Replacing old duct work is not a difficult proposition for a homeowner, but it will require a certain amount of skill to complete. Since it is a replacement there will not be a need to add the extra work of reducing the flow out of the furnace or air conditioner. You will basically be replacing the trunk line and the vent lines. Measurements and hanging them under the house will be the most difficult parts of the job.
Remove all the old duct work and dispose of it properly or according to your local zoning laws. Measure all the runs that you will need to make. This will help you when you get under the house to have everything at the proper length before starting. Cut all the ducting to the correct length and place in the crawlspace.
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Hang the trunk line. This is the large shaft that comes directly off the furnace or air conditioner. Use the straps to hang the trunk line along the floor joists. The screw is normally a Phillip's head screw; you will need a Phillip's head bit to attach the straps that hold the trunk line to the joists. Make sure the supports are every other floor joist since this will cut down on rattling.
Cut all the holes in the trunk line where they will exit and run to the floor mounts. You may not have had to remove the floor mounts, but if you have, it is best to go through and mount them to the sub-floor before you start hanging the duct work. It will give you an extra support.
Clamp the farthest vent line into place. There will be clamps included in any duct work system. Tape around these clamps with the duct tape. This will ensure that no air escapes, making the system more energy-efficient. Attach the vent to the floor mount the same way. It should fit right into the tube and clamp down. Seal with duct tape. Continue this process until all the vents are finished.
Support the new duct work with the support straps. These will be hung along the floor boards. Since the duct work will actually fit into the cavity between joists, you will simply screw the supports into the floor joists. These should be every 4 feet or so apart.