There are two main problems to be handled:
1) Configuration of the silo so that it flows as desired.
2) Design of the resulting silo.
There is actually an ASME short course available on #1.
On the second item, the main issue is that there is no end of variation of details, so it's hard to make one spreadsheet or software that handles it all. Skirt supports are far and away the simplest to design, but people don't like them due to access limitations. There are all kinds of leg details used on silos, and probably each could be evaluated in multiple ways. Adding in potential vibration, lack of symmetry, thermal effects, etc., complicates it all more.
Gaylord and Gaylord had a silo design book. One thing I ran across in that is one set of equations for product pressure are recommended. Then about two pages after that, "So-and-so recommends THESE factors" and using those factors, you get completely different results. The conclusion is that there is a fairly large potential variation in the actual loads produced on the silo.
I believe it was the "Structural Engineering Handbook" that had a nice section on designing the lower shell using two stiffeners and treating it as a beam. But, when I looked at that, they never said what to do about torsion in that beam- which turns out to be a major item. So be aware that some of the methods out there are not exactly perfected, either. See my separate post on Bednar's leg-design procedure, which is another similar example.