 Okay. All right, we'll continue with tap threads and in case you're wondering what page you were, you're on, those of you who have joined us for this session is page, should be page 926. And now tapping is done with either by hand or by machine. And the bulk of the metal, though, is taken out with the tap drill, of course, which has a diameter equal to or slightly greater than the root diameter of the thread. And of course we covered the number of chamfered threads and so on. And then the bottom tap, one of the things I wanted to mention there is that I guess in some cases you have to even take a, they have the 120 degree cone, I think, on the bottom of them and you have to grind it off, I think, sometimes. If you really want to get all the way down to the bottom of a hole. Now here's ACME threads and those are kind of an oddball type, but nevertheless they've been around since the 1800s. And they're used for transmitting power on like on jacks and perversing motions on machinery. In fact, those of you who've ever leveled a house or something with a house jack, they are ACME threads. They're kind of a square cut type thread. And scissors jacks sometimes have ACME threads on them. They have a general purpose fit class of 2G, 3G and 4G, with 2G being the sloppiest and 4G the tightest. And they have a series of diameters and threads that are to be used whenever possible and they call it centralizing for the tolerances. And they have the three classes and the 2C, of course, is the worst and the 4C is the best depending on what you want as far as backlash or anything like that goes. And the same tolerance designations are used for both internal and external threads. Now here they are, as you can see, they're kind of a square type thread. Very thick stubby and transmit a lot of power. And in this case, they really don't have much of a radius in the bottom because they make them so strong that they figure that they'll carry the load. And of course, there's no impact loads normally on these because it's something that you're turning so slowly that you don't generate any impact loading. Then we go to stub act me. It's about the same thing as the other one except that it has shorter height on the threads. And let's see, this is the one I believe, no it isn't either. I was thinking one of them, the English and the Americans have a different setup on it. But the stub act me, the regular is .5 pitch while the stub is .3. And if you turn over, you can see the difference on the next table. You see it really just has shorter threads on it in this direction. And of course, all the different thread geometries and everything are on there and the pitch diameter and all that you can look up at your own leisure when you feel that you need something to help your insomnia. Ah, buttress threads. They have been around a long time too and they're kind of special and they're used where loading is in one direction. Typical examples are airplane propeller hubs, columns for hydraulic presses, and breach assemblies of large guns. They have a flat angle on the loaded side of only 7 degrees from the perpendicular and in a pressure angle of 45 degrees. And this is the one that the British and the Americans differ on, the height of the threads. .4 pitch and 6 tenths pitch. What the US prefers the .4 and the British believe the use of the .6. Now I'm sorry, Americans use the .6 and the British use the .4. But anyway, a guy pointed out an example of these to me here while back that they had a press in their plant. That they had to fix and he found that it had these oddball threads on it called buttress threads and he knew that I was into fasteners. He said, you ever hear of buttress threads? I heard of them. They're not very common. And you see there are kind of odd here. Here's that 7 degree angle on the pressure face of them here. This is two different pictures from a ANSI spec, I believe. One shows threads with a radius up here. The other one shows threads with no radius. And they have their use and the thing of it is this guy found out with his press. If you want to fix them, these are normally machined cut on. There's no no taps, no dies, no nothing for them. You have to fix them yourself, random in place. Now if we go to cross-sectional areas for thread calculation. You have different cross-sectional areas for tension and shear stress calculations. If a fastener is loaded in shear with no threads in the shear plane of the hole, then the full shank area can be used for the shear stress calculations. For tensile stress, you use a minimum area through the threaded portion of fastener, but it's not a circle with a diameter equal to the minor diameter because since you have a root on one side and a thread on the other side, you get slightly better benefit than that on the diameter. So you get an effective diameter that's slightly larger and there is a formula for calculating it. There are a number of formulas as far as that goes, but here is a common one in which n is the threads per inch in the English system and d is the shank diameter, so you have, this is your correction factor here for the fact that you're not using the full diameter of it. And then for metric fasteners, you have this for the correction factor where p is the thread pitch in millimeters and d is the shank diameter in millimeters. And in the appendices, which