We've decided that we can fit four 4' x 4' gardens in the Strip Garden area. My father-in-law was in town this week and he helped me to build our frames.
Mel's book says you only need a 6" depth and that you can stack boxes in order to grow plants like carrots that require deeper soil. We decided that we didn't want to deal with that so we bought 12" deep two by fours.
Here's what the frames looked like after construction.
I didn't take a good picture of the construction, but here's what the frame looks like empty.