Slide a flat bar underneath the ends of each cross brace, and carefully pry them up to remove them, one at a time.
Remove all of the nails from ends of the braces and any stray nails that may have been left in the floor joists, using the claw end of a hammer.
Place the braces, one at a time, on the table of a miter saw, with the mitered ends facing up. Adjust the miter saw to cut at the same angle as the mitered ends. With the miter saw, saw the 2-by-2-by-96-inch boards to the length of each respective brace that requires replacement.
Fit the replacement braces in place between the floor joists, one at a time. Hammer two evenly spaced 8-penny nails through each end of the braces into the joists to secure them firmly in place.
Slide a flat bar underneath the ends of each cross brace, and carefully pry them up to remove them, one at a time.
Remove any stray nails that may have been left in the floor joists, using the claw end of a hammer.
Measure the length of the basement along one wall that runs perpendicular to the direction of the floor joists, using a tape measure. This is the measurement required for the strapping boards.
Lay out the strapping boards on a work surface. Measure and mark the strapping boards to the measurement from Step 3, using a tape measure and pencil.
Place each marked strapping board, one at a time, flat on the table of the miter saw. Cut each strapping board to length, using the miter saw.
Hold each strapping board perpendicular across the floor joists, one at a time. Space the strapping boards every 16 inches on center across the entire width of the basement.
Hammer two 8-penny nails through the strapping boards into the floor joists at each intersection along the entire length of the boards.