you people don't have, we'll be getting later, we have a derivation of this tension formula for calculating the cross-sectional areas. Now here's a little handy-dandy formula for calculating thread pullout. And this is one that I've never seen in a textbook. I got it from some of the people I worked with at Martin Marietta. It's for shearing off threads in a hole where normally when you tap into a hole, the material you're tapping into is weaker than the fastener. So you're concerned about how long the thread engagement you have to have to keep from pulling anything out. So this formula helps you to conservatively arrive at that. You have pi times a mean diameter, and the mean diameter is usually pitch diameter, and you have an allowable for your material in shear, whatever it is. If you're working with yield, you put in the shear yield allowable. And if it's ultimate, you put in the ultimate allowable. Then the length of engagement. Now that length of engagement is the length of full thread engagement. The denominator has the three in it. If you were going to be totally theoretical about it, you had a perfectly mated threads, then that figure could go down as low as two, because actually if you visualize it for a moment what you're doing, you're pulling out a little cylindrical shell. And if you had things exactly at the pitch diameter so that the external internal thread were the same, then you would be splitting that little shell between the two of them so this factor could go all the way down to two. And since threads don't make that way, the three is put in as a fudge factor, as I have mentioned here. And there are some other methods given in H28, Milhambock H28, for calculating pull-out. And once again, some of them are a lot more complicated than what I've done here. If you have a chance to do it, it will work, so you can go ahead and go with it. Now moving into the TIG resistant bolt section, of course people usually don't even think about that, and it gets them in trouble. But if you have cyclic loading on a joint, then you need to minimize the stress risers created during the manufacturing cycle. And of course some of these are the threads, thread run-out, thread fillet radius, and work hardening through forming the bolts. So you also have to monitor the installation of the bolt closely to minimize the cycling modes. And of course one of the things that you do is this is one of the cases in which Murphy can tighten them up tight. Because with a fatigue joint you want it to be as tight as possible, because it cuts down on the cyclic loading. Now, one of the things you can use of course is the fasteners with cold or old threads, because that gives you the residual compressive stresses in the thread surfaces, and gives them more fatigue resistance because fatigue only works in tension. So as long as you keep things in compression, you're all right, it's just like with glass, they don't worry about cracks in glass if it's in compression because it doesn't do anything, it's just in tension. Well it's the same way here, if fatigue is compression is fine, but tension is where it gets you in trouble. So some of these fasteners, as I mentioned earlier, you actually have to cold roll the threads in order to get it up to the strength that you want it, so that's a good fatigue bolt. Also the J threads are better than regular threads in fatigue, because they have the larger root radius. Then here's one of the other problems that you can run into that people ever once in a while forget about is the elongation limits on materials. One of the rules of thumb on designing fasteners is don't use a material at a strength level that has an elongation below 10%, because when you get down below 10%, your stress risers become much more important. As a matter of fact, H11 tool steel, which is used for high strength fasteners, can get you in trouble and some of the aerospace companies are backing off on using it at the real high strength because of that, because it goes down about a 7% or 8% elongation and when you get down that low, then you can get brittle failures. Now, J threads as I mentioned are better, and using countersunk washers under the heads to minimize the washer contact with the fillet radius. And then if you really want to get sticky and have a super duper fatigue type bolt, you can undercut the shank down to the same diameter as the minor diameter of the threads, and this does away with your stress concentration on your thread run out. You don't have any run out then because you just have a smooth shank and when the thread runs out, it runs out on top of the thing more or less. So an undercut diameter fastener is better in fatigue than a regular fastener where the shank diameter is normally equal to the major diameter of the threads. Now, the hardness of nut less than bolt hardness. That one can be very much a problem in some cases. Since the bolt load is initially reacted on the first one or two threads and that has to deform something in order to spread it out, you want your nut to be softer than the bolt so you can spread your load out. And a rule of thumb is that the maximum hardness of the nut should not exceed the minimum hardness of the bolt. And that's even stretching it. Normally you would want it to be, for instance, a 160 KSI bolt to use a 125-145 nut on it in order to distribute