Jet fuel burns MUCH hotter than a building fire would. The building fire would be wood, carpets, lamps.. many things that, while burn, do so very inefficiently. So, the intense heat warped and eventually made the steel support beams fail.
As far as falling sideways, the building was made to take a plane hit. It happened in the '40s to the Empire State Building, so knowledge of it could happen was known, and planned for, in advance.
What they didnt plan for was a plane loaded with enough fuel to fly over the ocean to crash into it. As stated the fireproofing, which is intended to insulate the steel from extreme heat, was blown away during the impact.
The building was built in a grid of squares of support beams. Newer buildings are built the same way but with X's to give added structural support with less weight (The Malasian towers for example). With the box pattern of the WTC, top-down collapse is what would happen if one or two layers of boxes were taken out. If it was supported with the X pattern it would twist, hopefully keeping just enough integrity to save it from complete collapse (though falling sideways is much more of a threat because of the twist).
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What is the melting point of steel (specifically the steel alloy used in common steel reinforcement for buildings)? What is the burining temperature of jet fuel?
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I can tell you that jet fuel WILL cause damage. If you look at how jet engines work, the flame never even touches or comes close to the casing of the engine itself. They use very high pressures around the combustion chamber to keep the heat from touching the walls, and forcing the flames out the rear.