It is not possible to support a horizontal beam from one end, and the same is true for an I-Beam. I believe this can also be proven for a pipe, but that proof is just outside of my reach.
But all of these proofs depend on uniform density of the beam. If we remove that assumption, the very method of proof no longer holds.
Can we design a boxy* truss of reasonable materials that when supported from one end is horizontal within margin of error of construction? That is, we can ignore Agravado's number, imperfect cuts, imperfect welds, uneven density, etc, but we cannot simply make it so strong that the bending is below margin of error. I'm expecting any such truss must consist of struts of different thicknesses.
Any truss would have the bottom row of struts bending down between the pins on both ends. We can ignore this and say it's horizontal when all the pins are at the same height.
This problem as no practical use. For practical purposes we would just mount a tiny bit higher and use turnbuckles on the diagonals to fine-tune the resulting beam height at the end.
* I mean to eliminate the trivial solution of running a guywire from the end back to the support beam high above.
OK truss formation: XXXX>