Speaker 1: If I were to ask you a deceptively simple question,
Speaker 1: like when you stand on the floor, why don't you
Speaker 1: fall through it?
Speaker 2: You'd probably think it's a trick question, right.
Speaker 1: Or maybe something I don't know five year old might ask.
Speaker 1: But the truth is, getting to the real scientific answer
Speaker 1: to that simple question took humanity thousands of years.
Speaker 2: It really did. And what's wild is that for centuries,
Speaker 2: like even during the construction of the great medieval cathedrals,
Speaker 2: which are just absolute architectural marvels. Oh, the builders didn't
Speaker 2: actually know the math or the physics behind what they
Speaker 2: were doing. I mean, if you pulled aside a medieval
Speaker 2: master mason and asked him how a massive, you know,
Speaker 2: thousands of tons stone vaults stayed up in the air,
Speaker 2: he'd probably tell you he'd just followed the traditional rules
Speaker 2: of his.
Speaker 1: Craft, just like rules of thumb, Yeah.
Speaker 2: Rules of thumb. And beyond that, they believed the building
Speaker 2: was essentially held up by the grace of God. They
Speaker 2: relied entirely on trial, error and.
Speaker 1: Faith, which is frankly pretty terrifying when you think about
Speaker 1: walking into one of those cathedrals today. So today we're
Speaker 1: diving into the actual science of elasticity. We're drawing from J. E.
Speaker 1: Gordon's classic engineering text Structures or Why Things Don't Fall Down,
Speaker 1: and we've tailored this deep dive specifically for you, whether
Speaker 1: you're an engineering student grinding through your first structural mechanics course,
Speaker 1: or maybe a young professional designing your first real world.
Speaker 2: Project, or honestly, just a fiercely curious learner who wants
Speaker 2: to understand how the physical world works without getting bogged
Speaker 2: down in a swamp of impenetrable jargon.
Speaker 1: Exactly so, to understand how those massive suspension bridges and
Speaker 1: towering skyscrapers stay standing, we have to start with that
Speaker 1: fundamental question about why you don't fall through the floor.
Speaker 2: And as with so many foundational concepts and physics, it
Speaker 2: all starts with Isaac Newton and well a famously cantankerous
Speaker 2: scientist named Robert.
Speaker 1: Hook Right, because Newton's third law of motion is absolutely
Speaker 1: non negotiable, like every action must have an equal and
Speaker 1: opposite reaction, Right, So, in structural terms, every single push
Speaker 1: must be matched by an equal and opposite push.
Speaker 2: Precisely, if you weigh, say, two hundred pounds, and you
Speaker 2: stand on the floor, your feet are pushing down with
Speaker 2: two hundred pounds of force. So for you to stay
Speaker 2: right where you are not sinking into the ground, that
Speaker 2: floor has to push back up with exactly two hundred pounds.
Speaker 1: The force just has to balance perfectly.
Speaker 2: It has to. If the floor only pushes up with
Speaker 2: like one hundred and ninety nine pounds, the structure is
Speaker 2: failing and you're falling through it. If it magically pushed
Speaker 2: up with two hundred and one pounds.
Speaker 1: It would literally launch you into the air exactly.
Speaker 2: It would just launch you.
Speaker 1: Okay, but hold on, I get the physics of the
Speaker 1: balancing act. But how does an inanimate piece of wood
Speaker 1: or you know, a slab of concrete know how to
Speaker 1: push back? It doesn't have muscles, it's just dead material. See.
Speaker 2: That is the exact paradox that Robert Hook solved. Hook
Speaker 2: realized that solid materials must actually change their physical shape
Speaker 2: in order to resist a force.
Speaker 1: Change their shape how well.
Speaker 2: The classic example from Gordon's text is hanging a simple
Speaker 2: heavy brick from a string tied to a tree branch.
