Force required to bend a bar 90*

[rn14]

I have an interesting problem which is fairly basic but not something we are required to think about too often and I may therefore be oversimplifying it.
I guess some fabricator needs to bend a 1 1/2" dia. A36 bar (not rebar). The bend is 90*. The fabricator is not sure his machine can do it and wants an estimate of the force required. I am pulling from some old memories of a limit states class I took and it seems that I could just determine Mp for the bar, which I could do by hand or use the shape factor for a circle (I think 1.7?). Once Mp is reached the section will be fully yielded and can be bent with essentially not additional force. Have I forgotten about some assumptions that would cause my estimate of force to be way off?

 

[csd72]

For A36 the yield strength is 36ksi but the ultimate strength is 58ksi.

This means that the bar will start to bend from above 36ksi and from strain hardening the resistance will increase up to 58ksi as bending continues. Keep in mind that these are minimum strengths so you probably should allow for an additional 20% to be sure.

You are correct that you should use the plastic modulus,but I would use M = 1.2ZFu as noted above where Z = (PIxd^3)/32

 

[rn14]

I basically have three numbers for him.
1.)Force using Mp
2.)Force using Mp*1.5 to include some strain hardening
3.)Force using Mp=1.2*Z*Fu

I think 2 will actually be in the ball park depending on the actuall properties of the steel used.

 

[JStephen]

The 36 ksi is the minimum, and it'll normally run a fair bit above that.

You're calculating the moment to bend it, but he's likely pressing it into a V-shaped block or something to actually bend it, so you need to convert that moment into a force.

 

[rn14]

Ya, I converted them to forces. The are actually bending it by applying a force to it 64" from the fulcrum.

 

[miecz]

I think you want the plastic section modulus as [π]d[³]/6.

 

[miecz]

Oops, I guess that's d[³]/6.

 

[csd72]

miecz,
thats for a square section, not a circular!

 

[Tomfh]

plastic section modulus for a square is d^3/4

 

[csd72]

Oops! your right you Americans and your darn S and Z being around the wrong way!

In the UK and Australia S is the plastic modulus and Z is the elastic modulus. I thought I had got used to the american method but it catches me once again.