Alternator or battery gone bad?

Ford Focus 2011 mk3 1.6 tdci. While driving the power steering started malfunctioning and i got all kinds of warning lights in the dash. Pulled over and the car battery was to weak to turn over the engine. Got the car home and took out the battery and charged it from 9v to 12.5. Drove the car normally for like 30min then it was out of power again and the car stopped. Measured the battery while running and got 11.9v. Any ideas?