Building a Popsicle-Stick Bridge
The goal: to build the strongest possible bridge to take a matchbox car, using wooden popsicle sticks. Constraints:
The bridge must span a 55cm gap
No more than 100 popsicle sticks may be used
The sticks may not be cut
Only white glue may be used
Construction paper may be used for the deck only
The test load is applied to a 4cm-wide section at the top of the arch. The test jig looks like this:
(Well-built bridges can support over 200kg - the weight of two adults)
A bit of thought, or modelling with a computer-aided design program, shows that the bridge can be reduced to a simple triangle. The force required to break a well-constructed bridge is orders of magnitude greater than any other forces acting on it, such as its own weight, the weight of the toy car, "wind load" etc.
This is not the case for a real bridge, of course, which must be designed for a variety of vehicle loads, wind loading, snow or ice buildup, earthquakes and so on. Also, because of the power law (mass increases as the cube of the size, while strength increases as the square of the size), small structures are much much stronger than their full-size counterparts.
A bit of simple physics (or CAD software) will put numbers to the forces. Simple analysis treats the sides as rigid bars, and the corners as free pivot points. One lower corner is fixed to the support, while the other is allowed to slide. The base of the triangle is in tension, while the sides are in compression. The higher the triangle, the less tension in the base. The limiting case for an infinitely high triangle is zero tension in the base, and half the test weight in compression in each side. If the triangle is made lower, the forces increase. In the limit of a zero-height triangle, they become infinite....
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