The thicker the boards, the less need for bracing to prevent bowing. If you are using 1" boards, then I recommend bracing along the sides. If they are at least 2 inches thick, you will probably be OK, however store-bought dimensional lumber of 2 x 4 is going to be 1 1/2 x 3 1/2. I have 4 x 8 x 12 raised beds made from Tamarack wood that is a true 2 inches thick, and I did not add any middle braces. I have had no problem with bowing. Besides the true 2 inch thickness of the boards, I believe another reason I have not had any bowing is because the soil mixture is never walked on so it doesn't get packed down, and it is rather fluffy and light...even in the Spring, I can easily dig with my hand right down to the bottom. I would recommend something like Tamarack over Cedar just because it will be cheaper. Depending on where you live, it may be harder to find, though. I got mine from a local guy who mills his own logs.
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