Last post for tonight - just a summary of points I wish everyone would understand:
1.
All orthogonal coordinate systems are equivalent. None is more accurate than any other. Some are more practically useful for a given task due to their reducing computational complexity.
2. The
Center of Stiffness is a concept that is dealing with the
torsion a structure exhibits when its Center of Mass experiences a lateral force, e.g. wind or a seismic event. It is a point about which a rigid plane rotates once you subtract the translations.
2a. Hulsey's model and presentation do not look at any torsion that any WTC7 floor experiences. Therefore,
Center of Stiffness is irrelevant in our current context.
2b. The CoS changes within the floor plane as well as relative to the fixed ground over time as the structure heats, deforms, and elements change their elastic modulus due to heating. It is thus a poor choice as origin for Hulsey's coordinate system: Any displacement of an element in that system might capture the motion of the CoS, not of the element.
3. Hulsey really says that, as the structure is heated and it expands, a
Center of Thermal Expansion emerges, which he locates vaguely in the region where he observes the least lateral movement. This is something that his model is actually concerned with, and so this is what he actually means, even when he switched to the term "center of stiffness".
3a. However, I do not believe that "the point that does not move relative to the fixed ground" is the same as CoTE. So you
can't identify the CoTE by this property.
3b. As a corrolary, I am totally convinced (and betting a 20-pack of beer) that
Hulsey's actual coordinate system for slides 77ff is locked to the ground. Any and all talk of these centroids is thus technobabble, irrelevant, perhaps designed to confuse and bamboozle.
4. The structure of the NIST models - it's not understood by Hulsey, and not understood by his fans.
Chapter 8: Some preliminary models to find parameters, areas to look more closely into, get a feel for how the structure might behave. The lessons-learned flow into the following chapters, not the models themselves!
Chapter 9: Fire model - how fire moves around the floors, consumes fuel, releases heat accordingly, and spreads hot gas. The output of this Chapter is the input for Chapter 10.
Chapter 10: The heat distribution through time from Chapter 9 is taken as input and a model computes how the structural elements - steel and concrete - heat up and cool down over time, individually element by element, and within elements. The output of this Chapter is the input for Chapter 11.
Chapter 11: The 16-story ANSYS model: It is pinned to the ground, pinned to the floor above (the 17th?), and otherwise modelled completely. Only within a region in the east of the building does NIST model connections such that they are susceptible to various failure modes developed in Chapter 8. Outside that area, the model is of course complete and flexible and responds to heat and gravity and changing loads, the only thing is that connections cannot fail. It is difficult to see why this should be a problem to Hulsey, who confirms that no connections fail. Anyway, Chapter 11 takes the element temperature histories over several hours from Chapter 10 as input. Its output is information of which connections HAVE failed due to heat-induced stresses. The output of this Chapter is the input for Chapter 12.
Chapter 12: Full 47-story LS-DYNA model. This model is initiated with the accumulated damage from Chapter 11, the heat pattern from Chapter 10 after 4 hours for Case B fires, two or three different scenarios of structural damage from the WTC1 collapse, and gravity. Note: At the time the LS-DYNA simulation actually starts, all damage from heating has already occurred! (This means: Immediately upon starting the sim run, all beams and girders not vertically supported start falling from where they had been connected). This model needs not take heating histories into account, because it only models the rapid collapse phase - 18 seconds or so - during which no element is expected to cool or heat significantly! This model then computes how the dynanic impacts of rapidly moving members affect other members that may be weakened by heat or damage accumulated in the ANSYS model.
I hope that helps.