Properties of Materials

Hello CET 135 students. We are looking at the fourth chapter of the building instruction textbook and I wanted to give you an overview. Of course I don't read all of these slides. You have plenty of reading ahead of you in any case. Excellent textbook. A few, not spelling errors so much, but a few typos here and there. Maybe table 3.5 instead of 3.1. Maybe They get a width wrong here or there, but I guess it's kind of a game if you find a couple errors. There's nothing huge, nothing that you can't figure out pretty easily. But if during your readings you do come up with an issue, then just let me know, and I should be able to figure out pretty quickly. All right. So let me give you a little overview of this chapter on properties of materials. So... We say that materials are classified by their physical properties, which makes sense because we're asking them to do a physical job. So, for instance, when you're ordering concrete, you have a certain load-bearing capacity for them. You have different additives that actually change the physical properties of the cured concrete. Steel structures, you know, nano carbon fiber structures, things like that, carbon nanofibers, you know, different types of plastics, those types of things. So elasticity and plasticity is a thing and it doesn't just have to be something that's made to stretch or compress or something that is obviously a polyvinyl or anything. So you'll see that as we go through. So just basic, a little bit of physics review, if you will. So compressive force is of course if you're taking something and you are providing pressure on it and then tensile under a lot of tension, right? It is when you're trying to stretch something. So a rope here of course would have really no resistance in this direction, but plenty of resistance when it's under tension and that's why it is used for suspension. So cables, same thing, suspension bridges, cabled. So you normally would use something like a column or if you're holding something above your head, you're under compression and you can see that compression and tension oftentimes take place at the same time. Your textbook will talk about being in static equilibrium and that simply means that all forces are balanced out. That's the equilibrium and that you're not moving and that's pretty much the goal of buildings is to be in static equilibrium. And I say buildings, but we can also talk about bridges and other structures that you don't want to move. And by the way, there are plenty of nice simulations out there where you can simulate tension and compression for structures that you build as bridge building simulations and games and things like that all the time. Interactive physics is a great one. If you can find the demo version of that, it's pretty cool. So again, suspension bridge is here. You have compression and you have tension acting all throughout. So think about that the next time you go across a bridge. What is the primary source of stability? Compression, tension, or fair enough, equally shared combination of both. All right, so this is actually the formula for stress, which is defined as force over area. So if you take a material and you apply a force to it, either by tension or compression, the area is actually that little cross-sectional area there. So if I were to cut through, I'd see a circle there, right? So with that area, I'm applying a force over it. Now this is where it gets confusing. If you do have a physics background at all, then you'll realize that the units or the variables here are actually a little mismatched for how you would see it in a physics class, where P would be pressure, which is force over area. So if you have that background, don't let it confuse you. F here is stress, and it's little f. All right, so just a little bit of an example here, and it helps you understand a little bit on units where we go from psi, but we're actually looking at now. Kpsi or Ksi showing in this case thousands of pounds per square inch Kpsi or kips. sometimes. But basically you can see that there's the stress, there is the weight in this case 500 pounds or force and it's being suspended from a cable in some way and you have a cross-sectional area of half an inch and so if you look at it and you do the geometric calculation there, pi r squared, remembering the radius is half of the diameter, then you can figure out what the cross-sectional area is. And here's where I'll also remind you of a place where you could get confused. Your textbook is going to use a lot of English units. And so if you've taken a physics class before where you're using metric units all the time, then your thinking is going to have to be adjusted for this because we still use a lot of English units along the way. And sometimes we use a mix of units. So you might talk about pressures in pascals, which is newtons per square meter. So I don't want to overwhelm you with a lot of unit talk, but just be aware that there are opportunities for you to get confused and so you got to be on the lookout for that. By the way, this cable if it's being put under tension, there's that cross-sectional area at any point, it's going to want to stretch. It's going to be slightly ductile, but it's going to want to deform. along the way. It's going to go over what we call elongation and that could be pretty temporary. But if it's put under enough of this stress, then it is going to be permanently deformed, which we'll talk about during this video. So that goes into the failure point. So there's a point at which you really can't return. and you can't support any tension anymore and so that's where we go for tensile strength. So if you get to the point of failure, so it's fine at 500 pounds, but then we reach the maximum point of a thousand pounds for this particular cable, it's a nice round number. We assume that the cross-sectional area doesn't change until dramatically at the point of failure here and so we can say that it's doubled. it's stress at that point. So there are some nice graphics which I'll show you here as well. So we're going to be making as part of the class a concrete test cylinder and if it's virtual, which it is for you guys, then you're going to create a smaller version but it really falls into the same idea. You go ahead and you have a cylinder made of this. It's just a very cylindrical form. It's filled with and then you do basically vibration and tamping for the most part. And then you put it in the test apparatus, which is basically just a huge hydraulic or pneumatic cylinder compressor. And it goes to failure. So you