Tritanium is 21.5 times harder than diamond; also, in 2364, Federation hand phasers were unable to melt centimeter-thick tritanium plate. Bulkheads of Galaxy and Intrepid class starships are made from tritanium; also, greater resillience of GCS and especially SCS to damage suggests their hulls are at least partially composed from tritanium.
Given known output of hand phaser, we can take some guesses. If we assume that hand phaser can melt 1 cubic centimeter of tritanium per second, then we have energy required to melt tritanium as being 168 to 673 MJ per cm^3.
Duranium is used in portions of interiors of Galaxy class starships; also, hull of Intrepid-class starship is composed from duranium. Duranium is also interfering with sensor scans - 2 meter thick duranium composite used in access tubes aboard DS9 makes scanning of interior of tubes impossible, even by station's own sensors, but is, in terms of damage resistance (be it to weapons or physical impacts) inferior to tritanium.
