Truncated Cone Under Compression Loading

[Bower7]

Hi All!

Does anybody have a good reference for stresses in a truncated cone under a compressive load on the smaller diameter?

 

[chicopee]

Do research on bins and bunkers and the ASME section XIII on cone designs. Altho. the ASME section XIII primarily deals with internal pressures, their code may have information on external loads. I suggest that the Pressure Vessel Design Handbook by Bednar may be of value in your research. Subject on Bins and Bunkers design that I have is on rectangular and square structures detailed in the Tubular Steel Structures by the James E. Lincoln Arc Welding Foundation but Appendix A has in figure 16 a design which shows an inverted cone subject to a load on the small end which has a flare.

 

[MJCronin]

Does Roark have something on this case ??

As I understand your question, you are interested in elastic instability, correct ???

MJCronin
Sr. Process Engineer

 

[GregLocock]

Solid or a shell?

Cheers

Greg Locock


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[Bower7]

Thanks for the replies!

I’m not familiar with the ASME code but I’ll have to take a look on Monday.

I’m more interested in stress distribution rather than instability. I have a FEM model and need to do some verification calcs on it. NASA has a nice paper on instability, but unfortunately no information on stress distribution. I have checked in Roarks (albeit an older version) but strangely didn’t find a case that fits the bill. I’ll have to try find a newer version.

This is a thin truncated conical shell.

 

[GregLocock]

Is the minimum diameter reinforced or is it a pure shell?

Cheers

Greg Locock


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[Bower7]

Minimum diameter is reinforced, maximum diameter can be considered fixed to the ground.

 

[robyengIT]

in Roark's there is this (you can change sign of the load)

 

[dhengr]

Bower7:
With your lack of any fundamental understanding of your problem, why would we trust that your assertion of fixity at the base can be trusted? That would be a function of the relative stiffness of the various parts at that joint, and the exact means of their attachment. Why wouldn’t this be treated like a thin shell tube (a tube column) under a compressive loading? Although, you haven’t bothered to give any dimension, thicknesses, loads, engineering details, etc. Are we dealing with a 100 ton load and 2” thick shell or 100lbs. and .125” thick shell, there is a difference in how you would approach the problem. Is the loading concentric and uniform? Then the loading (bearing stress) would be B[sub]f[/sub] (lbs./inch) or B[sub]si[/sub] (lbs,/sq.inch) = P/(circumference)(shell thickness) at the top. The axial force/stress in the shell would be slightly larger B[sub]f[/sub] or B[sub]si[/sub]/ cosθ, where θ is the cone angle from the vertical. Then, depending upon the length of the tube, the diameter and thickness of the tube, you do have buckling issues which must be evaluated.

 

[btrueblood]

Chapter 14 Elastic Stability, Table 35 of Roark's has an equation for the buckling of the truncated conical shell, ends held circular - for various combinations of axial load and internal/external pressure. They include a knockdown/safety factor based on a fairly large number of tests.

 

[dvd]

This seems similar to behavior of a belleville washer.