Cylindre buckling under axial load

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Discussion Overview

The discussion revolves around the buckling of thin cylinders under axial load, exploring theoretical formulations and experimental observations. Participants reference various sources, including classical theories and experimental results, while expressing skepticism about the accuracy of theoretical predictions compared to real-world experiments.

Discussion Character

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

Main Points Raised

  • One participant presents a formula for buckling stress derived from Timoshenko's theory, noting discrepancies between theoretical predictions and experimental results.
  • Another participant cites a source indicating that experiments typically yield only 15 to 50% of the theoretically predicted values, suggesting that the initial experiment's results are within this range.
  • A participant questions the derivation of the presented formula, indicating it applies to long tubes and referencing historical work by Prescott.
  • Further sources are shared that criticize the reliability of elastic theory for cylinder buckling and emphasize the need for experimental corrective factors that vary based on conditions.
  • Concerns are raised about the sensitivity of buckling behavior to initial conditions and geometric imperfections, suggesting that design should consider these factors.
  • One participant critiques the experimental method used to test the buckling of a soda can, implying it lacks rigor.
  • Another participant expresses disappointment over the tone of the discussion, indicating that comprehensive theoretical analysis exists, including experimental data across various materials.

Areas of Agreement / Disagreement

Participants express differing views on the reliability of theoretical models versus experimental results, with no consensus on the adequacy of existing theories or the validity of the experimental approach. The discussion remains unresolved regarding the best methods for predicting buckling behavior in thin cylinders.

Contextual Notes

Participants highlight limitations in current theories and the variability of experimental results, indicating that predictions may depend heavily on specific conditions and material properties.

Enthalpy
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Hello everybody, and a happy new year!

Found in Dubbel (Taschenbuch für den Maschinenbau) page C47 7.3.2 the axial load that buckles a thin cylindre. This is not Euler's buckling of a long compressed beam, but probably from Timoshenko's theory for shell buckling applied to a thin cylinder.

The book gives:
σ = e/R*E/(3(1-μ2))0.5 where σ is the stress,
and taking Poisson's coefficient μ as 0.33 I obtain
σ/E = 0,612*e/R
and
F = 3,845*e2*E.

As I mistrust buckling computations, I stepped on a soda can over bathroom scales and got instead
F = 0,68*e2*E
far less...

I use this lower value now for my computations, but maybe I botched the experiment? I measured the thickness properly with a micrometer at several positions, tried to step slowly and vertically...

Do you have more experimental values, or different formulas from a theory?

And if someone steps on a can, please mind your ankle, I hurt mine.

Thank you!
 
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Enthalpy said:
Do you have more experimental values, or different formulas from a theory?

"...experiments usualy give only 15 to 50% of that predicted theoretically; moreover, the observed buckle pattern is different from that predicted by the theory..."
http://www.dtic.mil/dtic/tr/fulltext/u2/a801283.pdf

Your 0.68/3.845 = 18% is between 15 and 50%, so your experiment was OK :smile:
 
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Enthalpy
σ = e/R*E/(3(1-μ2))0.5

Have you seen the derivation of this formula?

It is for a long tube of dimensions where axial length > 10√(eR/2)

It was presented by Prescott in 1924, but he does not claim originality for it.
 
Thank you!

Meanwhile I've also seen
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690013955_1969013955.pdf
http://shellbuckling.com/papers/classicNASAReports/1969NASA-TN-D-5561-Peterson.pdf
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930084510_1993084510.pdf

Which tell in essence the same picture:
- Elastic theory is b**cks for cylinder buckling
- Experiments are not reproducible, even for plain metal
- Introduce an experimental corrective factor much smaller than 1
- This factor depends on everything

Imagine for a cylinder with stiffeners, or of composite...
Build it first, measure, and only then make predictions?

A few considerations:
- My book isn't as good as I had thought...
- We have no theory for that in 2013! Shame.
- Once again, models are necessarily right - when Nature wants to conforms to them.
- Nasa and Naca documents from pre-computer era, when people made measurements, are a treasure. Fabulous to have them online.

OK, I have the necessary information to go further, thanks!
 
Enthalpy said:
We have no theory for that in 2013! Shame.

There's nothing wrong with the theory. The "only" difficulty is that this (and other related problems in continuum mechanics) are VERY sensitive to initial conditions and geometric imperfections. For thin cylinders, St Venant's principle often doesn't apply, therefore "local" deviations from a mathematically perfect structure have "global" consequences.

The solution is the same as for any other engineering problem: never "design" things that you can't analyse.

Imagine for a cylinder with stiffeners, or of composite...
Build it first, measure, and only then make predictions?
Stiffeners make the problem a lot simpler. One way to proceed is design a frame structure that carries the loads without buckling, and then cover it with a (non load carrying) thin cylinder.
 
Stepping on a soda can placed on a bathroom scale is not exactly the ne plus ultra of experimental procedure.
 
enthalpy
Which tell in essence the same picture:
- Elastic theory is b**cks for cylinder buckling
- Experiments are not reproducible, even for plain metal
- Introduce an experimental corrective factor much smaller than 1
- This factor depends on everything

I was disappointed to see this tantrum in response(?) to my civil question about the derivation of a formula that you yourself posted.

I got The Theory of Elastic Stability down from the shelf this morning.

There is a whole chapter devoted to this subject including a derivation of your formula (referenced to a 1910 paper in German) and a considerably more advanced analysis.

The authors also offer considerable experimental material, including test results on a variety of materials from steel to brass to rubber. There is also discussion of these results and comparison with theory.

Is there any point in my further contribution to this thread?
 

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