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Help for bending moment calc with Roark's Formulas
2

Help for bending moment calc with Roark's Formulas

Help for bending moment calc with Roark's Formulas

(OP)
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.

RE: Help for bending moment calc with Roark's Formulas

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

Mra = -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 Mra 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.

RE: Help for bending moment calc with Roark's Formulas

(OP)
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?

RE: Help for bending moment calc with Roark's Formulas

The correct formula is Mra=-q(a2-ro2)2/8a2 that leads to Mra=-qa2/8 for a full load.
The stress is σ=6M/t2 as you may find in Roark's introductory notes.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Help for bending moment calc with Roark's Formulas

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.

RE: Help for bending moment calc with Roark's Formulas

(OP)
Thanks to both of you, that simplifies matters greatly.

RE: Help for bending moment calc with Roark's Formulas

(OP)
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?

RE: Help for bending moment calc with Roark's Formulas

The minimum required thickness for a blank in ASME B31.3 is tm=dg√(3P/16SE) where dg is the diameter at the gaskets and SE is the allowable stress.
From the formulae in my previous post σ=6Mra/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 tm 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
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

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