So steel doesn't melt but just weakens or steel does melt?
OK, here is a quick 101 for laypeople on steel, temperature and strength:
The strength of any given steel* depends on its temperature. Generally, any increase results in a loss of strength. Steel is for example stronger at 68°F/20°C than it is at 70°F/21°C. The difference is just very very small, of course.
Metallurgists know how to look up how a given steel performs at what temperatures. So for example, at 500°C, it may have only 70% of the strength it has at 20°, or 65%, or 75%. (I am making these numbers up at this point - this is only illustration).
Or, to take a different viewpoint, a given steel may go under 50% of original strength at 800°C, or at 750°C, or 850°C (again, making up these numbers, just to give you the idea).
Iron melts (becomes liquid) at a bit over 1500°C, and so do many steels, but this temperature is irrlevant for the fire performance of structural steel that has to bear any load at all, as it will deform long before becoming liquid. Think of butter: Fresh out of the fridge it will resist a knife pretty well, at 86°F/30°C it becomes soft and hardly resists your knife anymore, but it doesn't melt until hmmm say 113°F/45°C. Think of structural steel as butter straight from the fridge, and steel involved in a building fire as butter in a warm kitchen. It doesn't melt, but it isn't able to carry much weight any longer.
To assess the arguments about steel and office fires, here is one last piece of information you need:
Office fires always generate temeratures above 250°C, frequently above 600°C, can reach 1000°C in some spots if the fire is large (as they were in the WTC), but is highly unlikely to reach 1500°C.
Conclusion: In any office fire, expect steel to lose strength significantly, but don't expect it to melt.
Because of this, structural steel gets covered with a layer of fireprotection - that is an insulation made of heat-resistant fibers. This fire protection delays the heat-up of the steel in case of fire. The aim is to prevent reaching a certain dangerous temperature for a specified time, for example 90 minutes or 2 hours. Such requirements are laid down in Building Codes which construction firms have to obey. The aim of this rating is to allow time for evacuation, and to give the steel a better chance of survival, as 90 or 120 minutes is a realistic time by which fires in a given location die out or get sufficiently under control by fire fighting efforts. In the Twin Towers, much of the fireproofing was removed by the plane impacts, so all bets of steel survival in fires were off.
* There are of course various kinds of steel, optimized for various purposes: Depending on its intended use, steel can be made more or less flexible, harder or softer, easier or harder to work with, more or less resistant to corrosion, having a higher or lower melting point, and of course more or less expensive, etc. This is achieved by mixing in other materials such as carbon, sulfur, or other metals such as molybdanium, nickel etc.