What Could Have Caused an Error in Experimental Buckling Load Calculation?

Click For Summary

Discussion Overview

The discussion revolves around the discrepancies observed in experimental buckling load measurements for a tube of circular cross-section under compressive axial load, specifically addressing why the experimental value exceeds the theoretical prediction. Participants explore potential sources of error, including experimental setup, measurement techniques, and material properties.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant notes that the experimental buckling load is 2.34% larger than the theoretical load and questions possible causes for this discrepancy, such as the position of strain gauges or the data acquisition program.
  • Another participant suggests that being within 2.34% of the theoretical load indicates a successful experiment and attributes potential errors to material imperfections or geometry rather than a specific anomaly.
  • Some participants argue that a measured result exceeding the theoretical value is unusual and warrants further investigation into the load application and measurement methods.
  • Concerns are raised about the accuracy of measurements, particularly regarding the load application and the possibility of stiction affecting results.
  • Several participants discuss the idealized conditions under which theoretical buckling loads are calculated, emphasizing that real-world imperfections in geometry and material properties typically lead to lower actual buckling loads.
  • One participant proposes that measurement errors, particularly in dimensions, could explain the observed discrepancy, suggesting that the experiment may not have been performed correctly.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the discrepancy, with some suggesting it is a general experimental error while others emphasize the anomaly of a measured value exceeding the theoretical one. No consensus is reached regarding the primary cause of the discrepancy.

Contextual Notes

Participants highlight various factors that could contribute to measurement uncertainty, including the precision of strain gauge placement and the accuracy of material property measurements. The discussion acknowledges the complexity of accurately measuring buckling loads in practical scenarios.

Who May Find This Useful

This discussion may be of interest to researchers and practitioners in structural engineering, materials science, and experimental mechanics, particularly those involved in buckling analysis and load testing of structural components.

ads.
Messages
8
Reaction score
0
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.
 
Engineering news on Phys.org


ads. said:
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!

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

ads. said:
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?

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.
 


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


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.
 


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.
 


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.
 


Dr.D said:
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.
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:


Dr.D said:
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.

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

CS
 


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


Dr.D said:
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.

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


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


The uncertainty in ANY of the measurements you take can do it.
 
  • #13


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

Similar threads

Calculating the strain in three different ways - experimental error?
  • · Replies 1 ·
Replies
1
Views
3K