I found some pictures of the corrugated metal raised beds I made last year.
Here is a picture of one of my new 4X4 foot X16 inch high corrugated raised garden bed. In this picture, I have added about 8-10 inches of hügelkultur wood and organics as filler to the bottom of the raised bed.
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Here is a picture after I filled the top 6-8 inches with a 1:1 mixture of my chicken run compost and top soil. I planted strawberries in this bed and they really grew well last summer.
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Like I said, I just used scrap lumber I had behind the garage to make the 2X4 frames which I then attached to the 4X4 corner posts. I used pocket hole screws for everything on the framing to hold it together. I bought a small bag full of roofing sheet metal screws with gaskets to attach the metal to the wood frames. I built each of these 4X4 corrugated metal raised panel garden beds for less than $25.00 each because I did not have to buy any wood.
Would love to see some pictures of your build and your experience using the 2X2 raised beds. Maybe a new thread on the subject. Depending on how you use the wood from the pallets, just be warned that reclaiming pallet wood can take more time and effort that you might think. Some of the pallets I have tried to disassemble have had some funky type of nails that made it very difficult to take the wood off. Other times, the wood would break into pieces and left me with nothing useable. I imagine you can save money using reclaimed pallet wood, but be prepared to put some sweat equity into the project.
There are a few YouTube videos of using pallet wood to make some nice raised beds. Worth a look to consider your options. Here is one guy I like to watch. This was his pallet wood build.