see how it fractures. But then you can actually, because of the force sensors, you can actually determine and track that point at which it has. has failed. So I say force, but really you're talking about a stress point, right? So force over some area, which we have the area here. Alright, so looking at the dimensions of that six inches is kind of standard there in terms of the diameter. And so you can easily figure out the area pi r squared, r being in this case three inches. And just again, be very, very careful as you're going through the practice exercises and as you're going through any later exercises and including the tests, that you keep very close track of your units, because I might want to do something in centimeters or meters, but we're going to be given data or given data tables that show us things in PSI and other units. that are in the English system. So just be careful. So there's a value for comparative strength. It's the load at failure versus the area of the cylinder and that's how you would figure out when this failed. So another idea except in reverse is tensile strength and so you actually can reach a point where whatever, called a test specimen, whatever material you're stretching here, it's going to be able to... test that deformation. And then of course you can go on and go through failure for that as well. But here is the elongation. So things that are under compression. they do not elongate, they actually shorten, right? But things that are under tension, they're going to elongate. And so if it's highly elastic, then it can elongate a great amount. That's that delta L change in length. There's the original length, L0, L original. It can go under a great deformation and then return back, or great elongation, I should say, and then return back. But otherwise, more brittle and less ductile materials are going to deform less, which can be a good thing. However, you reach that failure point at a much shorter length. So this is called strain. So you've learned about stress, and now we have strain. And you want to remember these, and you want to remember the ratio between them, and I'll talk about that as well. But strain is very simple. For something that's linear, it's going to just be the change in length over the original length. So it's really, it's almost a percentage of change. All right, so there's a little epsilon symbol here for that. And so you've got your delta, it's the same thing. Delta L, it's the triangle L, this one's the same thing. The change in length over the original length. So just two ways of looking at it. Don't get confused, it's exactly the same formula. So you can see that steel versus say brick is going to have a very different amount of strain that's needed before failure or that's permissible before failure. So that makes sense. You can imagine why we don't hang things from columns. They're really only good for compression. Masonry doesn't do very good under tension. I already talked about ductility and the warning I should say for ductile materials is that they begin to stretch and stretch and stretch. And when you stretch something that's made out of something real, not in the ideal world, but the real world, it's going to get thinner. Brittle materials don't give you that benefit. They're not going to really get thinner before they break. And if you think about these things on a really small scale. then it makes sense the way that things are bonded. If it's just steel then you've got iron atoms for the most part, maybe with some impurities there. And they're bonded pretty well and they have a lot of mobility, but things like brick and clay and those types of things, they don't quite have that amount of bond there. So this is stuff you learned back in grade school about mobility and malleability. Just a little bit of review for you. I'll let you review the video on your own in the PowerPoint on stress and strain diagrams, but you can see here that there's this nice even ratio of stress to strain. And if you've ever heard of Hooke's law, H-O-O-K-E apostrophe S, Hooke's law, Hooke spent a lot of time looking at springs and things that are elastic, whether they stretch or then compress or both. And this is very, very, very similar to that Hooke's law formula that you may be familiar with from fundamental physics. And then you reach a point of failure in the end. And there's this wonderful, interesting characteristic curve that happens. It's a little bit different for each material. So some materials reach this Y point sooner than others. Some have a much longer slope, but it just depends on the elasticity of the material. Now, plasticity, have you ever heard the plasticity of someone's brain, their mental state? It means that you're able to learn and learn and learn, and your plasticity, for most people, goes down as you age, which means that your mind can't really create additional neuroconnections and such. So it's the same thing with materials. Some materials have higher or lower plasticity, the ability to go over, go under a lot more of this stress, if you will. So the ratio of stress to strain would give it a value of E, we say, and it's different for very, very diverse materials. Everyone has its own characteristic line here before, of course, you reach the ultimate point of failure. And then for concrete, again, a characteristic curve here. You can reach the point of compressive strength, and then you reach the point of failure. Everything has, every material has its own characteristic stress-strain curve or diagram. All right. Stop hiding that. There we go. So materials are going to deflect. if they're underweight and a lot of times it's really just the weight of themselves and what is attached to them. So if you remember from the previous chapter you were looking at loads and so let's say that we had a beam we went by unit length there was say we took a foot of of a beam as an example and then you would look at what was above the beam what was below the beam and You took all of those unit loads and you would find the overall load that it was responsible for, the tributary load. So it's very similar here. In the ideal world, nothing bends under stress, right? But in the real world, of course, everything bends even under its own weight. So an example, From my experience would be if you're laying brick, so you use what's called a Mason's line. And so you have two little blocks of wood and then you have a string that goes between them and they're under very, very high tension, but you'll always have to account for the fact that even the string itself has its own