WEBVTT 1 00:00:00.080 --> 00:00:03.799 If I were to ask you a deceptively simple question, 2 00:00:04.000 --> 00:00:06.639 like when you stand on the floor, why don't you 3 00:00:06.639 --> 00:00:07.200 fall through it? 4 00:00:07.360 --> 00:00:09.640 You'd probably think it's a trick question, right. 5 00:00:09.560 --> 00:00:11.960 Or maybe something I don't know five year old might ask. 6 00:00:12.480 --> 00:00:16.160 But the truth is, getting to the real scientific answer 7 00:00:16.160 --> 00:00:20.000 to that simple question took humanity thousands of years. 8 00:00:20.199 --> 00:00:23.239 It really did. And what's wild is that for centuries, 9 00:00:23.399 --> 00:00:26.679 like even during the construction of the great medieval cathedrals, 10 00:00:26.719 --> 00:00:31.079 which are just absolute architectural marvels. Oh, the builders didn't 11 00:00:31.160 --> 00:00:34.280 actually know the math or the physics behind what they 12 00:00:34.320 --> 00:00:36.600 were doing. I mean, if you pulled aside a medieval 13 00:00:36.640 --> 00:00:39.119 master mason and asked him how a massive, you know, 14 00:00:39.359 --> 00:00:42.159 thousands of tons stone vaults stayed up in the air, 15 00:00:42.439 --> 00:00:44.799 he'd probably tell you he'd just followed the traditional rules 16 00:00:44.880 --> 00:00:45.159 of his. 17 00:00:45.159 --> 00:00:47.240 Craft, just like rules of thumb, Yeah. 18 00:00:47.119 --> 00:00:50.439 Rules of thumb. And beyond that, they believed the building 19 00:00:50.560 --> 00:00:53.079 was essentially held up by the grace of God. They 20 00:00:53.119 --> 00:00:56.240 relied entirely on trial, error and. 21 00:00:56.280 --> 00:00:59.000 Faith, which is frankly pretty terrifying when you think about 22 00:00:59.039 --> 00:01:02.399 walking into one of those cathedrals today. So today we're 23 00:01:02.439 --> 00:01:07.480 diving into the actual science of elasticity. We're drawing from J. E. 24 00:01:07.560 --> 00:01:12.920 Gordon's classic engineering text Structures or Why Things Don't Fall Down, 25 00:01:13.400 --> 00:01:17.000 and we've tailored this deep dive specifically for you, whether 26 00:01:17.040 --> 00:01:20.920 you're an engineering student grinding through your first structural mechanics course, 27 00:01:21.319 --> 00:01:24.040 or maybe a young professional designing your first real world. 28 00:01:23.920 --> 00:01:27.959 Project, or honestly, just a fiercely curious learner who wants 29 00:01:28.000 --> 00:01:32.200 to understand how the physical world works without getting bogged 30 00:01:32.239 --> 00:01:34.719 down in a swamp of impenetrable jargon. 31 00:01:34.959 --> 00:01:39.159 Exactly so, to understand how those massive suspension bridges and 32 00:01:39.760 --> 00:01:43.079 towering skyscrapers stay standing, we have to start with that 33 00:01:43.120 --> 00:01:45.799 fundamental question about why you don't fall through the floor. 34 00:01:46.159 --> 00:01:49.079 And as with so many foundational concepts and physics, it 35 00:01:49.120 --> 00:01:53.280 all starts with Isaac Newton and well a famously cantankerous 36 00:01:53.319 --> 00:01:54.719 scientist named Robert. 37 00:01:54.439 --> 00:01:57.560 Hook Right, because Newton's third law of motion is absolutely 38 00:01:57.560 --> 00:02:00.599 non negotiable, like every action must have an equal and 39 00:02:00.640 --> 00:02:03.760 opposite reaction, Right, So, in structural terms, every single push 40 00:02:03.840 --> 00:02:05.959 must be matched by an equal and opposite push. 41 00:02:06.280 --> 00:02:10.360 Precisely, if you weigh, say, two hundred pounds, and you 42 00:02:10.400 --> 00:02:13.520 stand on the floor, your feet are pushing down with 43 00:02:13.560 --> 00:02:15.960 two hundred pounds of force. So for you to stay 44 00:02:16.039 --> 00:02:18.759 right where you are not sinking into the ground, that 45 00:02:18.800 --> 00:02:21.879 floor has to push back up with exactly two hundred pounds. 46 00:02:22.000 --> 00:02:23.960 The force just has to balance perfectly. 47 00:02:24.039 --> 00:02:26.000 It has to. If the floor only pushes up with 48 00:02:26.199 --> 00:02:28.800 like one hundred and ninety nine pounds, the structure is 49 00:02:28.800 --> 00:02:31.560 failing and you're falling through it. If it magically pushed 50 00:02:31.599 --> 00:02:33.240 up with two hundred and one pounds. 