At ten feet they won't sag noticeably under their own weight, but that doesn't mean they'll remain straight. It's very likely that they'll warp, twist, bow and otherwise deform somewhat as they dry out. How straight do you need them to be?

Thanks sooooooo much for your response, Joh!

To keep that likely warp, twist or bowing to a minimum, would it help ANY to screw two or three short sections of 4x4's between the 2x4s along the 10-foot space, sandwiching the two 2x4's together? Or would it then still warp, twist and bow together.

While my proposed ?structure?, LOL, will be otherwise and additionally attached to a larger existing garden trellis to stabilize it THAT part, please consider this proposed section a free-standing garden structure that will be seen mainly from the front, the front being the 12-foot length).

PT wood is designed for ground contact. The load capabilities are reduced because the chemicals weaken the wood. 2x4 PT are some of the sorriest boards ever. They commonly break where there is a knot. Heart Redwood or Clear Vertical Grain Douglas Fir would be stronger. You can paint or seal it for water protection.

To get strong straight boards:
When you buy a board, look at the end grain. Get the boards with the most growth rings, spaced tightly together. Throw back ones that have the center of the tree, they will twist the most. Big surface knots are also to be avoided.

Thanks, aidan, for the "strong straight boards" advice. We'll use painted vertical grain Doug Fir for the 2x4s.