 All right Well, we'll maybe we'll talk after class that you have to speed a little bit But for your information, too, I'm taking this class and dynamics So if you don't want to be caught on camera, don't come up here They for this homework set I put up Spolt chat both editions of the book both the seven Sammy eight edition book I just put them up there That's some of you mixed and matched some of you. I don't know what you did so You can now check your problem see if you did okay on right any questions Where are we still let's see We're still a bit away from the first exam, so we're okay And you click everybody's TJ Right. That's where you go by TJ. Yeah, that's that's You're out you officially appeared so is that your full official name? We'll find out what it that's DJ. He's your little brother I don't know. What's what's de-steem TJ doesn't stand for anything I That's always amazing when people Name a kid something and then immediately go to some nickname of that. Why didn't you just name them then the first place? My brother is not Daniel. He's Dan because that's what my folks wanted at all So are you the junior? Yeah, so are you DJ? Yes Okay Well, people will be able to track you All right, if you remember we were working on on Tuesday on Strings we come up with one and Like the stresses there's more than just one but all we had on Tuesday We come up with on Tuesday was what we call The normal string. Oh by the way all the Videos I think are up to date on itunes you You miss something But you guys want to don't miss a what you can't you can catch up the entire semester Only take about eight hours to download But how long they took me to upload? I need to download Press them and upload and all that took about four hours a class hour The thing I had two days to do nothing All right, we had the normal strain remember what that was what was our symbol for normal strain Excellent actually I believe a lower case epsilon to find as This is this is what we're finally doing here is actually looking at how these materials these engineering materials Deformed so we're looking at deformation of these materials For the most part in engineering sense what we're looking at is elastic deformation It's okay with it's it's not that it's okay that these things to form is that it's unavoidable When things are under some kind of load There's going to be some kind of deformation in these realistic materials in these real life materials that we're finally looking at What what is the the design concern is that we Understand these deformations allow for them and then expect them to disappear when the load disappears Just like when we unload a spring we expect it to go back to its rest length. That's kind of the thing We're expecting here that these materials Will respond to this load respond predictably to this load And then respond to Predictably to the removal of that load. So this was our first real look at a material in deformation under load Remember how it was defined from Tuesday? Not new notes What did you do on Tuesday? Dell Over L Dell being the amount of the deformation in our simplest picture We imagine some piece under some simple axioload whether it's Tensile load like I drew there or a compressive load. It doesn't really matter what happens is in tension we expect a an elongation of The material and that will make them the strain positive L being The original length so it's the change in length over the original length often Often put as it as a percentage if you look through some of the problems yet in this or You remember the load that we did on Tuesday These are very small numbers on the order of 10 to the minus 6 So very very small numbers as we're finding out as we go through this stuff We really got to keep an eye on The units anyway, so let's warm up problem So here's a here's some kind of axial some kind of some kind of member Under some axial strain and We're going to look at two of the possible deformative responses of this One let's imagine Well, we don't imagine it does that it elongates by some measure But since the volume is constant Not only does it elongate But it's going to narrow down a little bit It is a very same thing when you when you stretch a rubber band or something if you look at it closely If you stretch it enough you'll see that not only does it get longer, but it also gets narrower So we're going to look at this response. Of course exaggerated in this picture Start with an original length of 500 millimeters We have an elongation here of 300 micrometers an original diameter of 16 millimeters and A change in diameter We may all call that Dell sub D for the change in diameter minus 2.4 Micrometers so in this case we have actually two strains we need to look at we need to look at the strain in the Length direction the axial direction, but we also need to look at the strain Across the diameter So just as a warm-up sort of get used to the numbers again that we're working with here That's your warm-up problem in here yet. I put the Solutions from both addition sets up there Remember, I don't grade these so much for specific Content you can check the results itself as much for for Your ability to lay out a problem of solution Itself that we may have a focus a little bit better. That seems you can see some of the numbers now. So First couple days are a little sketchy All right easy numbers to work with You need to keep track of the the magnitude of these things but also and I kind of took care of it for you anyway take care of the Plus in the minus signs because we do have strain possible directions. We got to know which of this class is on the scene I don't remember that first day Never in the same sense for it Degree you were what? Yeah, I didn't get to do that physics one this year because I preempted That with an email to everybody's was it jettison couple From a distance, which is you know, it's kind of like firing somebody fire somebody without an election will come in The eyes a lot easier Remember that if you ever become a manager somewhere hello Brandon We got everybody here today Cancel class and celebration All right, what do we got should all agree certainly we can divide two numbers by two numbers DJ GDX has this calculator here today, so There's no trouble then Do you agree? Everybody agree? You don't know That we got a little Terrorist cell over here and a little terrorist cell over here and the gulf between New is Micro tends to be about the the magnitude of these these