If you have a cantilevered beam with one end fixed to a wall and the other end free, and there is a moment acting on the free end, where will the beam fail?

If you have a cantilevered beam with one end fixed to a wall and the other end free, and there is a moment acting on the free end, where will the beam fail?

I think it would fail at the fixed end. If you were to draw the moment diagram for the situation where you only have an applied moment, you’d see a constant moment throughout the beam. That being said, you have the additional moment created from the actual weight of the beam as you move farther out towards the beam tips which adds additional stresses at the fixed end. So on that basis, you’re most likely to fail there.