the load. Now, this court case that I mentioned to you earlier, the chair failure, that was the thing that caused that chair to fail was that the furniture manufacturers don't have too many fatigue engineers on the job. They go out to the hardware store and buy whatever is cheapest and they bought the bolts from one place and the nuts from another place. And this deformed thread nut in deforming it, they had actually work hardened it to where it was harder than the bolt. So what it did when they put it on, it just stripped the threads of the bolt as it was going on. And then in a matter of about six months, this guy's brand new chair fell apart and sent him for a ride. So he sued the furniture company. And that's where I got in on it. But use a desirable joint loading diagram. Now, you want a fastener joint stiffness ratio of five or higher, and we'll go through some of the things on calculating joint stiffness, fastener stiffness, and so on, to minimize the cyclic loading on the fastener. And coming back again, I keep repeating this one, but it's worth repeating, avoid tapped holes if you can. Don't use them unless you have to. I was on a design review here one time in which this young engineer came up with a design and he had heard that when you used aluminum, you were supposed to use inserts. So instead of bolting through, he put through holes in but tapped them for inserts because after all, you're supposed to use inserts and aluminum. But if you have a chance to use through bolting, that is the most efficient, most trouble-free way of doing it, regardless of what you're bolting in. All right, now the tapped holes are cut rather than rolled, and the radius of a tapped hole is not measured normally. If you want it measured, it's a lot of trouble. So you can get all sorts of undetected stress risers because think at it from a practical standpoint. You've got a quarter-inch hole. The inspector is going to go up and look down in it and say, yep, there's a hole there. It looks all right to me, and that's about the amount of inspection you'll get on it. Now, use a lot of small diameter bolts if you can in order to give you a more elastic system because that gives you a better ratio of bolt joint stiffness to fastener stiffness. And of course, that kicks the labor cost up so that you have to wet to see what you're going to do in order to make the joints survive. Now, the other thing you have to do is consider the thermal loading in the joint. Remember I mentioned earlier about using Belleville washers to give you a longer spring constant, if you will, and a bolted joint to take the thermal cycling? And particularly if the bolt and the joint materials are different, then you have to watch it closely. We had a problem on the Centaur vehicle when they were using good old A286 bolts on aluminum flanges. The only thing is they tightened them up, torqued them down at room temperature. Then when they tanked up with liquid hydrogen and liquid oxygen, the temperature went down to something like minus 300. The aluminum shrank and it started leaking because the bolts got loose. So they like to never hit a happy balance on that of getting bolts. In fact, they had to get higher strength bolts so they could crank the torque up so that the thing would be all right at room temperature and still not leak at the cryogenic temperature. So this is a problem you have to be careful about. Then here's the other thing that you should do. This is one of the few places that I agree with some of the automotive companies on. It is torque the fasteners close to the yield point if it's a fatigue joint. And if you do enough testing to determine where it is, then you can torque up to 90 to 95 percent of yield. And the higher preload decreases the cyclic loading. And I have some figures here to indicate this. If you want to leaf back and forth between 10.7 and 10.8, or I'll tell you what, if you will go to the next page with the graph there and then Betsy can keep hers where it is, there we go. Now we can work back and forth. On here, here is the initial loading, here is yield. So here is the initial loading before you put an external load on the thing. Now when you put the load on, the cyclic loading on the fasteners is just the part between here and here. So as you will see when I show the next one of these where I deliberately put the two points closer together you get a lot less cycling. Then this is the clamping load remaining when you go all the way up to yield. Now this represents the stiffness of the bolt and this represents the stiffness of the joint. So if you get a better ratio between the two and lean those lines over a little bit you get less cyclic loading on the bolt when you apply an external load. Now if you go over here we are toward above yield because here is the yield point, there is above yield. Then on this one we really applied a load that took it way above yield and failed it, it separated. So now if you look at the 10.9, there I put the initial preload and yield are fairly close together. So you see the cyclic loading is just between here. So therefore you get less cyclic loading with the higher torque on the fasteners. Now this figure was overtarked. If you notice it is kind of wiggly here. Betsy overtarked it trying to scan it into the scanner and it wouldn't scan in right. Okay moving on now to