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Plate four points bending equation for a plate

  1. May 15, 2012 #1
    Hello,

    I am no mechanical engineer and my knowledge in bending is limited to Euler-Bernouilli beam theory.

    I wish to analytically calculate the normal stress of a plate bent by four points bending. I have already calculated this stress for a beam.

    However I cannot apply the beam theory to a plate.

    Does someone know a tutorial or an article giving specifically the four-points bending of a plate and its solution?

    Thank you
     
  2. jcsd
  3. May 15, 2012 #2

    PhanthomJay

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    :eek: That's a tough one that i don't think even Roarke's Stress and Strain covers. This old timer took graduate courses in Theory of Plates and Theory of Elasticity eons ago. All I remember is a bunch of unsolvable partial differential equations.
    Stay away from square or rectangular plates supported on 4 corners. Consider a statically determinate circular plate instead, supported at 3 equidistant simple supports, then get a copy of Roark's book. Beyond that, i cannot help, sorry.
     
  4. May 16, 2012 #3
    Well Roark's is definitly the go to book but like PhantomJay I dont remember seeing that in there but you never know.

    My solution would be use FEA. I know you wont get an analytical solution but you may be able to validate it via a simple experiment.
     
  5. May 17, 2012 #4
    "Theory of Plates and Shells", Timoshenko & Krieger

    Article 49, p 218 in my copy

    "Rectangular Plates Having Four Edges Supported Elastically or Resting on Corner Points with All Edges Free"
     
  6. May 17, 2012 #5
    Nice reference thanks.
     
  7. May 17, 2012 #6
    Roark is oft quoted at PF, (as here) however a much more modern book ( and at least twice as thick) is

    Formulas for Stress Strain and Structural Matrices

    Pilkey

    go well
     
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