Reply #1: Why is it ludicrous?

[AZCat]

I find it quite the opposite. Perhaps an explanation is in order.

A few definitions
stress: The force applied to a material divided by the area over which it is applied. For beams (columns) the area used is generally the original cross-sectional area. Stress has units like pounds (force) per square foot (area) or "psi" in Imperial units and newtons (force) per square meter (area) or "Pascals".

strain: The normalized change in a dimension of a member (length, for example), or (new dimension - old dimension)/old dimension. Strain is unitless but often can be seen labelled as inches per inch or something like that. This is basically a measure of how much a beam is stretching (under tension) or squishing (under compression).

A quick assumption
The weight held by the remaining structural members didn't change (much) during their failure, so we can treat it as a constant.


In materials science, there is something known as "Young's Modulus", or the "Modulus of Elasticity". This is the number that, for particular kinds of materials, defines a quasi-linear relationship between stress and strain. In other words, if you know how much force is being applied to a beam, you can figure out the change in length.

This quasi-linear relationship only lasts over a certain range of stresses, because the material begins to undergo some changes that affect how it reacts to stress. An example "stress-strain curve" can be seen at the wikipedia. Notice the initial linear region and how it tails off until the point labelled "Fracture". The maximum stress doesn't always occur at that point, but it does in this graph.

That maximum stress point is what we are concerned with. If we assume that the cross sections of the structural members in the WTC don't change during failure, then the stress applied to those members is dependent only on the weight carried by each member.

If structural members begin to fail they no longer can carry the weight they previously did, and that weight is shifted to other members increasing the stress on each of them. If a large number of the members are already loaded close to their ultimate strengths then failure of a few members can cause a cascade of failures, and it can occur very rapidly. In fact, the speed of the failures feeds itself because the strain of the members causes heat buildup within the member itself, and under the appropriate conditions it can be adiabatic and can cause "strain hardening" in the member, particularly around stress risers.


If you have any questions please don't hesitate to ask. I may not have explained everything clearly.