But this if this is a three and a half inch leg This is first hole is out here at two inches and there is only one hole You can't get two holes in that one Here's the solution the gross area comes from page one dash 46 Nominal strength is equal to this comes from table bloody blah and There's your two and a half out of table out of Page one dash 46 the table on that page gives you 90 kips of nominal strength for gross section yield Moving on to net section fracture the book the the specs always call it next net Section rupture, but our book kind of flip-flops between the tubes. So don't be confused Here's the gross area Here is the diameter of the bolt plus a sixteenth worth of fit plus a sixteenth worth of damage Times the thickness of the angle That's this little area right here. This picture shows two holes in there Can't get them in there It won't fit So it leaves you a net area to 2.125 square inches Please reduce that strength by 15% you say why because Times that area gives you this much Strength net section that net section since it's so short can be run all the way up to the ultimate strength You don't have to limit it to f sub y 58 1.08 oh six hundred and forty seven kips Then we go back and say what's this times point nine and what is this times point seven five? Point nine is eighty one point seven five is seventy eight net section fracture controls the situation so you must make piece of ultimate your request for ultimate load less than your design strength Less than a resistance factor times the nominal strength So you start getting familiar nominal strength Design strength those kind of names you're going to be confused So our design strength is seventy eight point five. It's a smaller resistance He says when only dead load live load a presence You don't have much choice but have one and two because all the others are for snow and wind and rain and earthquake And if you don't have any of that Then you're not going to have to check those equations He assumes you know how and almost all the problems in here just have live and dead load in them Here is where he got his numbers for for those angles here was his gross area For a three by three by three eighths inch angle Two and a half square inches. I remember that's right Here is X bar You would use this X bar in calculating you in his case. He just says you as point eight five Pretend it is so we didn't really need X bar, but there it is on the next page And here are those dimensions on Where you can put these holes And if the holes are given in a problem, well, then that's where he's going to put them whether it's very workable or not But on the last page of your angles, you have a small table tells you workable gauges in angle legs So if you have a five by something Angle and you want to put a single set of holes in it you come down to a five inch Angle that's the leg size and If you only want to put one set of holes in it, that's G G You'll put them at three inches. That's where you ought to put them. That's where everybody expects them to go They'll fit nicely and get a wrench on them No problem If you need to jam two rows of bolts in here on a five inch leg Then they recommend that you here's the long leg you go at G1 and G2 So on a five inch leg you go two and one and three quarters Two to the center from the back and another one and three quarters to the next set of holes If you want to stick two rows of holes in a four inch angle leg Good luck And you have no numbers you can't do it they just not gonna fit you might you could get them in there You could drill them in there, but when the guy with the wrench comes at you swinging it Then you'll know you shouldn't have put the holes there and with the bolster He can't get the stuff in there to connect it up That's on page 1-48 last page of the angles Now back to our problem Our problem still had the loads to be calculated 1.4 dead the dead was 35 kips For 49 worth of total load. That's during construction during the life of the building When load really got way out of hand I very rarely see this happen 1.6 live could be the guy miscalculated the dead load by 20% It's a 66 kips. You must take the larger of the loads that you calculate You take the smaller resistance and the larger of the load your factor of safety. There's your factor of safety there's your factor of safety and There's your factor of safety and it's Safe they've been doing this now for 20 years 30 years Since 66 calculators is less than how much what is that number called? Design strength, that's correct. Are you sure that's not nominal strength? Yes, he says okay. Yeah, it's not nominal. It's nominal. You can't use you got a multiply times their resistance factor Here's a pair of double angles back to back He asks you to assume that the effective area is point seven five of the nominal We'll get into how to calculate you shortly Most people and I would suggest they have double angle stuff back there was sometimes kind of hard to remember How to use it if I were you if you had two angles I just go get one angle strength and then when you're totally finished multiply times two Howdy Same thing growth section yield yield times growths area 36 it must be a 36 steel that angle is a Five by three by five sixteenths long legs back to back means he's laying the five inch dimension Back to back and he is sticking the unconnected element, which is three inches long out That's a good idea Gross area for that angle is two point forty one square inches I don't know if I bothered getting the table for all of them. I just get usually one to show you how So you pull that out of the angle? Properties you're gonna get eighty six point seven six kips worth of gross section yield Now considering the holes in there there are two holes in a single angle The dimensions where they're at that doesn't matter, but it is a five inch angle So this one's it to that was at one point seven five The size of the hole The bolt is a half inch so add an eighth to that four eighths plus an eighth is five eighths There's your five eighths Thickness of the angle T is five sixteenths inch thick There's two of them That's not times two of them There's not two angles are there. What do we agree to do before we started? Only do one what is that two for? That's right. There's two holes drilled in that angle. Okay Times two is subtracted from the gross leaving you this much net The net is to be multiplied times you Soon you'll be able to do this without his help and asking you to assume gives you this much steel Nominal strength is that much steel one point five one four one point five one four Times the ultimate for piece a thirty six steel gives you eighty seven kips of strength Back on the previous page. We had eighty six point seven six There's your eighty six point seven six on this one have eighty seven point eighty one There's your eighty seven point eighty one. This one is not too bad. Please knock it down by ten percent This is not too bad. Please reduce it by twenty five percent seventy eight sixty five there's your strength And he says since sixty eight point sixty five point eighty six less than seventy eight where the seventy eight come from Regional problem on the next page Okay, okay. Yeah, then it is acceptable and Two times that That's because you got two angles before you go home. I don't know. I guess I just those are pretty I think I guess I drew another one. All right now then effective area Several of these things you have outstanding elements that aren't connected and they reduce the joint efficiency That's called shear lag Because what happens is you have a little oh, I know I did that you have a little element in