Barre chords are transpositions of open chords; the root note stays on the same string:  

 - An open E chord has the root on the 6th string, and so does any E-shape barre chord.  
 - An open A chord has the root on the 5th string, and so does any A-shape barre chord.  
 - An open D chord has the root on the 4th string, and so does any D-shape barre chord.  

Any open chord that you can transpose as a barre chord will follow the same rule, e.g. a C chord has the root note on the 5th string (third fret), so a C-shape barre chord also has the root on the 5th string (third fret above the barre).  

This is of course also true for the scale degree of the notes played on the other strings in the chord; which strings play the root, third, fifth, seventh, ... in an open chord doesn't change when you play that shape as a barre chord.