 Howdy. Any question? Yeah? What's on the ratio that you said that's only like equal to like 0.3 around that area? You ever take a little bit? Yeah. Yeah, if you look in the back of the book, that's just what's shown. Also, of course, notice that for SI English units, there is no difference. Because there is really no units left for strain anyway. And this is strain divided by strain. In fact, that's where we're picking up then, again, right now. What's on the ratio? We just defined that on Tuesday. What was the symbol for it? I think it's, no, it's probably not new. If I remember now, no is like that. Well, whatever it is. It's boo. That's what it is. It's boo. Defined as, do we, you got it? You're looking at it? Lateral strain. If we give some definition to it in terms of direction. We had a pipe that we looked at. And if we just give it some axial direction. That was the direction of the force being applied. It can be, again, tension or compression. And then the transverse directions. Or it might even be easier if we do it more like this. If we look at a cylindrical solid that is stressed. In fact, we did this problem. And then when it elongates. Now we have an axial stress, sorry, strain, defined in the usual way. And then a transverse strain would lay all in some, so this would be del x, this is length x. This then would be del in the radial direction. And that just emphasizes the way we're looking at most of our materials. That there is no preferred orientation for the radial direction. This implies that maybe the strain in the y direction is different than that in the x direction. Sorry, the strain in the y direction might be different than that strain in the z direction. Which could be the case. There are materials where we would need to define a Poisson's ratio for the y direction that would be different than that for the z direction. We're not going to look at those materials. That's for advanced mechanics of materials. And beyond what we want to work with. So maybe if we just put this as a strain in the radial direction, then it reminds us that it doesn't matter what that radial direction is. It could be in any direction around there. A little different than might be implied here. We were going to say for our class that any strain in the y direction is the same as the strain in the z direction. Remember what I called a solid that does such a thing? Isotropic. Most of our materials will be such. What is the big material that we're familiar with where there might be preferred directions? Especially since if any of you buy lumber, and you know the growth rings, if you buy lumber you can buy it taken from a particular part of the wood. You might hear a Poisson lumber and that type of thing. Because wood taken from one section is going to be different than wood taken from a different section. Because it does have directional properties there. It's especially true in wood. If you look down the length of it, it's very rare that wood is cut such that the grain goes across the piece. Because then it's very weak for its usual purpose, which is a structural material. The grain in wood is almost always run down the piece. And the purpose of plywood is to even overcome that directional bias. Plywood is different layers with the grain running in one way in a very thin sheet. Then another sheet is glued over that has the grain running in a different way. And then another sheet is glued over and they can put even other directions. You do multiple layers of that in plywood with all those grain layers in different directions. In plywood it really doesn't matter what direction. You lay the piece into its purpose when you install it because it's got no directional bias to it because of the grain in the wood. So we're going to look at isotropic materials, ones that have no particular directional bias. If you get into this in advanced studies and even you can imagine the things that are now done with carbon fiber where laying down the fabric in the particular directions greatly enhances the ability of the structure to absorb particular stresses. A great example of that nowadays is in bicycles where almost all the high-end bicycles now are carbon fiber with the bias of the fiber fabric itself laid down in particular ways, in particular parts of the bicycle to absorb the different strains and stresses and all the different types of uses of the bicycle. So we'll revisit right here just to kind of get us going again a problem we did look at, I believe last week it was just like this cylindrical piece here. I'll even give you the same numbers. We're just going to take it a little bit farther. The original length was 500 millimeters and a diameter 16 millimeters. Everybody will know what OD means, you know what? Outside diameter. That's not a concern with a solid cylindrical piece like we have here because there is no inside diameter but very shortly we're going to be looking at tubular materials and we'll have an outside and an inside diameter and it'll be important to us which is which. And then we put that under some kind of axial load and it caused it to, of course that's greatly exaggerated, caused it to react in that way. And we had an axial elongation of 300 