so the first gate to brace on Black Gate (gothmog's tent gate) can't be repaired because the chest doesn't work. You should check the second one aswell, just in case (the warg pits)
On Minas Tirith (main gate), braced wood does 0 impact on gate. it gives me points when someone bashes it, but it doesnt add health to the gate. it just ignores it.
Then we retreated to the second flag, where the gate could be closed and opened independently of the wood right inside it: