Help for bending moment calc with Roark's Formulas 2

[Guest102023]

I have a circular, flat strainer plate that is fixed at the periphery and loaded by internal hydrostatic pressure. The arrangement, mounted between flanges, is just like a blind flange, only thinner. I am seeking the bending moment at the periphery, and it is not obvious in Roark's Formulas which one to use.
At this moment (sorry) I am staring at Table 11.2, case 2e.

 

[btrueblood]

brim,

Not sure where you are, but you may be at the wrong table. In my copy (6th edition), I'm at Table 24, case 10.b. This gives

M_ra = -q(a² - r₀²)/8a²

where q is the distributed (constant) pressure loading from r₀ to a, r₀ being the inner radius of the pressure load, and a is the outer radius of the circular plate. If the pressure is acting across the entire plate, set r₀ = 0. Note that M_ra has funky units - it's a moment per unit line load per unit^2 thickness dimension. The explanation of finding stresses from the moments is given at the start of the table.

 

[Guest102023]

I have the 7th edition, but I will search on that formula.

1 minute later:
You are exactly correct. I had scanned only through the sketches, of which only the simply supported variant is shown.

I assume that once I have Mra, the stress will come from the simple beam equation?

 

[prex]

The correct formula is M_ra=-q(a²-r_o²)²/8a² that leads to M_ra=-qa²/8 for a full load.
The stress is [σ]=6M/t² as you may find in Roark's introductory notes.

prex
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[btrueblood]

No, don't use the beam equations with the table formula bending moments. See the start/header of the table for more info. on the formulas and how to calculate the stress. Prex gives the right formula.

 

[Guest102023]

Thanks to both of you, that simplifies matters greatly.

 

[Guest102023]

prex,

I followed both formulae and I am getting a ridiculously high stress from the second one, plugging in a pressure drop of only 3 psi.

The local authority reviewer insists on including bending stress in the CRN application and I am stuck. Any suggestions?

 

[prex]

The minimum required thickness for a blank in ASME B31.3 is t_m=d_g[√](3P/16SE) where d_g is the diameter at the gaskets and SE is the allowable stress.
From the formulae in my previous post [σ]=6M_ra/t²=3qd²/16t², so you see where's originating the formula above (of course a is radius and d is diameter).
If you have a thickness lower than t_m from the formula above, then you are in troubles. I'm also assuming that your strainer has no holes at the periphery, otherwise things would be even worse.

prex
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