Bending pipe - compression and tension

[mrmojorizing]

Hi,

I'm a bit confused. Say you're bending a cylindrical pipe (tube, hollow cylinder). So the neutral axis of the pipe will be in the middle of the pipe and all the material on the inside of the bend (to one side of the neutral axis) will be in compression, while all the material on the outside of the bend (on the other side of the neutral axis) will be in tension.

Now imagine you have a rectangular steel plate (a rectangular steel slab) and you bend it. The neutral axis will be in the middle of the plate and all the material on one side of the neutral axis will be in compression, and on the other side will be in tension.

My question is this: when you're bending a cylindrical pipe you can imagine the pipe walls being composed of tiny rectangular plates, each of which has its own neutral axis. Each tiny rectangular plate if bent on its own would have compression on one side of the neutral axis and tension on the other. This would seem to indicate that on one side of the neutral axis (axis of the pipe not of a rectangular plate) there is both tension and compression, since the pipe wall can be imagined to be made up of tiny rectangular plates, each of which has its own neutral axis. Yet if you look at the pipe alone, without imagining that the walls are made up of tiny rectangular plates there is supposed to be only tension or compression on one side of a bent pipes neutral axis. So this is a paradox which i don't get. What am i doing wrong? See pic below if you don't get my question.

https://docs.google.com/file/d/0B8Ru4CVOjev0aUpsbVk2cGl3aTQ

 

[SteamKing]

Sorry, no pic attached.

 

[Chestermiller]

For a given cross section shape, there is only one neutral axis for the overall cross section. If you look at the little rectangles in the pipe, the stress and strain are indeed varying (but just a little) over the cross sections, but the averages are not zero. On the outside of the bend, they are all in tension, although the tensile stress does vary slightly with distance from the neutral axis (of the overall cross section), with portions of the rectangles further from the neutral axis having more stress and strain, and portions closer to the neutral axis having less stress and strain.

Think of bending a deck of cards. Why is it easier to bend an ordinary deck of cards than it would be if you glued all the cards together? This should give you a hint about your question.

Chet

 

[Jupiter6]

Hi,

I'm a bit confused. Say you're bending a cylindrical pipe (tube, hollow cylinder). So the neutral axis of the pipe will be in the middle of the pipe and all the material on the inside of the bend (to one side of the neutral axis) will be in compression, while all the material on the outside of the bend (on the other side of the neutral axis) will be in tension.

Now imagine you have a rectangular steel plate (a rectangular steel slab) and you bend it. The neutral axis will be in the middle of the plate and all the material on one side of the neutral axis will be in compression, and on the other side will be in tension.

My question is this: when you're bending a cylindrical pipe you can imagine the pipe walls being composed of tiny rectangular plates, each of which has its own neutral axis. Each tiny rectangular plate if bent on its own would have compression on one side of the neutral axis and tension on the other. This would seem to indicate that on one side of the neutral axis (axis of the pipe not of a rectangular plate) there is both tension and compression, since the pipe wall can be imagined to be made up of tiny rectangular plates, each of which has its own neutral axis. Yet if you look at the pipe alone, without imagining that the walls are made up of tiny rectangular plates there is supposed to be only tension or compression on one side of a bent pipes neutral axis. So this is a paradox which i don't get. What am i doing wrong? See pic below if you don't get my question.

[PLAIN]https://docs.google.com/file/d/0B8Ru4CVOjev0aUpsbVk2cGl3aTQ[/QUOTE]

I can't see your pic though I'll say volumes have been written about bending metals.

Sheet steel bending allowances are usually based on something like a 44% of the material thickness as far as the actual neutral axis(inside radius). This is not something engineers came up with on paper, the brake operators had a lot of input in this. So abandon the idea of a 50% neutral axis because it does not work in real life with sheet. Bending with or against the grain also affects the force required.

With pipe and tubing it gets far more complicated. The material will flow giving you a bevel based on your bend radius, material, and length of the bent leg coming off the mandrel centerline.

My point is even with the best mechanical systems we have to bend pipe the bend axis will vary as the pipe itself is 1. captured 2.forced along the mandrels 3. Released off the mandrels.