You can use 2x4 or 2x2, for short spans. Some use solid wood boards for the horizontals, some build ladders, then hang the assembly from the floor above as a unit. Some use a pair of left-over I-joists, if deep enough. Be sure to install fire-blocking above the unit when running perpendicular to the joists (as in the picture -top right side, between the joists) to stop any fire from spreading more than 100 sq.ft. If no blocks present, fire in the enclosed chase will spread to the whole floor system in minutes, popping up all over the house. And then your homeowners insurance would not cover the loss because the framing was not to code. This on fire blocking from kctermite: http://www.diychatroom.com/f98/how-fireblock-framing-37190/
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