Remove the damaged floor joist by cutting the screws or nails that connect it to adjoining structures. Insert a metal cutting blade into your reciprocating saw. Insert this blade into the joint between the outside edge of the floor joist and the adjoining side of the rim joist. Cut through the screws that hold the wood in place. Cut all additional screws that attach the floor joist to the subflooring and support beams.
Detach the damaged floor joist from the overlapped or abutted floor joist it attaches to, using a screwdriver to remove screws or a hammer to pull out nails. Use a crowbar to pull apart any stubborn nails or screws. Tap the loosened floor joist with a hammer to knock it away from the seal plate and rim joist. Remove the freed floor joist from your work area.
Measure and cut the new floor joist to fit in the space left by the removed joist. Cut off any cut or broken nails from the subflooring with the metal blade of your reciprocating saw to provide a smooth surface for the new floor joist. Sweep away any wood particles, dust and debris.
Apply an even bead of construction adhesive along the top side of the new floor joist. This will adhere to the subflooring and help reduce squeaking. Place the edge of the floor joist against the rim joist and seal plate, attaching it back in place with screws. Attach the opposite end of the floor joist to the abutted or overlapped floor joist and any support beams that it rests on. Insert the screws at an angle to run them through both pieces of wood.
Attach the new floor joist to the subflooring from the room above. Locate the floor joist by measuring from the walls to the joist. Work casing nails between the nap of the overlying carpet. Drive these headless nails all the way into the subflooring and the underlying floor joist. Use a nail set to insert the tops of the nails beneath the surface of the floor.