type of numbers in the strain Calculation so everybody agreed that this little this little conclave Here and over here this group's not talking to each other. You'll sit together, but you're going to communicate with each other Jake's Desperately trying to cross the goal and trying to try to reach out of hand That's had nothing to do with it What do we have on this one remember there are thousand different ways to present it your choice So Pat, what'd you do? 60% 60% if it was that long it's now this long 300 micro meters. Yeah, watch this stuff This is this stuff is very very sensitive to them the magnitude on these numbers That's the thing you have Whole bunch of different ways to present back one of I guess the accepted way is just to say 600 Micros, but I think that agreed with what everybody said the six times 10 to the month fourth It's it's a it's a bit of a It's a well, it's a bit of a hangover a hold over Whoops a bit of a hold over from the old days that generally try to keep the The powers on the 10 to multiples of three That's where the best known Science si prefixes are it's a bit of a whole over from the years the days when we used to use slide rules to calculate this stuff So rather than a six take six times ten minus four six hundred times ten to the minus six Or six hundred micros is generally a little bit more acceptable though. Your number wasn't all just to make communication with the Old white man you're going to be working with when you actually get to an engineering firm because that's what the vast overwhelming of Presenting them are you'll be able to communicate with them? How about the strain in the diameter? diametral direction Jake No, I just want the answer. That's what you got all the answer boom The new guy making friends fast By when you have DJ is negative remember we need to know what direction this goes in One way to pretend Micro all right, so good start on This simple Division of one number by another It's been back to the days teaching math one away We're gonna do that stuff with them. All right That's just a review or reminder for us now. We'll look at the other type of strain that we look at in this class Again like this one Very very much depends upon your ability just to see the geometry in the in the problem So we'll start with a look at a simple Element of some type whether this is actually a piece of the material or represents the physical Description of a small square on a material which is one way that these type of strains are are determined for the purpose of illustration will imagine that one side is Secure to some immovable object of some kind and that there's some shearing force Across the top we'll give it a side a height of L there The width is not a concern to us in this At least in the geometry shown, but the height of it is the response of this then is For this element to deform in That way due to this shear stress, so this is called shear strain What we're concerned with here is the response in an angular way, so We'll again call that Dell Book this orientation we tend to call that Dell x so the shear strain then is Defined as that's a lowercase gamut This will be the average shear strain defined as that deformation Over the original like essentially what that is then is The is the tangent of that angle that's formed For very very small angles, and you can check this on your calculator if your calculator set to radians for very very small Angles the tangent and the angle are the same You set your calculator radians put in a very very very small angle Take the tangent of that you'll get essentially the very same number back except for several Several decimal places down the road So it's an angular deformation as you might expect from the response in the material to shear Deformation if we if we look at the limit as L approaches zero of this average shear then we get the the Precise shear at that angle that can be more of a concern if we have a material That responds in a slightly different way than the implied shear It could depend upon the material it might even depend upon how the material is fastened down where it might deform something like that where then we do have a Different angle of the shear down here, then we would have got We would have gotten if we take in the average We're not going to concern ourselves too much with that kind of precise detail Since this is an introductory class into this so there's there's I guess the notion sort of of a instantaneous shear just like we had when we develop the Calculus of limits in the first place All right some of the some of the greater details of this if you remember also on Tuesday we set up a look at the Shear across an entire element Determine that there could be shear stresses like that Under that kind of load the material will Deform again in a highly exaggerated sketch Would deform something like that Remember we're talking about very very small Deformations or couldn't possibly sketch those bless you so we're very much concerned with With the full picture here So this is a a deferment a change in a 90-degree angle in response to these Shear stresses so it's the 90-degree angle then minus Minus the shear that we're seeing back here So if you think about the geometry a little bit If we brought this down so that these bottom two surfaces are the same we Pretty much have this same drawing here So it's just a in essence a slightly different way then to to look at the two different problems another possibility is That the shear stresses are in the other direction then the response of the material is Hard to draw yeah, I might do something like that under shear stresses in the other direction this will give us a positive shear stress response this we consider a Negative shear spot the shear stress response But either way they're they're calculated in the same way. How you doing your technical free-hand sketching? Oh, and are you in that? You're doing better More and more cognizant of what you're putting down a little bit Okay, all right, so that's that's the setup for it for for these problems again, it's a lot of the problem is just a Geometry problem So we'll look at a couple simple setup simple possibilities of What we can do with these all right, so imagine we have a thin plate of some some rectangular size 720 by 480 millimeters in original unstressed Dimension and then due to some applied load we get a response again, of course Exaggerated something like see that All right, so I'm still happy. I