Speaker 2: When you hang that brick, the string actually stretches, it
Speaker 2: gets physically longer. And it's this very stretching, this deflection
Speaker 2: that allows the string to pull upward against the downward
Speaker 2: weight of the brick.
Speaker 1: Wait, are you saying that everything around us, from a
Speaker 1: heavy oak desk to a solid concrete wall, is essentially
Speaker 1: acting like a trampoline or a stiff spring.
Speaker 2: Basically, yeah, because.
Speaker 1: When I step on a concrete floor, it certainly doesn't
Speaker 1: feel like it's bending.
Speaker 2: It doesn't feel like it's to us, right, because we're
Speaker 2: big and the bend is tiny. But at a microscopic level, yes,
Speaker 2: it's absolutely acting like a spring.
Speaker 1: Wow.
Speaker 2: Every single structure, no matter how rigid it seems, deflex
Speaker 2: when a load is applied to it. Deflection isn't a
Speaker 2: flaw in the design, it's you know, it's the fundamental
Speaker 2: mechanism by which a material carries a load.
Speaker 1: So when that concrete floor pushes back up against your feet,
Speaker 1: it's because your weight has bent the concrete ever so slightly.
Speaker 2: Exactly. The chemical bonds between the atoms of the creator
Speaker 2: being physically stretched apart or compressed together. They're resisting that
Speaker 2: change in distance using electromagnetic forces, and that atomic resistance
Speaker 2: is what we experience as the material pushing back.
Speaker 1: Okay, so if everything is essentially a giant matrix, of
Speaker 1: microscopic springs. How do structural engineers actually measure this without
Speaker 1: losing their minds? Because Gordon points out that early scientists
Speaker 1: got completely stuck here.
Speaker 2: Oh, they totally did, and it held the science of
Speaker 2: elasticity back for generations. Early scientists were trying to calculate
Speaker 2: the strength of an entire bridge or an entire rod
Speaker 2: all at once.
Speaker 1: We can't do that.
Speaker 2: No, you can't, because the forces aren't distributed perfectly evenly.
Speaker 2: It wasn't until scientists zoomed in and developed the concepts
Speaker 2: of stress and strain to look at what was happening
Speaker 2: inside the material at one specific, tiny point that the
Speaker 2: math finally worked.
Speaker 1: Let's break those two terms down, actually, because in everyday
Speaker 1: conversation people use stress and strain interchangeably.
Speaker 2: Oh constantly.
Speaker 1: Yeah, I might say at a stressful day at work,
Speaker 1: or I'm under a lot of strain. But in engineering
Speaker 1: those words mean two very different, highly specific.
Speaker 2: Things, very different. Let's start with stress. So in engineering equations,
Speaker 2: stress is the load or the force divided by the
Speaker 2: cross sectional area. It measures how hard the atoms at
Speaker 2: a specific point inside the material are being pulled apart.
Speaker 2: Think of it as the invisible internal pressure.
Speaker 1: So like, if you hang a five kilogram brick from
Speaker 1: a string that's exactly two square milimeters thick, the stress
Speaker 1: is two point five kilograms per square millimeter. Nailed it, Okay,
Speaker 1: So stress is the invisible force. Then what is strain.
Speaker 2: Strain is the physical result of that force. It's the
Speaker 2: increase in length divided by the original length. Meaning if
Speaker 2: a one hundred inch string stretches by one inch under
Speaker 2: the weight of that brick, the strain is one divided
Speaker 2: by one hundred or point zero one.
Speaker 1: Oh, So it's a percentage exactly.
Speaker 2: Strain is just a ratio, a percentage of stretch. It
Speaker 2: doesn't have units like pounds or kilograms. To put it simply,
Speaker 2: stress tells us how hard the atoms are being pulled,
Speaker 2: and strain tells us how far they actually pull apart.
Speaker 1: And when you put those two concepts together, you get
Speaker 1: another major engineering term, right, Young's modulus, which if I'm
Speaker 1: understanding right, is essentially a material stubbornness score.
