You cannot take a piece of a hut off on Yom Tov as you are breaking a house. However, taking wood next to the wall is permitted.

Wood pieces which are scattered in a field are muktza. If you gathered them, they are not muktza. In an enclosed area, even if the wood is scattered, they are not considered muktza.

R’ Yehuda says an enclosed area means that it is close to the city. R’ Yosse says if it has a lock, even it is just in the techum [2000 amos], it is permitted.

Beitzah 4:3

You cannot take wood from a beam or from a beam that was broken on Yom Tov as they are considered mukstza.

Even the wood that you use for fire, you cannot cut it with a normal ax.

In the case of a locked house with a weak door, where the door gets broken down, the food in the house is permitted. Reb Meyer says you can even knock down a weak door.