51 00:02:33.039 --> 00:02:35.319 It would literally launch you into the air exactly. 52 00:02:35.400 --> 00:02:36.439 It would just launch you. 53 00:02:36.599 --> 00:02:39.039 Okay, but hold on, I get the physics of the 54 00:02:39.039 --> 00:02:42.240 balancing act. But how does an inanimate piece of wood 55 00:02:42.400 --> 00:02:44.919 or you know, a slab of concrete know how to 56 00:02:44.960 --> 00:02:48.240 push back? It doesn't have muscles, it's just dead material. See. 57 00:02:48.280 --> 00:02:51.599 That is the exact paradox that Robert Hook solved. Hook 58 00:02:51.719 --> 00:02:55.360 realized that solid materials must actually change their physical shape 59 00:02:55.400 --> 00:02:56.879 in order to resist a force. 60 00:02:57.120 --> 00:02:58.919 Change their shape how well. 61 00:02:58.960 --> 00:03:01.960 The classic example from Gordon's text is hanging a simple 62 00:03:02.120 --> 00:03:04.719 heavy brick from a string tied to a tree branch. 63 00:03:05.080 --> 00:03:07.400 When you hang that brick, the string actually stretches, it 64 00:03:07.400 --> 00:03:11.879 gets physically longer. And it's this very stretching, this deflection 65 00:03:12.400 --> 00:03:15.479 that allows the string to pull upward against the downward 66 00:03:15.520 --> 00:03:16.199 weight of the brick. 67 00:03:16.599 --> 00:03:19.120 Wait, are you saying that everything around us, from a 68 00:03:19.159 --> 00:03:22.879 heavy oak desk to a solid concrete wall, is essentially 69 00:03:22.919 --> 00:03:26.639 acting like a trampoline or a stiff spring. 70 00:03:26.919 --> 00:03:28.439 Basically, yeah, because. 71 00:03:28.240 --> 00:03:30.520 When I step on a concrete floor, it certainly doesn't 72 00:03:30.520 --> 00:03:31.319 feel like it's bending. 73 00:03:31.479 --> 00:03:33.159 It doesn't feel like it's to us, right, because we're 74 00:03:33.159 --> 00:03:36.240 big and the bend is tiny. But at a microscopic level, yes, 75 00:03:36.280 --> 00:03:38.000 it's absolutely acting like a spring. 76 00:03:38.120 --> 00:03:38.439 Wow. 77 00:03:38.639 --> 00:03:41.800 Every single structure, no matter how rigid it seems, deflex 78 00:03:42.240 --> 00:03:44.960 when a load is applied to it. Deflection isn't a 79 00:03:44.960 --> 00:03:47.560 flaw in the design, it's you know, it's the fundamental 80 00:03:47.560 --> 00:03:49.879 mechanism by which a material carries a load. 81 00:03:50.080 --> 00:03:53.000 So when that concrete floor pushes back up against your feet, 82 00:03:53.360 --> 00:03:56.639 it's because your weight has bent the concrete ever so slightly. 83 00:03:56.879 --> 00:04:00.439 Exactly. The chemical bonds between the atoms of the creator 84 00:04:00.479 --> 00:04:04.240 being physically stretched apart or compressed together. They're resisting that 85 00:04:04.360 --> 00:04:09.520 change in distance using electromagnetic forces, and that atomic resistance 86 00:04:09.599 --> 00:04:12.240 is what we experience as the material pushing back. 87 00:04:12.520 --> 00:04:15.919 Okay, so if everything is essentially a giant matrix, of 88 00:04:16.000 --> 00:04:21.240 microscopic springs. How do structural engineers actually measure this without 89 00:04:21.279 --> 00:04:25.439 losing their minds? Because Gordon points out that early scientists 90 00:04:25.759 --> 00:04:27.000 got completely stuck here. 91 00:04:27.040 --> 00:04:29.360 Oh, they totally did, and it held the science of 92 00:04:29.360 --> 00:04:33.519 elasticity back for generations. Early scientists were trying to calculate 93 00:04:33.519 --> 00:04:36.319 the strength of an entire bridge or an entire rod 94 00:04:36.399 --> 00:04:36.959 all at once. 95 00:04:37.000 --> 00:04:37.959 We can't do that. 96 00:04:38.079 --> 00:04:41.439 No, you can't, because the forces aren't distributed perfectly evenly. 97 00:04:41.920 --> 00:04:44.800 It wasn't until scientists zoomed in and developed the concepts 98 00:04:44.839 --> 00:04:47.480 of stress and strain to look at what was happening 99 00:04:47.600 --> 00:04:51.720 inside the material at one specific, tiny point that the 100 00:04:51.720 --> 00:04:53.000 math finally worked. 101 00:04:53.319 --> 00:04:56.040 Let's break those two terms down, actually, because in everyday 102 00:04:56.079 --> 00:04:59.839 conversation people use stress and strain interchangeably. 