Speaker 2: Stubbornness score, that's a great way to visualize it. Yeah,
Speaker 2: Young's modulus represents the stiffness of a material. It's the
Speaker 2: ratio of stress to strain, meaning if you apply a
Speaker 2: massive amount of stress, like a huge and visible force,
Speaker 2: and the material only experiences a tiny bit of strain
Speaker 2: or stretch. It has a very high Young's modulus. It's
Speaker 2: incredibly stubborn.
Speaker 1: This leads to another pair of words. People constantly mix
Speaker 1: up right, strength and stiffness.
Speaker 2: They are absolutely not the same thing. Strength is the
Speaker 2: ultimate amount of stress needed to physically break a.
Speaker 1: Material, to actually snap it right.
Speaker 2: Stiffness that Young's modulus we just talked about is how
Speaker 2: floppy or rigid a material is before it reaches that
Speaker 2: break up point. Gordon uses some brilliant every day examples
Speaker 2: to illustrate this.
Speaker 1: Oh, the cracker one.
Speaker 2: Yeah, think of a dry biscuit or a cracker. A
Speaker 2: biscuit is stiff, you know, it doesn't bend or flop
Speaker 2: at all, but it's extremely weak. It snaps with almost
Speaker 2: no force.
Speaker 1: Where's something like steel is both stiff and strong right, And.
Speaker 2: On the flip side, nylon is very flexible, meaning has
Speaker 2: low stiffness and a low stubbornness score. But it's incredibly.
Speaker 1: Strong because you can stretch a nylon climbing rope significantly
Speaker 1: without it breaking exactly.
Speaker 2: And finally, raspberry jelly is flexible and weak. By separating
Speaker 2: strength from stiffness, engineers gained a scientific language to describe
Speaker 2: exactly how any material will behave under a load.
Speaker 1: So we have the math, we can calculate stress, we
Speaker 1: can measure strain, and we know our material stiffness. You'd
Speaker 1: think structural engineering is perfectly solved and completely safe. At
Speaker 1: this point. You would think so like you just calculate
Speaker 1: the stress, make sure it's lower than the breaking strength
Speaker 1: of the steel in your golden but meticulously calculated structures'll break.
Speaker 2: And often with catastrophic, terrifying results. The problem is that
Speaker 2: the beautiful, clean math of Hook and Young assumes a
Speaker 2: perfect material. It assumes the steel or the concrete is
Speaker 2: entirely uniform. But in the real world, perfection simply doesn't exist.
Speaker 2: Every single material.
Speaker 1: Has flaws, and in nineteen thirteen, a guy named ce
Speaker 1: Inglis discovered something deeply unsettling about those everyday flaws.
Speaker 2: He did. Ingliss mathematically proved that a tiny defect like
Speaker 2: a microscopic scrash, an air bubble in the cast metal,
Speaker 2: or a small rivet hole, acts as a stress concentration.
Speaker 1: A stress concentration.
Speaker 2: What does that look like think about a fast flowing river.
Speaker 2: If you drop a large boulder in the middle of it,
Speaker 2: the water doesn't just stop right, it diverts and rushes
Speaker 2: violently around the sides of the boulder. Force flowing through
Speaker 2: a solid material does the exact same thing when it
Speaker 2: hits a hole or a crack.
Speaker 1: So all that invisible force gets crowded into a bottleneck exactly.
Speaker 2: And because of that crowding, the dress at the very
Speaker 2: microscopic tip of a crack can be one hundred to
Speaker 2: one thousand times higher than the stress and the rest
Speaker 2: of the surrounding material. Wait.
Speaker 1: Wait, so if I have a steel beam that's theoretically
Speaker 1: only holding ten percent of its maximum capacity, a microscopic
Speaker 1: scratch on the surface could be experiencing forces one thousand
Speaker 1: times higher yep, Meaning the atoms right at that scratch
Speaker 1: are effectively pushed past their breaking point.