weight and it's going to deflect downwards from that. Very simple example for the layperson, you take two telephone poles, Utility line runs between them and you can see a little downward deflection. Some of it's by design, of course, but even if they tried to get under very high tension, there's going to be some deflection in there. Right, so you can see a foam example. You can see there's compression here and it's under tension here and this plays out a lot in bridge building and span building. And of course, depending on the dimensions of the material, you'll have this neutral axis. All that really means is that that's the one that experiences the least deformation. It's not so much under compression, not so much under tension. It's right there in the middle, so it's an equilibrium, if you will. And a good point that that slide made too is that everything's in three dimensions. So you can try to simplify things in one dimension for very, very thin materials. For flat materials, you can simplify things in two dimensions. But for materials that cover a large span height-wise and length-wise, you have to think then in three dimensions as well. All right, so just another view, some examples. You know, we make the move from traditional framing, and then we have learned, of course, over the years, you can do lamination and you can reduce materials, which also reduces the weight. Just... from themselves, which allows them to have a lower personal embodied load and then the benefits are pretty obvious there in terms of material use and an overall load. So that's the idea of the I-beam. Okay, so again you hollow things out, less weight, less mass, less weight, less personal load if you will, and or embodied load. and then you are able to again use not 100% necessarily, but very very similar tensile strengths and resistance to deformation and deflection. Plus the added benefit is, depending on on how you're using these, you can sometimes use these gaps or very often use these gaps for the passage of conduits. Just depends on how it's used and those are designed in. All right so reinforcing bar is important. You look up rebar and concrete if you're not familiar with that what that is. A nice table to show us a little bit. There's a stacked effect here. This is really sheer right talking this is a dramatic example but you can take a stack of books if you will and you can see that if you apply a force to the top We'll just take a single book here. I'll take your textbook. How about that? Take your textbook. And I apply a force to it and you can see that that tangential force or that sheer force causes a deformation and it's not in one dimension now, I've done it now in two dimensions. And there are some fancy words for that from physics, but for the most part you just need to think of these as sheer stresses. So there's some bolts here, for instance. I'll give you a funny example. When I was first learning how to ride a motorcycle, I hopped on to a little Honda Rebel and I was trying to shift gears and I actually the first time I tried to shift gears I actually Sheared the bolt that held it together. So the gear shifter actually fell completely down. It was pretty embarrassing, but you never forget So you got to really think about these as you're building something or assembling something and they're selected based off of the properties of the metal and also the physical dimensions Which are very important and then of course you think of you compare that to the load. They're called fasteners So all this goes to show is that depending on the materials you have to um be aware of their different amounts of ductility or plasticity or brittleness and that there are ways of reinforcing these and you have to think about directions as well. We've talked about that a little bit in the past, more about test cylinders, more in terms of fastening. So some pretty good examples of failure rates here. So there's that necking idea. That's the visual cue that we were talking about before. You're not going to go back from that, by the way, but it might not completely fail until you get a little bit of a warning. If it were, for instance, a safety feature. Let's go back to our OSHA training right or look towards it, I guess, in most people's cases. If you are looking for signs of wear on, say, well, for OSHA 30, we're talking about crane safety a lot of times. So if you're looking for signs of wear on the lanyards and such for cranes, then you might see this necking as an example. And you want to make sure that you replace that and put it out of service. So buckling is kind of the opposite there and so there are ways to mitigate that as well, which you might be more familiar with because a lot of you have seen basic traditional stud work for the most part and you don't just have to think up and down in terms of compression right there's side to side motion as well and your textbook does a pretty good job of explaining this too right so multiple ways of supporting reinforcements. A little example here for you. This actually will help you a little bit with one of the later lab activities. So I would go through this for the most part, but this is just that example that's in the textbook as well. So my biggest thing here, is just don't get confused by the symbols because it's pretty straightforward. So structural safety, you talk about the safety margin, it's the actual strength versus the required strength. So in other words, how close are you to the limitations of this material or structure? And then the factor of safety is, you know, what's that failure stress? Remembering what stress is, right? The force over the area and and then versus the allowable stress. So, again, how close are you to the point of? failure. These are going to be ratios, so it's going to be basically a percentage or multiples, I should say, how far off you are. So again, YouTube video here available for you to talk about thermal expansion. If you build anything and you have changes in temperature, even just from night to day, but mostly seasonal. then you're going to get expansion or contraction. So there are plenty of classic examples out there. If you go over a bridge, then you see the teeth. And in the wintertime, the length of bridge was really what you're concerned about is the length because it's a much longer area there. And the same percentage of expansion is going to make much greater change. Then the teeth are much further away. So you see gaps. So you're riding across on a motorcycle and you notice it. You drive across. cross on a car and you don't probably. But