103 00:04:59.240 --> 00:05:00.000 Oh constantly. 104 00:05:00.160 --> 00:05:01.920 Yeah, I might say at a stressful day at work, 105 00:05:02.000 --> 00:05:04.639 or I'm under a lot of strain. But in engineering 106 00:05:04.759 --> 00:05:08.600 those words mean two very different, highly specific. 107 00:05:08.279 --> 00:05:11.879 Things, very different. Let's start with stress. So in engineering equations, 108 00:05:11.920 --> 00:05:14.920 stress is the load or the force divided by the 109 00:05:14.959 --> 00:05:18.519 cross sectional area. It measures how hard the atoms at 110 00:05:18.560 --> 00:05:21.759 a specific point inside the material are being pulled apart. 111 00:05:22.160 --> 00:05:25.079 Think of it as the invisible internal pressure. 112 00:05:25.519 --> 00:05:28.759 So like, if you hang a five kilogram brick from 113 00:05:28.759 --> 00:05:32.439 a string that's exactly two square milimeters thick, the stress 114 00:05:32.480 --> 00:05:36.199 is two point five kilograms per square millimeter. Nailed it, Okay, 115 00:05:36.360 --> 00:05:39.399 So stress is the invisible force. Then what is strain. 116 00:05:39.800 --> 00:05:42.439 Strain is the physical result of that force. It's the 117 00:05:42.480 --> 00:05:45.480 increase in length divided by the original length. Meaning if 118 00:05:45.480 --> 00:05:48.160 a one hundred inch string stretches by one inch under 119 00:05:48.160 --> 00:05:51.040 the weight of that brick, the strain is one divided 120 00:05:51.079 --> 00:05:53.079 by one hundred or point zero one. 121 00:05:53.199 --> 00:05:55.199 Oh, So it's a percentage exactly. 122 00:05:55.279 --> 00:05:57.920 Strain is just a ratio, a percentage of stretch. It 123 00:05:57.959 --> 00:06:01.399 doesn't have units like pounds or kilograms. To put it simply, 124 00:06:01.519 --> 00:06:03.720 stress tells us how hard the atoms are being pulled, 125 00:06:03.839 --> 00:06:06.120 and strain tells us how far they actually pull apart. 126 00:06:06.560 --> 00:06:08.480 And when you put those two concepts together, you get 127 00:06:08.519 --> 00:06:12.600 another major engineering term, right, Young's modulus, which if I'm 128 00:06:12.639 --> 00:06:15.560 understanding right, is essentially a material stubbornness score. 129 00:06:15.600 --> 00:06:18.199 Stubbornness score, that's a great way to visualize it. Yeah, 130 00:06:18.279 --> 00:06:21.519 Young's modulus represents the stiffness of a material. It's the 131 00:06:21.639 --> 00:06:25.480 ratio of stress to strain, meaning if you apply a 132 00:06:25.639 --> 00:06:29.199 massive amount of stress, like a huge and visible force, 133 00:06:29.600 --> 00:06:32.720 and the material only experiences a tiny bit of strain 134 00:06:32.839 --> 00:06:36.279 or stretch. It has a very high Young's modulus. It's 135 00:06:36.319 --> 00:06:37.439 incredibly stubborn. 136 00:06:37.600 --> 00:06:40.120 This leads to another pair of words. People constantly mix 137 00:06:40.199 --> 00:06:42.399 up right, strength and stiffness. 138 00:06:42.600 --> 00:06:45.639 They are absolutely not the same thing. Strength is the 139 00:06:45.800 --> 00:06:48.600 ultimate amount of stress needed to physically break a. 140 00:06:48.560 --> 00:06:50.720 Material, to actually snap it right. 141 00:06:51.240 --> 00:06:54.399 Stiffness that Young's modulus we just talked about is how 142 00:06:54.480 --> 00:06:57.399 floppy or rigid a material is before it reaches that 143 00:06:57.480 --> 00:07:00.920 break up point. Gordon uses some brilliant every day examples 144 00:07:00.920 --> 00:07:01.680 to illustrate this. 145 00:07:01.879 --> 00:07:03.000 Oh, the cracker one. 146 00:07:02.920 --> 00:07:06.120 Yeah, think of a dry biscuit or a cracker. A 147 00:07:06.160 --> 00:07:08.720 biscuit is stiff, you know, it doesn't bend or flop 148 00:07:08.759 --> 00:07:12.199 at all, but it's extremely weak. It snaps with almost 149 00:07:12.240 --> 00:07:12.879 no force. 150 00:07:13.079 --> 00:07:17.000 Where's something like steel is both stiff and strong right, And. 151 00:07:16.959 --> 00:07:20.120 On the flip side, nylon is very flexible, meaning has 152 00:07:20.199 --> 00:07:24.399 low stiffness and a low stubbornness score. But it's incredibly. 