Speaker 2: Yes, and that's the reality of the built world. We're
Speaker 2: literally building our modern cities and vehicles out of materials
Speaker 2: that are already full of microscopic cracks, and we're just
Speaker 2: managing the physics to ensure those cracks don't spread. And
Speaker 2: the person who figured out how to manage that spreading
Speaker 2: was a Griffith who looked at the problem through the
Speaker 2: lens of energy.
Speaker 1: Let's unpack Griffith's energy approach, because this feels like the
Speaker 1: core of modern fracture mechanics.
Speaker 2: It is. Think of a structure carrying a load like
Speaker 2: a bridge supporting cars, as a giant reservoir of stored energy,
Speaker 2: which we call strain energy. Okay, it's identic to the
Speaker 2: tension energy stored in a wound up rubber band or
Speaker 2: a drawn bowstring. It's just sitting there waiting to be released.
Speaker 2: If the structure breaks, that stored strain energy has to
Speaker 2: go somewhere.
Speaker 1: It gets converted into what Gordon calls fracture energy. Like
Speaker 1: he uses that stored energy to violently tear the chemical
Speaker 1: bonds apart and create a new crack.
Speaker 2: Surface decisely now, Griffith found that short cracks are usually
Speaker 2: perfectly stable. Why because to rip those chemical bonds apart
Speaker 2: requires a certain amount of energy, and a tiny crack
Speaker 2: just doesn't release enough of that stored strain energy to
Speaker 2: pay the cost of tearing the bonds.
Speaker 1: Ah, So the surrounding material is essentially holding it together.
Speaker 2: Right. But and this is where the math gets terrifying.
Speaker 2: Once a crack grows to a very specific size, known
Speaker 2: as the critical Griffith crack length, the economics of the
Speaker 2: energy flip.
Speaker 1: Meaning the release of the stored strain energy suddenly becomes
Speaker 1: greater than the energy needed to rip the material apart.
Speaker 2: Yes, the moment it hits that critical length, it's energetically
Speaker 2: easier for the material to break than to stay together.
Speaker 2: At that point, the crack becomes completely self propagating.
Speaker 1: It just takes on life of its own.
Speaker 2: It feeds on its own released energy, speeding up through
Speaker 2: the material at the speed of sound, resulting in an explosive,
Speaker 2: catastrophic failure.
Speaker 1: And the most tragic real world example of this in
Speaker 1: the sources is that a havevilin Comet airplane disasters in
Speaker 1: the nineteen fifties. Yes, this was the world's first commercial
Speaker 1: jet airliner. It was supposed to be the future of aviation.
Speaker 1: But these planes kept mysteriously exploding mid air, falling out
Speaker 1: of the sky into the ocean, and nobody knew why.
Speaker 2: It was one of the greatest mysteries in early aviation.
Speaker 2: When investigators finally dredged up the wreckage and reconstructed the
Speaker 2: fuselage like a giant jigsaw puzzle. They found the culprit.
Speaker 2: It all started at the windows.
Speaker 1: The windows.
Speaker 2: The original Comet featured square windows. Every time the plane
Speaker 2: climbed to altitude, the cabin was pressurized, blowing up like
Speaker 2: a balloon, and then depressurized when it landed.
Speaker 1: So thousands of cycles of inflating deflating.
Speaker 2: Right and the sharp corners of those square windows acted
Speaker 2: as massive stress concentrations. Microscopic fatigue cracks started forming at
Speaker 2: the tiny rivet holes near those corners. Oh no, because
Speaker 2: the cracks were so small, inspectors couldn't see them. But
Speaker 2: with every flight, the cracks grew a tiny fraction of
Speaker 2: a millimeter. Eventually, while cruising at thirty thousand feet, one
Speaker 2: of those hidden cracks reached the critical Griffith cracklength math flip.
