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I am building a cantilevered second floor deck with overall dimensions of 6'6" out and 15' wide and has a glue lam support at 3'6".  Nothing but mamico and wood handrails above.  We are using 2x12's for joists on the deck which meet silent floor joists at wall.  My question what is the minimum my 2x12's can run inside beside the TJ's.

RE: cantilever

Consider that you have 2 points of connection for the extension of the 2x12 inside the TJ.  The first connection let's consider to be the rotation point, the second will be the shear point.  This will result in a point load on the TJ and the 2x12 equivalent to cantilever moment at point 1 (if assumed to be fixed for the moment) divided by the lap distance beside the TJ (the teeter-totter approach!).  You need only resolve this distance for the added load on the TJ and the 2x12.  Then you may add fasteners in between the two points to distribute that load for additional safety factor.

That's the simplified, back of the napkin approach.

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