Circular Flat Plate

[mmaurigi]

I need to calculate the thickness of a circular flat plate. This is a false bottom in a pressure filter. The plate is welded inside the vessel all along the circumference. The plate also has a 10" pipe welded to its underside for center support. I have a 5th ed. of Roark's, and I think the calculation in that edition that applies to my situation is in Table 24, Case 3h, Fixed Outer Edge, Fixed Inner Edge. The information about my plate is:
Outside Rad., a = 59.5"
Inside Rad., b = 5.375"
Pressure, q = 15psi
Material is SA36 C/Stl.
Poisson = 0.3
E= 30,000,000 psi

I went through the formulas to calculate the constants C2, C3, C6...etc

When I get to the moment calculation, I come up with a negative value for the moment. Solving for t, you can't take a square root of a negative number.

If someone out there has a 5th Edition of Roark's could you look at case 3h and using my values above, tell me what I'm doing wrong.

Thanks

 

[JStephen]

The moment can be positive or negative. Just use the absolute value for finding thickness.

The negative moment just means it's in the opposite direction, so that one face of the plate is in tension instead of the opposite face.

If the plate does not have a hole at the center, you could also use the equations for a full plate, calculate deflection due to the uniform load, then calculate a line load at the pipe radius to make that deflection cancel out at the inner pipe. Perhaps more work, but should be more accurate, particularly if the plate thickness comes out much larger than the pipe thickness.

 

[prex]

Don't take the fixed condition at the edges, this is unrealistic. A fixed condition means no rotation at all, but your weld at the periphery (particularly if welded on one side only) and the shell wall will rotate. Also in the center there will be some rotation, though much less than at the outer edge.
If you take the supported-supported condition you'll be on the safe side. The suggestion by JStephen is a good one if you want more realism, but still with a hinged outer edge.
In the first site below, under Plates -> Simple bending -> Annular pl. , you find calculation sheets equivalent to Roark's formulae.

prex

http://www.xcalcs.com

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[cbrn]

Hi,
other possible approximation of your "real-life" connection: calculate for clamped, calculate for hinged, and average the two. In many cases that leads to results very close to the experimental.

Regards

 

[40818]

I agree with cbrn, take the average of FF and SS.
You could also check for the max stress/deflection under simply supported, and also the edge fixity stress due to assuming its fully fixed.
Or do an FE model to checkl your handcalcs and also derive accurate edge fixity rotations