Circular Flat Plate
Circular Flat Plate
(OP)
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
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





RE: Circular Flat Plate
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.
RE: Circular Flat Plate
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 : Online tools for structural design
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads
RE: Circular Flat Plate
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
RE: Circular Flat Plate
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