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Cylindre buckling under axial load

  1. Jan 3, 2013 #1
    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!
     
  2. jcsd
  3. Jan 3, 2013 #2

    AlephZero

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    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:
     
  4. Jan 3, 2013 #3
    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.
     
  5. Jan 3, 2013 #4
    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!
     
  6. Jan 3, 2013 #5

    AlephZero

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    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.

    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.
     
  7. Jan 4, 2013 #6

    SteamKing

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    Stepping on a soda can placed on a bathroom scale is not exactly the ne plus ultra of experimental procedure.
     
  8. Jan 4, 2013 #7
    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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