Speaker 2: In a fraction of a second. The crack fed on
Speaker 2: the strain energy of the pressurized cabin. The fuselage ripped
Speaker 2: entirely open, and the planes exploded, which is.
Speaker 1: Why every commercial airplane today has rounded windows to eliminate
Speaker 1: those sharp corners and disperse the stress. Actually, it really
Speaker 1: puts into perspective that modern engineering isn't about finding perfect
Speaker 1: crack free materials. It's about designing structures so that the
Speaker 1: critical crack link is long enough, say a few inches,
Speaker 1: so that an inspector can easily spot it and ground
Speaker 1: the plane long before it explodes.
Speaker 2: It's all about managing the enova flaws and knowing that
Speaker 2: these cracks are always waiting in the wings. Structural engineers
Speaker 2: have to be incredibly strategic about how they apply forces
Speaker 2: to a material in the first place. You can't just
Speaker 2: throw massive steel beams at a problem and hope for
Speaker 2: the best, right.
Speaker 1: You have to understand whether the structure is going to
Speaker 1: be pushed, pulled, or slit exactly.
Speaker 2: Let's walk through those three main types of forces compression, tension,
Speaker 2: and sheer.
Speaker 1: Yes, because structures behave radically differently depending on which one
Speaker 1: they're facing. Let's start with compression, which is pushing materials together. Okay,
Speaker 1: if I'm looking at a massive medieval stone tower or
Speaker 1: a huge brick wall, my intuition says that the stones
Speaker 1: at the very bottom are in serious danger of just
Speaker 1: being crushed into dust by the incredible thousands of tons
Speaker 1: of weight pressing down on them.
Speaker 2: It's a completely natural assumption, but it's actually wrong.
Speaker 1: Really.
Speaker 2: Yeah, when short fat blocks of a brittle material like
Speaker 2: concrete or stone fail in compression. They don't simply squish
Speaker 2: flat like a marshmallow. They fail by sheer ring diagonally.
Speaker 2: The material slides away from the pressure along a forty
Speaker 2: five degree angle.
Speaker 1: Okay, but what about the tall towers.
Speaker 2: When you move to tall structures like your medieval tower
Speaker 2: or a cathedral wall, they almost never crush. The actual
Speaker 2: compressive stress at the bottom of a brick wall is
Speaker 2: usually a tiny fraction of the crushing strength of the
Speaker 2: stone itself.
Speaker 1: Then why do walls fall down because they tip over?
Speaker 2: It's exactly like a toddler stacking wooden toy blocks too
Speaker 2: high and slightly crookedly.
Speaker 1: Oh so it's an issue of instability, not material strength exactly.
Speaker 2: In masonry, engineers talk about the thrust line and the
Speaker 2: middle third.
Speaker 1: How does that work.
Speaker 2: Imagine an invisible vertical line representing all the downward force
Speaker 2: of the wall's weight. That's the thrust line. As long
Speaker 2: as that thrust line pushes straight down through the middle
Speaker 2: third of the wall's base, the wall is perfectly stable.
Speaker 2: The mortar joints between the bricks are entirely in compression,
Speaker 2: just happily getting squeezed together. Okay, But if the wall
Speaker 2: leans or a massive gust of wind hits it, that
Speaker 2: thrust line wanders outside the middle third toward the edge
Speaker 2: of the wall.
Speaker 1: And when that happens, the physics changes entirely.
Speaker 2: Right, The joints on the opposite side of the wall
Speaker 2: actually go into tension. They try to pull apart, since
Speaker 2: mortar is fantastic at being squeezed but terrible at holding
Speaker 2: things together. In tension, the joint racks open like a hinge,
Speaker 2: and the wall just pivots and tips over.
Speaker 1: Okay, so that's thick walls. But what if the compression
Speaker 1: member is something tall and thin, like a metal pole
Speaker 1: or a strut.
