Will my raised flower bed design be sturdy enough?
The floor is marginal, the deflection is almost an inch. This might be tolerable, but deflections also put a lot of stress on the screws. Damp soil weighs more than water, 96 lbs/ft3 according to one website, so it could be worse than these calculations.

Floor calculation:



Another concern is the strength of the corners. If this stand isn't level, there will be tremendous forces on the corners. Even if it starts level, settling could make it un-level. I would sink PT 4x4s 3 ft into the ground in the corners (or maybe 6 total), so there is no chance of the corners rupturing and it falling and hurting someone.

I don't know how to account for the corrugated steel, so I didn't calculate the side strength. 

Edit for new design:

Floor calculation:



2x6 side rail calculation:



Both of these calculations are OK. I can't comment on the remainder of the design without seeing a detailed diagram. I don't know how to analyze screw and bolt strength, so I wouldn't necessarily be able to confirm a complete design anyway.

If you are going to rest the 2x6 on top of the 4x4s, you need to be sure that there is no chance that it can slip off.