I don't think you'll find a simple, good solution by hand.

You can take each face individually, treat it as a flat plate, apply whichever of Roark's formulas seems to fit the best, and check loading in that way.  Check it assuming simply supported and with fixed edges, and assume your case is somewhere in between.

You can isolate a section out of the box, treat it as a square frame, and design for bending in that direction.

You can treat the faces as slats running in the short direction, check reinforcing in that direction, then treat as slats crosswise and check reinforcing in that direction.

Roark may even have some equations for a rectangular tank which could be applied.

In any case, you may be able to come up with a satisfactory design by hand, but you could have some pretty wide variations between the design and FEA model.

This kind of problem is vastly simplified in many cases when the reinforcement required by loading falls below the required minimum areas- then you can make some pretty appoximate, but conservative assumptions, and still have a reasonable design.

Isn't this a relatively straightforward box culvert design scenario?  Just consider a 1m length of box culvert unit and carry out an analysis for all the different loading combinations that you have, and design for the worst case bending moments and shear forces for the walls, roof, and base.

The Reinforced Concrete Designers Manual has worked examples for this type of design. (UK publication).

Valleyboy

I did look at the Reinforced Concrete Designers Manual (not sure what publication) but I was unsure whether or not I could consider this a straightforward rectangular culvert due the massive size of the structure. Though sectioning the model into 1m length box culverts may be a fair approximation. I'll try that out.

You should be able to check your FE results against the tables in this book   

http://www.cement.org/bookstore/profile.asp?store=&pagenum=1&pos=14&catID=&id=192

It's set up for liquid retaining tanks, and I think your worst case will be when the tank is empty. So in that case your moments will be opposite of the table moments. I will have to look if the aspect ratio goes as high as the tank you have.