Jet fuel cannot melt steel beams (~1,400 C) unless it reaches sufficiently close its adiabatic flame temperature (~2,200 C). However, the World Trade Center fire was not the conditions required to reach adiabatic flame temperatures. The WTC fire was fuel rich and combustion poor, which is why it bellowed so much black smoke. Incomplete combustion not only reduces the amount of heat rendered, but reduces the flame temperature because the incomplete products will need to also be heated as well. Convective losses were also quite significant furtherly reducing the steady state flame temperature.
The WTC fire was still quite hot reaching as high as about 1,000 C in some regions though the steel beams would not have been uniformly exposed to such temperatures whether by location or the integrity of the insulation material protecting them. So no, the WTC fire did not melt the steel beams to any significant degree. What the fire did do was drastically weaken the strength of the beams, for instance butter in your fridge is much harder than butter left out on the counter. Also, inhomogeneous temperature exposure further weakens steel due to thermal expansion. Even this however is not the whole story. The reduction in strength of steel at high temperature is a well known fact and the WTC was designed (like any modern building) to have some protection from reduced beam integrity in the situation of fire. This might sound odd, but a commonly overlooked contribution to the ultimate collapse of the towers was the damage they sustained from the plane's initial impacts. The WTC suffered massive internal damage from the impact itself.
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