We are familiar with the core remnant of the Twin Towers, which stood in excess of 40 stories several seconds after the main collapse had reached the foundations. I think question of how it collapsed under it's own weight deserves a separate thread.
For reference, here are videos of the core remnants
WTC1
Source: https://youtu.be/7W0-W582fNQ
WTC 2
Source: https://www.youtube.com/watch?v=75X3auwx_kQ
Here is my preliminary attempt at a response.
But I need more information for a more complete response. Specifically, I need core column specs to calculate gyradius. I also need beam specifications to calculate bending resistance.
Also, it would be better to have criticism from experts like @econ41
For reference, here are videos of the core remnants
WTC1
Source: https://youtu.be/7W0-W582fNQ
WTC 2
Source: https://www.youtube.com/watch?v=75X3auwx_kQ
You've implied that after the core columns lost lateral support of the floors, they would fail also, but I don't think you cited anything to back that up. The core columns were laterally braced between themselves.
Here is my preliminary attempt at a response.
First of all, the core columns were mostly 'braced' by floor beams and slabs. These things provide only limited bending resistance compared to the deep spandrel plates of the exterior walls.
With that said, let's demonstrate that the core could collapse without lateral bracing.
Consider a 40 storey, 480ft remnant whose base load is just 10% of normal at 1.8 to 2.1ksi. I don't know the gyradius, but it's probably in the range of 1-2ft. So let's use this handy derivative of the self-buckling equation
Slenderness² × base strain = 7.8373
Slenderness = 361 to 335
So gyradius = 1.3 to 1.4ft
FOOTNOTES
1. Wikipedia gives self buckling equation
Length³ × density × gravity × area = 7.8373 × elastic modulus × area moment of inertia
Length × area = volume
Volume × density = mass
Area moment of inertia = gyradius² × area
Mass × gravity / area = base stress
Base stress) elastic modulus = base strain
Length / gyradius = slenderness
Therefore we get
Skenderness² × base strain = 7.8373
2.The core columns were mostly made of 36 and 42 ksi steel, with a load factor of 50%. Hence the base stress values
But I need more information for a more complete response. Specifically, I need core column specs to calculate gyradius. I also need beam specifications to calculate bending resistance.
Also, it would be better to have criticism from experts like @econ41
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