micrometers, radial minus 2.4 micrometers. We did this very problem last week. You pull out your notes or boot up your laptop to pull down that video except I don't remember which day it was. We did this very problem and actually came up with these different stresses in a different direction. Sorry, there's different strains. So you can either thumb back and find that or calculate it in about three seconds anyway. But from this we can get two other things now that we didn't have before. So now we can find Poisson's ratio. We can even determine what Young's modulus is from this test. So do both of those. Get you kind of warmed up here because man we got a killer problem coming up. It's going to set you back a couple hours. Bob's question is what's the micro stand for? Help them out. Ten to the negative six. Ten to the negative six. The way I remember that Bob is that if I see a micro I remember it means ten to the minus six. That's how I remember it. This is a little help to you there. Go to the library. Yeah, because a lot of times somebody will get up and go to the bathroom and leave their calculator sitting there and then you just take it. Oh, I don't condone that. Do you have one just didn't bring it? Yeah, no, it's all right with those developments. And over there is it. Oh, by the way, I think we have a test coming up next week. First exam for, yeah, Tuesday for these first three chapters. So it'll be up through push-on ratio. I don't think we'll, I'm across much new on Monday. For you new guys, my tests are open, both open notes. Since it's only a one hour class sometimes it's tough to give you enough time. So what I will typically do, does anybody have a class right after this? Because what I've done before when somebody did one, we only had one hour but then there was a test after this I'd give usually two in class problems and a take home problem to do. Would you rather just sit and work for a little extra time on Tuesday or have two in class and one take home? There's one vote take home. I think you said in class. Did you just threaten him? Do you want to? So you say in class, you say take home. Preference, two in class, three in class, four in class, wishy-washy. Four, actually the wishy-washy came close. Wishy-washy is a stronger vote voting block than you were. All right, so we'll do in class. By that I mean maybe 20 minutes extra. I would hope you wouldn't need more than that. I'm not trying to trick you on that. He's just trying to see the basics of what we're doing so we can keep going. What comes up next depends, of course, on a lot of this stuff. I don't know what we've been doing over it. All right, you had those from last week, I hope. If not, they're pretty easy to come up with again. I think TJ, you were the only one who wasn't here. What we get for the axial is just the 300 micrometers divided by the original length. Watch your units a little bit. Remember what units specifically we used on that problem last week? Remember there were thousands of choices. 600 micros is left okay. I think even radians is tacked on some of those sometimes. I don't know how much sense that makes. It's not an angular measurement. Lots of different choices. And for the radial strain, the change regional dimension, this is exactly as we had last week. Same units. Anybody get something different than that? Usually what I'll probably do on a test if you have to come up with these, which you could expect it might be likely, I'll give you particular units for two reasons. One is just to make sure you can handle the conversions because there's a lot of different possibilities here. And when you get to working in some place if you're working in this, they're not going to ask you to give it to, to do it in any units you feel like. You're going to have to give it to the units that are standard in whatever company you're working in. That way when you communicate with somebody else, they all, you all agree on what you're talking about. Also makes it a little easier for me to grade and we're always interested in something that makes things easier for me. Anybody have Poisson's ratio? Point who? Point two five. Right in the order of what we're looking for. The main thing you have to do is watch your units. If they're the same top and bottom, then there's no worry. Oh wait, isn't it minus point two five? That's just why we have the absolute value here on the term. Remember getting the habit of putting a zero in front of your decimal place. It's just the professional way this is done. I won't take off for it. It's just, it's one of those little things I try to give you to keep your, there's just a lot of little tricks and traps and pitfalls that can happen to you as a working engineer and I'm hoping you're going to devoid some of them. That's one of them. Getting the habit of putting in that lead zero. Wouldn't be a trouble here because anybody working with this would know that Poisson's ratio of 25 doesn't make any sense. Figure was point two five. But getting the habit of doing that itself anyway. Anybody find Young's modulus? If so, how? Find the stress they just got. That would be, well I gave it, yeah I didn't write it up here but did give you that low