in the summertime everything expands and so imagine my fingers getting very slightly thicker then you see the teeth the gaps between the teeth are not quite as pronounced. That's just an expansion gap. So concrete same thing you can cut them you can put you know wooden expansion in you can put asphalt expansion and foam expansion plastic expansion it just depends. You can just have a gap there. You can have an edge joint. Same thing. Large brick buildings. There's certain, based off of code and general manufacturer's practice for things, you have certain lengths of a material that you're allowed to use or material system that you're allowed to use before you account for expansion. Even roofing materials, you have a certain amount of gap that's required. in the substrate, right, which would be the plywood or planking or whatever you're using underneath. It's all because things are responding to the temperature. So again, we live in the real world. This is not an ideal world. What I mean by ideal is things stay static. It's a very dynamic world and so the materials are going to change and you need to be able to respond to that. Alright, so thermal expansion, there's some nice formulas for it. The big thing is that this is delta. Just means change in. It's the same thing as this little guy except lowercase versus uppercase. And this is the change in temperature. This is going to be the change in length. So you could just as easily call this triangle L. It's the same exact thing. And then there's one alpha here. That's just the letter A basically in Greek. And then there's the original L. So again, Don't get confused because the variables sometimes look a little different from each other from time to time. These are scientific notation forms. Also engineering notation, if you will, because it's a multiple of three. But the big thing is, is that it's easy enough to plug and chug numbers in if you just have one unknown. So let's say you know the original length of something. You know the coefficient of expansion here. right? There's also the coefficient of compression. You can use the same thing or coefficient of, yeah, same thing, the coefficient of expansion. And so the same rule applies here. You know a final temperature, you know an initial temperature. So let's say that it's 20 degrees Fahrenheit out. Remember we're using the Fahrenheit scale for these, that's important. and then it goes up to 50 degrees Fahrenheit outside. We're getting close to those temperatures here today actually. So the final was 50, the starting was 20, so 30 degrees would go right here. Alpha is given as somewhere within this range. It depends on the type of steel and then the original length would have to be given to you. Then you could figure out what the change in length is. Now here's the thing, if you're asked what the new length is, You have to take this change in length and add it to the original length. All these symbols are easy to get lost in, but the whole point is that whether you're expanding or you're contracting, use that thermal coefficient and you can find all of these coefficients in some table somewhere, right? Well, here's an example. Glass, steel, aluminum. polyethylene, wood. It says wood along the grain, right, because it was a biological material, an organic material, and so the grain has a different coefficient of expansion than across the grain because of the way that the celluloid constructs are made. I don't mean to get too wordy for you on that one, but... The way the cellulose is laid out. And so across the grain is different than along the grain and that's just because across the grain you're cutting across little teeny threads, but along the grain they're huge long threads, right? All right, so different expansion coefficients. And actually I'll show you a demo of that too along the content. All right, so there are limits to all of these. You can estimate these. The longer it is, the greater the overall change in length will be, not as a percentage, but as a final measurement. There are plenty of examples here. And then we talk about methods of heat transfer. So thermal conductivity just means that heat flows between things that are in physical contact with each other. So... the whole idea is that if I touch something hot, then that material is vibrating very quickly, right? That's the whole point about heat. And so if I touch it, I'm not vibrating as quickly on the small scale. My little molecules aren't vibrating, at least compared to the hot stove. And so they're vibrating my molecules on my hand, and I don't like that because I like my molecules to stay as still as possible compared to my, how they originally were. So then they fly faster and if it's too hot then they fly away and that's called being Really badly burnt and if it's just a little bit too hot and they melt right because I'm changing the structure again A YouTube video for you to watch I won't read everything Completely, but this has very practical Very practical applications in the building sciences. So you have these things called R-value and U-values. And U-values are basically the inverse of the R-value. U-value is all about transmittance and R-value is all about resistance. And so you put in insulation in a home and you say, well, I want as high an R-value as I can get. Well, there's actually a limit to how valuable that is, depending on where you are in the world and local weather patterns and things. or temperature zones rather, but if you can find say an R value, then you can tell that the U value is going to be the inverse of that. So inverse is one divided by the original value. So again, lots of examples for you that you can go through. I won't ruin all your reading by doing that, but if you come across an example in the textbook that you're really not sure about, show me exactly where you're having an issue and I'll explain it in a different way. possibly less worthy. We'll see. All right, so that's where we are, and I will also provide you a couple demonstrations as we go along, but if you have questions, let me know, and I hope that this overview helped you at least understand that as complex as the chapter content might be, There are reasons behind it. Things make physical sense. So I encourage you one last time, always ask, does this make sense? I don't mean does it click in your head. I mean, when they make a claim in the textbook or in a video or in a resource that I give to you, does it match your own understanding of the world around you? Because this class is all about real physical materials and experiences. All right.

