Nope nope nope. You wont be manufacturing a 20 beam out of 14 joists. The probable plan would be for one of those four 14 foot joists being anchored to the house and the other three to be sistered together to make your 14 beam that will be parallel to the house but probably about 17 away from the house. Joists will be suspended by joist hangars attached to the ledger board at the house and then will run over top of the triple-laminated beam. Attaching the ledger board to the house has a number of important considerations such as a flashing to keep precipitation controlled and fasteners of sufficient strength and length anchored into the existing framing rather than merely the exterior sheathing.
No offence, but based on these questions I think you should have an experienced person helping or advising, or hire a professional. It will be easier than having it done again as not all of your material will be able to be re-used.
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"The trouble with people idiot-proofing things, is the resulting evolution of the idiot." Me
Last edited by CaberTosser; 07-08-2018 at 10:35 PM.
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