Building Bridges - The Science of Beams

07 June 2009



PaperA sheet of paperA chasm - we used a couple of box files 21cm apart
Weight for beamA weight - I used a bottle hanging on stringSome tape


The idea is to build a bridge across a 21cm chasm which will hold as much weight as possible, using only one sheet of A4 paper.  You can use some tape to hold it together, but not to act as part of the structure.


A sheet of paper doesn't make a very good bridge, and can't even hold its own weight.

A square tube

A square tube is quite rigid until it folds slideways into a parallelagram when it becomes only slightly stronger than the sheet of paper, supporting a little over 100g of water

Triangular tube

A triangular tube doesn't collapse sideways and supported about 300g of water


A round tube supported about 1.2kg of water

Triangle of tubes

A triangle made of two tubes and a strip of paper supported over 2kg of water - at which point we ran out of water!


Paper is an interesting material, it is very strong in tension - if you clamp it correctly a sheet of A4 paper will support over 200kg.  However it is very flexible, so if you compress paper it will just buckle and fail at very low forces.

Paper is strong in tension
Paper is very strong in tension
Compressing paper
Because it is so flexible it is very weak in compression

Paper is so flexible, not because the material is particularly soft, but because it is so thin. If you bend something the material on the outside of the curve is stretched and the material on the inside of the curve is compressed.

If the beam is very shallow,  the change in length is very small, so you aren't stretching or compressing the material very much, and it doesn't push back hard. On the other hand, a thick beam will have very large changes in length, so it will be very stiff.

Bending a thin beamBending a thick beam
In a thin beam the inside and outside of a curve only change length slightlyIn a thick beam the change in length is large.

This means that a major way of making a beam bridge stiffer is to make it deeper. One obvious way to do this is to make a square tube. This would be very stiff if it didn't have a major weakness.

There is nothing to stop the square turning into a parallelogram and going flat, and therefore very flexible.

Square TubeSquare tube failing
A square beam would be strong if it didn't fold sideways into a parallelogram and become flat

A triangular beam is a lot stronger, because the triangle can't change shape without distorting its sides.  However because the sides are very flat, they can bend and allow the corner to buckle under load.

Triangular tubeTriangular tube failing
A triangular paper beam is quite strong, but eventually the sides bend and the corner buckles

A tube is very strong because the paper is all curved in one direction and it can't curve in another without stretching or tearing. However if you use it as a beam you are squashing it, and eventually it will go flat enough to bend in the wrong direction

A tubeThe tube under loadTube buckling
A tube is very strong as the paper is all curved in one direction so it can't curve in another. But loading it as a beam causes it to flatten and then it gets weak.

A tube however is very strong is straight compression, as there is no force trying to flatten it. so if you can devise a structure with tubes in compression and something else in tension it can be very strong.

One way of doing this is to make a triangle out of two tubes and a strip of paper to hold the bases together at the bottom. This is very strong although if you wanted to make the structure stand up on its own you would probably have to give it more legs.

Triangle of tubes




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