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Shell Loading

Shell Loading

Shell Loading

Is anyone aware of an analytical (non-FEA) solution of how to calculate the allowable forces and or moments that can be imposed on a roof manway of an API 650 oil storage tank?  The roof is a self supporting cone design, and the manway is not located in the center of the roof.  I think the failure mechanism would be local buckling of the roof plates, due to the compressive loading, large (local) radius of curvature, and thinness of the roof plates.  Any help would be greatly appreciated.  I’d even settle for the double infinite Fourier series type of solution that is common in analytical plate/shell mechanics.

RE: Shell Loading

Your best bet is to use a FEM program.  STAGS is one thatI believe could be used.  The fact that you have an offset cylindrical body intesecting a conical body, makes the intesection difficult to prescribe.  There is an analytical method of oblique cylinders.  A polish paper in the 1950s made an attempt to solve this problem.  I used a shell of revolution code to match the boundary conditions.  The solution was somewhat good, but not exact enough.  Dr.Charles Steele (Stanford Univ) while  developing FAST4 permitted such an analysis of two cylinders intersections using asymptotic expansion methods. Dr Enerst Paxson (Stanford) in his PhD distertation used expansion methods for the cylindr and cap intersection problem.  Very mathematical and very difficult to set up.  If you wish to persue any of these methods, I can give you the references at a later date.  A FEM model is perhaps the easiest.

RE: Shell Loading

You might try using WRC 297 (Local Stresses in Cylindrical Shells Due to External Loadings on Nozzles).  There is actually a free program available to perform this check at www.xcalcs.com .

RE: Shell Loading

Thanks to meca for the citation.
However the self supported cone roof of an API 650 tank is normally much closer to a flat plate than to a cylinder, so I'm afraid WRC297 is not very suitable.
As far as the bending moments on the manway are concerned I would suggest the use of trunnion formulae you can find in the Roark (Flat Plates chapter).
For the axial load I can't find a specific suggestion. By the way this type of structure will support only a very limited axial load. I suggest that the value is the allowable (live load + dead load) insisting on nozzle, that load being determined with the formula applicable to self supported cone roofs using the actual thickness, provided a reinforcing plate of area equivalent to the nozzle opening is used.
I'm afraid this is not very useful, but I can't find a simple method to prove any higher resistance (and wonder if a much higher resistance would be calculated by a detailed analysis).

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