153 00:07:23.759 --> 00:07:28.040 Strong because you can stretch a nylon climbing rope significantly 154 00:07:28.120 --> 00:07:29.839 without it breaking exactly. 155 00:07:30.240 --> 00:07:34.600 And finally, raspberry jelly is flexible and weak. By separating 156 00:07:34.639 --> 00:07:39.079 strength from stiffness, engineers gained a scientific language to describe 157 00:07:39.120 --> 00:07:41.800 exactly how any material will behave under a load. 158 00:07:42.319 --> 00:07:44.879 So we have the math, we can calculate stress, we 159 00:07:44.920 --> 00:07:48.600 can measure strain, and we know our material stiffness. You'd 160 00:07:48.600 --> 00:07:51.720 think structural engineering is perfectly solved and completely safe. At 161 00:07:51.720 --> 00:07:53.959 this point. You would think so like you just calculate 162 00:07:53.959 --> 00:07:55.839 the stress, make sure it's lower than the breaking strength 163 00:07:55.839 --> 00:08:00.879 of the steel in your golden but meticulously calculated structures'll break. 164 00:08:01.000 --> 00:08:04.959 And often with catastrophic, terrifying results. The problem is that 165 00:08:05.000 --> 00:08:07.920 the beautiful, clean math of Hook and Young assumes a 166 00:08:07.959 --> 00:08:11.560 perfect material. It assumes the steel or the concrete is 167 00:08:11.759 --> 00:08:15.720 entirely uniform. But in the real world, perfection simply doesn't exist. 168 00:08:15.800 --> 00:08:17.240 Every single material. 169 00:08:16.839 --> 00:08:20.160 Has flaws, and in nineteen thirteen, a guy named ce 170 00:08:20.360 --> 00:08:24.199 Inglis discovered something deeply unsettling about those everyday flaws. 171 00:08:24.240 --> 00:08:28.000 He did. Ingliss mathematically proved that a tiny defect like 172 00:08:28.040 --> 00:08:31.000 a microscopic scrash, an air bubble in the cast metal, 173 00:08:31.079 --> 00:08:34.120 or a small rivet hole, acts as a stress concentration. 174 00:08:34.519 --> 00:08:35.600 A stress concentration. 175 00:08:36.159 --> 00:08:38.840 What does that look like think about a fast flowing river. 176 00:08:39.279 --> 00:08:41.559 If you drop a large boulder in the middle of it, 177 00:08:42.039 --> 00:08:45.840 the water doesn't just stop right, it diverts and rushes 178 00:08:46.000 --> 00:08:49.600 violently around the sides of the boulder. Force flowing through 179 00:08:49.639 --> 00:08:53.000 a solid material does the exact same thing when it 180 00:08:53.080 --> 00:08:54.360 hits a hole or a crack. 181 00:08:54.759 --> 00:08:58.080 So all that invisible force gets crowded into a bottleneck exactly. 182 00:08:58.399 --> 00:09:00.840 And because of that crowding, the dress at the very 183 00:09:00.840 --> 00:09:03.759 microscopic tip of a crack can be one hundred to 184 00:09:03.840 --> 00:09:06.519 one thousand times higher than the stress and the rest 185 00:09:06.519 --> 00:09:07.919 of the surrounding material. Wait. 186 00:09:07.960 --> 00:09:10.919 Wait, so if I have a steel beam that's theoretically 187 00:09:10.960 --> 00:09:15.159 only holding ten percent of its maximum capacity, a microscopic 188 00:09:15.200 --> 00:09:18.600 scratch on the surface could be experiencing forces one thousand 189 00:09:18.600 --> 00:09:21.799 times higher yep, Meaning the atoms right at that scratch 190 00:09:21.840 --> 00:09:24.480 are effectively pushed past their breaking point. 191 00:09:24.679 --> 00:09:27.039 Yes, and that's the reality of the built world. We're 192 00:09:27.080 --> 00:09:30.639 literally building our modern cities and vehicles out of materials 193 00:09:30.679 --> 00:09:33.279 that are already full of microscopic cracks, and we're just 194 00:09:33.360 --> 00:09:36.080 managing the physics to ensure those cracks don't spread. And 195 00:09:36.480 --> 00:09:39.159 the person who figured out how to manage that spreading 196 00:09:39.440 --> 00:09:42.279 was a Griffith who looked at the problem through the 197 00:09:42.360 --> 00:09:43.240 lens of energy. 198 00:09:43.679 --> 00:09:46.960 Let's unpack Griffith's energy approach, because this feels like the 199 00:09:47.000 --> 00:09:49.279 core of modern fracture mechanics. 