strength building exercises
 

I look for exercises to build my strength in playing bar-chords. I am trying and trying but they somethings keep on sounding "rattling".

Trying and trying is the best "exercise" you could do. The strength will come with time. Be patient and don't get frustrated.

With barre chords, the issue isn't necessarily strength, unless your action is too high. Usually, it's a problem with technique.

If some of the strings sound muffled when you strum, you may not have your fingers close enough to the fret, or you may be muffling the string with the finger on an adjacent string (that one is not unique to barres). If the string(s) that are fretted by your index finger are the muffled ones, try rotating your index finger toward the nut slightly so you are fretting with the side of the finger.

Also, practice barres further up the neck. Barring an F chord, right next to the nut is harder than, for example, an A on the fifth fret or a C on the eighth. When you get those chords to sound right, then gradually move toward the nut.

It also helps if you have your thumb securely anchored on the back of the neck.

Ken

What ken said is real important.You definitely want to be "squeezing" with your thumb.It would be like taking all 4 of your fingers and opposing them with your thumb.

Its easier for me if I put my fingers closer to the actual fret.Its like when you use a capo.You place it as close to the metal part of the fret as you can.Not the space exactly between the frets.That will pull the string and throw you out of tune....What I'm getting at is dont squeeze to hard but hard enough so that you dont buzz.Also,Keep your finger pressure straight down.Dont bend the strings,that'll throw you off too.
You may want to consider dropping your tuning down a half step or a whole step and gradually work your way back up to concert pitch.Or you can start with light gauge strings an d work your way back up.
one thing is for sure heavy strings sound better than lights.

Muggy