I have had many 20 minute connections from B-->F and vice versa. Have always made them. Out of breath at times, but never missed the flight (and they've been from the farthest point to the farthest point - no shuttle bus either ).

Relax. This is not an issue - people at ORD do this every day. . .as others have already said - if you miss your connection then it's UA's responsibility to get you on another flight.