Pole bending

[Changabooniggiwan]

Settle an argument for me, would you?

I have a 1m rod - a cylinder of steel with a radius of 1cm. Using a machine of some sort, I bend the rod round to form a complete circle.

What is the external diameter of the said circle?
What is the internal diameter?
Is the steel now less dense at the outer edge and more dense at the inner edge?
Could the two ends of the rod actually meet without deformation of their shape?
If they do deform, what shape would the end profiles be?

[Zag]

I don't actually know, but I don't think you're going to change the density of steel with that process. (If you had asked me this question a few years ago, I could have told you for certain -- my father was an expert in these things when he was still alive.) Steel would need massive pressure to change its density. Since the pressure that you're creating has elsewhere to go, it won't do it.

I suspect that the difference in length between the inner and outer circumferences will be corrected for by distorting the cross-section of the rod. Your resulting cross-section will now be an oval or an oblong of some sort. The "extra" matter along the inner circle will push out in the z direction, and the missing matter along the outer circle will come from shrinking it both in the z-direction and the radius.

If you could somehow reshape the rod but still contain it in something that would protect the circle shape of the cross-section, that something would have to apply massive pressure, as I said. The resulting pressure would probably melt the steel slightly, which then would re-form in the circle you've created. You'd still have uniform density, just a new shape, as if you had cast it in that shape in the first place.

Again, this is speculation on my part, especially the last paragraph.

[ctrlaltdel]

you dont specify the "bending machine". if the "machine" can melt the cylinder and cast it again as a torus, no problem, just calculate the final dimensions for the same volume of steel.

if it is a cold process, i think you would end up distorting the section shape. get a play-do cylinder, bend it in half at 180 degrees. thats the sort of distortion you will get on your originally circular section shape.

as for the precise dimensions of the final shape, that would heavily depend on the specific steel and its properties - i.e. how much distortion theres going to be.

btw, bending steel rods will, i think, always include significant heating of the rod.... http://www.ehow.com/how_5869685_bend-metal-rod.html

or just ask these guys to measure it for you http://factory.dhgate.com/bending-machinery/steel-bar-bending-machine-gw40/gw50-p37637528.html