Tapered Beam Deflection Coefficients

[Joblack]

I have been working on a project where we need to check the deflection of a tapered beam and I have been looking up in Roark's "Formulas for Stress and Strain" Table 13a at the deflection coefficients for an end loaded cantilever beam look wrong or the table header has a typo as he has Inertia at Fixed End divided by Inertia at Free End of say 2 gives a deflection multiplier of 0.579 which would then reduce the deflection if you using the inertia at the fixed end to calculate the deflection, or am I wrong in this assumption and that to calculate the deflection of tapered beam you use the inertia at the free end in which case Roark's table would be correct.

 

[prex]

Look in the first site below, under Beams -> Tapered :you'll be able to cross check Roark's results.

prex

http://www.xcalcs.com

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http://www.megamag.it

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[Cockroach]

If ever there was a time for finite element, then this would be it. Run a SolidWorks model using COSMOS.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[GregLocock]

Tapered in depth, or width? I can assure you that a linear taper in wdth is a solvable equation, since I solved it last week, and I'd be a bit surprised if the depth case was any harder.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[jte]

Take a look at your strength of materials book and look for energy / virtual work methods. An integral or two later you're done.

However, since I'm far more proficient at SolidWorks / Cosmos than calculus, I'd take Cockroach's approach myself...

jt