Bending a pipe

[KevinH673]

If you are bending a pipe similiar to this picture:

http://image.shutterstock.com/displ...-of-a-powerful-man-bending-a-rod-33069904.jpg

Do you still analyze it as a cantilever beam held on both ends?

I would assume you would use stress for a bending beam:

Stress=M*y/I

where y=diameter/2, I=pi*d^4/64, and M is the moment of the force to the middle. Is this correct?

 

[btrueblood]

Your equation works until the beam begins to permanently deform. Then, the material behavior takes over, and the equations change a bit. Google plastic hinge.

 

[KevinH673]

Is the above equation analyzing it as a cantilever? My book doesn't mention end constraints.

This stress will be before any plastic deformation occurs. Thanks for the help.

 

[btrueblood]

The equation converts bending moments to stresses. Whether the beam is a cantilever or not affects how the moments arise, and where the moment will be a maximum.

I'd say your beam is a case of a free beam with equal and opposite applied bending moments, not a cantilever.

 

[KevinH673]

I agree with that, looking through my handbooks it seemed a cantilever equation was incorrect. Seems obvious, but was worth it to ask. Thanks for the help!

 

[rb1957]

actually, a cantilever would be a fine approximation, if you took into account the symmetry of the problem.

because of symmetry, the bar is cantilevered at the CL and loaded at the end.

trick question, how is it loaded ? force or moment ??

 

[KevinH673]

Trick question because one creates the other? I'd say it's easier to analyze this as a moment, no?

You're right on the cantilever approach, if you split the pipe in half, as you said. Interesting because I wouldn't have thought to solve it like that.

 

[KevinH673]

Also, I've looked in two of my books and neither seems to give a good explanation of the Stress=My/I equation's derivation. Does anyone have a link explaining how to derive it? I've done a quick Google search without luck, but I honestly have not really dug around. Please, no one spend any time trying to find this, as I can do it after work, but if anyone has a good source in their bookmarks and wouldn't mind sharing, I'd love to read it!

 

[flash3780]

There's always Wikipedia...

http://en.wikipedia.org/wiki/Euler–Bernoulli_beam_equation

A theory of elasticity book might give you a more detailed explanation.

 

[rb1957]

actaully, the "strong man" is only applying a moment at the ends. it'd be different if he was pulling the pipe down with his head as a 3rd point. of course he could be applying an axial load on the beam, so that it buckles like a column.

 

[flash3780]

Do you still analyze it as a cantilever beam held on both ends?

The way I would analyze the bar would be to recognize symmetry. The center of the bar has a zero slope condition, and it turns out to be the same as a cantilevered beam with a moment load applied to the end. This case is often referred to as "simple bending" and sig = My/I is appropriate.

Of course, the guy could be applying an axial load as well, which would have to be accounted for...

Useful link:

http://www.roymech.co.uk/Useful_Tables/Beams/Beam_theory.html