I doubt there is a defined answer to this, not without an analysis of the piano in question, and it seems like a bit of a waste of time to try and figure out how much pressure is required to break your piano. It happened to me once when I was a teenager. Pain in the arse, string slipped over the entire set and the whole instrument became completely unplayable until the tech came to restring it. Buzzzz buzz buz.
Also..I went to a concert quite some time ago now where the pianist told us that she once played a concert on a fairly dilapidated instrument and a leg broke mid performance sending the piano to the floor.wouldnt that be just a bit frustrating..
What does it take to break a string?
Agreed. Corrosion is probably the main culprit, especially at the contact points like hitchpins, coils, V and capo bars. Hard playing on a healthy string will probably snap the hammer shank before snapping the string. No a pianos limits in terms of volume and projection and don't play harder. Its fruitless.