Bending Moment for Solid Circular Plate 2

[cap4000]

Does anyone have a formula for the bending moment for a circular plate with a concentrated load in the center. I have a few books on this issue but they are not clear. I also have Ram Advanse which can do a shell analysis. I can only model a square plate. Any tips will be greatly appreciated.

 

[prex]

Any elementary book on plate theory will give you that.
For a simply supported plate the radial moment is
M_r=P(1+[ν])log(R/r)/4[π] and of course it goes to infinity at the center.

prex

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[cap4000]

Thanks. I have the Cook and Young books whereby they know its infinity as you say. They do have there own formula to eliminate this infinity result but it was removed in a later edition.

 

[rb1957]

roark has a solution ... probably just like your text's "removed" solution ... replace the "point" load with a pressure applied to a very small area ... r' = sqrt(1.6*R^2+t^2)-.675t

but remember this is a plate solution, watch for large displacements, > 0.5t, which cause appreciable stresses on the mid-plane (not accounted for in plate analysis).