
Paul K. answered 06/29/22
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it's actually really interesting how they represent this in the video. Initially from your question I was thinking they simply folded the paper flat several time to thicken what we could call the "road" of the bridge. However they almost roll the sides. It makes a good analogy for load barring beams of wood in a house. I'm not sure if you've ever seen someone or a show remodeling a house but often if someone wants to remove a wall they need to reenforce where the wall was to make sure the floor above or just the roof doesn't fall in. And these beams that they use are super heavy and really thick. You can't simply use a regular beam of wood because it can't hold the weight of the house. As you put stress on a beam of wood, just like the initial paper it buckles and in the case of the wood it will tare. On a micro scope level the wood molecules that are all stuck together in the beam start to bend and the ones on the outside of the bend will be pulled apart. However if you make the wood thicker all those strands of molecules work together to hold more stress. This is similar to the paper. you add more layers of paper and you have more layers to take the stress. it's similar to trying to rip a book in half compared to one single sheet of paper. Additionally the folds can be looked at as almost rounded over on a very microscopic scale, which would add more strength because circles are one of the strongest shapes.
If we look back at the design of the bridge in the video you can notice that he does have those folded sides perpendicular to the road of the bridge. If you fold those sides down they won't hold as many pennies. The force of the pennies on the paper is pointed downward, so the stress on those sides will be downward. This means you want the thickest part of your load barring beams(the folded paper sides) to be inline with your force to help distribute that force to the cups.