I agree with
xongsmith on most points.
This is not part of my common experience.
The statement of the problem is incomplete.
Based only on the picture, and assuming that the ends are just sitting there, it looks as if the beam would warp enough for one of the ends to slip off its support.
I'm guessing that is not what you are asking, though it illustrates the incompleteness.
Otherwise, I would expect it to fail near the center. There are upward force at A and B, that counter the downward forces (plus the weight of the beam). Between the upward forces and the downward forces, we have attempt to rotate the left part and the right part in opposite directions. That is, the combined effect will be to warp the beam. This attempt to warp will be resisted by the tensile strength of the beam, and I'm pretty sure that will be at a max near the mid point.
Jesus was a liberal hippie