Science Puzzle
Which Way Up Is a Plank Stiffer?
A plank of wood 10 centimetres wide and 2 centimetres thick bridges a gap, with a heavy weight in the middle. You can lay it flat, or stand it up on its narrow edge so it's 10 centimetres deep.
Which way up will the plank bend less?
The Answer
On its edge. Stood up, this plank is about 25 times stiffer than when it lies flat.
When a beam bends, its top is squeezed and its bottom is stretched, while the middle hardly changes at all. Wood far from the middle has to squeeze or stretch the most, so it does most of the work of resisting the bend. A deep beam puts its wood a long way from the middle. A flat plank keeps all of it within a centimetre of the middle, where it can barely help.
Engineers have a rule for this: a beam's stiffness rises with the cube of its depth. Standing the plank on its edge makes it 5 times deeper (5 × 5 × 5 = 125 times stiffer), but also 5 times narrower, which divides that by 5. That still leaves 25.
That's why the joists under a floor are always laid on their edges. Steel beams take the idea further: an I-shaped beam puts most of its metal in a flange at the top and another at the bottom, as far from the middle as possible, joined by a thin web. Try it with a ruler. Flat, it bends easily; on its edge, you can hardly bend it at all.
The principle: Bending stiffness depends on depth. A beam's resistance to bending rises with the cube of its depth, so the same material is far stiffer standing on its edge.