The question of the sagging floors in the WTC.


Something just came to mind that I cannot explain. Maybe someone with structural engineering skills kan explain this to me.

According to NIST, as far as I’m right here, part of the collapse of the twin towers was the fact that the floors sagged due to heat, and this pulled in with considerable force on the outer columns.

Can someone please explain to me how a sagging (softer) floor can pull more inwards on a perimeter column than a straight one? We are not adding any force to the floor, it just expands as it is no longer as rigid. The load on the point where it is connected to the perimeter column must be the same.

Of course it would be different if the sagging was due to added weight (downward force) to the floor, but this is not the case.

If i hang a narrow line between two small trees and I grab onto it and hang, it gives way and there is some pull on the trees as well as some sag in the line. If I do the same with a thicker line it does not give way that much, but shouldn’t the pull on the trees be the same? They are supporting the same weight. (Mine)

I cannot wrap my mind around this theory. I bet it has something to do with vectors though 🙂

Help

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3 thoughts on “The question of the sagging floors in the WTC.

  1. Not 100% sure of this but I’ll try to explain it. The truss spanning between the perimeter columns and the core columns is like a simply supported beam. You can (very roughly) approximate the effect of heat on the beam as a hinge dividing the beam in two (to simulate the loss of stiffness). The same load (mostly self weight) which without hinge would cause only vertical reaction on the supports ( on the perimeter columns in this case), now with a hinge at mid-span will generate both vertical and horizontal reaction, in particular the horizontal reaction vectors will have the same magnitude but opposite direction.

    To understand the situation I will make a very simplistic but effective example that could make the concept easier to understand. Think of of your harm, perfectly horizontally stretched, with your hand holding a door handle, while carrying a heavy bag on your elbow. The inside of your elbow is directed upwards and the door is closed but free to open if pulled. Your arm is simulating the truss, the bag is simulating the truss self weight (assuming it as concentrated in the midspan), your hand on the door handle is the connection to the perimeter column. If you keep you elbow very stiff, the door will remain closed, because the weight of the bag will be distributed vertically between your body and the door without any horizontal reaction. But if you suddenly start to loosen a bit your elbow, allowing it to bend (simulating the loss of stiffness in the truss steel due to the heat), your hand will start pulling and the door will open. No force is added, it was only added a degree of freedom to the system.

    Obviously the actual situation was much more complex, with not a single mid span hinge but a continuous loss of stiffness etc, but the idea is roughly the same: as the steel started softening, a horizontal reaction on the columns was created. The same effect would have been on the core columns (the other support of the truss). In the WTC the inward force was estimated to be 14 kips (62 kN) on the columns.

    Geez, would have been so much easier to explain it with a sketch haha 😉 Hope I got it right

  2. Giorgio, thanx! I think my brain is beginning to get it now. If i have a plank between two small trees and sit on it, the trees should not bend towards me. If I replace the plank with my hammock the trees wold flex more inwards. Plank=rigid floors, hammock=”soft” floors.

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