200 00:09:49.360 --> 00:09:52.720 It is. Think of a structure carrying a load like 201 00:09:52.759 --> 00:09:56.960 a bridge supporting cars, as a giant reservoir of stored energy, 202 00:09:57.000 --> 00:10:00.519 which we call strain energy. Okay, it's identic to the 203 00:10:00.559 --> 00:10:03.159 tension energy stored in a wound up rubber band or 204 00:10:03.159 --> 00:10:06.320 a drawn bowstring. It's just sitting there waiting to be released. 205 00:10:07.039 --> 00:10:10.200 If the structure breaks, that stored strain energy has to 206 00:10:10.240 --> 00:10:11.000 go somewhere. 207 00:10:11.200 --> 00:10:14.759 It gets converted into what Gordon calls fracture energy. Like 208 00:10:14.919 --> 00:10:17.919 he uses that stored energy to violently tear the chemical 209 00:10:17.919 --> 00:10:19.759 bonds apart and create a new crack. 210 00:10:19.480 --> 00:10:22.879 Surface decisely now, Griffith found that short cracks are usually 211 00:10:22.919 --> 00:10:26.759 perfectly stable. Why because to rip those chemical bonds apart 212 00:10:26.799 --> 00:10:29.440 requires a certain amount of energy, and a tiny crack 213 00:10:29.600 --> 00:10:32.919 just doesn't release enough of that stored strain energy to 214 00:10:33.080 --> 00:10:34.720 pay the cost of tearing the bonds. 215 00:10:34.799 --> 00:10:37.679 Ah, So the surrounding material is essentially holding it together. 216 00:10:38.200 --> 00:10:40.840 Right. But and this is where the math gets terrifying. 217 00:10:41.320 --> 00:10:44.200 Once a crack grows to a very specific size, known 218 00:10:44.240 --> 00:10:47.440 as the critical Griffith crack length, the economics of the 219 00:10:47.559 --> 00:10:48.600 energy flip. 220 00:10:48.600 --> 00:10:52.519 Meaning the release of the stored strain energy suddenly becomes 221 00:10:52.600 --> 00:10:55.399 greater than the energy needed to rip the material apart. 222 00:10:55.559 --> 00:10:59.759 Yes, the moment it hits that critical length, it's energetically 223 00:10:59.799 --> 00:11:02.480 easier for the material to break than to stay together. 224 00:11:03.080 --> 00:11:06.279 At that point, the crack becomes completely self propagating. 225 00:11:06.480 --> 00:11:07.879 It just takes on life of its own. 226 00:11:07.960 --> 00:11:10.440 It feeds on its own released energy, speeding up through 227 00:11:10.440 --> 00:11:13.759 the material at the speed of sound, resulting in an explosive, 228 00:11:13.879 --> 00:11:15.000 catastrophic failure. 229 00:11:15.360 --> 00:11:17.799 And the most tragic real world example of this in 230 00:11:17.840 --> 00:11:21.039 the sources is that a havevilin Comet airplane disasters in 231 00:11:21.080 --> 00:11:24.120 the nineteen fifties. Yes, this was the world's first commercial 232 00:11:24.240 --> 00:11:26.639 jet airliner. It was supposed to be the future of aviation. 233 00:11:27.320 --> 00:11:30.639 But these planes kept mysteriously exploding mid air, falling out 234 00:11:30.639 --> 00:11:32.720 of the sky into the ocean, and nobody knew why. 235 00:11:33.120 --> 00:11:35.360 It was one of the greatest mysteries in early aviation. 236 00:11:35.960 --> 00:11:39.720 When investigators finally dredged up the wreckage and reconstructed the 237 00:11:39.720 --> 00:11:43.360 fuselage like a giant jigsaw puzzle. They found the culprit. 238 00:11:43.799 --> 00:11:45.320 It all started at the windows. 239 00:11:46.000 --> 00:11:46.679 The windows. 240 00:11:46.759 --> 00:11:50.480 The original Comet featured square windows. Every time the plane 241 00:11:50.519 --> 00:11:54.200 climbed to altitude, the cabin was pressurized, blowing up like 242 00:11:54.240 --> 00:11:57.320 a balloon, and then depressurized when it landed. 243 00:11:57.679 --> 00:12:01.120 So thousands of cycles of inflating deflating. 244 00:12:00.759 --> 00:12:03.679 Right and the sharp corners of those square windows acted 245 00:12:03.679 --> 00:12:08.559 as massive stress concentrations. Microscopic fatigue cracks started forming at 246 00:12:08.559 --> 00:12:11.639 the tiny rivet holes near those corners. Oh no, because 247 00:12:11.679 --> 00:12:14.519 the cracks were so small, inspectors couldn't see them. But 248 00:12:14.639 --> 00:12:17.360 with every flight, the cracks grew a tiny fraction of 249 00:12:17.399 --> 00:12:21.440 a millimeter. Eventually, while cruising at thirty thousand feet, one 250 00:12:21.480 --> 00:12:25.200 of those hidden cracks reached the critical Griffith cracklength math flip. 251 00:12:25.519 --> 00:12:27.480 In a fraction of a second. The crack fed on 252 00:12:27.519 --> 00:12:30.960 the strain energy of the pressurized cabin. The fuselage ripped 253 00:12:31.080 --> 00:12:34.279 entirely open, and the planes exploded, which is. 254 00:12:34.200 --> 00:12:37.759 Why every commercial airplane today has rounded windows to eliminate 255 00:12:37.759 --> 00:12:41.399 those sharp corners and disperse the stress. Actually, it really 256 00:12:41.440 --> 00:12:45.399 puts into perspective that modern engineering isn't about finding perfect 257 00:12:45.440 --> 00:12:49.399 crack free materials. It's about designing structures so that the 258 00:12:49.480 --> 00:12:52.559 critical crack link is long enough, say a few inches, 259 00:12:53.080 --> 00:12:56.000 so that an inspector can easily spot it and ground 260 00:12:56.080 --> 00:12:58.200 the plane long before it explodes. 261 00:12:58.399 --> 00:13:01.799 It's all about managing the enova flaws and knowing that 262 00:13:01.840 --> 00:13:05.200 these cracks are always waiting in the wings. Structural engineers 263 00:13:05.240 --> 00:13:08.639 have to be incredibly strategic about how they apply forces 264 00:13:08.679 --> 00:13:11.080 to a material in the first place. You can't just 265 00:13:11.120 --> 00:13:13.840 throw massive steel beams at a problem and hope for 266 00:13:13.879 --> 00:13:14.799 the best, right. 267 00:13:14.799 --> 00:13:16.480 You have to understand whether the structure is going to 268 00:13:16.480 --> 00:13:18.480 be pushed, pulled, or slit exactly. 269 00:13:18.559 --> 00:13:22.519 Let's walk through those three main types of forces compression, tension, 270 00:13:22.759 --> 00:13:23.360 and sheer. 271 00:13:23.879 --> 00:13:27.000 Yes, because structures behave radically differently depending on which one 272 00:13:27.000 --> 00:13:31.360 they're facing. Let's start with compression, which is pushing materials together. Okay, 273 00:13:31.639 --> 00:13:34.559 if I'm looking at a massive medieval stone tower or 274 00:13:34.559 --> 00:13:37.919 a huge brick wall, my intuition says that the stones 275 00:13:37.960 --> 00:13:40.279 at the very bottom are in serious danger of just 276 00:13:40.320 --> 00:13:43.679 being crushed into dust by the incredible thousands of tons 277 00:13:43.720 --> 00:13:45.200 of weight pressing down on them. 278 00:13:45.279 --> 00:13:48.000 It's a completely natural assumption, but it's actually wrong. 279 00:13:48.639 --> 00:13:48.919 Really. 280 00:13:49.039 --> 00:13:52.679 Yeah, when short fat blocks of a brittle material like 281 00:13:52.759 --> 00:13:56.960 concrete or stone fail in compression. They don't simply squish 282 00:13:57.080 --> 00:14:00.960 flat like a marshmallow. They fail by sheer ring diagonally. 283 00:14:01.639 --> 00:14:04.559 The material slides away from the pressure along a forty 284 00:14:04.559 --> 00:14:05.480 five degree angle. 285 00:14:05.879 --> 00:14:07.360 Okay, but what about the tall towers. 286 00:14:07.720 --> 00:14:10.679 When you move to tall structures like your medieval tower 287 00:14:10.840 --> 00:14:14.480 or a cathedral wall, they almost never crush. The actual 288 00:14:14.519 --> 00:14:16.879 compressive stress at the bottom of a brick wall is 289 00:14:16.960 --> 00:14:20.279 usually a tiny fraction of the crushing strength of the 290 00:14:20.279 --> 00:14:20.960 stone itself. 291 00:14:21.080 --> 00:14:23.759 Then why do walls fall down because they tip over? 292 00:14:23.919 --> 00:14:27.000 It's exactly like a toddler stacking wooden toy blocks too 293 00:14:27.080 --> 00:14:28.559 high and slightly crookedly. 294 00:14:28.879 --> 00:14:32.320 Oh so it's an issue of instability, not material strength exactly. 295 00:14:32.480 --> 00:14:35.240 In masonry, engineers talk about the thrust line and the 296 00:14:35.279 --> 00:14:35.840 middle third. 297 00:14:35.879 --> 00:14:36.639 How does that work. 298 00:14:36.879 --> 00:14:40.559 Imagine an invisible vertical line representing all the downward force 299 00:14:40.720 --> 00:14:43.519 of the wall's weight. That's the thrust line. As long 300 00:14:43.559 --> 00:14:46.120 as that thrust line pushes straight down through the middle 301 00:14:46.120 --> 00:14:49.679 third of the wall's base, the wall is perfectly stable. 