Intense fire from the jet fuel did not melt the steel structure of the towers, but did heat it to a temperature where it was weak enough to buckle under the weight of all the floors above it. This would be a catastrophic event that would happen at once. One side of the structure would buckle near the impact/fire zone, and the other three corners would also buckle nearly simultaneously.
At this point the building's floors above the impact zone become a solid body, essentially a vertical wrecking ball weighing thousands of tons, which crushes the lower floors as gravity does its work.
It is no coincidence that the South Tower only took 50 minutes to collapse (despite the plane going in at an angle), while the North Tower took 90 minutes to collapse even though the plane hit the building square and caused massive structural damage. The South Tower was hit on floor 75, while the North Tower was 90 or so. The South tower had 15 more floors of building as dead weight on top, and its critical stress level as the temperature was raised from the fire was reached sooner.
This is just engineering. It was discussed literally within minutes of the first tower collapsing.
1985 Honda VF1000R, 1990 Ducati 851, 2008 YZ450F