That orange thing might have been a drawing tool called a flexible curve, and they might have edited out the tedious footage of the teacher bending it to the right shape.
I stand with you- once one has done a thing a number of times- it is unlikely that one WOULDN'T know what would happen! Murphy is always there, however...
A few years ago I was idly thinking about arch bridges and the fact that the Earth's surface beneath the bridge also has a curvature - granted not much, but it's there. So the longer the bridge the more the Earth curves beneath it. Take this thought to its logical conclusion and you have a bridge that goes right round the Earth and needs no supports. It becomes a giant hoop that just holds station. But an observer might look up at it and say "why doesn't it fall down?". Answer: because for that to happen, on the other side of the planet, It would have to fall up!
Vsauce covered this in his video "Which way is down?". Ironically, this bridge would appear extremely uneven and undulating, due to having to match the forces of gravity as well.
@@Renteks- I watched the video now. When you say "extremely uneven" I think this is a huge exaggeration.. Vsauce mentions a figure of "almost 100m", but he doesn't point out that this would be stretched over many hundreds of miles and probably not detectable to the human eye. Apart from that there would be other problems with gravitational perturbations from neighbouring astronomical bodies - i.e. the Moon, the Sun, Jupiter, etc - and hence for these and for other other engineering reasons the only shape to build such a hoop would be circular. But this is all just an academic thought exercise anyway, because according to my estimates there is no building material even remotely close to being able to withstand the colossal circumferential compressive stresses that such a structure would develop. No, not even remotely. Some other engineering trickery would have to be employed. Would be a totally cool thing though.
I have a feeling that if the arch wasn't assembled correctly, it wouldn't take 1kg, so he was more making the comment that he wasn't sure he'd assembled it correctly.
The arch only works this way if the two lower blocks are rigidly connected to each other. In this example with a shelf. Do the same experiment without a shelf, with two separate blocks at the bottom, then the thrust force will push them apart and the arch will collapse. That is why we see in medieval arch architecture, steel cross-connections between the two ends.
Wow amazing. Imagine a walking bridge built like this, and you can feel it move disconcertingly as you cross it! Only faith in engineering can steel your nerves 😅
I came here hoping to hear the word “voussoir”. I was not disappointed! (I worked at a Voussoir factory where no-one but a French software engineer called them voussoirs.)
Wow. Way better visual than anything i saw at Penn State. I would like to build some larger models. Maybe sandpaper on the surface or magnets to help initial assembly. I wonder if theres some Higher level mechanics like a Lagrangian of the centers of mass and friction at tangent points to help describe the “thrust curves” that develop
If some of the slats are loose between the voussoir and the abutment this would indicate the surfaces are in fact slightly UN-PARALLEL, because clearly it would not be able to be removed ...the lecturer actually confirms some of the slats were loose.
I always wondered how the French word "voussoir" translated in English. I got my answer: it doesn't. Though in French, when it's part of an arc, the proper word is claveau (same etymology as clef, key). Voussoir is normally refering to an element of a vault.
I'm currently on a youtube binge / rabbit hole, but this was very informative and interesting. I've always had an intuitive sense of forces in structures, but seeing the force vectors and the thrust line over a whole arch is very interesting, and kind of makes me want to program a physical simulation to represent different weights and thrust vectors over arches.
Interesting thought, I figure that would mainly force the material to be under constant pressure in thr tops and bottoms, eventually thst would weather away until the forces are more spread out again.
@@GundamReviver my logic was to induce a prestress into the material, and make it more stable. The idea being just the opposite of the convex faces. This would enhance resistance to not only the linear stress, but to lateral and torsion stresses. No swing, no twist, no bounce. Seems to make sense.
@@dangeary2134 nah, but did start out with a degree in engineering stuff 😂 I figure you are correct in that it would have increased regidity since indeed it would be pre stressed, but thst added hardness would Probabaly mean the "points" pushing against each other would get immense force on them and break and crumble quicker. Also it's like nearly afternoon here, haha, welcome to the internet: it's always daytime somewhere.
There are two types of friction. Normal friction requires movement to be occurring which isnt happening in this situation, and then Static friction which resists initial movement between the blocks slipping. Static friction would just resist any slipping and equally cancel it out. While it does technically exist in the model, it doesnt actually have any notable effect and so it can be pretty much ignored for the sake of simplicity. It only really matters if the slipping force is enough to overcome the static friction.
I am not sure if at 2:40 the picture is complete: Aren't there frictional forces at both contact points too? - Intuitively, I would guess the whole arc would not be stable if the surface (of the contact points) would be (ideally) slippery.
I think there are no major frictional forces in this static system. A friction force perpendicular to the thrust line would result in rotation of the block, we can see this when he adds a weight and all the blocks rotate to a new stable position.
@@joshdaly2343 Try to build the arch using slippery soap blocks. I am pretty sure it will not hold. Generally, the two planes defined by two contact points on a block are not parallel, hence the two forces will create an outward (or may be rarely an inward) force expelling the block. Yes, this is countered by the gravity of one block, but I am pretty sure that there are also fricitional forces at each of contact points.
@@sakudoo if the soap blocks had the same shape and density as the wooden blocks in the example, then arranged in the same shape they would still hold the arch. It would be very hard to do not (mainly) because the lack of friction, but the fact that there's only one "thrust" line for a particular arrangement of blocks. That's why the arch changes shape when a weight is added so it reaches its unique thrust line whete there's no friction.
Had same question. I think you could add the friction forces to the three forces they drew, and add more terms to the equilibrium equation. But, those terms will cancel out. The component of gravity perpendicular to the surface equals the normal force they have drawn, and the component of gravity parallel to the surface equals the friction force, neither of which they drew. At both left and right points. So, my guess is that friction is indeed there and critical to the arch. I didn't look it up though, so this might be bogus.
There is. The video is misleading. Any undergrad student should point out that normal force is perpendicular to the contact surface in case 1 where cardboards were used for top bricks. Thus friction force introduced by normal force is used to counter gravity. I was so surprised no one pointed it out.
@@xiaojiang2610how can a normal force, which is perpendicular to the surface, introduce a friction force, which is parallel to the surface? The whole point of arches is that they act in pure compression, hence there is no need for friction force. For the second arch in the video, if there were friction forces, the blocks would rotate (as they do briefly when he adds a weight and they come to equilibrium in a new shape with zero friction forces)
Никогда у вас не получиться изготовить в идеале точки соприкосновения, то ,что несут они разные (переходящие) нагрузки_это Да, но приходится вернуться в начало этого предложения
That is the answer for an infinitely flexible member like a cable. But the stiffness necessary to keep an arch from buckling will allow shear and bending forces to develop. This alters the mathematical solution.
@@gregoryford2532 but why? don't tell me the English people did not have arches until the French came. The word "keystone" is English, so why having a weird French word for the other stones in the arch?