302 00:14:50.279 --> 00:14:53.600 The mortar joints between the bricks are entirely in compression, 303 00:14:54.000 --> 00:14:57.159 just happily getting squeezed together. Okay, But if the wall 304 00:14:57.279 --> 00:15:00.600 leans or a massive gust of wind hits it, that 305 00:15:00.720 --> 00:15:03.799 thrust line wanders outside the middle third toward the edge 306 00:15:03.799 --> 00:15:04.240 of the wall. 307 00:15:04.320 --> 00:15:07.159 And when that happens, the physics changes entirely. 308 00:15:06.879 --> 00:15:09.159 Right, The joints on the opposite side of the wall 309 00:15:09.200 --> 00:15:12.240 actually go into tension. They try to pull apart, since 310 00:15:12.320 --> 00:15:15.480 mortar is fantastic at being squeezed but terrible at holding 311 00:15:15.519 --> 00:15:18.879 things together. In tension, the joint racks open like a hinge, 312 00:15:19.159 --> 00:15:21.120 and the wall just pivots and tips over. 313 00:15:21.320 --> 00:15:23.639 Okay, so that's thick walls. But what if the compression 314 00:15:23.679 --> 00:15:26.120 member is something tall and thin, like a metal pole 315 00:15:26.240 --> 00:15:26.840 or a strut. 316 00:15:27.279 --> 00:15:30.279 That introduces a different failure mode called buckling, which was 317 00:15:30.320 --> 00:15:34.399 mathematically defined by Leonhard Euler. A thin pole under compression 318 00:15:34.399 --> 00:15:37.320 doesn't crush either. Instead, it bows outward. 319 00:15:37.440 --> 00:15:39.639 Oh sure, like a plastic ruler when you push the 320 00:15:39.720 --> 00:15:40.279 ends together. 321 00:15:40.600 --> 00:15:44.159 Yes, perfect example. And the insidious thing about buckling is 322 00:15:44.200 --> 00:15:46.480 that once it bends, even a fraction of a millimeter, 323 00:15:47.000 --> 00:15:49.480 the weight pushing down now has a tiny lever arm 324 00:15:49.559 --> 00:15:53.080 to pry the pole further outward. The more it bends, 325 00:15:53.360 --> 00:15:56.440 the longer the lever arm gets magnifying the stress until 326 00:15:56.440 --> 00:15:58.039 the pole violently snaps. 327 00:15:58.639 --> 00:16:01.480 So if compression has all these tipping and buckling issues, 328 00:16:02.120 --> 00:16:04.759 why do engineers ever bother with pulling things apart? 329 00:16:05.159 --> 00:16:09.559 Why use tension Because tension members like the steel cables 330 00:16:09.559 --> 00:16:12.799 on a suspension bridge, can be incredibly lightweight. Since you're 331 00:16:12.840 --> 00:16:15.600 pulling them taut, you never have to worry about them buckling. 332 00:16:15.879 --> 00:16:20.200 You can use relatively thin, light cables to span massive distances. 333 00:16:20.279 --> 00:16:23.039 That sounds great, it is, but tension has a severe 334 00:16:23.159 --> 00:16:25.200 hidden cost the end fittings. 335 00:16:25.360 --> 00:16:27.840 Ah, you have to attach that highly stressed cable to 336 00:16:27.879 --> 00:16:29.639 something solid without ripping it out. 337 00:16:29.799 --> 00:16:33.679 Exactly, Transferring a massive tension load from a thin cable 338 00:16:33.720 --> 00:16:37.720 into a solid frame safely without creating terrible stress concentrations 339 00:16:37.720 --> 00:16:41.600 at the bolt holes requires heavy, complex, and highly expensive 340 00:16:41.639 --> 00:16:42.360 metal fittings. 341 00:16:42.480 --> 00:16:43.039 That makes sense. 342 00:16:43.440 --> 00:16:46.799 Nature actually ran into this exact same engineering problem with 343 00:16:46.840 --> 00:16:50.879 our own bodies. Our muscles pull on our bones using tendons, 344 00:16:51.159 --> 00:16:54.440 which are biological tension cables. Oh wow, But to avoid 345 00:16:54.559 --> 00:16:56.960 ripping the bone apart at a single point of attachment, 346 00:16:57.480 --> 00:16:59.840 Nature splays the end of the tendon out like a 347 00:17:00.519 --> 00:17:03.679 distributing the pulling load across a wide area of the bone. 348 00:17:03.759 --> 00:17:07.480 It's just brilliant biological engineering. So we have compression pushing things, 349 00:17:07.519 --> 00:17:10.680 tension pulling things, and finally we have sheer forces. 350 00:17:10.880 --> 00:17:13.799 Shear is when materials slide past each other, like the 351 00:17:13.839 --> 00:17:16.519 two blades of a pair of scissors, and sheer forces 352 00:17:16.559 --> 00:17:20.680 are tricky because they actually create tension and compression simultaneously 353 00:17:20.799 --> 00:17:23.759 at forty five degree angles to the direction of the slide. 