fastener torque which is 11.1. Now determination of torque values is one of the most difficult and controversial aspects of fastener design. And if you talk to Murphy he says if tight is good a little tighter is better. But it doesn't always work out that way. Murphy is the guy that runs the wrenches. But the variables involved the joint material strength, the coefficient of friction between mating surfaces, the effect of friction between the bolt head and nut or its mating surface, and the effect of coatings and lubricants on the friction coefficients themselves. Because the amount of lubricant you put on changes it all together. Now the percentage of bolt tensile strength that you want for preload. That is something that is difficult. One of our guys just to show you how things can vary. One of our guys had some stainless steel bolt and nut assembly. That had been locks cleaned. Now locks cleaned is like ultrasonically cleaning your jewelry or something like that. It is clean clean. And he was required to have it that clean so he went to assemble it. He had used up his allowable torque before he got it seated because dry clean stainless on dry clean stainless has a real high coefficient of friction. So this just shows you what you can do going to an extreme. Now the other thing is what is the distribution of total torque to tension, shear and friction. You know when you torque up a fastener that you have a certain torque value applied. But you don't know how much of it went into tension, how much of it went into shear, and how much of it has lost the friction. But it all has to be accounted for. Then the other thing is the relative spring rates of the bolts and nuts and the joints themselves. And then accounting for the running torque of the locking devices. All those different methods of locking themselves have what is called a running torque that has to be accounted for. Now head friction. If the fastener is tightened from the head, the bearing surface for the bottom of the head becomes a big part of the friction load. That's why that having a smooth washer, hardened washer under the head is a good idea. Even if you don't necessarily have to have it, it's good because it gives you a hardened surface that will have a lower coefficient of friction than the joint material itself. Plus the washer will deter or prevent embedment of the head where the joint material is softer than the bolt, which is usually the case. Now if head friction locking is desired, then you can maximize that head friction. Remember earlier I covered the serrated head that you could use without a washer or don't use any lubricant on the thing. And then of course you will use up more of your torque on friction and have less in it and actually load which you have to account for. Nut friction, pretty much the same thing. You can go either way, you can maximize it or minimize it by using lubricants and stuff like that. And the nut usually contains a locking device. It's easier to install a locking device on a nut normally than it is on the bolt, so most of the nuts carry the locking device. So the running torque of the locking device, and I'll go through definitions on it, but the running torque is the amount that it takes just to seat the thing down to the surface. And it's usually a small fraction of the total. Now the K factor, people say T equals two-tenths FD. And that two-tenths is used religiously. Well that two-tenths is this budge factor, which has this formula right here. And for those of you who have a copy of my fastener manual, I had the right calculations in the manual, but I had the wrong terminology. I had a Greek psi for this angle here, it should have been lambda according to the formula, and the calculations were done right, but the terminology was wrong in it. Anyway, this is the formula that you use for calculating that K factor. Now, the d sub m is the mean thread diameter, which you use pitch diameter for. Lambda is the thread lead angle, and mu here is the friction coefficient between threads, and alpha is the thread angle. In this case, since you have a 60 degree angle, it's half of that, which is 30, and mu sub c is the friction coefficient between the bolt head or nut and the clamping surface. So if you throw all those together, and you're able to determine them well enough that you have some confidence in them, then you run a calculation and get an actual value for that K factor. Now, I did some calculations using these coefficients of friction, and in this case I used identical ones, although you could have different ones for the between threads and between the bolt or nut. And look at the variation that you can get with the variation in friction coefficient. You see, the K factor, the .2 that we use, is actually a little bit high because it would be somewhere in here would be a more realistic value. However, one of the objections to using zinc plating is that the friction coefficient with zinc can vary enough that that value can go anywhere from .4 up to almost 1. So now when you do this, then most of the torque that you're applying is going into overcoming friction, and your axial load on the fastener isn't very much. Here are some torque definitions, and these are courtesy of SAE AS1310 and Marshall Standard 486. And some of them have been cleaned up slightly to make them a little more readable