Why are bridges made of triangles?

01

The idea

A triangle can't change shape

Push the corner of a square and it leans over. A triangle's sides can't change length, so its angles can't change either.

02

Play with it

Push the frame, then add a diagonal. Blue members are pulled, red ones pushed.

Try this · 0/3Watch the square foldStop it foldingFind out what two diagonals do

03

Now a bridge

Many triangles in a row. Drive the load across and watch which members work hardest.

04

The rule

Each joint balances

\begin{aligned} \textstyle\sum \force{F_x} &= 0 \\ \textstyle\sum \force{F_y} &= 0 \end{aligned}

A 45° diagonal against a push H

\force{N} = \dfrac{\force{H}}{\cos 45^\circ} = \sqrt{2}\,\force{H}

Pulled members can be thin (rods, cables). Pushed members must be thick enough not to buckle. That's why truss bridges have chunky top chords.

05

Your turn

▲ Build1/3

To do

A thin rod is great at being pulled, useless at being pushed (it bends like a noodle). Which diagonal should it be? The push is 10 kN from the left.

= Solve2/3

To do

A square frame with one 45° diagonal is pushed sideways with $\force{10}\,\mathrm{kN}$ . What force is in the diagonal?

A square frame with one 45° diagonal is pushed sideways with $\force{2}\,\mathrm{kip}$ . What force is in the diagonal?

◆ Pick3/3

To do

06 · Takeaway

Triangles can't fold.

\sum \force{F_x} = 0, \quad \sum \force{F_y} = 0

Related: why thin columns suddenly fail · why supports push back.