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You might be ok if the skins are properly bonded to the framework as that's how torsion boxes work, though I'd have more of a framework grid internally. As said though it's a long span.
For reference I build a 3m x 2m torsion box to use as a base for a router sled and it flexes less than that when only supported by sawhorses. I did use a 10cm frame though.
I’m making a couple of torsion box alcove shelves.
2.3m span with 30x30 battens which are fixed together and to studs.
It’s solidly attached but I can flex the middle of the span up and down by 5mm with my hand. Is that going to sort itself out with 12mm ply glued and nailed to top and bottom?
Wondering if I need more spans or worst case some floor braces?