Replying to Plywood backing necessary?

I just built two 8 foot boxes, and I'm about to put the topsheet on the second box. For the first box, I put 2x4's along the width of the box directly underneath the topsheet. I put a 2x4 every foot, but now I just read some threads saying that it's a good idea to put a piece of plywood between those and your topsheet to provide support for the plastic so it doesn't crack. Is that so necessary that I should take off my topsheet and put some plywood in there?

The boxes are 8 feet long, 1 foot wide, with 1/2" HDPE