6 Replies Latest reply on Sep 2, 2008 1:04 PM by 19411

Beam Theory vs Code Results

Ben Floan Aug 28, 2008 6:36 PM

In the static verification problems found in the online help, there is the "T" cantilever beam given. At the given length, 2000in, the results compare quite well with the beam theory which gives deflection = PL^3/3EI ~ 0.06%. However, if one shortens the length of beam from 2000 to 1000, to 500, to 250in error increases to 0.86%, 4.19%, 17.71% respectively. Why?.. is this a limitation in the code or theory (Euler-B vs Timoshenko)? Any input on this would be much appreciated.

Ben

Beam Theory vs Code Results

Anthony Botting Aug 28, 2008 7:20 PM (in response to Ben Floan)

Beer and Johnston (2nd Ed, pg 195) infer that the B/E beam-bending theory is valid only where Saint-Venant's Principle holds. That is, points being measured are "far enough away" from the influence of end-effects.
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  Ben Floan Aug 28, 2008 7:45 PM (in response to Anthony Botting)
  
  Anthony,
  
  T beam width is 200in and height is 60in..... so are you saying this is not related to differences in E/B and Timoshenko theory but rather load concentration?
  
  Thanks again,
  
  Ben
  
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    Ben Floan Sep 2, 2008 11:35 AM (in response to Ben Floan)
    
    Jason,
    
    Thank you very much for that clarification and sketch....was a great help.
    
    Regards,
    
    Ben
    
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Beam Theory vs Code Results

Anthony Botting Aug 28, 2008 9:06 PM (in response to Ben Floan)

Hi Ben: According to Beer and Johnston, they are saying the theory's validity is not valid near load (or restraint) application areas. The term "near" is not defined further.
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Beam Theory vs Code Results

19411 Aug 30, 2008 4:17 PM (in response to Ben Floan)
For Euler Beam Theory you will see that the error is no longer negligible when the length/thickness ratio is less than 8 as a rule of thumb.

thickness=(largest cross section dimension)=200in
Length=2000in, 1000in, 500in, and 250in

Ratio=Length/thickness=2000/200, 1000/200, 500/200, and 250/200.
Ratio = 10 , 5, 2.5, and 1.25

In engineering terms, the transverse shear distorts the transverse cross section for short beams. In Euler beam theory one of the assumptions is that the cross section stay perpendicular to the neutral axis and it is still plane. See the picture below.

BeamTheory.jpg 59.7 KB
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Beam Theory vs Code Results

19411 Sep 2, 2008 1:04 PM (in response to Ben Floan)

Ben,

I made a slight mistake in the picture. I edited it.
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