Beam loading formula from machinery handbook

Jan 29, 2004 3 Replies
L

Not being a mechanical engineer, I was looking at simple beam deflection calculations in the machinery handbook and was wondering why there seems to be a discrepancy from posted formula on various sites.



For instance, for a beam with a single support and uniform load, the handbook states for maximum deflection:



ymax (at end) = (wl^3)/(8EI)



the formula ymax = -(w * l^4) / (8 * E * I) at x = l



from



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agrees with the results from beamboy and other postings. I also measured it experimentally.



So I guess the question is l^3 vs l^4 unless E or I are calculated differently in the handbook??



thanks.


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J

That's a cantilevered beam with uniform loading.

The 2nd formula is correct. I've checked 2 of my books.

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B

Looks like different definitions for "w".

In one case (wL^4), w is load per unit length. In the other (wL^3) , w is total load.

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B

As the saying goes: Who ya going to call: Marks Handbook or a private web page and some posters?

Next: I hope you can distinguish between 2nd moment, initialized as 9th letter of the alphabet, upper case I and length, initialized as 12th letter, lower case l . But I think you can.

Last, I hope you are accounting for uniformly distributed load vs. point load - which accounts for a factor of 3/8 in deflection, but I think you are.

That leaves the one definition that you are probably forgetting. A uniform load, which is often given as load per unit length (along the cantilever) versus a uniform load totaled over the whole length. The difference introduces a factor of l

Brian W

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