What stick said, plus a dado on the side-ways stringer, plus glue, lots of glue. But I also doubt it will support itself, let alone anything set on top of it. You might get a little more strength if you use three pieces in a U configuraton, or if you put a third stringer on top, like an I beam. The crossed stresses in the three pieces of the I beam should help cancel each other out resulting in less twisting. But sagging will be your main problem, especially over time.
If it is outdoors, use waterproof glue. If outdoors, a water proof coating might be wise.
I have a grid of 2x2s about 14 x 10 feet, on which I stretched shade cloth for an open area over a patio. There are 3 long stringers, one on each side, one in the middle. I used some existing, very twisted 2x2s under the grid that were already in place to span the bottom. Straightened them as much as possible and put one long deck screw in the middle to attach them to the middle stringer. Amazingly the twists have completely straightened out (rains and sun) over time. So depending on what you're making, attaching the T or I beam to whatever it supports may help strengthen it and keep it from twisting.
Personally, I'd make this using shorter lengths of a harder wood and overlap the joints so they don't meet in the same place. I think you are going to have a much easier time finding sufficient material with appropriate grain if you go for shorter pieces. For the top and bottom of the I, or the cross on the T, I'd select grain that was perpendicular to the flat side. For the I or stem of the beam, I'd look for grain that was parallel to the flat surface. With the I beam construction, you could use a really good ply, which will be dimensionally stable as well as very strong. The edges in the vertical piece buried in a groove will protect it from moisture. Screws through the whole beam and into whatever the beam supports will also help prevent warping.
Whatever approach you take, Glue and screws will turn it into a solid piece. If you use a shallow dado to set the tall dimension of the I beam in place, you'll get a little more glue surface, which will help strengthen the final result.
How, exactly will you be using this?
Last edited by DesertRatTom; 05-28-2015 at 07:26 AM.
Reason: fpr clarity