This is the email I sent on this very subject:
"Hello Naganarayana
In ASME Section VIII, Division 1, you will find in Appendix 1-5 and Appendix 1-8 the cone to cylinder junction analysis. Where the cone is attached to the cylinder, there is an inward force all the way around the junction which is pulling the cylinder radially inward. This force has to be counteracted by a junction ring which prevents the collapse.
I have been an engineer for a long time. In my early years, I worked in Cape Town, South Africa. I used to visit the wineries. At those wineries, the wined was stored in stainless steel tanks with shallow cone bottoms. Sometimes when the tanks were completely filled, the bottoms would collapse. I was called in to solve the problem. By knowing why they collapsed, I was able to solve the problem. I simply told them to put a certain size ring at the junction, and the collapsing no longer occurred.
A little knowledge goes a long way."
Now, in the case of tanks that did not fail, either you were lucky, or the forces in the cone were not sufficient to cause collapse (I have no way of knowing). There is an analysis of shallow cones in the API 650 storage tank code. If you go to Appendix F in that code, you will be able to do the cone junction analysis.
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Sincerely,
Ray Delaforce
CADWorx & Analysis Solutions
Hexagon PPM