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Euler's buckling formula
Thu, 2008-12-04 05:59 - Fanfan WANG
Hi, everyone,
I am new here. Now I am doing a research which is related to the Euler's buckling formula. It is known that when the cylinder is thick enough, Euler's buckling formula is no longer valid. I want to know in which region of slenderness(aspect ratio) of a cylinder or column that the Euler's buckling formula is valid. Is there any analytical study or numerical results about it? Is there any suggestion or paper I can find?
Thank you very much!
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slenderness limit on Euler's buckling formula
Euler's buckling formula is based on Euler-Bernoulli beam theory, which does not account for the effect of transverse shear deformation. This effect is significant for non-slender beams, or in this case, non-slender columns. So, to find the buckling load for non-slender columns (if it exists), you will need a beam theory for non-slender beams (e.g. Timoshenko). It would seem to me that the same slenderness limit on Euler-Bernoulli beam theory would apply to Euler's buckling formula.
That makes sense
If course, it is of note that the less slender a member becomes, the less susceptible it is to buckling. Is there an obvious case where one would expect buckling to be the failure mode in a member for which Bernoulli-Euler beam theory is unreasonable?
Engineering classification
Dear Hugh Wang,
For a column of length L and cross section radius of gyration rho, it is possible to distinguish 3 failure regimes under compression:
For unstable cross-sections, e.g. thin C beams, local buckling may appear, thus reducing the strength of the column.
Well, I hope this helps.
Regards,
Julian
Books and reference
Dear Julian,
First, thank you so much for your answers.
Second, is there any book or paper regarding to your answer? Since I am writing a paper and I need accurate and precise reference. Thank you.
Best regards,
Hugh
Introductory book on buckling
Dear Hugh,
Any undergraduate book on aerospace structures should cover the basis of the topic. The book I mentioned before (Analysis and Design of Flight Vehicle Structures by E.F. Bruhn) is useful if you are interested in a "manual like" book for design purposes. Nevertheless, it is probably not the best book for learning the subject from scratch.
The book Buckling of Bars, Plates, and Shells by Robert M Jones is fully available online through Google Books and is probably better as an introductory book. That could be a good starting point for you.
Good luck!
Julian
Julian J. Rimoli - absolutely correct answer
where can I find that
Dear Julian J. Rimoli,
Thank you for you answer.
But I want to know the scale and marks of the axes. It is very important.
And where does this plot appear? Can I find it?
Thank you very much.
Best regards,
Hugh Wang