In this problem, we're told that we have a piece of pre stressed concrete. So we have is a slab of concrete. What happens is we take a metal rod, we stretch it and hold it, and then we pour concrete around it that concrete cure and then let release the rod. And then we have big plates here that are very stiff. So the rod will try to spring back to its normal length and in doing so will compress the concrete because the concrete concrete new sister, so in the and you'll have a rod through the concrete. That's intention and the country in compression, which is what you want, because medals are very good in intention and just concrete is very good and compression, but very does very poorly in attention because cracks brought me easily. So this piece of concrete. This conflict block is 1/2 1 1/2 meters long. It has a cross sectional area, 50 centimeters. The steel rod that goes through it has a cross sectional area, 1.5 centimeters squared. Um, it's steel. So Chung's module is is 200 acre Pascal's, their country. We're told it has a young marginalised of 30 Guica Pascal and we're told that the stress in the concrete after the after the Rod is concrete is cured and the rod is released. Is minus eight Mecca Paschal's. Now I've assumed that this 1.5 meters is the final link of the concrete. No, what we'll see is that it really doesn't matter. And then we've given in a linear approximation. We have very small deformation is whether we use the final length of the initial length. You'll see really makes no difference at all. Um, but I used the final in character kind of show that why that is so we know that the strain is the change in length over the initial length, which is the stress divided by the young's modules. Um, and we know that the change in length is the final length minus the initial all over. The initial is the strength. So if we have, if we have the initial link, it's easy to find the if you have the initial length, the stress and the young marginalised season to find the change in length. However, if you have their final link, the stress than the young evangelist. We need to do a little bit of algebra and we see that what we get is that the change in length change in length to equal the final length the times of stress all over the module is time plus this stress. And so that's what I have here for the concrete. Now why it makes very, very little difference is if you look at the magnitude of these two terms, Um, if this time gets anywhere close to being this, then you have strains on the order of one, which means that you're long past any kind of many. Your material behaviour on pretty much everything in this chapter is is no longer could assumption. So you can see that, really, this term had better be very small compared to this. And in fact, we had When we have here, um, basically, you know, orders of three orders of magnitude difference here. So we can pretty much neglect this term, which means that whether this is the initial length of the final thing is kind of material. So what we're asked for how much does the concrete compress after the after the tension in the rod is released, and we can pluck all our numbers in here, and we get that it compresses a 0.4 millimeters. So from the from the cured length to its final link, it is now. It's your point formula short, Um, and again, you can kind of compare that to this. You know, the initial length of the final link are almost indistinguishable from now. We're asked what the tension in the rod is. Well, if we look at a free by diagram of, say, the plate that the rod the rod is attached to when it's pulling the rod is pulling the plate this way, and the concrete is pressing on. It has a pressure that's equal to stress. That's pushing it out. And so the net to keep this an equilibrium, the net force from the concrete, which is this must equal the tension in the rod so we can plug in our numbers and we get that. That's 40 kilometers now. If no one asked for how how much? How long is the rod after it's been released? How much has it stretched from it? So there's there's kind of Ford in three different states of the rod. It's on stretched length. It's stretched length when you're waiting for the concrete secure. And then it's second stretch length after it's been released, and now the concrete is stretching. So it's this last stretch length that we want to find. So we know the stress in the in the Rod, his t two, the tension divided by its cross sectional area. And again we can use the formula like this and again. This term is negligible compared to this, and we can plug all our values. And then we get that this final value is is two millimeters. And so what that tells us is, is that the you need to stretch the rod 2.4 millimeters and while the concrete rich jury and then once we let it go, it rebounded back 0.4 millimeters by compressing the concrete