don't want Oh There's a All right, so that's a little better. There's there's the exaggerated response of this to some shear stress You can see we have two Places where we have the shear strain So we need to look at the response here. We'll call that 0.5 Millimeters and the one down here 0.25 millimeters. You can figure out the Shear strain from that Again, just a geometry problem One of the things we're looking for is the total Shear strain here where that gamma is two shear strains put together think about the geometry to change remember in that Original 90-degree angle always in this class and your others be very careful with your units We're talking about angular changes here Expression is it radians? Usual Love the idea of buying a fourth grade or a hundred dollar calculator I have to keep my editorial comments and my death threats really only two choices to make We tend to turn those two choices once right one's wrong. So let's see what we figure out which is which How you got that Left yourself bad notes. Do you ever look at your notes again? Oh But if you ever go to publish them for journals, you got that here to very strict DJ agree with anybody or still feeling kind of socially isolated Oh Do you agree this is my favorite group Never had force dudes on average Did you agree? Did you guys sort it out somehow? Yeah Well for you, and you're still not talking to TJ All right, let's see general definition whatever deformation we have here along the Topics that happens to be in the x direction Generally, it's on here. It's not too Terrifically important here 25 millimeters over there, and then the discussion the back here was which goes under it Would you finally decide what goes under that point five seven zero? 720 But where were the units? I'll just keep the units the same between the two And you'll be okay, and I'll just cancel and you left over whatever number you're left over What we get for that one is positive in this case? Yeah, six ninety-four of my brothers micrometers per meter or What are one of the other 25 different ways to look at it? Sigma two or a gamma two This year straight in the other direction. I guess that would be fine LX like that Hey, you know what to put for that. You guys agree on that one, too. Finally, who was right? It was wrong What he was right and wrong? Is this a positive or negative? This one's also positive by convention and so the strain in that direction then was 521 micros and then the total strain Was the sum of those two? Which is what 12? 15 an angular deformation your question was Units radians it if you put in degrees which you could I guess no reason not to but That's There's no reason to Since this is sufficient for or what's understood for the strength the sheer strength All right already tired two solid days and clearing my driveway since nobody came down for extra credit to help We a mile away like you don't it's in the sheriff file I think the sheriff knows exactly which one of you knows where I live and which one doesn't All right What in the tape back? What I know exactly what you said No on that one we did have that that If we wanted that angle, yeah It's it's a I know I find this a little bit confusing I don't know I don't this is not my my engineering background in this field, so I Find it a little bit confusing that all the different ways they report some of this stuff So I don't know sometimes it just seems like the game. All right, so it's Friday So let's do a Get out of class question. There's the original shape. It's a square Ten inches on the side. It's original unstressed for when stressed the response is In the y direction the response is something like this You can you can do an entirely different problem if you'd like from the response, of course exaggerated is something like that 0.2 inches That's 0.3. So I want you to find those Strains call this and down here also find Significantly that's a gamma key Along along one of the edges First person to get that it's million bucks Anybody gets a quarter in class gets to leave her been shown time and time again with the proper motivation People will rise to the channel Jury how many millions can you have It's pointless after you offer double figures for a number of millions not sure it's strain. This is remember. This is the normal strain Along one edge problem. What are you doing? Let's say you're not quite right. Good idea. I Would check it. It's not really good, but you got the right idea. Just check your numbers almost if you're having on it is with Not the upper number more. Let's see in the x-direction. It's Well, it's a decrease so it's a minus zero point three inches Okay, if you guys catch the minus But then remember you divide it by the original length the original length of that piece that now decreased by point three Is that piece there? That's the piece that that's the direction that decreased by The point three inches Doesn't matter you get the same thing That length across there is 207 then the same type thing in the y-direction only it's a positive increase Get these minus sign when Appropriate swear that's gonna be on my gravestone and finally missed a minus sign That makes sense now you see that and for the one on the edge It's the same type of thing the original length of an edge is 10 inches The new length of an edge is Whatever this full diagonal length is So you have to do a little category and they're I mean Come up with that Normal stresses. What was that? What's the new length of the edge? Are you doubled it? Yeah, you don't want to double that one It made sense to double the other ones if you wanted to but this one ten inches isn't actually double It's a single single length So yeah, take this decrease length over that increase length Yeah Yeah, but remember you don't want the original or you don't want the new length here you want to change Yeah Yeah, that's why I get point 066 Thank you All right, that's that's just stuff to work out right at the end now so Let's at least lay out how you're gonna find the shear strain remember this here's called theta p That's pi over two minus the shear strain. We're looking for So this is pi over to the original 90-degree angle minus Whatever that angle isn't you can figure that out from the geometry you're given So that that number there then is you take it back in the class on Monday. Oh No, we're looking more like micro rags. Well, hang on. Let me see. No, well, we're that's still pretty darn big by a factor of Something