Hello CET 135 students. We are looking at the fourth chapter of the building instruction textbook and I wanted to give you an overview. Of course I don't read all of these slides.

You have plenty of reading ahead of you in any case. Excellent textbook. A few, not spelling errors so much, but a few typos here and there.

Maybe table 3.5 instead of 3.1. Maybe They get a width wrong here or there, but I guess it's kind of a game if you find a couple errors. There's nothing huge, nothing that you can't figure out pretty easily.

But if during your readings you do come up with an issue, then just let me know, and I should be able to figure out pretty quickly. All right. So let me give you a little overview of this chapter on properties of materials. So...

We say that materials are classified by their physical properties, which makes sense because we're asking them to do a physical job. So, for instance, when you're ordering concrete, you have a certain load-bearing capacity for them. You have different additives that actually change the physical properties of the cured concrete. Steel structures, you know, nano carbon fiber structures, things like that, carbon nanofibers, you know, different types of plastics, those types of things.

So elasticity and plasticity is a thing and it doesn't just have to be something that's made to stretch or compress or something that is obviously a polyvinyl or anything. So you'll see that as we go through. So just basic, a little bit of physics review, if you will.

So compressive force is of course if you're taking something and you are providing pressure on it and then tensile under a lot of tension, right? It is when you're trying to stretch something. So a rope here of course would have really no resistance in this direction, but plenty of resistance when it's under tension and that's why it is used for suspension.

So cables, same thing, suspension bridges, cabled. So you normally would use something like a column or if you're holding something above your head, you're under compression and you can see that compression and tension oftentimes take place at the same time. Your textbook will talk about being in static equilibrium and that simply means that all forces are balanced out.

That's the equilibrium and that you're not moving and that's pretty much the goal of buildings is to be in static equilibrium. And I say buildings, but we can also talk about bridges and other structures that you don't want to move. And by the way, there are plenty of nice simulations out there where you can simulate tension and compression for structures that you build as bridge building simulations and games and things like that all the time. Interactive physics is a great one.

If you can find the demo version of that, it's pretty cool. So again, suspension bridge is here. You have compression and you have tension acting all throughout. So think about that the next time you go across a bridge.

What is the primary source of stability? Compression, tension, or fair enough, equally shared combination of both. All right, so this is actually the formula for stress, which is defined as force over area. So if you take a material and you apply a force to it, either by tension or compression, the area is actually that little cross-sectional area there. So if I were to cut through, I'd see a circle there, right?

So with that area, I'm applying a force over it. Now this is where it gets confusing. If you do have a physics background at all, then you'll realize that the units or the variables here are actually a little mismatched for how you would see it in a physics class, where P would be pressure, which is force over area.

So if you have that background, don't let it confuse you. F here is stress, and it's little f. All right, so just a little bit of an example here, and it helps you understand a little bit on units where we go from psi, but we're actually looking at now.

Kpsi or Ksi showing in this case thousands of pounds per square inch Kpsi or kips. sometimes. But basically you can see that there's the stress, there is the weight in this case 500 pounds or force and it's being suspended from a cable in some way and you have a cross-sectional area of half an inch and so if you look at it and you do the geometric calculation there, pi r squared, remembering the radius is half of the diameter, then you can figure out what the cross-sectional area is.

And here's where I'll also remind you of a place where you could get confused. Your textbook is going to use a lot of English units. And so if you've taken a physics class before where you're using metric units all the time, then your thinking is going to have to be adjusted for this because we still use a lot of English units along the way. And sometimes we use a mix of units. So you might talk about pressures in pascals, which is newtons per square meter.

So I don't want to overwhelm you with a lot of unit talk, but just be aware that there are opportunities for you to get confused and so you got to be on the lookout for that. By the way, this cable if it's being put under tension, there's that cross-sectional area at any point, it's going to want to stretch. It's going to be slightly ductile, but it's going to want to deform.

along the way. It's going to go over what we call elongation and that could be pretty temporary. But if it's put under enough of this stress, then it is going to be permanently deformed, which we'll talk about during this video. So that goes into the failure point.

So there's a point at which you really can't return. and you can't support any tension anymore and so that's where we go for tensile strength. So if you get to the point of failure, so it's fine at 500 pounds, but then we reach the maximum point of a thousand pounds for this particular cable, it's a nice round number. We assume that the cross-sectional area doesn't change until dramatically at the point of failure here and so we can say that it's doubled. it's stress at that point.

So there are some nice graphics which I'll show you here as well. So we're going to be making as part of the class a concrete test cylinder and if it's virtual, which it is for you guys, then you're going to create a smaller version but it really falls into the same idea. You go ahead and you have a cylinder made of this.

It's just a very cylindrical form. It's filled with and then you do basically vibration and tamping for the most part. And then you put it in the test apparatus, which is basically just a huge hydraulic or pneumatic cylinder compressor.

