Tragic Hero

My definition of a 'tragic hero' is someone who does good deeds, but at their own 'tragic' expense.  How can we relate this.  Well i see it related to Okonkwo in the sense that he was trying to save or protect his people, but he couldnt and killed himself at his own expense.  Tragic heroes often have many downfalls. Such as when Beowulf fought the dragon and died 'tragically' by being bitten. In the end, I believe my definiton of a tragoc hero almost can be related to every book weve read, and they seem to suffer something horrible at their own expense.