Science Puzzle
Cantilever Tension
A cantilever beam is fixed into a wall on the left and hangs in the air with a heavy load at its free right end. The load bends the beam downwards, so its top face is being stretched (tension) and its bottom face is being squeezed (compression).
If the beam were made of plain concrete, where would it crack first, and why?
The Answer
Across the top face, right next to the wall. The top is the side being stretched, and concrete is very weak in tension.
Concrete is excellent at resisting compression: you can squeeze it hard without cracking it. But it handles tension poorly: stretching pulls the material apart along its weakest points, and concrete has many tiny internal voids that become crack initiation sites under tension.
Why the top? Think of a diving board with someone standing on the end. It droops, and its upper surface curves over like the brow of a hill. The outside of a bend is always the longer side, so the top gets stretched while the bottom gets squeezed. Why by the wall? Every part of the beam has to hold up the load beyond it, and the further away the load is, the more leverage it has. At the wall it's working over the whole length of the beam, so that's where the bending and the stretching are greatest.
This is why reinforced concrete puts its steel bars where the tension is. In a concrete balcony or diving platform the main bars run close to the top surface. In an ordinary beam resting on a support at each end it's the other way round: the beam sags like a smile, so the bottom is stretched and the bars go near the bottom. Engineers call the two shapes hogging and sagging; working out which one a beam is doing is one of the first questions in structural engineering.
The principle: Stress distribution in beams. A cantilever loaded at its free end is stretched along the top and squeezed along the bottom, most of all at the wall. Concrete resists compression well but fails in tension, so a cantilever's reinforcement goes near the top; a beam resting on two supports is the other way round.