# Plate four points bending equation for a plate

1. May 15, 2012

### pierebean

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. May 15, 2012

### PhanthomJay

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.

3. May 16, 2012

### Dr Bwts

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.

4. May 17, 2012

### Studiot

"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"

5. May 17, 2012

### Dr Bwts

Nice reference thanks.

6. May 17, 2012

### Studiot

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