# Failure to Understand

1. Aug 4, 2004

### e(ho0n3

I'm having trouble understanding this question:

For a freestanding concrete dam of uniform thickness t and height h, what minimum thickness is needed to prevent overturning? Do you need to add in atmospheric pressure for this last part? Explain.

What do they mean by overturning exactly? And why would I need to find the thickness when I'm already given the thickness?

2. Aug 4, 2004

### arildno

On the face of it, this looks like a question about buckling strength, but I'm not too sure..

3. Aug 4, 2004

### Staff: Mentor

I presume "overturn" means just what it sounds like it means: knock over, topple.

When full, the water exerts a force on the dam. Is it enough to topple the dam? Think of the dam as a solid block. (Consider torques.)
The thickness is a variable.

An interesting problem.

4. Aug 6, 2004

### e(ho0n3

OK. I found the force of the water on the dam and where it acts. What I then did was, I calculated the torque about the tipping edge (assumming the block is already in tipped state) and set this greater than zero. Solving for t, I obtained

$$t > \sqrt{h/3}$$

Am I correct?

5. Aug 6, 2004

### Staff: Mentor

Don't you find it odd that your answer shows no dependence on the mass of the dam or the density of the water?

6. Aug 7, 2004

### e(ho0n3

That and the units don't make any sense. Hmm...What to do?

7. Aug 7, 2004

### e(ho0n3

OK. I made some dumb mistakes but now I have the answer, which is

$$t > \sqrt{\frac{\rho_w}{3\rho_c}}h$$

where $\rho_w$ is the density of water and $\rho_c$ is the density of concrete.

Last edited: Aug 7, 2004
8. Aug 7, 2004

### Staff: Mentor

Now you got it.