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Once the bracing is replaced and any problematic wiring has been removed, take out the drywall and insulation around the area to be replaced. Use a chalk line and reciprocating saw to keep your drywall cuts as straight as possible (Image 1). Tear drywall from ceiling (Image 2) and replace insulation that has fallen as needed.
You should build your support beam in advance of removing any support to eliminate the down time between the removal and replacement of support. Measure the length of the space to be spanned and allow at least 8" extra for setting on top of supports on each end.
In this demonstration, we used used 2" x 8" lumber with a piece of 1/2" plywood sandwiched in between to create the support beam. Cut the 2" x 8" lumber to proper lengths. Then, with a table saw, cut the 1/2" plywood into pieces 7 1/8" wide -- slightly less than the width of the 2" x 8"s. Cut enough plywood to extend the whole length of the 2" x 8"s. Lay the pieces of plywood between the two 2" x 8"s, making sure the plywood does not extend outside the edges. First, apply a generous amount of wood glue for extra reinforcement; then nail both sides of the new beam with 1-3/4" nails, using 3 or 4 nails per foot for strength.
Use a circular saw to take out the area under the joists where the new beam will fit. If necessary, cut through the joists to allow enough space for the beam to fit.
Angle the crown (the natural curvature of the boards) upward to keep the ceiling from bowing. Then attach the beam to the joists with nails. For added support, nail a joist hanger under each joist into the beam, making sure the hangers do not extend below the new beam.
Once the beam has been secured, remove the bracing and replace the drywall.