Hi, I'm Hally. Welcome to Project Strange. Lots of questions around the structures in our world. Like, who made them, how they made them, and why they made them. And Project Strange is our attempt to find these answers through understanding structural engineering. This episode we're trying to understand elasticity. But first, let's talk about history. In 1727, the Swiss mathematician and mechanician Leonard Euler, who was taught mathematics by Johann Bernoulli. Euler. Euler. Euler. So that there was a linear relation between stress and strain. This equation today used to quantify the elasticity of a material is called Young's modulus. Euler and Jacob Bernoulli, Johann's older brother, introduced the idea that at a given section along the length of a beam, there were internal tensions, amounting to a net force and a net torque. But get this. Euler also introduced the idea of compressive normal stress as a pressure in a fluid in 1752. Did you know that steel is the most elastic material? When you think of elasticity, you immediately think of elastic bands, which are always made out of rubber. What makes steel more elastic than rubber is at the root of elasticity, which is the ability for material to regain its original shape when the pressure is removed. Steel has the highest Young's modulus value of any other material. Therefore, making it the most elastic. So next time you want to shoot a rubber band at your friend, you still instead. Actually, wait, don't do that. The French engineer and physicist Charles Leigh Gossett and Column was apparently the first to relay the theory of a beam as it bent elastic line to the stress and strain in an actual beam in a way never quit achieved by Bernoulli. And although possibly recognized, never actually published by Euler. And now I'll pass it off to Peyton with the interview. Tristan! What? What is elasticity? To an engineer, literally everything is a spring. Even things that you don't think are springs. Big things, small things, bananas are springs. Even rocks. We don't think of a rock as stretchy, but when you apply a pressure to rock, all the atoms and molecules arrange in such a way that there is small deformation, even if it is very small. And a spring can be defined by two attributes. One is how much it stretches and how much force you need to stretch it. This is a spring. This is a spring. This is a spring. This is a spring. The whole world is a spring. Buildings are springs. The rocks are springs. The ground is springs. And this is how we evaluate them. This piece of wood has no load on it. So we put a piece of duct tape where its position is. And when I load it up with a metal weight, it displaces. It deforms. It is in a different shape. And we can measure that. How much it displaces. And if I put on a second weight, it's good to have too. We see that it is displaced approximately an equivalent distance with double the weight. So let's graph that. A spring, as I said, is modeled based on how much strength it requires to stretch it. Or in our example, how much force was exerted by gravity. And we can measure that and call it F. Don't need to know exact amounts right now. We're just measuring the amount of force. And on our graph, we're comparing it to deformation. How much it moves. And with a zero force, it was at a certain location. And then when I added one weight, gravity caused it to displace banana for scale. So I'm going to draw a banana here that we have displaced at one banana per steel plate. And now I put on the second plate and it displaced. There are two bananas for two steel plates. And what we see is it's a straight line. And that's known as Hooke's Law. Hooke's law states that the amount of movement is proportional to the amount of force applied for a pure elastic system. We use elastic systems every day in our life. This sock is an elastic system. Where'd you get that from? Got another one. Got a whole bag of them. We have elastic waistbands on a lot of our clothes. They are very stretchy. But if you extend them beyond their stretchable limit, they don't go back to the same shape that they were before. You can see this one is stretch wider than it's original shape. We like things that are elastic and we know that if we stretch them too far, they don't behave as they used to. And beyond this ideal elastic that Hooke talked about, we know that is the plastic region where it does not return back to its original shape. But we're talking about elasticity. But this isn't good enough because using Hooke's law, we can predict how much an object will stretch under how much force. This concept was expanded to modulus of elasticity or Young's modulus. If I know the stretchiness of one piece of material, and I know how much force it takes to stretch one piece of material, half the length of a similar material would stretch half as much. But conversely, if I have two pieces of material, it will also stretch half as much. So Hooke's law is very dependent on the material and the shape and how many of it you have. So we use stress and strain. As Dr. Hunt explained, stress is how much force is applied per area. And strain is how much stretch is applied. Using stress and strain, we can change force into stress, and we can change deformation into strain. And using those two concepts, we find that our graph essentially stays in a straight line just as it was before. And this is more useful to us because this is a material property, so it does not depend on the shape or the number of objects you have. It depends on the material, so we can compare one type of steel to another type of steel. Similar area, but this also works for steel of different shapes, different areas, and different materials that are the same size in shape. And using elasticity of different materials, we can make predictions about how a building will perform. I designed a large warehouse, and in the wind, the braces elongate and contract. I designed a four-story wood building with a rooftop burden, and we use Young's Modules or Modules of Lasticity to determine how much the wood structural columns will shrink under the weight of the building. We can use Young's Modules to predict how much a building will move under different sources of load. Well, how do we use it in our everyday lives? We use Modules of Lasticity when we wear our clothes, and they stretch to conform to our body shape. We use Modules of Lasticity when we put springs on our cars and on our bikes to make sure that the shape of the road is smoothed out as we travel. And using Modules of Lasticity, we can predict the performance of not just springs, but of our materials. Modeling things as springs is very helpful because springs are very simple. Springs elongate and contract with the force imposed on them. And this allows us to make predictions of how things will both change shape and distribute load amongst the members. So if something is very stretchy, it will cause a lot of movement, or it will transfer the force to an adjacent member. Modules of Lasticity allows us to calculate just how much force is transferred, or just how much movement is caused. Is there such thing as too much elasticity? Absolutely. You need to select the stiffness of the members that you are for its intended purpose. If you have too much flexibility in spring in your car, your car will bounce too much when it hits above. Similarly, you want a building to be able to sway and deflect when in the wind, because rigidity sometimes concentrates loads in small elements that can't take the load. But if you design a flexible system, it's more resilient and able to distribute loads into where you are hoping that the load would go. So you design your force system so that the building moves and deflects in the way that you've predicted it to. Is there such thing as too little elasticity? Yes. Too little elasticity is typically associated with rigid elements, and when you have a rigid element beside a flexible element, the rigid element attracts more force to it, because it is the stronger support, and it is deflects less under a load. If you have a flexible banana and a steel element, and beside each other, and you load it up, the steel element will take the majority of the force, because the flexible element will deflect under the stress applied. So basically, elasticity is the ability for materials to return to its original shape after the pressure is removed. Understanding the behavior of materials under a load is essential for building safe structures. Engineers need to ensure that the materials they use can support expected loads of excessive deformation or failure. In engineering, the elasticity of a material is quantified by the youngest modulus, which measures the amount of stress needed to achieve a unit of strain. A higher modulus indicates that the material is harder to deform. The SI unit of this modulus is the Pascal, PA. The material's elastic limit or yield strength is the maximum stress that can arise before the onset of plastic deformation. Its SI unit is also Pascal, PA. Does your brain feel bigger after this? I know mine does. Thanks for tuning in. Make sure to smash like and subscribe button on your way out, and as always, enjoy the process. Have you ever built something that wasn't strong or reliable? Yes.