Stresses in Column-Supported Silo Cone Bottom

[TankDude]

I am analyzing a small silo with a cone bottom that is being supported by four columns. The cone has a compression ring located approx. 1/3 down from the straight shell to cone junction that consists of two circumferential plates with stiffeners located where it rests on the columns. I have analyzed similar silos in the past, however the major difference is the location of the compression ring. Typically the shell-to-cone junction is where the column tie-in is located and thus reinforced. Does anyone have any thoughts or good references for checking the bending that the column reactions exert on the cone plate? Thanks in advance.

 

[chicopee]

Perhaps I am off on this approach. Since you already know the bending moment on an elemental strip on the ring and the tank I would look at the "all too familiar" formula (fmax=6Mmax/bt^2) normally used on a base plate welded to a cylindrical shape is welded to. I would assume the bending moment only to be within the area of contact between column and ring and this contact area to be projected on vessel wall (obviously very conservative).

 

[JStephen]

Assuming the cone is not too flat, use the API-620 approach to find membrane stresses, treating the area above and below the ring as different freebodies, and neglect the bending (IE, do it the same as you would a compression ring). Perhaps keep compressive stresses in the ring fairly low to allow some conservatism.

If the cone were flatter, you could use the flat plate equations from Formulas for Stress and Strain, but they would likely give you some unreasonable results.

 

[JStephen]

I just noticed Roark's Formulas for Stress and Strain does include some information on bending in cones. It only includes loads at the open ends of cones, but it might be possible to apply two such cases to treat the inner and outer parts.