here and The load comes down, you know, it's really I guess you should show us in his intention the tension load comes down and here's the little element and it pulls in some direction on that little element and Then as you go down here The shear stress is a little different as you go down Into the thing because the shear stress in this one is guaranteed zero because it's touching the air and so the shear trying to get down in here actually lags and So that you can get this condition of no stress no tension stress at all Where there's guaranteed no tension stress because nothing's connected now I have ways of Computing that First off in sixteen point one dash twenty-seven. Yeah, I knew I'd get to all of these things where they're coming from You'll find his insistence that you reduce the net area by Shear lag factor and Get an effective area one that you can really use in your calculations for strength or Welded connections The effective area is going to be the gross area not the net area because if it's welded you have no holes So in a welded connection the net area Minus no holes is the gross area Therefore the effective area but the effective area can still be reduced for instance You can have a plate and I think that's also something I showed up here No, I still have holes But if you weld this plate and this is the only place you can weld it is at the bottom and maybe on the sides You still have this problem with the stress can't get through the air down into the plate So when it's welded or bolted you can lose strength due to this you factor Now we break these you calculations into two general things Number one we know what it is if you just tell me what you're doing if you're doing an angle And you'll tell me the angle and you tell me how many bolts you're going to use The length of the connection then I've I got a really good equation. You can calculate you right on the money very close But if you say well, I've got the angle I'm trying to design the angle But I don't know what size bolts I'm going to use and I don't know how many bolts yet But then I'm going to just have to give you an approximation of what we find for that kind of a structure So it's pretty well broken up into if you really already know the connection Then this is a category that these three categories you'll use These things need to be scratched out. I don't know if they are in your book now or not things change If the connection is unknown and you say yeah, well if I don't know the connection How can I know the connection so I'm trying to design the connection well Then I'm I'll give you some alternate values that you are permitted to use in the design and then when you Find out what you're planning on using then you actually got something to sink your teeth into probably ought to come back here and Design it with the numbers that I'm that are correct Not just these should be pretty close another reason you probably want to do that as You might imagine these numbers have to be pretty low Because it's gonna have to cover all the things all the ranges and we say well, okay Just make him use a point six No matter what he usually gets it'll always be better than that The equation they found after years of study and a bunch of other equations that worked out Okay, but this one worked better is you is equal to one minus How far Does the centroid of the unconnected elements stick up in the air? What a dumb thing to do? Divided by how long is the connection? So here we go Here's what the person did they have an unconnected outstanding element There's your X bar Now in the book it may be listed as Y bar because the book this Shows all of his angles, you know sitting some way. I don't know which way Do you know it depends long leg up long leg down or whatever? But if you're looking for This number here in the angle sitting in this direction say that's the five inch leg and that's the eight inch leg He's gonna list that Y bar That's to him. It's Y bar when you say well, no, no, no I'm gonna lay it on the plate this way and I want X bar That's why bar out of the tables. You have to orient the book to fit your needs and L is how far it is from here to here? and if you're willing to extend this gusset plate on out and Put some more holes in it What happens to L? For the dang equation there it is look what happens to L L gets big X bar for that shape stays the same you subtract less Loss of strength you don't have as much loss of strength you get a bigger number and use a bigger number That says it should be because as the connection gets longer The load has more time to duck down into the plate below That's on our page 51 more information on page 51 a it's on page 16.1 dash 28 And this is a segui's equation 3.1. He refers to it later X is the distance from the center of the connecting shape to the plane of the connection and L is the length of the connection and Yes, sir L is from center to center of the bolts Center to center of the bolts if you say well gee I've got an extra Foot of angle over here. Well, I don't know why you got an extra foot of angle over there You know maybe your dad sells angles, but you don't get to count it in the length of the connection Yes, but nobody would do that Because nobody would do that. All right now then here are the real values of you Above here are the ones they really tell you what the things are but you got to really tell him the angle You're gonna use and you got to tell him the plates you're gonna use and that kind of stuff Down here if you say I don't know Well, then we're gonna let you use some approximate numbers For example for a wide shape miscellaneous shape American standard or HP shapes or T's cut from them It is incidentally once you find out the what you really gonna do You go back here to case two where I numbered the same things You welcome to use these numbers up these equations, but if you don't know what's going on then If your flanges are connected with three or more fasteners in the direction of the loading That's not too bad three fasteners be a lot better if you had four or more fasteners And if the B sub F of the flange is greater than two-thirds of the depth you get to use this But if it's not you get to use this they're trying to find Ranges of things where you can just go ahead and pick a number to get started with Good equation is this one here where you take one minus X bar over L Here for example, here's an angle. This is the one that makes the most sense. There's your X bar Here's your X bar where you put it The L is the length of the connection between the boats There's your L one minus says all tension members Says, please don't use this for plates and don't use it for Holostructural shapes where the tension load is transmitted to some but not all of the cross-sectional elements That's how you got in this problem in the first place Our longitude and the wells and these things take some thought You know, you really do have to sit down and look at what he is Telling you and where you go in these things All right Thank you for coming the half that's here. Thank you, sir Yes, sir All right, let me I'm gonna be doing clean it cleaning up here, but I'll listen I Do not My office hours are Excuse me. You're in my way Shame on you Is it Yeah, well, it's for this problem here is that and you said this turned out not to be steel Yeah Yeah, so I don't know why you're not right that doesn't make any sense to me except probably the solution manual the guy Just used to eat for steel because he's so used to it, which is wrong So, you know, you know, I gotta get this done. I'm sorry. See I get off on these things That's not come I say I won't answer questions