Re: What designs I.e. shapes are the strongest to build with

Hi, Mystery Student!

These tower-building contests are pretty popular. I have included a link to a site describing a spaghetti bridge contest.

Look at the successful towers and see how they were done.

First: A tower is mostly loaded in Compression, that is, the main members are usually being pushed on. Structural members fail differently depending on if they are pulled apart or pushed together. If the load is in tension, the member will snap at its thinnest part. If it is loaded in compression, though, it will fail by bowing out, or buckling.

To demonstrate this, take a long, thin piece of balsa. Stand it up on a table, and push down on it gently but firmly. It will resist for a bit, then suddenly bow to one side (take care not to let it snap). Try a shorter piece, and you'll have to push harder before it bows.

The formula that describes a column's strength is Euler's Formula:

Load =A* C * pi^2 * E (r/l)^2

A = area of the piece making up the column
E = modulus of elasticity of material
c = constant for end fixity: 1 when the column end can rotate, 4 for when it is fixed in place, 9/4 for one of each
r = radius of gyration
l = length of the column between bracing members

This formula was developed for columns much larger than yours; you don't need to solve it. Just look at what it says about how columns support loads. Notice that the load-carrying capacity of the column is affected by if the ends are fixed or free to rotate. Also the strength decreases as the square of the length, while increasing by what is called the Radius of gyration. This last is a property of the column's shape. Generally put, the farther the material making up the column is located from its center, the stiffer it will be. For example, a column made up of four pieces of balsa each 2 millimeters on a side, but spaced apart by 2 mm, has a radius of gyration of 4 mm, while a column made up of the same four pieces glued together has an R of only one mm.

You should also know that a triangle is the most efficient shape for constructing any structure. A truss bridge, for example, is a series of triangles, and radio towers are made up of columns braced by diagonal members that form triangles.

Here are a couple of answers from MadSci about trian gles and towers.

Finally, all engineering is compromise. You have to have enough material where it's needed to carry the load, but not more than necessary. So: I'd suggest trying a three-legged tower, since three legs are more stable than two or four. Then the columns need to be large enough to support the load, possibly gluing two, three or four pieces into one column, spaced a bit apart to give them a greater radius of gyration. Then the length of these colums must be reduced by bracing them together by cross-pieces, with triangles made up of diagonals between. The more you have, the better, but too many will increase weight without contributing to strength. Having the columns plumb, i.e., straight up and down, is stronger; battering them , that is tilting them inwards an inch or so in a foot of height, adds stability with little usage of material. Take care to make your joints as strong as you can.

Those are a few suggestions; the execution is up to you. Make an accurate sketch of your tower ideas, get a LOT of that balsa wood, build the tower to your sketch, and load it up very slowly. When it fails, pay particular attention to HOW it failed. Did it buckle, twist, fall over sideways? Did a member or a joint fail first? Now figure out how to reinforce the part that failed. More balsa? Where? Test that tower until it breaks, and see how it failed. Keep doing this -- and keep careful notes on each failure, so you can look back and see what you've tried already -- until you have an efficient, strong tower that will carry the load and carry off the prize.

And if you don't win -- what did the guy who did win do different? Try something like that next year! Never give up!! Good Luck!!

P.S. Here's information on Balsa: http://www.iswonline.com/wwp/w om/balsa.htm