Plate four points bending equation for a plate

AI Thread Summary
The discussion centers on the challenge of calculating normal stress in a plate subjected to four-point bending, with the original poster lacking expertise in mechanical engineering and relying on Euler-Bernoulli beam theory. Participants suggest that traditional beam theory may not be applicable to plates and recommend consulting Roark's "Formulas for Stress and Strain" for guidance, although its coverage on this specific topic is uncertain. An alternative solution proposed is the use of Finite Element Analysis (FEA) for validation through experimentation. Additionally, references to Timoshenko & Krieger's "Theory of Plates and Shells" and Pilkey's "Formulas for Stress Strain and Structural Matrices" are mentioned as potential resources. Overall, the discussion highlights the complexity of the problem and the need for specialized resources or methods.
pierebean
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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
 
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pierebean said:
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
: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.
 
Well Roark's is definately the go to book but like PhantomJay I don't remember seeing that in there but you never know.

My solution would be use FEA. I know you won't get an analytical solution but you may be able to validate it via a simple experiment.
 
"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"
 
Nice reference thanks.
 
Nice reference thanks.

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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