Force to Straighten Curved Beam 4

[ryldbl]

I have a 25' round steel rod with a diameter of 1.125". This rod is not straight, but rather has a radius of curvature of "p". Does anyone know how to calculate the axial force necessary to straighten the rod? I don't know a formula to determine lateral deflection in a curved beam due to axial tension.

When I say "straighten" I mean elastically deform the rod into a straight beam, not permanently yield the rod to a straight condition.

 

[JStephen]

If the bar is bent has something yielded? In a real world situation...

Presumably, if the bar was made perfectly straight and is not curved, then it has yielded.

You get the faces of the bar or plate to the yield stress when you roll it. But it will spring back somewhat, and the residual stresses are not necessarily close to the yield point afterwards. In other words, you could apply some amount of tension without anything yielding.

In a real world situation, this wouldn't be a problem- get 90% of the deflection out and call it done.

 

[GregLocock]

You could cast it to a bowed shape, nothing's yielded then.

Well, I'm glad nobody called me on the superposition thing, as I've forgotten how I did it!

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[ryldbl]

Sorry, I've been out of the office for the past week. Wow, I never would have thought there would have been so many posts...this is great! You've all come up with some enlightening theories, I wish I could have provided some more detail earlier but here it goes...

The application is a continous sucker rod string in an oil well. For those who are unfamiliar, a contious sucker rod string is a length of steel rod ~3,000 to 7,000 ft long which is used to connect a prime mover at surface to a pump underground. When the rod is transported to the well site, it is wrapped onto a large spool. When this is done, a slight amount of yielding occurs resulting in a slightly bent rod string.

It is imperative that the rod string be as straight as possible when placed in service. Every rod string will have a certain amount of axial load applied by the sub-surface pump. This has lead to the question: how much load is neccessary to straighten a rod with a given radius of curvature?

The 25' length was arbitrary and I only proposed it because this is the length that I am trying to get some tests done on. My thinking was that if I could get a methodology from you all I could apply that to any length.

In short, the load conditions are: The beam is pin supported at the top end and hangs under its own weight. I know that the weight of the rod alone is not enough to straigten it. I do not know the exact radius of curvature.

 

[IFRs]

Can you just reverse bend it slightly as you install it to straighten it out?

 

[ryldbl]

There are a lot of ways that we could remove the bend, but this is a theoretical question bound by the fact that the rod is bent and there is an axial load applied.

 

[EnglishMuffin]

For a "back of the envelope" ball park estimate, you might consider something like P = 8*del*E*I/(e*L^2), where E I & are the usual, del = required lateral translation at middle of length L, and e = eccentricity of axial load P. This equation is basically from Timoshenko, and is for a short thick column, assuming the rod starts from an unstressed elastic deflection shape and not a circular arc, and that it takes the same amount of force to bend it back as it did to deflect it. Obviously I cannot justify this equation rigorously on these terms, but for what you are doing, it might be a good enough indicator - at least it stands up to dimensional analysis and rough logic. The interesting thing about this equation is that the longer the rod, the less the load has to be to make the rod straight for a given mid point lateral translation, (presumably approximately within an amount "e"). What it amounts to is that for such a long rod, you may not have to worry. It all depends on what you mean by "slightly bent".

 

[unclesyd]

I'm glad you came back with that description as I've been looking for an article that I have on uncoiling/unwinding wire for heading machines.
I'll keep looking

 

[rb1957]

i agree with unclesyd, thx for the added info ryldbl. i think we'll have to retrace some steps, because now we have a plastically deformed rod (so there is an internal stress field) and i think the original "elastic" reference is no longer accurate, rather it should be "plastic", no?

also, surely this problem has been uncountered before, as it sounds (to the uninitiated) to be a stadnard operation.

also, is the rod really axially loaded ? sure there is the weight to be considered, and sure the rod is being "forced" into its hole, but is "driven" a better description ... isn't the force applied to the rod being reacted dynamically (with movement of the rod) ?

i think unclesyd will come up with the answer (whihc i think is a couple of idler wheels.

 

[prex]

EnglishMuffin, that formula comes from this one:
f=ML[sup]2[/sup]/8EJ
This represents the center deflection of a simply supported beam under the action of two equal end couples M, so I suppose that in your reference the eccentricity e is at both ends of the beam, from what M=Pe.
Don't want to propose again my conclusions, that were clearly completely wrong , however note that in my first post I proposed P=24EJ/L[sup]2[/sup] for the straightening load.
However ryldbl I understand now that with such a load and no initial eccentricity (except beam deflection) one would reduce the deflection to some 20% of the initial value, so that the beam would hardly be defined as straight. The load to straighten it to say 1% is really much higher and of course it is impossible to have it fully straight.

prex

http://www.xcalcs.com

Online tools for structural design

 

[ryldbl]

I still think that we are dealing with the elastic range. The rod has been plastically deformed slightly, but the axial force applied to the rod string should not be enough to yield the rod - only elastically straighten it somewhat. In other words, when the axial load is removed, the rod should return to its plastically deformed, slightly curved state.

Yes, there is axial load applied to the rod. The application considered here is not the reciprocating up and down beam pumps that you typically see in oil fields, but rather a PC pump where the rod is rotated to operate the pump. Thus the rods is exposed to a constant torque - something which I do not want to consider in this discussion - and a significant axial pulling force caused by both rod weight and pump operation. This is key, when the pump is operational, is directly applies a large axial load to the rod string.

 

[rb1957]

is the rod "freely" rotating under the torque, or does the pump react the torque, in which case there'll be a large torque wind-up (no?)

also, we're getting into the words a little more ... how much is "slightly", describing the plastic deformation ? i suspect that the 7000' of rod is coiled for transport, say a diameter of 25', and uncoiled at the site; now we're into a non-linear model of how the rod coils and relaxes. and how straight is "somewhat"; we've spent quite some time discussing gettting a mathematically (perfectly) straight rod from a deformed rod ... i suspect we're into another problem ... how much force is required to push the slightly deformed rod down its hole ? how much bigger is the hole (than the rod) ?

prex, you sounded a little defensive; i don't think there's any need to be, we're all trying to solve a question with little information (that's not a shot, ryldbl) and i think we're all taking our best shots and learning from them. hopefully we're not learning not to shoot !