Cylinder stresses in flowing system

[aspearin1]

I need to find some sort of correlation to estimate the buckling forces for the following conditions:
Perforated SS (.040 thickness) cylinder with a welded seam. This cylinder undergoes a uniform stress around its periphery (outside of cylinder) via flowing water (pressure). I need to be able to estimate the maximum allowable water pressure above which this object will buckle, taking into account material, surface area, geometry, and if possible weld type. Any help would be appreciated.

aspearin1

 

[bvi]

There may be some more theoretically correct approach, but my inclination in this type of problem would be a simple approximation. Determine an equivalent thickness for the cylinder based on the hoop stiffness of the perforated cylinder. In other words, an unperforated cylinder with the same hoop stiffness as the perforated cylinder. This should simply be an area ratio calc. Then use the effective thickness in a standard cylinder buckling calc (e.g. per Section VIII, Div 1, which includes appropriate safety margins. I would also go back to theoretical buckling papers for cylinders to confirm hoop stiffness is the critical parameter.

An additional check would be to make sure the individual ligaments do not buckle under the compressive loads they are subject to (beam buckling). Rather than sweat it too much, assume the beam length is the hole diameter, the width is the minimum ligament width, the end conditions are pinned, and see if it works, with adequate safety margin. If it doesn't, work the problem in more detail.

 

[prex]

I wouldn't take an equivalent reduced thickness as proposed by cb4: as the critical pressure for elastic buckling depends on the cube of the thickness (that is on the bending stiffness), that procedure would be excessively safe, unless buckling is in the plastic region.
My proposal is that an effective elastic modulus is determined simpy multiplying the actual one for base material by the ratio of unperforated area to full solid area of tube. This will in practice reduce the critical pressure calculated for a solid cylinder by the same ratio.
Then a plastic critical buckling pressure should be calculated with the procedure suggested by cb4, or in other words: take an equivalent thickness reduced in proportion to the ligament width to hole pitch ratio.
Then the minimum of the two critical pressures will be used.
Hence ASME VIII procedure is not suitable in this situation, as it mixes up the two phenomena of elastic and plastic buckling into a single check. The separate formulae available in many textbooks for critical pressures should be used.
I agree also with the remark of cb4 on the stability of the single ligaments, but would also add that they are curved and this could have a non negligible effect on the calculation (depending on hole diameter to pipe diameter ratio).

prex

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