previous, previous problem a couple weeks ago or two weeks ago I guess, I did this problem. This kind of thing could be used I guess as an aid in trying to identify an unknown material thing that's done forensically. Give it to me if you would please in units of gigapascals. Do I have a calculator either? No, nothing. You should have a leather, you know a holster for it. I mean your engineering students, we used to have to carry slide rules like that. We could handle it. You know it's at home on my desk. You didn't forget your half gallon of blue drink. DJ's got both calculator and his morning drink. There's no try. Dewey's got calculator and two morning drinks. I don't know what is, there's something about this side of the room over here. Yeah, yeah. When you forget here you got it. I found, I remember finding the joys of circular calculators because they can be made pocket size and you don't have to run out the end of the slide rule and change the calculator. Well you don't even know what I'm talking about. So slide rules are great. It's one of those skills that all the old engineers would say, oh kids these days should have done it the way we did. Got it? What did you check with? You don't have calculator. I do have slide rule in my office but that helped. Actually I've got my grandfathers. In order to increase the significant figures the only thing you could do is just make slide rules bigger and bigger and bigger. I've got my grandfathers. It was about this long and had a magnifying glass over the hairline so we could read it even more, even more precisely and add more significant figures to it. You guys are calculating something. I'll go get it and show it to you. And a gold embossed case. It brings tears to my eyes. Double sided. It's got signs, cosines, square roots, cube roots. It's got everything. More than you'd ever possibly use on here. I'm sure there are calculator games. I don't know what they were. My grandfather received the first master's degree awarded by Caltech in 19. What do you got? You got a calculator. What did you get? In gigapascal. What was 100? You can get that. You got something different. Let's check. Let's check. Did you do the stress separately? No trouble other than it's killing it. Area is sometimes trouble here for students. What do you use for area? R squared, I hope. But we've got, remember, the original diameter over 4d squared. There we go. So we're automatically in Pascale's, Pascale's a Newton per meter squared. Those numbers look okay. The stress out separately. You don't have to, certainly. You can put the values into here. Sometimes it just works better going from a larger problem to two smaller ones is all. 0.49? Scowls over here, including some me. You got what? 59.68 times 10 out of 6. But I got 59.7 and then what? Positive 6. We have negative, couple negative things on the bottom. And that's in Pascale's. So that's 59.7 mega Pascale's. We now have 59.7 Pascale's. Divided by the strain in the axial direction, because we're looking at the axial stress. Those have got to match. 600 times 10 to the minus 6. Micros. Those cancel then, the 10 to the 6. Cancels the 10 to the minus 6. Yeah, I hope not. And then that gives you, we'll just call that 60. So we have 1 tenth. That's 10 to the 12th. What's a gigapascale? 10 to the ninth. So if we move this over on 3 Pascale's, then what's a gigapascale? So does that look about what you got? Not a lot of precision required in these numbers. So 99.97 is kind of a wasted effort and ink. Like remember, we're going to build a big factor of safety on there anyway, usually, if you were actually in the design of this. So don't belabor the point with a lot of details, especially if you haven't. Slide rule, which automatically takes care of significant figures as you go. You just can't read the crap off the screen. You guys can read it. Through that calculation, do you have to have the stress in the microbes? Because if you had a... It's just like no units. If you take off the microbes, it's 600 times 10 to the minus 6th meters per meters or inches per inches. Okay. Yeah, if you don't change it back to this. Percent is kind of like a unit itself. If you put percent, if this value in the terms of percent, then you've got Pascals per percent, technically. Generally, I think on these things, if you convert down to the base unit as you go, you generally have a little bit less trouble. Once down to the base units, take it all the way through, and then once back up to the requested units, you're generally okay. Or if I don't specify, or if you go to work in this field and it's not specified, you can leave it like this. It's not wrong. But as you can see, we got a lot of changing back and forth from very small to very big units. And that's not going to change. There's times when we'll have very normal numbers, but there'll be a lot of times when we're working with very small and very big units. All right, so here's a nice new problem for you. I have a beam here of three meters in length. Stencil right on the side of it, how big it is there. Supported by two cylindrical posts. Looks like grass, doesn't it? It's a bit out of my green chalk. That would really help. Notice the two posts