This chord diagram is from the GarageBand chord trainer (I'm a beginner). How is it possible to put a barre down on the third fret without also muting the top E string?
I use this kind of "A-shape" barre chord all the time, although I must admit I rarely teach it to students. I actually find it easier than using fingers 2, 3 and 4 to play the three fret 3 notes. All you have to do is bend your third L.H. finger backwards, so that the joint nearest the knuckle moves forwards and away from string 1.
Here's a picture of me using this technique:
Not everybody can do this but the trick is your finger forms a 2nd, partial barre at the 3rd fret, but bends so it raises above the highest string. Some people play A like this as standard however I believe it partly comes down to luck how long your fingers are, how practical this technique will be.
Check out this awful drawing:
Both answers are great, but do you know there are other ways to play this chord here. The index barre can be over all 6 strings, which can all be strummed. It just gives an inversion of Bb. 3 fingers can be used, on 2nd, 3rd and 4th strings. Otherwise, two fingers can be used, with two strings held down by one finger, and the other with another finger. As Bob says, it's hardly a beginner's shape, but I also use it in preference to my other suggestions. It's o.k. to mute the top string, which note is actually replicated an octave lower.
The shape is of course movable to make any major. Try it around frets 6-8, where there might be more success as the fretboard is a little wider.
I have seen people who can get that F on the first (highest) string, but it is almost freakish.
Usually that highest string is muted for me. Also, I would never fail to barre the sixth (lowest) string. Just remember in this voicing, your root note is on the fifth string. If you are "boom chucking" (playing root/chord/fifth/chord' etc.) it puts that lower fifth tone right where you need it.
This chord is excellent for adding sevenths, both flat and major, as well as the sixth, up on top where they can be featured. If you need a six string Bb, go on up to the sixth fret and barre E-style.
I remember not liking this chord, and the F on the first fret, but time and practice will make it all second nature. Work away. You will get there.
A friend o' mine did the double barre in a song many years ago and I was like, "Whoa, what's that?" He showed me and I went home and practiced it until my fingers ached, then practiced more.
It's great to have that major chord at such a quick flick from the majors above it G to C, A to D, etc.. Nice for speed songs like punk rock too. Attack it and make it yours.