Physics Inertia Problem: Time Required for a Building to Collapse?

Question

A 100 story steel frame building had a very intense fire on the 80th floor. That fire caused the complete and instantaneous collapse of the steel support on floors 79, 80, and 81. After those three floor collapsed, the weight of floors above caused the 78th floor to collapse, and then the 77th floor, and so on.

Ignore friction and the energy required to break the steel frame. Assume that the mass of each floor is the same. Please take into account the inertia of each floor.

How long does it take for the building to collapse?

How would friction, the pulverization of concrete, and the breaking of the steel frame affect the speed of the collapse?

Answer 1

There is also an implicit presumption that each floor is fully independent of the ones below, which is not correct. The impact forces of the floors above propagate through steel and concrete substantially faster than the physical collapse speed.

The speeds of sound in concrete and steel both exceed 3000 m/s:
http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html

That means that damage to ALL floors below the collapsed ones would have occurred concurrently with the collapse itself.

Answer 2

Since you're obviously talking about the World Trade Center, I'll post a different but relevant calculation I did a while back, to debunk the idea that the collapse must have been a detonation:

Actually, the amount of energy present in the building itself is adequate to explain most of the destructive force. Consider: the buildings each had a mass of 450,000,000 kg. Assuming this is evenly distributed, a height of 415 meters means each has a potential energy of about 9.15e11 J. Combined this means
1.83e12 J.

By comparison, a kiloton of TNT has an energy of 4.184e12 J. In other words, the total energy of the collapse comes to something like 0.4 kilotons. The nuclear bomb that vaporized Hiroshima had an estimated energy of 15 kilotons. In other words, there's more than enough energy present in the buildings to do things like pulverize concrete into dust, sever steel columns into tiny chunks, etc.

Answer 3

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