Plastically Deformed Steel Tube - Radius of Curvature to Straighten

[tr450]

A hydraulic steel tube of diameter 10mm and wall thickness 1.5mm has been bent to a radius of 100mm. Calculate the reverse radius of curvature that needs to be applied to straighten the tube.

M/I= σ/Y = E/R


I am really struggling on the above question. I think I need to read off the stress/strain graph for steel to try and work the formula backwards. I believe that the material will also see the Bauschinger effect which will further complicate the working?

Any help would be greatly appreciated.

 

[tr450]

Hi,

I'd be really grateful if anyone could help with the above as I'm really struggling. Any help would be really appreciated.

Cheers.

 

[tr450]

To try and better explain the question I believe the only way to straighten the tube will be to apply a reverse bending moment at each end of the tube. As the tube has yielded and undergone plastic deformation then the only way to straighten this will be to 'overbend' it past straight; otherwise it it will elastically spring back to a slightly less radius of curvature (assuming that it has started to see plastic deformation).

What I need to do is find away of ascertaining the amount I need to overbend it by. If I work out the strain required to straighten the beam then what needs to deternmined is by how much the strain needs to be exceeded by to achieve a straightened tube. Is this the correct way of looking at it?

 

[nvn]

tr450: Do you think a simplistic approach would be acceptable? You have the curvature (κ₁) to bend the tube to a straight position (while load is still applied, not yet released). Hint 1: Do you think you should add to this the curvature (κ₂) corresponding to ____?

Or do you think the first sentence of the problem statement might mean the applied load currently bending the tube is still being applied right now, and not released yet?

 

[tr450]

nvn - I think a simplistic approach is definitely okay as a starting point, I can always try and expand on whatever I come up with initially. To confirm, the load has been removed from the tube.

If I can work out the curvature k2 to add onto the 100mm radius k1 then this would be the way to go. If I work out the strain on the inner radius of the tube and then ascertain the stress from the youngs modulus I will be able to check to see if it has plastically deformed again. If not then I can work out the stress needed to reach plastic deformation and from that get the radius k2. Do you think this would be the correct way of looking at it?

 

[nvn]

tr450: I am currently thinking that is perhaps sounding OK.

By the way, see item 2 in post 3940543.