Mastics and tapes do not hold ducts together. To secure most duct joints and duct sections you need to use screws, staples and draw bands. Screws are often the only way of preventing joint separation and movement.
Securing insulation to the ducts
It's not just the ducts that need to be secured. Insulation materials used around the ducts should also be properly secured by using pressure-sensitive tapes and draw-bands, or rust-resistant wire, staples or even nails.
Pressure-sensitive tape is mostly used in foil-faced insulation materials. The tape should be wrapped several times (3, at least) around the duct surface.
Draw bands and multiple-staggered wraps of tape are used to secure the overlap of the insulation material around the joints. Other fasteners are mainly used with unfaced materials, and applied along the whole length of the insulation, every 15-20 inches or so.
Screws are particularly useful to secure duct boots and around the joints, in round sheet metal ducts using sleeves and fittings.
Images credit: DOE
For vertical connections, install screws in conjunction with draw-bands, to prevent slippage: see image above.
Draw-bands are used to join two flexible ducts or to join one flexible duct section to other type of duct. In this case, the flexible duct is fitted over a collar and attached with two draw-bands: the first to secure the inner lining and the second to attach the outer insulation jacket.
Staples and Tape
Fiberglass duct boards can be fastened using embracing staples. If the use of staples is not feasible, try pressure-sensitive tapes.