Engineering

Why bridges are made of triangles: a square folds, a triangle cannot

A bridge truss of lime-green rods and pins, built from triangles, beside a faded square that has folded out of shape
30seconds
The 30-second version

A square made of four pinned rods folds flat at the slightest push, but a triangle of three rods cannot change shape at all. That one fact is why bridges, cranes and roof frames are built from triangles.

Drag the joints of a rod frame, add and remove rods, and watch a live count of how many rods a shape needs to stay rigid (2 × joints − 3). Then chain triangles into a Warren truss and try to fold it.

Deep dive · 3 min
Deep dive · 3 min

More in Engineering

View all →
Why Taipei 101 hangs a 660-tonne ball in its upper floors: the tuned mass damper At the top of Taipei 101 a 660-tonne steel ball hangs in plain view. It is not decoration: it is a tuned mass damper that swings against the building and can… Engineering4 min read Why airliner windows have no corners: stress piles up at the tightest curve Cut a hole in a stretched plate and the force has to squeeze past it, so the metal beside the hole carries far more stress than the rest. For a round hole in a… Engineering5 min read Why steel beams are shaped like an I: the same steel, 25 times stiffer Put a beam across a gap and it sags: the top edge is squeezed, the bottom stretched, and the steel in the middle does almost nothing. That is why girders are… Engineering4 min read Why a stone arch stands without glue: Hooke's upside-down rope A stone arch has no glue, yet it stands for centuries because every block is only ever squeezed. In 1675 Robert Hooke hid the secret in an anagram: as a… Engineering5 min read Why a squeezed ruler bows sideways: Euler's buckling and the hollow tube Squeeze a ruler between your palms and it doesn't crush: it bows sideways and gives way. That's buckling, and it decides how slender a column can be. Euler… Engineering4 min read Why every bridge is made of triangles: a square frame folds, a triangle can't Push on the corner of a square frame and it folds flat. Push on a triangle made of the same sticks and nothing moves. The reason is simple: three side lengths… Engineering4 min read