because they've gotten kind of out of hand. So just for torque itself, of course it's a force times a distance, and you have a moment arm, which is the length of your torque wrench, and then a force that you put on it. And if you have a torque wrench, it will register the amount of torque that you're putting on, or if you have one of the old do-it-yourselfers, it has a needle on it, and you measure it by deflecting the rod. And that one is a plus or minus 40%, depending on whether you can hold it in place long enough to read it while you're doing the torquing. The applied torque is the torque transmitted to the fastener of the installation tool, and then the running or prevailing torque is the amount to overcome the locking device itself. So just to seat the fastener. And here are some other definitions, the double torque or retorque to seat materials being joined where you had interferences or sheet gaps or form and place gaskets and stuff like that. And also where you've torqued around one time in a circle of bolts, and then you need to go back and check them. The no-load torque is the torque required to overcome kinetic friction between mating threads without a locking device, and that is usually, unless you have threads that are damaged or something, that is usually next to nothing. Then the installation torque, design torque applied in a tightening direction and includes kinetic-static friction, self-locking features, and required to apply a desired axial load to the fastener assembly. So it's measured in the tightening direction only. And of course the thing that is usually indeterminate, or not indeterminate, but hard to determine is how much axial load do you really get for a given torque? And here's limiting torque and so on, which you can read through these multiple torques required to seat parts where you have heavy interferences in an assembly. And one of these has to do with where, if you're torquing fasteners on a flange, or if you're torquing the lug bolts on your car or something, you know you always torque 180 degrees apart. And after you get them snugged down so that you get the effect of the adjacent fastener to the one that you're torquing down to make sure you get it tightened down. If you tighten them down and then tighten one down and the one next to it will have a slight amount of loosening due to the give of the flange itself. So you have to go back and recheck them. In fact, the guy by the name of George Bible, formerly of the University of Akron, came up with a computerized program on dealing with large flanges, and we're talking near six-foot flanges or something like that, on the iterative process for doing the torques on them to get them all torqued down within satisfactory limits, and gave a presentation one time at the Voting Technology Council. Now here's the seating torque, and that's just to bring the bearing faces into a seated position, and then the brake loose torque, torque required to loosen the fastener from its installed position. There's various other definitions that get too confusing, and Harold Casper and I went through them and eliminated some of them that created too much confusion. Now here's the big question, what part tension? And that's the most unpredictable one, and the clamp load in general only represents something like 10 to 25% of the applied torque, because the rest of it is used to overcome friction and various other things in the joint. So, but the thing that you've got to look at is just because you put a certain amount of torque into a fastener and it doesn't have a lot of axial load on it, doesn't mean that that torque went away. It's still in there, in shear, or somewhere it has to be accounted for, so that's why you've got to be careful on overturking stuff, and you've got to combine stresses and check them all against the total strength of the fastener. So, and of course this is the thing here that the von Miesi stresses can be calculated and compared to yield and ultimate strength of the material. So, or for those of you who feel academically inclined, you could use a Mohr's circle and take shear and tension and plot them out and get all that sort of thing, but stress ratios work better. So, and there are torque values and these are tongue-in-cheek nominal ones for both inch and metric fasteners in the appendices which you will get later. Torque accuracies. It's only as good as the type of measuring device in the operator. And of all these methods, the worst one of all is the impact wrench. Joe Greenslade, who is a writer in the fastener world, put out an article here sometime back that I got a chuckle out of. I believe it was titled, Impact Wrench, The Engineer's Worst Enemy, because the impact wrenches that these grudges use are never calibrated probably. And they put them on real good and tight. And then you need a truck breaker bar to get your lug nuts loose on your car when you go to take it off. So, that's the worst one. And if a torque wrench is used to apply torque, the applied torque should be at least 70% of full scale of the wrench. In other words, don't use a 175-foot-pound torque wrench with a number-eight fastener, because there's no accuracy there, just like it is with any other reading. If you're doing instrumentation, you try to get, say, 70% of full scale in the range of your actual measurements that you're