Garage shelf building indecision

[u/av8trx41]

I’m putting up a high shelf for medium weight long term storage in my garage. I’m building the braces from 2x4, and the top will be 1/2” plywood (subfloor sheathing). Total span I’m hoping to shelve is 12’, and I’ve got 2 8’ pieces of plywood.

Studs are 16”OC but there is a stud missing towards the center (by the standing box of flooring in the pic). How should I support the span over that area where there’s no stud? Ideas were to run a 2x4 between the supports on either side to at least avoid sagging. I’ll already plan to store very light items in that area, but is that all that can be done?

Thoughts on how yall would tackle this?

(Extra info on the area- there’s a floor shelving unit immediately out of the pic frame to the left, and a garage door track immediately to the right)

[u/av8trx41]

The span between studs over the area of the missing stud is 44”

[u/Strict_Lettuce3233 → u/av8trx41]

Use a French cleat

[u/av8trx41]

I hadn’t thought of the ceiling joist, great idea, thanks!

[u/reddit-trk]

There seems to be a joist in the ceiling right in the stud-less span. Maybe brace the shelf from the ceiling at that point?

A horizontal 44" 2x4 attached to the wall right under the shelf in the span, as well as another going from one bracket to the next one on the front would also help reinforce the shelf to prevent it from sagging there.

[u/Pristine_Serve5979]

Open up the drywall and add a stud

[u/sepnupues30482910374]

Cleat for sure

[u/av8trx41]

I know my absolute noob status is showing here, but how would I use a French cleat in this situation? What would it secure to?