# Is it easier to break 1 2inch boards or 2 1inch boards

1. Feb 20, 2013

### Howlin

Hi

I have been doing taewkon do and seen people break boards and I want to know is it easier to break say 1 2 inch thick pine board or 2 1inch pine boards assuming that the boards are uniform and have no knots in them and that the 2 1 inch boards are on top of each other with no gap inbetween them?

I have tried looking up online this question but I can't find an answer. If anyone could even send me to a page that has the force required to break a board of different thicknesses , that would be greatful.
Thank you

2. Feb 20, 2013

### jbriggs444

Two boards bonded together back to back are stronger than two unbonded; twice as strong.

One way of seeing this is to think of the board supported at the ends (or at the edges if you're doing karate) with a weight in the middle. The board will flex under this weight. The top of the board will be in compression. The bottom of the board will be in tension.

With two boards separately, the top of each board individually will be in compression and the bottom of each board individually will be in tension. The thickness of the board controls how much leverage these forces have to resist the flexing.

With two boards glued together, the top board will be in compression and the bottom board will be in tension. The thickness of the two boards together then controls how much leverage these forces have to resist flexing.

Two boards together have twice the thickness of one board alone. So there's twice the leverage and twice the yield strength. If you look up the beam strength formula, you'll see that it goes as the square of thickness. So if the question is: "how much force is required before the boards break" then the answer is that two together are stronger than two separate.

There are other questions that could be asked. Based on a cursory analysis, the "stiffness" of two boards together is four times as great as the stiffness of one alone. So it only takes 1/2 as much displacement to make the combined board yield. That means that the energy it takes (yield strength times yield displacement) to break two boards together is roughly the same as the energy it takes to break two separately.