User talk:Gpayette

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Athosanian (talk) 14:22, 4 May 2009 (UTC)Hello, Greg, I see your writing in page "Euler–Bernoulli beam equation" saying that "For thin beams (beam length to thickness ratios of the order 20 or more) these effects are of minor importance." would you help to tell me how do you know the length to thickness ratio for thin beams? Usually the textbook say that a beam can be looked as a thin beam when its length >> thickness and no exact ratio number. Thank you very much for your reply!

Hello. As alluded to in the section you cite, the Euler-Bernoulli beam theory accounts for deflections due to beam bending (i.e., due to internal moments), but it does not include deflections as caused by internal shear forces. For long and slender beams, the effects of internal moments are usually much more pronounced on the overall beam deflection than the effects of internal shear forces. To really know when the shear forces are important (i.e., when the beam is no longer a "thin beam"), it is necessary to compare results obtained using the Euler-Bernoulli beam theory with a more advanced theory such as the Timoshenko beam theory (which does include shear force effects). A general "rule of thumb" is that when the ratio of the beam's length to it's thickness is less than about 20 (Theory and Analysis of Elastic Plates and Shells, J. N. Reddy), shear forces are significant and the beam is no longer "thin". For a more rigorous assessment, it is necessary to consider specific boundary and loading conditions for the particular beam in question. However, I think the rule of thumb I mentioned (L/h > 20 => thin beam) is a pretty good assumption for most circumstances. I hope this is helpful for you. Gpayette (talk) 05:01, 5 May 2009 (UTC)

Athosanian (talk) 11:56, 10 May 2009 (UTC)Thank you very much for your reply. It is very helpful.