Two shapes that do not fold
Why Do Bridges Have Arches and Triangles?
Almost every bridge in the world is made of arches, triangles or hanging cables, and each is a way of turning bending into squeezing or pulling.
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Step 1 of 5
Bending is the hard case.
A loaded beam is stretched along its underside and squeezed along its top at the same time. Most cheap materials are good at one of those and bad at the other.
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Step 2 of 5
An arch turns it all into squeezing.
Curve the path and the load travels down the curve as pure compression into the ground. Stone and brick are enormously strong in compression, and that is why old bridges are arches.
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Step 3 of 5
A triangle cannot change shape.
Push on a square frame and it folds into a diamond. A triangle cannot deform without one of its sides changing length, so a truss of triangles is stiff for very little metal.
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Step 4 of 5
A cable does the opposite job.
A suspension bridge hangs the deck from cables, so the span is held by pure tension. Steel in tension is the strongest cheap thing we have, which is why the longest bridges hang.
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Step 5 of 5
Every bridge also has to survive itself.
Past a certain span most of a bridge's load is its own weight. Making it longer means making it heavier, and that limit decides which of the three shapes is used.
Wind, not weight, brought down the most famous bridge failure. A deck can be strong enough to hold anything and still be shaken apart by a steady breeze.
The short version
Bridges use arches, triangles and cables because each turns bending, which materials do badly, into squeezing or pulling, which they do well.
Try it yourself
Make a square from four strips and pins, then add a diagonal. One folds, one does not.