making, because you don't, since the tolerances are a percentage, you do not want to be measuring in the bottom 10% of your scale when you're making readings on anything. Now, here is a table with approximate values for torque measuring methods versus the accuracy and cost. Now, you see the feel there in which the guy just says, well, I've been doing this for years, so this is about what this should have on it. A cheap way of doing it, and if you've been feeling those joints for years like that, a lot of the times it will suffice. I don't use a torque wrench on my car unless there's a specified value called for, like a tie rod end or something like that, where you have to go to a high torque value, then I get out the torque wrench, otherwise I don't. Impact wrench, and it's probably even worse than that, but that's the value that some of us had agreed to before. The torque wrench that actually gives you a reading, about plus or minus 25, turn of the nut. Now that's a method which I will cover later, which is fairly accurate as long as you want to use it, but you probably wouldn't want to use it because you go above the yield on the passenger. Then these load indicating washers, they give pretty good accuracy, but of course the amount of labor involved runs a cost up. Remember I covered those, the one that had the little bumps on it and the other one that had the little internal bushing that you compressed. Fastenery elongation, now that can be used if you are say, bolting a flange and you have a guy there with a scale, an accurate scale, he can actually measure fastenery elongation as long as he subtracts out the dead part that didn't expand on it. And get some idea as to where he's at on it. But then you can go to string gauges. Now string gauges are real accurate, but the only thing is, how do you do it? How do you put string gauges on a bolt that you're installing down in a hole? It's kind of hard to do. So what you normally do with the string gauges is if you're really interested in finding exactly what you want, you put them on one of the bolts and test it under the same conditions as nearly as you can to duplicate the actual installation. And you get a torque reading from that and then use that torque reading on the bolt you're going to install. Then of course the other thing was these direct tension indicating bolts which is kind of a string gauge type setup. So I will cover some of those in further text here. Now torque striping, that is used a lot by the aerospace companies for after you have decided the final torque value on a fastener, you actually just take a marker of some kind, they used to use a paint and now we use a blue sharpie pen to mark across the head or the nut straight across onto the surrounding surface. Now this is a visual indication if the thing switches position on you because it will show up because the two marks don't line up anymore. And that is a very common thing in the aerospace world, that way you can look in later and see whether anything has changed on your installation. Now joint relaxation, that's not what you're going to after today. It's defined as the unloading of a fastener after its final torque due to a number of contributing factors. And here are some of the major factors, embedment of the washer, the head or the nut in the joint material, yielding of a high spot or a blemish on the head, nut or washer or joint surface after final tightening, and untwisting of a fastener from initial torsion where the shank had an interference bit in the hole so you cranked it down but a lot of that went into putting some torsional twist into the fastener. And so after the thing settles down it kind of makes its way back, creeps back to a equilibrium position and in doing so that will lessen the load on the fastener itself. And then creep of the joint material itself. Then here's the other thing I mentioned like the lug nuts on your car. Failure of the installer to re-torque a pattern of fasteners after initial installation to compensate for effects of adjacent fasteners to each other because when you compress the surface next to the fastener you torqued before then it changes the load on that fastener and you've got to go back and re-torque. Also here's why I don't like to go up to the yield point on fasteners. Inadvertently exceeding the yield point of the fastener during the initial torquing process. Now there you're in real trouble. In fact that's what they did on that first time around on that Centaur bolt problem I was talking about with the cryogenic temperatures. They said well we'll just increase the torque. So they increased the torque and they were yielding some of the fasteners. When they checked them again they were down to something like 40% of the initial load so they had to go to higher strength fasteners. Then the other thing is critical joints should be inspected for relaxation a few hours after installation. You go through and check them with the same torque and see if any of them have loosened up any. Now here's the turn of the nut process. And this is used in the construction business because it's something that visually you can do particularly with a big bolt. You tighten the nut above yield so what you do is you tighten it to what you think is about 75% of ultimate load. Then put a mark on it. Then turn the nut an additional 180 degrees. This