1. Dec 8, 2008

Hi,
I have a problem with the experimental buckling load that I have deduced for a compressive axial load applied to a tube of circular cross section. The buckling load is 2.34% larger than the theoretical buckling load! The beam is connected to supports via knife edges; these are rigid bodies and so will increase the overall buckling load of the beam. However using the correction factor deduced by Karman and Biot (1940) for this beam the buckling load is 1.000005 x P(theoretical), so the effect of hte knife edges can be considered to be negligible. What else might have caused this error? Position of strain gauges? Data acquistion program?

thanks for any help.

2. Dec 8, 2008

### Mech_Engineer

Re: Buckling

Ha! If you're within 2.34% of the theoretical load, I would call your experiment a success.

You're fighting for atoms in one spot when you could be off by significant margins in others. My guess is your material is not "perfect" and is slightly off either in its mechanical properties or its geometry. Being off 2% is a very small margin when comparing theoretical results to experimental results. Things like paralellism of your knife blades will have an effect on your results as well.

3. Dec 9, 2008

Re: Buckling

Lol, thanks. So it looks more like general experimental errors rather than anything in particular.

4. Dec 9, 2008

### FredGarvin

Re: Buckling

You can introduce more error than 2% just in the lay up and connections of the strain gauges. I would pat myself on the back for having a correlation that good.

5. Dec 16, 2008

### Dr.D

Re: Buckling

I think you guys are missing the point. He said his measured result was ABOVE the theoretical value, and that is a true anomaly. I have made quite a few buckling measurements, and I have never, ever, gotten a measured result higher than the theoretical value. I think the question is an entirely valid question, and worthy of some serious consideration.

I have to suggest that you go back over your load application/load measuring situation. Are you measuring load right on the column itself, or are you measuring it on a ram that loads the column? If on a ram, could part of the load be shunted into the support by stiction?

You definitely have a strange result that ought to be explained.

6. Dec 16, 2008

### FredGarvin

Re: Buckling

I'm sorry, but in all of my years in testing, I have been in very few situations where a measurement uncertainty could not be bilateral. Perhaps you can expand more on why the uncertainty in a measurement of force can not be more than the theoretical value?

I can think of a few scenarios off the top of my head that would explain that. I have already listed one.

7. Dec 16, 2008

### PhanthomJay

Re: Buckling

If the measurement of I, L, E, or the value of K, was off by over 2%, that would, in addition to other factors previously cited, explain a mere 2% plus or minus error, wouldn't it? Please clarify your response, thanks.

Last edited: Dec 16, 2008
8. Dec 16, 2008

### stewartcs

Re: Buckling

I don't find it strange at all. There are many reasons (some listed) that would cause such an error.

CS

9. Dec 16, 2008

### Dr.D

Re: Buckling

In an absolutely perfect setup, that is a perfect column with perfect loading, etc. -- no imperfections in geometry, material, anything, -- then presumably the column remains in place and the mode of deformation is axial compression until such time as that becomes a higher energy state than bending would require. At that point, axial compression becomes unstable and the column buckles. This is absolutely the highest possible buckling load for the column.

The sort of idealized state postulated in the previous paragraph never exists in reality. There are always imperfections, in the material, in the geometry of the column, in the geometry of the loading. All of these things combine to give an actual buckling load that is lower than the ideal buckling load in every case. In fact, what they almost always come down to is that the really is not an instability problem at all but simply a bending problem with a very tiny initial moment arm arising only from the geometric imperfections.

The bending problem always begins with at zero force - zero deflection and rises from there. The true buckling problem shows zero deflection until the critical load is reached at which point the load begins to increase. The bending curves are always below the buckling curve.

10. Dec 16, 2008

### stewartcs

Re: Buckling

This presupposes that one has actually measured the column particulars exactly correct, which is almost never the case. Hence, the "theoretical" critical load may certainly be lower than the actual.

CS

11. Dec 16, 2008

### Dr.D

Re: Buckling

So Stewartcs has proposed an explanation in that the dimensions, etc. were not correctly measured, i.e. that the experiment was not correctly performed and someone made measurement errors with a micrometer. This is a plausible explanation, I suppose. I have never seen it happen, but that does not mean that it could not happen.

12. Dec 16, 2008

### FredGarvin

Re: Buckling

The uncertainty in ANY of the measurements you take can do it.

13. Dec 17, 2008

### Mapes

Re: Buckling

Also note that a radius measurement error $\epsilon$ would result in a buckling load error $>4\epsilon$ because $I\propto r^4$.