are not the same length. Slightly different lengths on those. Remember what we're looking at lately has a lot to do with 220 millimeters. This one's 210 millimeters in length. Exactly right there. Of course, he's drawing to the scale. Both of them have the same diameter. Paid out of 14, 6 aluminum. We're throwing numbers around like that. You know, you're in Starbucks or something. Just drop that. You've been working with them. The girls love it. Doobie, you're married to it. Awesome stuff. Doobie's now thinking, God, I wish I was single just to hear that kind of phrase. Start throwing this stuff around. It's a big deal. All right, so there we go. We'll label this one this side over here, A. And that's I, B. How does that work for a creative part of this class? The problem you've already checked is 2014 T6 aluminum in there. So you might need some of those numbers. Otherwise, well, maybe I'd throw that in as red herring. It would have been a red herring in statics when we didn't need that type of thing. But in this class, we're finally talking about real engineering materials and how we're going to use them. All right, an 80 kilonewton load is placed on there. Perhaps a generator or an engine or something put there at some unknown spot. Remember, for right now, we're not allowing the beams in any of these problems to bend. They will shortly here in class. But for right now, consider that the beam AB itself is rigid. Once loaded like this, the beam, however, will displace down a little bit. I want you to find two things. Find X. You're going to need that anyway. I also want you to find the diameter of A after it's loaded. After the 80 kilonewton is placed there, such that the beam remains horizontal. You either want to tip one way or the other. Remember, once this is compressed, it's going to cause the leg A to bulge out a little bit. We'll assume it's uniform along the length. Hopefully because you'll add that onto the original diameter of 30 millimeters to get the loaded diameter. You're going to have to find del. Take out a little map for ourselves here. You've got to find DA. That's going to come from finding del in the radial direction. That can come from the strain in the radial direction. Where can that come from? This Poisson's ratio. Where can that come from? Nothing. Just look up this and go from there and finish up. What are you going to do with it though? We want to pull this out of Poisson's ratio. We're going to need the strain in the other direction to pull this out. We're going to need the strain in the X direction, the change in length in the X direction. Where will that come from? The requirement that this load be kept, or the beam be kept level. A partial solution. Especially in here, Jake, you were saying something about the elasticity. The elasticity and the stress. The stress is going to come from the load that that post is bearing and that's going to come from the static view. What about the coffee pot over there? If you have it all set up, I'm happy to turn it on for you. So by the time you get in here, it's all done. Buy the coffee then. The last time students fired it up. Endurable fat. Maybe on a day that has a little more downhill to it. This one is still a little upheld. I did the solution maps with health. I know that a lot of times when I look at it, even still, I look at sample problems or solutions in a book. How are the students supposed to know that's what you do? They always put in this first step and they don't say how they know that was the first step to take. So I've had this idea that solution map would help, but I don't know how to show it. I haven't come up with a good form of solution map. This is kind of okay. There's a flow chart. I'm going to do both until it joins. I'm going to do some pieces of this at the same time. If I find the reactions, then I have to go change your grade from last fall in statics. The placement of the load x to find the reactions. You need to find at least the reaction F A to find the stress. Use that with the Young's modulus to find the strain. You don't need to find all three. You still need three equations to find the one we know or the one we need. So what was one of the equations? The forces have got a sum to zero. Very permanent loners. I can thrive right with it. At least know what the other two equations are. You're going to need this load F A, the placement to make sure that the beam stays level. So what are the three equations? Some of the moments. Some of the moments about B. We don't need B. We do need A. So that would certainly help. But what's the third equation? The equation to find that. Dell is not going to be part of it. The deformation. This is just pure statics. What we already summed the moments about B is summing the moments about A an independent equation. Remember when you need three equations, they have to be independent equations dependent to sum the moments about some other place on the same problem. So sum the moments about A or sum them about P or you can even do it about any other place. It doesn't matter. You just have to do it about some other place. It's just as easy as any. And you should be able then to find the load in F A or the reaction F A.