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API 650, Annex E, E. Allowable Longitudinal Stress

API 650, Annex E, E. Allowable Longitudinal Stress

API 650, Annex E, E. Allowable Longitudinal Stress

I'm trying to better understand the equations in E.
Can someone help me understand what's in the coefficient 10^6 of the allowable stress equation 10^6*t/D? I think it must be some derivation possibly including 1.33FY/(12D/t) (1.33 for ASD times yield stress, all divided by D/t).
Also, the equation GHD^2/t^2 is a limit to determine thin vs thick wall stress criteria (I think), but how does it relate to the common limit of R/t? GHD^2/t^2 appears to have pressure in the equation.

Thanks in advance for your insight.

RE: API 650, Annex E, E. Allowable Longitudinal Stress

I think it states that the equations have allowance for internal pressure which helps keep the shell from buckling; thus the pressure term. Those are for seismic compression, not general compression, and significant seismic loading requires that the tank have product in it.
There's a similar general-purpose equation for compression stress in thin-wall cylinders in API-620, in the allowable stress section of the standard.

RE: API 650, Annex E, E. Allowable Longitudinal Stress

Great tip JStephen. I see the max allowable compressive stress for longitudinal loads only, is 1.8X10^6t/R, and for longitudinal an circumferential compression stress, it's 10^6t/R. Still curious where the large 10^6 coefficient is derived from?

Thanks again!

RE: API 650, Annex E, E. Allowable Longitudinal Stress

See Chapter 11 in Timoshenko's Theory of Elastic Stability, Eq. 11-9, for example.
He comes up with critical buckling stress = E*t/R * sqrt(3*(1-nu^2)), where nu = Poisson's ratio. I'm not sure how that compares numerically. There's probably a factor in there to adjust from theoretical to reality, plus a factor of safety. Some of these theoretical buckling-strength derivations can be 50% off.
There's been no end of work on problems like this and external pressure buckling of shells, the latter problem being motivated largely by submarine design issues.

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