354 00:17:24.160 --> 00:17:26.839 This brings up a really fascinating distinction in the source 355 00:17:26.880 --> 00:17:32.880 text about the materials themselves, specifically isotropic versus anisotropic materials. 356 00:17:33.039 --> 00:17:37.079 It's a crucial difference. Isotropic materials like steel or glass 357 00:17:37.400 --> 00:17:40.279 have the exact same mechanical properties in every single direction. 358 00:17:40.400 --> 00:17:42.279 It doesn't matter which way you twist or cut a 359 00:17:42.319 --> 00:17:46.240 steel plate. The internal structure resists the forces the exact 360 00:17:46.319 --> 00:17:50.440 same way, but anisotropic materials behave very differently depending on 361 00:17:50.480 --> 00:17:53.880 the direction you apply the force. Wood is a great example. 362 00:17:54.039 --> 00:17:57.319 It's easy to split along the grain, but incredibly hard 363 00:17:57.359 --> 00:17:58.599 to snap across the grain. 364 00:17:59.279 --> 00:18:01.799 Gordon uses dressmaking to explain this, which I thought was 365 00:18:01.839 --> 00:18:04.359 such an elegant analogy. If you take a piece of 366 00:18:04.400 --> 00:18:07.519 woven cloth and pull it straight up and down parallel 367 00:18:07.559 --> 00:18:09.920 to the threads. It's very stiff, right, But if you 368 00:18:09.960 --> 00:18:13.559 pull it diagonally at a forty five degree angle, it 369 00:18:13.680 --> 00:18:14.759 stretches dramatically. 370 00:18:14.839 --> 00:18:17.640 That's because the threads act like a trellis scissoring past 371 00:18:17.680 --> 00:18:20.640 each other in sheer. And this is the entire underlying 372 00:18:20.680 --> 00:18:24.359 principle of the bias cut dress in fashion, cutting the 373 00:18:24.359 --> 00:18:26.680 fabric at an angle to the weave so it stretches, 374 00:18:27.079 --> 00:18:29.359 drapes elegantly, and clings to the body. 375 00:18:29.559 --> 00:18:30.000 Wow. 376 00:18:30.119 --> 00:18:32.519 Whether you are designing the wingskin of an airplane or 377 00:18:32.599 --> 00:18:35.319 a high end ball gown, you are managing the exact 378 00:18:35.400 --> 00:18:37.839 same physical forces of sheer intension. 379 00:18:38.519 --> 00:18:41.839 Okay, So considering all of these incredibly complex failure modes 380 00:18:41.920 --> 00:18:45.920 you know, oilers, buckling, sheer planes, critical Griffith cracks, it 381 00:18:45.960 --> 00:18:48.640 honestly feels like a miracle anything stay standing at all. 382 00:18:48.799 --> 00:18:52.000 It kind of is how do structural engineers actually design 383 00:18:52.039 --> 00:18:55.359 the things we interact with every day, like houses, floors, 384 00:18:55.400 --> 00:18:59.279 and furniture without them costing a fortune or taking decades 385 00:18:59.319 --> 00:19:01.119 to supercomput They. 386 00:19:01.039 --> 00:19:05.400 Use what is essentially an engineering cheat code. They prioritize 387 00:19:05.640 --> 00:19:07.279 stiffness over strength. 388 00:19:07.519 --> 00:19:11.920 Let's pause and really explore that, because intuitively, you'd think 389 00:19:11.960 --> 00:19:14.799 the ultimate goal of a brilliant engineer is to make 390 00:19:14.880 --> 00:19:18.160 a structure as mathematically efficient as possible. 391 00:19:17.839 --> 00:19:20.000 Right, like making it exactly strong enough. 392 00:19:20.079 --> 00:19:23.359 Yeah, you'd want every single joist, beam and bolt to 393 00:19:23.400 --> 00:19:26.839 be exactly strong enough to carry its intended load, saving 394 00:19:26.880 --> 00:19:28.599 weight and saving material cost. 395 00:19:28.799 --> 00:19:31.799 You'd think so, But a perfectly efficient structure is actually 396 00:19:31.880 --> 00:19:35.839 incredibly dangerous in the real world. Oliver Wendell Holmes wrote 397 00:19:35.839 --> 00:19:38.640 a famous poem about this concept called the one Hoss 398 00:19:38.720 --> 00:19:41.559 shay Oh, I've heard that. It's about a carriage designed 399 00:19:41.599 --> 00:19:45.000 so flawlessly that no single part was weaker than any other. 400 00:19:45.240 --> 00:19:48.119 The result, when it finally reached the end of its lifespan, 401 00:19:48.279 --> 00:19:52.039