The steel did not "melt"
Watch a blacksmith at work, and you will see that steel heated to red heat is so soft that it can be molded like putty by the blacksmith's hammer.
Furthermore, that once-strong steel, when cooled slowly, is so weak it can be bent with your bare hands (that's called "annealing").
Returning the steel to its prior strength and hardness requires re-heating it and "quenching" it by plunging it into water to cool it quickly.
Watch a blacksmith forge a knife. You will never again be amazed that the girders in the WTC -- when exposed to tons of burning jet fuel -- weakened to the point that the buildings collapsed.
Chemical Engineer Rosie O'Donnell has pointed out "fire can't melt steel".
But as you say, melting is not necessary for the girders to lose structual strength.
THE careful text-books measure
(Let all who build beware!)
The load, the shock, the pressure
Material can bear.
....