brings a bolt stress up above yield but below ultimate providing that the material is ductile so that yield and ultimate are far enough apart. Now that is not used in the aerospace world because you don't risk stuff like that. Aerospace torque values usually are 50 to 75% of yield depending on the application as to whether you have much tension on the joint or none and so on. So that because you still have to check for both shear and axial load. Now tightening faster beyond its yield is risky because it's so difficult to determine where yield is. This is why that if you go look at the definition of yield for a material in a something like meal handbook five you'll find that it's based on two tenths of a percent permanent set. Because you don't know that you're at yield unless you have the thing on a machine until after you've exceeded it because you're still going up on your elasticity curve. And until you peek out from the straight line you don't know you're above yield. So as I mentioned earlier the usual reason for going up close to yield is to minimize the fatigue effects on fasteners. But unless you have done an awful lot of testing it's not a good idea to go up to the yield point on a fastener. Now on joint stiffness we have alluded to it many times up to now and we covered the joint loading diagrams. And now we just look at the joint itself as we tighten the fasteners. John Bickford actually has used a spring type analogy on this which makes it easier to understand because you take a piece here that has three different cross sections. It's three different springs with three different spring constants. And so you can think of a joint or a fastener that way. And here is another one with the joint stiffness. Next page. I thought we'd had a stop, a glitch there and things. Okay. All right. This one's one on one but just leave that one up for anyway. Here is another thing that kind of shows you here the concept again of a large spring representing the joint and a fastener. It's a little tiny spring that's trying to compress the big one. And of course to keep the fasteners out of trouble you want their stiffness ratio to the joint to be a pretty large differential. And theirs is showing clamping force. All right. Now you can leave yours up over there. And we'll go to the next one here in which we look at a bolt. Remember in school you had calculating the expansion or tensile elongation on a rod. And the delta L or change in length was just PL over AE where P is the axial load. L is the elastic length and A is the rod cross section and E is the modulus of elasticity. And so if you apply this to a bolt you can calculate these delta L's for different cross sections and their lengths. And John Bickford uses an extreme here on the next page. In which he took a bolt that had been machined all over the place and he calculated a delta L based on all these different L over A ratios since P and E are constant. So that is how you can arrive at a joint stiffness value for the bolt. Now I mean the stiffness for the bolt. But now when you go to the joint there's where the authors disagree and there's all sorts of things. So here are three different types of models if you will that are used to calculate joint stiffness. The sphere although it was listed I couldn't find any equations for it. The cylinder is used a lot and the cone is used a lot. And there are various ways of calculating the stiffness. Now what I'm talking about is if you look at these the hole here represents the hole where the bolt would go through. Okay now John Bickford uses a cylindrical model with a modification for eccentric loading at or near the edge of the joint. That is if you are wanting to use a circle and the bolt is close enough to the edge that you can't get the diameter circle you want. You can put in a fudge factor for the fact that you're closer to the edge than you should be. And this brings up another standard which is used a lot in the industrial world but difficult to obtain. So I found out is the German standard Vern-Dutcher engineer or otherwise known as VDI since no way you can pronounce it. That is a standard for doing calculations on fasteners that are loading the joint stiffness and all that type of thing. And I have a copy of it but I had to get it through the back door because the library couldn't find a copy in English. Shigley who wrote a lot of books on engineering uses the cone frustum model with a cone angle of 45 degrees measured from the bolt centerline. And then NASA Langley had another setup using a straight cylinder with three different equations depending on the minimum edge distance of the shortest side of the joint. Then another guy by the name of Alexander Blake uses a cone angle with an angle determined by a line drawn from the outer edge of the flat of the head to the centerline of the clamp joint. So this is the clamp joint here to here and there's the centerline of it where the cone comes to. And then using all of this stuff, all of these measurements to calculate a joint stiffness. And he comes up with a nice little equation here and this is for a particular angle of 45 degrees I believe here. No I'm sorry this is the Shigley method on the cone. We have the other one I guess in the appendix. But you have an equation there that you can use to calculate the joint stiffness so that you can