And it goes to failure. So you see how it fractures. But then you can actually, because of the force sensors, you can actually determine and track that point at which it has.

has failed. So I say force, but really you're talking about a stress point, right? So force over some area, which we have the area here.

Alright, so looking at the dimensions of that six inches is kind of standard there in terms of the diameter. And so you can easily figure out the area pi r squared, r being in this case three inches. And just again, be very, very careful as you're going through the practice exercises and as you're going through any later exercises and including the tests, that you keep very close track of your units, because I might want to do something in centimeters or meters, but we're going to be given data or given data tables that show us things in PSI and other units.

that are in the English system. So just be careful. So there's a value for comparative strength.

It's the load at failure versus the area of the cylinder and that's how you would figure out when this failed. So another idea except in reverse is tensile strength and so you actually can reach a point where whatever, called a test specimen, whatever material you're stretching here, it's going to be able to... test that deformation. And then of course you can go on and go through failure for that as well.

But here is the elongation. So things that are under compression. they do not elongate, they actually shorten, right?

But things that are under tension, they're going to elongate. And so if it's highly elastic, then it can elongate a great amount. That's that delta L change in length. There's the original length, L0, L original.

It can go under a great deformation and then return back, or great elongation, I should say, and then return back. But otherwise, more brittle and less ductile materials are going to deform less, which can be a good thing. However, you reach that failure point at a much shorter length.

So this is called strain. So you've learned about stress, and now we have strain. And you want to remember these, and you want to remember the ratio between them, and I'll talk about that as well. But strain is very simple. For something that's linear, it's going to just be the change in length over the original length.

So it's really, it's almost a percentage of change. All right, so there's a little epsilon symbol here for that. And so you've got your delta, it's the same thing. Delta L, it's the triangle L, this one's the same thing.

The change in length over the original length. So just two ways of looking at it. Don't get confused, it's exactly the same formula. So you can see that steel versus say brick is going to have a very different amount of strain that's needed before failure or that's permissible before failure. So that makes sense.

You can imagine why we don't hang things from columns. They're really only good for compression. Masonry doesn't do very good under tension.

I already talked about ductility and the warning I should say for ductile materials is that they begin to stretch and stretch and stretch. And when you stretch something that's made out of something real, not in the ideal world, but the real world, it's going to get thinner. Brittle materials don't give you that benefit.

They're not going to really get thinner before they break. And if you think about these things on a really small scale. then it makes sense the way that things are bonded.

If it's just steel then you've got iron atoms for the most part, maybe with some impurities there. And they're bonded pretty well and they have a lot of mobility, but things like brick and clay and those types of things, they don't quite have that amount of bond there. So this is stuff you learned back in grade school about mobility and malleability.

Just a little bit of review for you. I'll let you review the video on your own in the PowerPoint on stress and strain diagrams, but you can see here that there's this nice even ratio of stress to strain. And if you've ever heard of Hooke's law, H-O-O-K-E apostrophe S, Hooke's law, Hooke spent a lot of time looking at springs and things that are elastic, whether they stretch or then compress or both.

And this is very, very, very similar to that Hooke's law formula that you may be familiar with from fundamental physics. And then you reach a point of failure in the end. And there's this wonderful, interesting characteristic curve that happens.

It's a little bit different for each material. So some materials reach this Y point sooner than others. Some have a much longer slope, but it just depends on the elasticity of the material. Now, plasticity, have you ever heard the plasticity of someone's brain, their mental state? It means that you're able to learn and learn and learn, and your plasticity, for most people, goes down as you age, which means that your mind can't really create additional neuroconnections and such.

So it's the same thing with materials. Some materials have higher or lower plasticity, the ability to go over, go under a lot more of this stress, if you will. So the ratio of stress to strain would give it a value of E, we say, and it's different for very, very diverse materials. Everyone has its own characteristic line here before, of course, you reach the ultimate point of failure. And then for concrete, again, a characteristic curve here.

You can reach the point of compressive strength, and then you reach the point of failure. Everything has, every material has its own characteristic stress-strain curve or diagram. All right. Stop hiding that.

There we go. So materials are going to deflect. if they're underweight and a lot of times it's really just the weight of themselves and what is attached to them. So if you remember from the previous chapter you were looking at loads and so let's say that we had a beam we went by unit length there was say we took a foot of of a beam as an example and then you would look at what was above the beam what was below the beam and You took all of those unit loads and you would find the overall load that it was responsible for, the tributary load. So it's very similar here.

In the ideal world, nothing bends under stress, right? But in the real world, of course, everything bends even under its own weight. So an example, From my experience would be if you're laying brick, so you use what's called a Mason's line. And so you have two little blocks of wood and then you have a string that goes between them and they're under very, very high tension, but you'll always have to account for the fact that even the string itself has its own weight and it's going to deflect downwards from that.

