this is probably irrelevant but I'd like to sort it out for myself. In a regular building with no fires.. the "center of thermal expansion" would be the same as the CoS, right? Because say we are in a heat wave (75F vs 98F outside temperature), then the building would expand thermally from the CoS. ??

obviously in a fire situation the pieces would expand where the fire is.

No. CoS and CoTE are distinct and different concepts.

The building would expand around the Center of Thermal Expansion when exposed to thermal loading - hence the word. The best way to think of CoTE is probably to picture the structure floating freely in space: It expands to all directions, like a balloon when you inflate it, and somewhere there is a center that doesn't go any direction. The structure experiences no total angular momentum here.

The Center of Stiffness is a concept that looks at torsion in a pinned structure: Suppose the ground underneath the building accelerates laterally due to a seismic event. This is a lateral force that acts on all mass points equally (equal acceleration), so you can think of the force as acting on its Center of Mass. Now, most structures are not uniformly or symmetrically stiff: Let's say the left side is build relatively stiff, and the right side is built relatively elastic. Then the entire structure responds laterally to the seismic event, but the elastic side more so than the stiff side, such that the elastic side moves farther. This means: The structure actually rotates a bit - or since it is pinned to the ground, the structure experiences torsion (what's the verb for "torsion"? The action of going into torsion?). The Center of Stiffness now is the point around which the upper level that you are looking at (an upper floor, the roof...) rotates, its pivot, and you find it by subtracting the translation of that plane relative to the ground.

If the Center of Stiffness happens to be the same as the Center of Mass, then no torsion occurs. Also, if they are not the same, but the force vector, emenating from CoM, points directly at or away from CoS, not torsion occurs.

Now, combine the two concepts:

When you heat a building that is pinned to the ground, it is not free to expand (assuming that the ground remains cool and does not expand). This induces internal stress in the structure similar, but not same, to the way a lateral seismic force induces lateral, and by way of differential stiffness, torsional stress.

I think, analogous to the CoM/CoS relationship, the following is true about the CoTE/CoS relationship:

If the Center of Thermal Expansion is the same as the Center of Stiffness, then thermal expansion will not result in torsion. Otherwise, some torsion will occur.

It would, in general, be quite an amazing coincidence if CoS and CoET were the same in a complex and asymmetric structure as the WTC7 building. So Hulsey is almost certainly wrong to insinuate that the two can be used equivalently in his model.

On account of heating, whether in Hulsey's model or NIST's, or in reality, the building experiences some torsion. I think this is apparent in Hulsey's slide 77, where, on the east side, the borders between two colors run roughly north-south, and in the SW corner, they run roughly perpendicular to that (although I couldn't tell from this where the pivot point might be, i.e. the CoS). In addition, the floor expands in general, in all directions, and again, it would be difficult to tell where the center of that is, which would be the CoTE.

Obviously, Hulsey's map does indicate displacement relative to

*something*. Since deformation due to Thermal Expansion is modulated by torsion through diffential Stiffness, it would probably require a very complex mathematical analysis to disentangle CoS and CoTE, which is why I bet a 20-pack of beer that Hulsey determined, nor measured from, neither, and instead measured everything relative to the ground. And in his talk, he merely SPECULATES that the area that moves least relative to the ground is where the CoS, or the CoTE, might be found if he looked for it. It's probably not completely wrong to start looking in that region, but he is, with good reason, very vague about the precise location of that center - and goes on to invalidly conflate the two different centers.

I think he wants to direct the audience's attention to a rather trivial point: That the espanding slab moves a greater distance the farther away it is from some center. And then went on to confuse himself that measurements are actually relative to the center.

But neither the CoS, nor the CoM, nor the CoTE, are points that fixed relative to the ground as the building is heated.