If you are going to attempt to frame around a tree, you must understand that a tree’s root system is extensive and may be damaged by any surrounding footings. Begin by running a beam in front and behind the tree between two double joists running perpendicular to the house surrounding the tree. Joists can now terminate on either side of the tree with their load being transferred around the tree. You should also install diagonal supports at the corners between the beams and the tree to define and approach the round opening for the tree.
Allow a little room for expansion, as the tree will continue to grow. Your decking can run past the framing near the base of the trunk. Building a deck around a tree will also affect how much water will reach the base of the tree. Including a tree in your design can be an interesting feature, but you must be careful not to damage the tree in construction or it will all be for naught.