Here is an example of what happens when you remove material from only one side of a piece of lumber. This is a piece of red oak has been in my shop for a couple of years and was flat. It is 30-1/2" long, 3 inches wide and 3/16" thick when I started work on it last night. Because the piece was too thin to run through my planer by itself, I attached it with double sided tape on a carrier board. I removed just under 1/16" of material from one side. When I finished up last night, I left the thin piece on the carrier board. This is what I found this morning when I went to the shop.
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The piece is bowed up 1/4" in the center of the 30 inch length. This won't present a problem as the piece is so thin and it will be glued in place when all is said and done.