API 650, Annex E, E.6.2.2.3- Allowable Longitudinal Stress

[Soln]

I'm trying to better understand the equations in E.6.2.2.3.
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.

 

[JStephen]

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.

 

[Soln]

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!

 

[JStephen]

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.