compare it to your fastener stiffness to decide whether you're in trouble or not. Now as far as the joint stiffness calculations go, here's one of the bad parts about it. The effect of adjacent fasteners on joint compression is not accounted for in any of these. So these are all empirical and they're only an indicator. Then unsymmetrical loading under a fastener due to edge distance or cutouts is not accounted for. In other words you're using a perfect cone or a perfect cylinder. And then if the bolt and joint materials are different, the stiffness calculations must account for the different moduli of elasticity for the materials. Now so you're in a little bit of trouble there on getting these however things could be worse. Here are some of the things you can do. First try just a simple cylinder with a radius equal to the shortest edge distance of the fasteners. This is called the Barrett theory of least work. Don't do any more than you have to to show something good. If this stiffness is satisfactory compared to the fastener, don't go any further, go with it. If the simple cylinder is not satisfactory, add a washer with a diameter larger than the fastener head to kind of spread out the radius on your cylinder, then check it for that. And check the compressive stress under the head contact area to make sure that the compressive yield will not occur under the maximum clamping load. And then if all else fails, go do the calculations if it is critical enough. Now in most cases you are not critical enough that you would have to go to a lot of lengths on the difference between the fastener stiffness and joint stiffness. Only in rare cases. Now one of the things that you want to be aware of is don't use a big fastener on a thin joint because chances are then the fastener is going to be stiffer than the joint and you're going to have trouble. You'll be in trouble on it. But you can check them and see what you've got and if your ratio is not too bad even for taking that shortcut method, say 5 or something between fastener and joint, go with it and it should be alright. Now in direct reading of fastener tension, this question is asked how can I determine the exact tension I have on a fastener for a given torque? Well a direct reading is possible but it's not economically feasible for most assemblies. The technology is there but you can't afford it. So the usual compromise is to test fasteners under the closest actual installation conditions that you can come up with and determine a torque value then use that torque value for your production assemblies. And so we'll cover a couple of the, couple or three here of the direct tension measurements. Now this one is ultrasonic. That's a good one. Transducers mounted to the head of the bolt. But as the bolt elongates, the travel time for the sound, you know, the way ultrasonics work, you bounce it off of the back surface and back. So if you increase the length of the thing, it takes longer for the ultrasonic wave to get there and back. So that is, you can get a direct correlation between the elongation of the bolt which knowing the cross sectional area will give you the stress. Well that's a very good thing but the major drawback to it is you've got to have a smooth surface to attach it to. Because if you remember even if you go in and have your heart checked or something like that that they use an ultrasonic fluid that they put on, on your body so that because you've got to have a medium for it to go through. So you have to have a nice smooth surface and then you have to have some sort of a gel on there to put your transducer on, get it to hold. So now what do you do if you've got a socket head bolt? You don't have any place to attach the thing. So then once the bolt is calibrated for a zero load, you have to disconnect the transducer in order to torque the bolt down to the load you want so that you can measure it again. So this one is a good method but it's not really practical to do in most applications. Next one is direct scaling. Now that we had mentioned that earlier in which where both ends of the installed bolt are accessible such as pipe plans you can actually measure the bolt and subtract out the dead areas that are on the outside of the nut, the head and so on and use the elongation there of the bolt to arrive at a load. Then of course these direct tension indicating washers that we covered in the washer section those are used successfully in the construction business because you take a feeler gauge and inspect, keep torquing until you get a gap of a certain size and you have the load that you want. Then we have this test machine by Ralph Schauberg of RS Technologies for Armington Hills, Michigan. He's one of my fellow compadres on the lecture circuit on fasteners. And he has a machine that you can throw a bolt in it and it will tell you for a given bolt the exact amount that you have for tension, the exact amount for head friction, the exact amount for nut friction. But the only thing is it will tell you for that bolt. It won't tell you about your total installation so what you have to do is take a bolt that you're going to use and decide what you want to load it to, put it in the machine and determine what torque it takes to give you that stress and then use that for your installation torque. We will take a break now and resume in a few minutes.