Triple beams for decks (3-2x’s) should be supported with 6×6 posts using a post beam connector bracket.  4×4 posts will not provide adequate bearing for a triple beam.   Do not notch the top of the post and through bolt the beam because the width of the triple beam will limit the notched section of the post down to 1″.  This does not provide enough strength to hold the beam in place.  A positive connection using a post beam bracket installed on top of the post and nailed to the side of the beam is the most secure connection.

Triple Deck Beam to Post Connection

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Triple Deck Beam to Post Connection

Here is an example of how to mount a 3-2×10 beam over a 6×6 support post to support a shed style porch roof.