Very simple example for the layperson, you take two telephone poles, Utility line runs between them and you can see a little downward deflection. Some of it's by design, of course, but even if they tried to get under very high tension, there's going to be some deflection in there. Right, so you can see a foam example.

You can see there's compression here and it's under tension here and this plays out a lot in bridge building and span building. And of course, depending on the dimensions of the material, you'll have this neutral axis. All that really means is that that's the one that experiences the least deformation.

It's not so much under compression, not so much under tension. It's right there in the middle, so it's an equilibrium, if you will. And a good point that that slide made too is that everything's in three dimensions.

So you can try to simplify things in one dimension for very, very thin materials. For flat materials, you can simplify things in two dimensions. But for materials that cover a large span height-wise and length-wise, you have to think then in three dimensions as well. All right, so just another view, some examples. You know, we make the move from traditional framing, and then we have learned, of course, over the years, you can do lamination and you can reduce materials, which also reduces the weight.

Just... from themselves, which allows them to have a lower personal embodied load and then the benefits are pretty obvious there in terms of material use and an overall load. So that's the idea of the I-beam. Okay, so again you hollow things out, less weight, less mass, less weight, less personal load if you will, and or embodied load. and then you are able to again use not 100% necessarily, but very very similar tensile strengths and resistance to deformation and deflection.

Plus the added benefit is, depending on on how you're using these, you can sometimes use these gaps or very often use these gaps for the passage of conduits. Just depends on how it's used and those are designed in. All right so reinforcing bar is important. You look up rebar and concrete if you're not familiar with that what that is.

A nice table to show us a little bit. There's a stacked effect here. This is really sheer right talking this is a dramatic example but you can take a stack of books if you will and you can see that if you apply a force to the top We'll just take a single book here. I'll take your textbook. How about that?

Take your textbook. And I apply a force to it and you can see that that tangential force or that sheer force causes a deformation and it's not in one dimension now, I've done it now in two dimensions. And there are some fancy words for that from physics, but for the most part you just need to think of these as sheer stresses. So there's some bolts here, for instance. I'll give you a funny example.

When I was first learning how to ride a motorcycle, I hopped on to a little Honda Rebel and I was trying to shift gears and I actually the first time I tried to shift gears I actually Sheared the bolt that held it together. So the gear shifter actually fell completely down. It was pretty embarrassing, but you never forget So you got to really think about these as you're building something or assembling something and they're selected based off of the properties of the metal and also the physical dimensions Which are very important and then of course you think of you compare that to the load. They're called fasteners So all this goes to show is that depending on the materials you have to um be aware of their different amounts of ductility or plasticity or brittleness and that there are ways of reinforcing these and you have to think about directions as well. We've talked about that a little bit in the past, more about test cylinders, more in terms of fastening.

So some pretty good examples of failure rates here. So there's that necking idea. That's the visual cue that we were talking about before. You're not going to go back from that, by the way, but it might not completely fail until you get a little bit of a warning. If it were, for instance, a safety feature.

Let's go back to our OSHA training right or look towards it, I guess, in most people's cases. If you are looking for signs of wear on, say, well, for OSHA 30, we're talking about crane safety a lot of times. So if you're looking for signs of wear on the lanyards and such for cranes, then you might see this necking as an example. And you want to make sure that you replace that and put it out of service.

So buckling is kind of the opposite there and so there are ways to mitigate that as well, which you might be more familiar with because a lot of you have seen basic traditional stud work for the most part and you don't just have to think up and down in terms of compression right there's side to side motion as well and your textbook does a pretty good job of explaining this too right so multiple ways of supporting reinforcements. A little example here for you. This actually will help you a little bit with one of the later lab activities. So I would go through this for the most part, but this is just that example that's in the textbook as well.

So my biggest thing here, is just don't get confused by the symbols because it's pretty straightforward. So structural safety, you talk about the safety margin, it's the actual strength versus the required strength. So in other words, how close are you to the limitations of this material or structure? And then the factor of safety is, you know, what's that failure stress?

Remembering what stress is, right? The force over the area and and then versus the allowable stress. So, again, how close are you to the point of?

failure. These are going to be ratios, so it's going to be basically a percentage or multiples, I should say, how far off you are. So again, YouTube video here available for you to talk about thermal expansion. If you build anything and you have changes in temperature, even just from night to day, but mostly seasonal. then you're going to get expansion or contraction.

So there are plenty of classic examples out there. If you go over a bridge, then you see the teeth. And in the wintertime, the length of bridge was really what you're concerned about is the length because it's a much longer area there. And the same percentage of expansion is going to make much greater change.

Then the teeth are much further away. So you see gaps. So you're riding across on a motorcycle and you notice it.

You drive across. cross on a car and you don't probably. But in the summertime everything expands and so imagine my fingers getting very slightly thicker then you see the teeth the gaps between the teeth are not quite as pronounced. That's just an expansion gap. So concrete same thing you can cut them you can put you know wooden expansion in you can put asphalt expansion and foam expansion plastic expansion it just depends.

