Minimum Flat Plate Thickness

[Nikk5]

Hi,
I need to obtain the minimum thickness of a flat carbon steel plate under the following conditions:

1) Circular bottom plate (radius = r) under uniform pressure P, and the plate is fixed at the periphery.
2) The plate is resting on the soil, and the soil has enough bearing capacity to prevent deflection of the plate.
3) Since I want my deflection to be "0", the plate will be only under simple compression load.

Is there any formula or method to calculate the required thickness under this conditions (compression load) ?

Thank you !

Nikk5

 

[IRstuff]

I don't think your conditions are sufficient. If you assume that the soil will not allow a deflection, then your plate can be an atomic monolayer. Moreover, your plate will sag, regardless; there is no possibility for a zero-deflection result. You must establish how much deflection you are will to allow that's non-zero.

TTFN
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[Nikk5]

Ok,
If I define a max allowable deflection "y"= 4", and my flat plate is 0.250 thick, 45' diameter, uniform pressure of 20 psi

How can I verify if thickness is ok ?. I have played with Roark's formulas but since deflection is quite bigger than thickness, they don't seem to fit.

Thanks,
Nikk5

 

[zekeman]

You want "worst case" the problem which is to assume a peripheral simple support, using Rourke or equivalent get the deflection as a function of R and the thickness.
Now equate that deflection to the allowed.

 

[IRstuff]

In the 6th edition, that would be table 24a Formulas for maximum deflection and maximum stress for flat circular plates of constant thickness with large deflection. The example in Mathcad has a modulus of 30 Mpsi, which results in a 3.049in deflection. max stress comes out to be 60.47kpsi

TTFN
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[rb1957]

"2) The plate is resting on the soil, and the soil has enough bearing capacity to prevent deflection of the plate."

if the soil is preventing the plate from deflecting, then the plate is merely transferring the pressure load from one face to the other ... 0.001" should be thick enough.

if the soil is not supporting the plate ('cause you're calcuating deflections from Roark) you should be aware that Roark's tables are based on plate bending, and if the defelction predicted is greater than the thickness then the plate is developing membrane loads (hoop stresses) and carryng the pressure as tension. and the fasteners around the edge need to transfer this load into the rst of the structure.




Quando Omni Flunkus Moritati

 

[IRstuff]

The OP has already stipulated a maximum of 4" deflection. If the soil is able to resist, that merely reduces the stress in the plate; the worst-case is still with the plate unsupported in the middle and not touching the soil.

btw, I entered 45-in as the radius, not the diameter, so the deflection is much smaller, more like 0.775-in, with 50.64-kpsi stress

TTFN
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[Jboggs]

The best way to guide your thinking on this is to ask yourself - exactly what failure mode are you trying to address? If the soil is supporting ALL the force of the plate, then the plate is under zero stress and the only thing it does is contain whatever medium is above it. The bottom line on this is that you need to re-phrase your question. Get more specific. What type failure are you trying to prevent?

 

[rb1957]

"The OP has already stipulated a maximum of 4" deflection" ... and the OP has already stipulated that the soil is supporting the plate with zero deflection ... pick one !

Quando Omni Flunkus Moritati

 

[dhengr]

Nikk5:
Are you talking about the steel bottom plate of a petroleum storage tank which is 45' in dia.? If so, that is a whole different animal than what everyone here is talking about. It’s basically a tension membrane supported out at the foundation and tank wall. The liquid loads are basically carried by the sub-soil under the floor plate, so there is no real plate bending. There may be some secondary plate bending due to detailing and welded joints however.

 

[fabtank]

I agree with dhengr that this sounds like the bottom plate of a steel storage tank. Typically this would be designed to API 650, which specifies a minimum thickness for bottom plates of 1/4" + corrosion allowance.