Deconstruct the coefficient "1/10000" in the API 650 required section for stiffener equati 1

[Soln]

I'm designing a tank with an allowable stress of 38000 psi. Can anyone help deconstruct the coefficient "1/10000" in the API 650 equation for determining required section modulus for stiffeners on p.5-70? Is there an allowable stress in there that I may adjust for the high allowable I'm using? I'm also suspicious that there may be an allowable stress in the equation for calculating the max height of unstiffened shell p.5-68. Or, it may simply be a function of modulus of elasticity (E), which won't help. I like being able to unwind the coefficients, so any help is much appreciated.

 

[JStephen]

I'm curious also. That equation has been around forever, but I've never seen a derivation.

Since it's used with the formed-plate windgirders, I would assume that the strength of them is governed by buckling rather than yielding, in which case, you wouldn't get much benefit from a higher-strength steel.

If you consider radial loading of the shell all around and check stability of the wind girder for buckling, you get a requirement for minimum moment of inertia, rather than section modulus. If you assume various distributions of wind loading and support on a circular ring, you get requirements for section modulus, but I haven't see a particular combination that gave me that coefficient.

 

[JStephen]

Aha, actually found an answer via Google!

From a previous post on this very site:
"The API equation, while based on an idealized wind load pattern, is not approximate. The section modulus requirements for tanks under 200 ft in diameter is intended to limit bending stresses to 15ksi."
Steve Braune
Tank Industry Consultants

And then a more complete description here:

http://mycommittees.api.org/standar...lts/Std 650/650-728 003 Study Wind Girder.pdf

And I note that the equation is not "approximate", although assuming that 25% of the load on the shell gets transferred into the wind girder would seem to be pure fudge factor, which explains why it can't be simply derived. IE, you can simply derive it if you are willing to take your final result and multiply it by some arbitrary number to match the equation you're trying to derive.