I'm wanting to build a 12'x12' root cellar out of foundation grade treated lumber. The walls are 2x8 construction 16" o.c. sheathed in .75" plywood.

Im planning on covering the top with 24 inches of silty clay loam soil. I estimated a dead load at 34,000 lbs or 222psf. There won't be a live load. Can anyone help me size my ceiling joists?

That is a tremendous dead load. Add water from rain or snow and it is even higher. Why so much dirt? I would consider thick expanded foamed Poly styrene billets with just a couple of inches of dirt. I cannot find a dead load over 100 PSF for comparisons.

I don't think a root cellar has to be this complicated. Mine is located in the basement under the veranda. It works.