Speaker 2: That introduces a different failure mode called buckling, which was
Speaker 2: mathematically defined by Leonhard Euler. A thin pole under compression
Speaker 2: doesn't crush either. Instead, it bows outward.
Speaker 1: Oh sure, like a plastic ruler when you push the
Speaker 1: ends together.
Speaker 2: Yes, perfect example. And the insidious thing about buckling is
Speaker 2: that once it bends, even a fraction of a millimeter,
Speaker 2: the weight pushing down now has a tiny lever arm
Speaker 2: to pry the pole further outward. The more it bends,
Speaker 2: the longer the lever arm gets magnifying the stress until
Speaker 2: the pole violently snaps.
Speaker 1: So if compression has all these tipping and buckling issues,
Speaker 1: why do engineers ever bother with pulling things apart?
Speaker 2: Why use tension Because tension members like the steel cables
Speaker 2: on a suspension bridge, can be incredibly lightweight. Since you're
Speaker 2: pulling them taut, you never have to worry about them buckling.
Speaker 2: You can use relatively thin, light cables to span massive distances.
Speaker 2: That sounds great, it is, but tension has a severe
Speaker 2: hidden cost the end fittings.
Speaker 1: Ah, you have to attach that highly stressed cable to
Speaker 1: something solid without ripping it out.
Speaker 2: Exactly, Transferring a massive tension load from a thin cable
Speaker 2: into a solid frame safely without creating terrible stress concentrations
Speaker 2: at the bolt holes requires heavy, complex, and highly expensive
Speaker 2: metal fittings.
Speaker 1: That makes sense.
Speaker 2: Nature actually ran into this exact same engineering problem with
Speaker 2: our own bodies. Our muscles pull on our bones using tendons,
Speaker 2: which are biological tension cables. Oh wow, But to avoid
Speaker 2: ripping the bone apart at a single point of attachment,
Speaker 2: Nature splays the end of the tendon out like a
Speaker 2: distributing the pulling load across a wide area of the bone.
Speaker 1: It's just brilliant biological engineering. So we have compression pushing things,
Speaker 1: tension pulling things, and finally we have sheer forces.
Speaker 2: Shear is when materials slide past each other, like the
Speaker 2: two blades of a pair of scissors, and sheer forces
Speaker 2: are tricky because they actually create tension and compression simultaneously
Speaker 2: at forty five degree angles to the direction of the slide.
Speaker 1: This brings up a really fascinating distinction in the source
Speaker 1: text about the materials themselves, specifically isotropic versus anisotropic materials.
Speaker 2: It's a crucial difference. Isotropic materials like steel or glass
Speaker 2: have the exact same mechanical properties in every single direction.
Speaker 2: It doesn't matter which way you twist or cut a
Speaker 2: steel plate. The internal structure resists the forces the exact
Speaker 2: same way, but anisotropic materials behave very differently depending on
Speaker 2: the direction you apply the force. Wood is a great example.
Speaker 2: It's easy to split along the grain, but incredibly hard
Speaker 2: to snap across the grain.
Speaker 1: Gordon uses dressmaking to explain this, which I thought was
Speaker 1: such an elegant analogy. If you take a piece of
Speaker 1: woven cloth and pull it straight up and down parallel
Speaker 1: to the threads. It's very stiff, right, But if you
Speaker 1: pull it diagonally at a forty five degree angle, it
Speaker 1: stretches dramatically.
Speaker 2: That's because the threads act like a trellis scissoring past
Speaker 2: each other in sheer. And this is the entire underlying
Speaker 2: principle of the bias cut dress in fashion, cutting the
Speaker 2: fabric at an angle to the weave so it stretches,
Speaker 2: drapes elegantly, and clings to the body.
Speaker 1: Wow.
Speaker 2: Whether you are designing the wingskin of an airplane or
Speaker 2: a high end ball gown, you are managing the exact
Speaker 2: same physical forces of sheer intension.
