Re: How do you make a strong bridge out of paper?

Hi Grace,

Great question!  Tubes and folds help make things stronger by changing the 
way that the load or the stress is applied to the material.  If you take a 
normal sheet of paper, it's got quite a bit of tensile (pulling) 
strength.  Try this: Take a fresh sheet of paper, grab two opposite edges 
about in the middle of the sheet and start pulling straight out.  It 
should take a lot of force to make it tear.  However, paper has virtually 
no compressive (squeezing) or flexural (bending) strength because the 
paper bends.  In engineering, this failure mechanism is called buckling, 
and it's the failure mechanism that structural engineers and architects 
worry the most about.

So for paper, as well as any material, by curving or folding the material 
in a particular direction, the compressive strength can be increased in 
that direction by preventing buckling.  Imagine that you're one of the 
millions of tiny fibers in the paper.  You're strong if someone pulls on 
you, but you bend really easily.  If all of the fibers in the sheet 
point the same way you do, then all of you are easily bent.  However, if 
you wrap the paper into a tube, then when a force is applied that would 
cause you to bend, some of the other fibers are rotated so that they are 
getting a tensile force, and they can support that easily.  So the paper 
tube can take forces in directions (Compression, Bending) that would cause 
a piece of paper to buckle.

There's a bunch of equations I could use here, but suffice it to say that 
larger diameter tubes are typically stronger than small diameter tubes, 
and thicker tube walls are typically stronger than thin walls.  

For any structure that you're going to build, you have to consider the 
weight, the cost, and the strength of the materials you're going to use.  
That's why hollow tubes and I-beams are always used in construction.  And 
not just when we build bridges, your bones are hollow for this same 
reason.  More strength for less material.

Here's one last thing to try.  Take an empty, undamaged can of soda 
outside.  Stand it on the ground.  Carefully put one of your feet on top, 
and slowly transfer all of your weight onto it until you're standing on 
one foot on the can.  It'll help if you have something to hold onto with 
your hands.  Have a friend or family member take a ruler (Or a pencil, or 
a stick, but definitely do NOT use their finger!) and tap the side of the 
can.  Once they hit the side hard enough to dent it, the can should 
quickly crush under your weight.  This illustrates how strong the can is 
when the tube is solid, and how much weaker it becomes once it buckles.  
The aluminum is like your paper, and is strong in tension, but not very 
strong under bending.  Next, grab another can, pre-dent the side, then try 
and stand on it.  It might not hold your weight at all.

Keep asking questions!

Jeff Yap
Mad Scientist

Related links:

American Architectural Foundation


M.N. Gogate's Glimpses of Structural Engineering


Free software to predict buckling


Bicycles and thin walled aluminum