Bending Stresses in Flat Plates using Roark's Formulas

[NoName1]

I am using Roark's 6th Ed for a flat plate with straight boudaries. I tried one case in Table 26 Case 8.b which is fixed on all four edges and has a uniform load over a concentric circle.

My question is why are the max bending stresses are not shown? The article for this table says that max stresses are included when available and critical cases otherwise. Max stresses are given for this load case with simply supported edges.

Thanks.

 

[Dinosaur]

I suspect the maximum stresses are on the boundaries for "large" diameter load circles, and may become maximum at the center for "very small" diameter circles; however, they may always be maximum on the edges. Think of a fixed-fixed beam with two equal point loads a set distance from the ends. Translate that behavior into a 3-D geometery as you describe. What do you get?

 

[MotorVib]

When I used Roark's for thin plates in the past it the max moment always depend on mounting holes locations and the boundary values. It don't take long to run both the inner and outer R moments. I only have thwe 7th and can't find the table that you are talking about.

Chris

"In this house, we obey the laws of thermodynamics." Homer Simpson

 

[JStephen]

Assuming this is the same as the load case in 5th Edition, I would assume maximum moment is at the center. I take "concentric" circle to mean a circle at the center. If the circle is "large", the load case no longer applies anyway.

 

[NoName1]

Thanks for the responses.

I did not explain myself well. For this case two stresses are given. The larger of the two is along the edge (which is where I think the max should be) and the other (lower)stress is at the center.

Is the formula for the stress along the edge actually the maximum eventhough the formula does not specifically state max? If is not, why are these formulas given (critical values?) instead of the maximum values.

 

[JedClampett]

I don't understand your question. The fifth edition has sigma b for the plate center and the middle of the long span. Did they leave this out in the sixth edition?
I've found that while Roark is a pretty good reference, you can't beat going to the source material. In this case, it's Timoshenko, "Theory of Plates and Shells."

 

[NoName1]

Yes it does say sigma b, but different load cases say Max sigma = ....

 

[JedClampett]

I'd assume that the stresses at the center of the plate and at the center of the long edge are the maximums.