These men are bracing the building with rebar
Braces are used to keep something rigid (reforzar)
The lid is propped up/propped open with a piece of wood
I have not heard shore up, it's not very common. Perhaps it's used alot in the construction business, personally I don't know
----ejemplos
The wind kept blowing the door shut so I propped it open with a chair.
The ceiling of the cave is composed of weak rocks, so when digging the miners brace the ceiling with rebar to keep it from falling.
Espero que te ayude