Almost Embarrassing - Moment for Constant Curvature? 1

[AggieYank]

How do you determine the moment for a shape that will be bent to a constant curvature. This would give it a constant moment along the length.

As an example. I have a solid steel bar, and want to bend it in the field to a radius of 60 feet. (It shouldn't matter, but there will be a series of supports holding the bar to the radius). The bar has a moment of inertia of 0.3 in4, and is made of steel.

It's easy enough to plug the problem into RISA or the like, but how do you solve this by hand?

Thanks.

 

[LowLax]

You know the I, E, length and deflection, so you could work backward and find a uniform load that would create that deflection. Then just calculate wl^2/8. But I'm not sure if what you are describing would be a uniform load.

 

[AggieYank]

Treating it as a simple span doesn't work. There isn't constant curvature in a uniformly loaded simple span beam. The maximum curvature occurs at the maximum moment (midspan), and that just isn't the case here.

 

[steve1]

I'm a little confused about what you are actually asking. In order to bend the bar you must apply a force. This force will produce a bending moment. When the bar is placed in service it will presumably be loaded with a set of external forces that will induce a different bending moment.

In addition to the above I would assume that the method of bending the bar would produce residual stresses.

I think we need more information from you.

Also:

Wouldn't a shape of constant curvature be a circle or some part of it?

 

[cooperDBM]

The basic moment-curvature relationship is 1/R = M/EI or M = EI/R.

Are you trying to hold this bar elastically to that radius, in which case you're building in this moment, or plastically deform the bar to that radius? You may have to apply a larger moment to yield the bar in order to deform it.

 

[AggieYank]

cooper, perfect. That's exactly the simple relationship I was looking for.

This bar will be fabricated straight, and field bent into this curvature creating residual elastic stresses in the bar. It will then withstand additional stresses created by loading.

Thanks for the advice everyone.

 

[rb1957]

are you going to bend the bar, then attact it to the supports (bend it for a 55' radius 'cause of elastic spring-back), or are the supports going to be keeping the bar in its new shape (that sounds like a pretty siginificant load)

how do you plan on bending it ? (i'd start in the middle, and work towards both ends at the same time)