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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