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Cylindre buckling under axial load 
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#1
Jan313, 11:42 AM

P: 661

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(1μ^{2}))^{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*e^{2}*E. As I mistrust buckling computations, I stepped on a soda can over bathroom scales and got instead F = 0,68*e^{2}*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
Jan313, 01:13 PM

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Your 0.68/3.845 = 18% is between 15 and 50%, so your experiment was OK 


#3
Jan313, 05:12 PM

P: 5,462

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. 


#4
Jan313, 06:44 PM

P: 661

Cylindre buckling under axial load
Thank you!
Meanwhile I've also seen http://ntrs.nasa.gov/archive/nasa/ca...1969013955.pdf http://shellbuckling.com/papers/clas...1Peterson.pdf http://ntrs.nasa.gov/archive/nasa/ca...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 precomputer era, when people made measurements, are a treasure. Fabulous to have them online. OK, I have the necessary information to go further, thanks! 


#5
Jan313, 09:06 PM

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


#6
Jan413, 12:48 AM

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Stepping on a soda can placed on a bathroom scale is not exactly the ne plus ultra of experimental procedure.



#7
Jan413, 06:47 AM

P: 5,462

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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