Most of the time it is a good idea to frame in around basement duct work, so that the sheet metal can be hidden behind a drywall or other type of wall covering. Even if you have no plans to spend any time in your basement area, you still might want to frame around the duct and cover the frame with a building material just to improve the efficiency of the heating system. If this case, there is no need to frame around a cold air return, just build a soffit to enclose the hot air runs.
Since most basement duct work usually runs along the floor joists of the first floor, framing should be a straightforward task that involves building a soffit type frame to cover the metal duct work. These frames can be built with 2-by-4s as your wood stock and No. 12 or No. 16 common nails as your metal fasteners. Build each side piece from the 2-by-4s as if you were building a wall except you will only need a single plate at the bottom and the top.The height of the mini-wall should just clear the thickness of the heat duct and then you can cut 2-by-4 cross pieces, which will run from one step-wall to the other just underneath the heating duct. Keep your framing units square with the plane of the ceiling and make sure the height of the step wall is the same over the course of a long run.
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There is one major obstacle that you might encounter when you frame around the basement ducts: the I-beam that often runs underneath the floor joists as a major support mechanism of the house. This large metal beam is also an obstacle for the sheet-metal technician, who installs the duct work, so the duct work is likely not to be run real close to the I-beam. If it is, you can make your framing box big enough to cover both the duct and the I-beam. If the house frame is sagging, however, the house may need jacking and this task often involves work on the I-beam. It is best to consult an engineer, if there appears to be a problem with a sagging house frame.
Your wall covering for the duct must be fireproof or fire retardant. Check the building code for specific building requirements. You may have to use fire retardant sheet rock around the duct work. As long as you are building duct work for forced air, this is not a big concern. However, if there is a wood burning stove in the basement, leave the duct work exposed, because the air from wood burning stoves can get superheated. As a result, special efforts are necessary for both installing the stove pipes and the walls that surround them. In any case, a complete understanding of the building code is necessary.