Speaker 1: Okay, So considering all of these incredibly complex failure modes
Speaker 1: you know, oilers, buckling, sheer planes, critical Griffith cracks, it
Speaker 1: honestly feels like a miracle anything stay standing at all.
Speaker 1: It kind of is how do structural engineers actually design
Speaker 1: the things we interact with every day, like houses, floors,
Speaker 1: and furniture without them costing a fortune or taking decades
Speaker 1: to supercomput They.
Speaker 2: Use what is essentially an engineering cheat code. They prioritize
Speaker 2: stiffness over strength.
Speaker 1: Let's pause and really explore that, because intuitively, you'd think
Speaker 1: the ultimate goal of a brilliant engineer is to make
Speaker 1: a structure as mathematically efficient as possible.
Speaker 2: Right, like making it exactly strong enough.
Speaker 1: Yeah, you'd want every single joist, beam and bolt to
Speaker 1: be exactly strong enough to carry its intended load, saving
Speaker 1: weight and saving material cost.
Speaker 2: You'd think so, But a perfectly efficient structure is actually
Speaker 2: incredibly dangerous in the real world. Oliver Wendell Holmes wrote
Speaker 2: a famous poem about this concept called the one Hoss
Speaker 2: shay Oh, I've heard that. It's about a carriage designed
Speaker 2: so flawlessly that no single part was weaker than any other.
Speaker 2: The result, when it finally reached the end of its lifespan,
Speaker 2: the entire carriage disintegrated into dust, all at the exact.
Speaker 1: Same instance, so no warning at all. None.
Speaker 2: If you build a perfectly mathematically efficient bridge and one
Speaker 2: unexpected gust of wind hits it, or a truck slightly
Speaker 2: heavier than planned drives over it, the entire structure shatters
Speaker 2: simultaneously because there is zero margin for error.
Speaker 1: So to avoid catastrophic instantaneous failure, we overbuild things.
Speaker 2: Yes, and we overbuild them specifically for stiffness in everyday structures.
Speaker 2: You know, the floorboards of your house, your dining room table,
Speaker 2: a wooden staircase. The design isn't dictated by the breaking
Speaker 2: strength of the wood. It's dictated by stiffness. Why stiffness, Well,
Speaker 2: a floor made of thin plywood might technically be strong
Speaker 2: enough to hold the weight of you and your family
Speaker 2: without structurally breaking, but it would sag and wobble so
Speaker 2: terrifyingly under your feet that you'd absolutely refuse to walk
Speaker 2: on it. To make the floor feel rigid, solid, and safe,
Speaker 2: builders are forced to use thick wooden joists.
Speaker 1: And because they made those joysts thick enough to stop
Speaker 1: the wobble, the actual internal stress, the invisible force pulling
Speaker 1: at the atoms, is incredibly.
Speaker 2: Low, precisely by designing for a comfortable level of stiffness,
Speaker 2: the stresses become so negligible that the ultimate breaking strength
Speaker 2: of the wood hardly matters at all. Even if that
Speaker 2: thick piece of wood is full of hidden microscopic cracks
Speaker 2: or knots, the stress is so low it will never
Speaker 2: reach the critical Griffith crack length. Oh I see, Prioritizing
Speaker 2: stiffness automatically creates a massive accidental buffer.
Speaker 1: Of safety that makes perfect sense for a house.
Speaker 3: Yeah, but you can't just use that cheat code forever, right, No,
Speaker 3: you can't, Like you can't just take the design of
Speaker 3: a sturdy wooden dining chair, multiply all the dimensions by
Speaker 3: a thousand and build a wooden skyscraper.
Speaker 1: Out of it.
Speaker 2: No, you absolutely cannot, and the reason for that dates
Speaker 2: back to Galileo, who realized a fundamental mathematical truth called
Speaker 2: the square cube law. As you scale any three dimensional
Speaker 2: object up, its volume and therefore its weight, increases by
Speaker 2: the cube, but its cross sectional area, which is what
Speaker 2: determines its structural strength, only increases by the square.
