Some Misunderstandings Related to WTC Collapse Analysis

[Tony Szamboti]

First thanks for attempting to make sense of my cartoon. It's a cartoon and obviously not a depiction of the actual dynamics but suggests/shows how the gavity forces work as the structure degrades.

axial strength refers to the ability of a column to resist or support loads applied directly above (compression)

A column's axial strength is limited by its slenderness ration.. stout columns are stronger then slender ones. Too slender will buckle from their own weight.. meaning that as the unbraced length increases... a given column section weakens ie supports less load and thus is more subject to buckling (failure)

The arrows are meant to indicate the direction of the loads...

When a column is removed if a multistory structure the column above it has no support and can't couple the forces (loads) to the foundation and the earth. These loads are then redistributed to columns that are coupled. The load has not changed... it has to and does find other paths.

you weigh 100 pounds and when standing each food supports 50 pounds. If you stand on a scale with both feet it shows 100. If you lift one foot it STILL shows 100 because all the 100 pounds are resisted by one leg.

Now if you lift the heaviest thing you can... say your dog which weighs 50#... each leg is at its limit of 75 pounds. On the scale it shows 150.

If you try to stand on one leg... you collapse... your leg would *buckle* at the knee and you'd call down and you would likely fall in the direction of the missing or lifted leg.

The twin towers had many columns and they shared the load carrying and when the columns were destroyed and weakened the load sharing was shifted all about. This caused uneven stresses and even warping, torquing and distortion and eventually collapse when the capacity was eroded below loads imposed. The failure rapidly propagates one this happens... the structure does not fall at once... but the propagation can be very quick when as more and more load is carried by fewer and fewer columns. This also introduces some eccentricity and tilt of the falling top... as it's almost impossible to have a completely symmetrical force/load redistribution.

We know the core collapsed first because we see the antenna begin to sink into the top... and this was followed by the release but inside the entire core up there and the floors were already probably dropping. The facade hung together because of the nature of the structure... structures without internal stress do not fall apart or even distort... they sort of float (as in free fall) When they meet resistance or forces they yield to them in some manner.

The disconnected mass of the top floors is what drives down through the tower destroying it.

Jeffrey, the cartoon depiction you show of the core load being transferred to the perimeter is appropriately named because what you show is impossible. As I stated to you when you e-mailed this to me a while back, the outriggers of the hat truss did not have anywhere near the ability to transfer the 12 stories of a central core gravity load to the perimeter columns. They would have immediately failed in bending had that entire upper 12 stories of core load been applied to them. The outriggers were only intended to provide counteracting moments to antenna wind loads by shifting them further outboard to the perimeter, where the force involved in the counteracting moment would be lower due to the greater arm involved.

The core did fail first and it was the pull-in it applied to the perimeter that caused perimeter failure. The proof for this is in the stagger between the core falling first (as evidenced by the antenna drop) and the exterior roofline line just a short time later being coincident with the exterior columns being pulled inward.

It is interesting that your "cartoon" does not get into the dichotomy concerning the lack of resistance by the columns in the building, which is clearly provable, by the measurements showing there was no deceleration of the upper 12 story mass after it started to fall, and the calculations based on the real columns, which say there should have been massive resistance by them in a natural fall.

It seems that you allow yourself much more freedom in your explanation than science would allow. Hence, your terming your explanation a "cartoon" is appropriate, as things often happen in them that are impossible in real life.