Why are bridge and roof trusses built from triangles?

A pinned triangle cannot change shape without changing a side's length, so it stays rigid.

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  1. Triangles use the least steel of any shape
  2. Triangles are easier to paint
  3. A pinned triangle cannot change shape ✔

Why: A square with pinned corners folds into a diamond. A triangle with pinned corners can only deform if a member stretches or shortens. Planar trusses are built from triangular subunits for this reason.

Huh, didn't know that: Three-dimensional space trusses use the tetrahedron, a triangular pyramid, as their basic unit.

The dad joke
Why do engineers love triangles? Every other shape keeps folding under pressure.
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References

Answer: A pinned triangle cannot change shape. A square with pinned corners folds into a diamond. A triangle with pinned corners can only deform if a member stretches or shortens. Planar trusses are built from triangular subunits for this reason.

  1. Engineering Statics (Baker and Haynes): 6.3 Trusses engineeringstatics.org/Chapter_06-trusses.html
    Simple trusses are made of triangles, which makes them rigid when removed from supports.
    Checked 2026-10-10.
  2. Engineering Statics (Baker and Haynes): 6.3 Trusses engineeringstatics.org/Chapter_06-trusses.html
    Planar trusses are two-dimensional trusses built out of triangular subunits, while space trusses are three-dimensional, and the basic unit is a tetrahedron.
    Checked 2026-10-10.

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