Speaker 1: Meaning if I take a wooden beam and perfectly double
Speaker 1: its size in every direction, the beam gets four times stronger,
Speaker 1: but it becomes eight times heavier, exactly.
Speaker 2: And if you triple the size, it's nine times stronger
Speaker 2: but twenty seven times heavier. The larger a structure gets,
Speaker 2: the more it has to fight its own immense weight.
Speaker 2: It becomes its own worst enemy.
Speaker 1: That explains so much.
Speaker 2: This is why you can't just infinitely scale up a bridge,
Speaker 2: an airplane, or even an animal without radically changing its
Speaker 2: architectural proportions. A mouse can have incredibly thin delicate legs
Speaker 2: relative to its body, But an elephant needs massive, thick
Speaker 2: tree trunk legs just to hold up its own bulk.
Speaker 1: Wow.
Speaker 2: Yeah, the square cube law forces engineers to abandon the
Speaker 2: simple cheat code of overbuilding when designing large scale structures.
Speaker 2: They have to rely on deep mathematical analysis to safely
Speaker 2: manage the massive self weight.
Speaker 1: It's incredible how all these pieces fit together. We've gone
Speaker 1: from Newton's simple balancing act to exploding jetliners, bias, cut dresses,
Speaker 1: and elephant legs.
Speaker 2: When we pull all of these concepts into the bigger picture,
Speaker 2: the core takeaway is that the physical world around us
Speaker 2: isn't assive. Structures only survived by actively deflecting, physically stretching
Speaker 2: and compressing at the atomic level to balance the forces
Speaker 2: acting upon them. We measure this intricate, invisible dance through
Speaker 2: stress and strain. But to keep our world safe, we
Speaker 2: must constantly guard against the magnification of stress caused by
Speaker 2: tiny cracks and defects. It's a careful, constant balance of
Speaker 2: precise fracture mechanics for the big things and practical everyday
Speaker 2: stiffness for the small things that keeps the modern world
Speaker 2: from falling down.
Speaker 1: And since we promised this deep dive would give you real,
Speaker 1: usable knowledge, we have a quick mental exercise for you
Speaker 1: to reinforce everything we've just covered.
Speaker 2: Yes, I want you to look closely at the physical
Speaker 2: chair you are sitting in right now, or the floor
Speaker 2: beneath your feet. Based on what we've talked about, ask yourself,
Speaker 2: as my weight pushes down, where exactly is the structure intension?
Speaker 2: Which parts are being stretched apart?
Speaker 1: Okay?
Speaker 2: And where is it in compression safely pushing together? And finally,
Speaker 2: if I'm magically doubled its size right now in every
Speaker 2: day men, according to Galileo's square cube law, how would
Speaker 2: those internal stresses change?
Speaker 1: It fundamentally changes the way you look at a room.
Speaker 1: And I will to leave you with one final thought
Speaker 1: to mull over the next time you are staring at
Speaker 1: a wall and you notice a tiny hairline crack in
Speaker 1: the plaster, or a small dentt in an exposed metal beam,
Speaker 1: don't just write it off as a meaningless cosmetic flaw.
Speaker 1: Definitely not recognize it for what it truly is. It's
Speaker 1: an active, invisible, desperate battlefield right at the microscopic tip
Speaker 1: of that seemingly harmless crack. Billions of atomic bonds are
Speaker 1: actively stretching to their absolute limits, fighting to manage a
Speaker 1: massive localized spike and strain energy. They are holding the
Speaker 1: line in real time to keep the entire structure from
Speaker 1: reaching its critical breaking point.
Speaker 2: There is a microscopic war going on all around us,
Speaker 2: every second of every single day. Just keeping the roof
Speaker 2: over our
Speaker 1: Heads, keep your eyes open to the invisible forces around you,
Speaker 1: and we'll catch you on the next deep dive.