You can just have a gap there. You can have an edge joint. Same thing.

Large brick buildings. There's certain, based off of code and general manufacturer's practice for things, you have certain lengths of a material that you're allowed to use or material system that you're allowed to use before you account for expansion. Even roofing materials, you have a certain amount of gap that's required. in the substrate, right, which would be the plywood or planking or whatever you're using underneath. It's all because things are responding to the temperature.

So again, we live in the real world. This is not an ideal world. What I mean by ideal is things stay static.

It's a very dynamic world and so the materials are going to change and you need to be able to respond to that. Alright, so thermal expansion, there's some nice formulas for it. The big thing is that this is delta. Just means change in. It's the same thing as this little guy except lowercase versus uppercase.

And this is the change in temperature. This is going to be the change in length. So you could just as easily call this triangle L. It's the same exact thing. And then there's one alpha here.

That's just the letter A basically in Greek. And then there's the original L. So again, Don't get confused because the variables sometimes look a little different from each other from time to time.

These are scientific notation forms. Also engineering notation, if you will, because it's a multiple of three. But the big thing is, is that it's easy enough to plug and chug numbers in if you just have one unknown. So let's say you know the original length of something. You know the coefficient of expansion here.

right? There's also the coefficient of compression. You can use the same thing or coefficient of, yeah, same thing, the coefficient of expansion.

And so the same rule applies here. You know a final temperature, you know an initial temperature. So let's say that it's 20 degrees Fahrenheit out.

Remember we're using the Fahrenheit scale for these, that's important. and then it goes up to 50 degrees Fahrenheit outside. We're getting close to those temperatures here today actually. So the final was 50, the starting was 20, so 30 degrees would go right here. Alpha is given as somewhere within this range.

It depends on the type of steel and then the original length would have to be given to you. Then you could figure out what the change in length is. Now here's the thing, if you're asked what the new length is, You have to take this change in length and add it to the original length. All these symbols are easy to get lost in, but the whole point is that whether you're expanding or you're contracting, use that thermal coefficient and you can find all of these coefficients in some table somewhere, right? Well, here's an example.

Glass, steel, aluminum. polyethylene, wood. It says wood along the grain, right, because it was a biological material, an organic material, and so the grain has a different coefficient of expansion than across the grain because of the way that the celluloid constructs are made.

I don't mean to get too wordy for you on that one, but... The way the cellulose is laid out. And so across the grain is different than along the grain and that's just because across the grain you're cutting across little teeny threads, but along the grain they're huge long threads, right?

All right, so different expansion coefficients. And actually I'll show you a demo of that too along the content. All right, so there are limits to all of these.

You can estimate these. The longer it is, the greater the overall change in length will be, not as a percentage, but as a final measurement. There are plenty of examples here. And then we talk about methods of heat transfer. So thermal conductivity just means that heat flows between things that are in physical contact with each other.

So... the whole idea is that if I touch something hot, then that material is vibrating very quickly, right? That's the whole point about heat. And so if I touch it, I'm not vibrating as quickly on the small scale. My little molecules aren't vibrating, at least compared to the hot stove.

And so they're vibrating my molecules on my hand, and I don't like that because I like my molecules to stay as still as possible compared to my, how they originally were. So then they fly faster and if it's too hot then they fly away and that's called being Really badly burnt and if it's just a little bit too hot and they melt right because I'm changing the structure again A YouTube video for you to watch I won't read everything Completely, but this has very practical Very practical applications in the building sciences. So you have these things called R-value and U-values.

And U-values are basically the inverse of the R-value. U-value is all about transmittance and R-value is all about resistance. And so you put in insulation in a home and you say, well, I want as high an R-value as I can get.

Well, there's actually a limit to how valuable that is, depending on where you are in the world and local weather patterns and things. or temperature zones rather, but if you can find say an R value, then you can tell that the U value is going to be the inverse of that. So inverse is one divided by the original value. So again, lots of examples for you that you can go through.

I won't ruin all your reading by doing that, but if you come across an example in the textbook that you're really not sure about, show me exactly where you're having an issue and I'll explain it in a different way. possibly less worthy. We'll see.

All right, so that's where we are, and I will also provide you a couple demonstrations as we go along, but if you have questions, let me know, and I hope that this overview helped you at least understand that as complex as the chapter content might be, There are reasons behind it. Things make physical sense. So I encourage you one last time, always ask, does this make sense?

I don't mean does it click in your head. I mean, when they make a claim in the textbook or in a video or in a resource that I give to you, does it match your own understanding of the world around you? Because this class is all about real physical materials and experiences.

All right.

Transcript for:Properties of Materials

Transcript for:
Properties of Materials