# Breaking the bottom board... when there's two

Watching a board-breaking ceremony at my martial arts school, I have seen something very weird no one can seem to explain: when a person attempts to break two boards stacked on top of each other (separated by pennies at the corner), there is a chance that the bottom board will break even though the top board remains completely intact. The movement used to break the boards is a palm strike (bring it straight up and drop it straight through the boards).

If my seventh grade knowledge is correct, the top board should receive the most force from the palm strike (and break first) and the bottom board should receive less force due to the initial resistance from the first board.

How is it possible to break the bottom board without the breaking the top board (that's not touching the bottom one directly)?

• Sort of vaguely related: physics.stackexchange.com/q/71661
– user10851
Mar 12 '16 at 3:11
• Maybe this is what's going on... As the top board is forced downwards, it receives an upward force from the bottom board, thus reinforcing it. It would be difficult to break the top board without the bottom one first breaking... as the bottom board helps the top maintain its rigidity. When the support is shattered, the top board can deform far enough to crack. Mar 12 '16 at 3:12
• Interesting, most of the time, it is the other way around. The top board breaks first then the bottom one breaks. This upwards force also allows the top board to be more easily broken. Mar 12 '16 at 3:13
• True. Perhaps then there's something else afoot. Let's see what others say. Mar 12 '16 at 3:15
• The bottom of the lower board is probably the part of the whole assembly that is subjected to the most tensile stress at the moment of impact. So it's possible that if the material is weak under tensile stress, that would be the first point of failure. I would think, though, that wood is fairly strong under both compression and tension, and would expect breaking of the bottom board or block to be more common with, say, ceramic bricks, which are generally strong under compression but relatively weak in tension.
– user93237
Mar 12 '16 at 3:24

Breaking happens on the outer surface, because of tension building up: a crack initiates, causes further stress concentration, and failure. Now when you have two boards, once they are pressed together the friction between them makes the two boards behave a little bit like a single thicker board.

And in the case of a single thick board, the center line (which is actually the point where the top and bottom boards are touching) is the line of zero strain: above it the board is compressed and below it the board is stretched.

If there is no friction, or the boards are very far apart, then this analysis doesn't hold - but with sufficiently small spacing and rough surfaces it does.

This assumes identical boards; of course it is easy to choose the properties of the two boards so the top one is more elastic (or thinner, or has higher fracture strength)

Perhaps this diagram helps:

Notice how the top board is bent through a bigger curvature - that should mean more bending stress, and therefore more tension on the lower surface of the upper board. HOWEVER: if the top board is touching the bottom board (as in this diagram) then NECESSARILY the outer curvature of the top board must equal the inner curvature of the bottom board - and without friction, that means the upper board experiences more stress and should break first. But if there is friction with the surface of the bottom board, that makes the two boards "move as one", with the tension in the top board canceling the compression in the bottom board, and the tensile stress being transferred to the new "outer" surface (that is, the bottom of the lower board).

• @user929304 May I recommend that you post that as a separate question (leave a link here) - it's a bit long for a comment and not very relevant to the present post. Dec 31 '16 at 13:12

Generally in cases where a board breaks, the force used to break the board stretches the board beyond its breaking point. That is when the board breaks. Now, when the first board stretches, the board below obstructs the first board. Due to this the bottom board breaks first, which gives space for the first board to break. Therefore the first board to break is the one below.