Bulk Solid Forces on A Rectangular hopper

[CardsFan1]

I am looking for a good reference to design bins and hoppers. I have a copy of ANSI/ASAE S433.1 "Loads Exerted by free flowing grain on bins".
But the document excludes mass flow hoppers. I think my hopper may be a mass flow condition. The sides are pretty steep. I have a copy of Gaylord and Gaylord "Design of Steel Bins for Storage of Bulk Solids" but it is very theoretical.( I'm still studying it). Im looking for a reference that is more "cook-book."

 

[r13]

I think this paper might get you to start. Link

 

[JStephen]

Several years back, I took a short course on flow of solids. One lesson from that was that for actual flow design, you need test data from your specific product (as opposed to looking up generic products in a reference book). For actually designing a hopper to flow, that is one of those fields where it is advantageous to do a whole lot of work in it, or none at all.

In that Gaylord and Gaylord book, in talking about Jannsen's equation, they say to use these two coefficients to determine pressures. Then a page or two over, they say "but so-and-so recommends THESE coefficients be used" and give some other values, which of course give you completely different results. The moral from that is that unlike a liquid tank, there are potentially large variations in the forces generated against the container.

For circular silos in smaller sizes (say, 12' or smaller), thickness will generally be governed by minimum thickness. And in applying Jannsen's equation, the general result is that more vertical drag on the shell produces less radial pressure and vice versa. So one approximation that can save a lot of time is to treat the product like a liquid to determine maximum radial load on the shell, and to assume the entire product is supported as a plug to determine maximum compression in the shell. If those two assumptions give you reasonable thicknesses, you should be good for any condition in between. If that approach gives you unreasonable thicknesses, then you need to look at it in more detail (but keeping paragraph #2 in mind!)

I believe there is a volume available through AISI by John Buzek, I would consider that as another source.

 

[human909]

The EU standard is far more modern and more comprehensive. If you do find a cook book let me know!

I do a fair bit of hopper design. Mostly I just calculate design loads and go from there. Sure there is a bit of number crunching but once you've done that then it just about getting the sheet thickness and stiffener spacing right.

 

[CardsFan1]

Thank you for all of the suggestions!
One take-away I get from Gaylord is that if it is a "shallow" bin, it is conservative to just use Rankine pressure formulas. I think my bin fits the shallow criteria, so I will pursue that route.
The S433.1 document states that it is not valid for mass flow hoppers. Is the hopper normal pressure higher in a mass flow than in a funnel flow?

 

[human909]

Sorry I meant to link this earlier.

https://www.phd.eng.br/wp-content/uploads/2015/12/en.1991.4.2006.pdf

Also this is a good summary of various codes:

https://core.ac.uk/download/pdf/82212409.pdf

Of course codes shouldn't be your only source but they can often be used (or overused) as a "cookbook".

Is the hopper normal pressure higher in a mass flow than in a funnel flow?

Yes. You have a significant change of direction in mass flow, particularly at the point of transition.

 

[CardsFan1]

human909, Thank you for the references. I skimmed through it, and it looks like it answers my question. I am not designing the function of the bin, only the checking the structural capacity.