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(OP)
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.

The design of conical roofs usually does not require high technology. Design is based on a uniformly distributed load acting on a cone with forces resolved to calculate periferal and hoop stress. Provided compression stresses are kept to reasonable values plate buckling is not a problem.
Small local loads are not likely to cause global collapse, and can be handled with reinforcing plates. Openings can be handled on an equivalent area basis.
1. - Treat your opening as a nozzle. Take a section through the nozzle and from three points calculate an average circle of curviture.
2. - Treat the nozzle as if it were on the side of a cylinder of the diameter just calculated. Use any pressure vessel text book for nozzle stresses.
3. - Because of the taper of the cone a horizontal section at the top of the nozzle will be shorter than one at the bottom. As a result local stresses at the top will be more concentrated than at the bottom. Use the ratio between top and bottom dimensions to give an approximate stress concentration factor.
4. - If you think in terms of plastic design, or yield line principles the plate will buckle in a series of diamond shaped areas. You can be quite crude in mathematical refinement and still come up with meaningful results.
5. - If you are working with large concentrated loads, or are worried about deflections, then analyse a 3-dimensional wire frame model, or use FEA. FEA was invented because the mathematics of some of these problems can get ridiculously complicated.

See also Mechanical Engineering section, where the same question has been posted.

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