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There are a couple issues here that need to be addressed.

1. I believe that you are overspanning your beam. Based on the 2006 IBC, a triple 2X12 beam can only span 7'2" if the beam supports two stories and the room is 20' in width (measured perpendicular from the beam). And it is possible that your room is even wider than 20'. Here is the table:

2. The table also says that you will need a minimum of two jack studs on each end of the beam. However, this assumes that you will have a continuous load path all the way to the foundation and ground. It sounds like you want to build a 'bracket" though. Does this mean that the load from the beam will pass to the bracket, from the bracket through the lag bolts, and then from the lag bolts to the existing 4x4? I would advice against this because it will induce a moment (rotational forces) in the 4x4. And it is very likely that the 4x4 was only intended to resist axial (straight up and down) forces.

3. If you still decide to go with your design method, have you considered the possibility of bolt bearing failure? In basic terms, this occurs when one side of the bolt hole (the holes in the wood) deforms due to the forces from the bolt.

If I were doing this project, I would figure out a way to shorten the beam span or invest in an engineered beam. I would also avoid the bracket support method and ensure a continuous and simple load path to the foundation.
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