Character Controller falling through..

Hello!

I’m making a simple platform game in which I am including elevators and beams that I rotate (on which the character can walk). The character moves forward all the time, like a lemming, and the player controls the diffrent objects (elevators etc.)
The problem I have is that if the elevator moves up, with the player on board, the character falls through the beam. The same thing happens when I rotate a beam upwards, with the character on it.
The character has a Character Controller attatched to it. Any toughts on how to solve this?

The 2D platformer tutorial have moving platforms, you could check that one.