Stress and Flexural Stress on a Rectangular Sheet with Vertical Brace

[Mandrill22]

Someone else created a formula to find the stress on one of the sheets of, what amounts to, a rectangular pressure vessel. There is always a vertical brace bar running up the middle of the sheet and, if the stress is high enough, 1 or 2 horizontal braces are added to the left and/or right side (see attachment for 2 horizontal braces).

The formula the other engineer created to find the flexural stress is:
F = PH^2 / 8Z

The formula he created to find the stress on the left side of the panel with no horizontal braces is:
S = P(L/2)^2 / 4(9.525^2(1+((L/2)/H)^2)))

For the stress on the top half of the panel when there is one horizontal brace, he put:
S = P(L/2)^2 / 4(9.525^2(1+((L/2)/2H)^2)))

Where:
9.525mm (3/8") is presumably the mat'l thickness.
P = Vacuum pressure MPa
L = Length of tank wall mm
H = Height of tank wall mm
Z = Wall section modulus mm^3

Two braces is the same thing, but with the height divided into thirds.

Are these formulas correct? I can't find anything similar online.

 

[marty007]

If you have access to ASME VIII-1, compare your formulas to those of Appendix 13 (Vessels of Noncircular Cross Section).

 

[Mandrill22]

Unfortunately, I don't have ASME VIII-1.

 

[JStephen]

You might also check the flat-plate formulas in Roark and elsewhere.

 

[SnTMan]

Please enlighten me, what is the difference between "stress" and "flexural stress".

Your equation for "F" look an awful lot like the usual plate formula.

Regards,

Mike

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[JStephen]

If you build a box and pressurize it, you get flexural stress from the bending on the flat plate elements, but also tension as each flat plate is restraining the plates at right angles to it. So flexural + tensile stresses, with the latter being fairly small.

 

[Mandrill22]

SnTMan, I suppose by "stress", he meant tensile or compressive stress? Presumably tensile. The formulas end up producing stresses of similar magnitudes.

 

[SnTMan]

Question was directed at the OP.

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[Mandrill22]

Right, I am the OP. The equations were written by someone else, which is why I used 'he'.

 

[SnTMan]

So really, only "he" knows.

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[Mandrill22]

I'm just asking if anyone recognizes where these formulas came from. It seems like a simple problem, but I can't find the formulas the engineer used anywhere online.

 

[SnTMan]

Shocking to think, but not everything is online

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[Mandrill22]

That's why I am asking here. It seems like one of the many engineers on here should know what formula to use.

The formulas in ASME VIII Appendix 13 gave me a negative bending stress of -2682 MPa and a membrane stress of 10 MPa, neither of which are correct. Both should be in the hundreds, or close to it.

I'm just considering a rectangular, flat, hot-rolled steel plate, fixed on all edges with a distributed load and trying to find the stresses on the plate. In reality the plate is twice the width, with a vertical rib running down the middle, but unless someone knows how to solve that, I'll just consider it two, half-width plates. I would really appreciate any information.

 

[SnTMan]

At a fairly casual look these formulae do not appear to resemble either the flat plate equations per Roark, or the equations in Appendix 13. I also now see I was mistaken in my statement about the equation for F resembling the plate equation.

As well, I find the definition of the section modulus ambiguous. Unit width? Which direction, L, H? Who knows?

You are going to have to get the "Someone else" to explain it.

Regards,

Mike

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[prex]

From your drawing I understand that you are checking a flat plate (the end cover of a rectangular vessel?) reinforced by ribs, so not a stayed vessel as I had understood by the first reading of your post: you should clearly state what you are after.
The formula for F fails dimensionally: it gives a force per unit volume, so what is it? A stress per unit length has no meaning to me. This formula resembles the one for a simply supported beam with distributed load: so it could be for checking the vertical middle rib. However P wouldn't be a pressure, it must be a force per unit length.
In the first formula for S the factor (L/2)/H appears to be a form factor, but then this interpretation fails in the second formula, where the form factor would be (L/H) , not (L/2)/(2H)
What you have seems garbage to me.

prex
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