Not a concept that I was familiar with relevant to this either. Heard of it, as centre of rigidity before.

Assuming that "rigidity" and "stiffness" mean the same her (if they don't, then the quotation defines something that is not "center of stiffness"), then the definition is pretty worthless, as it translates to "Center of Stiffness is the Stiffness Center". D'uh.

(above) + Lots of published papers showing examples of this. Centre of rigidity also refers to it.

http://debug.pi.gr/Default.aspx?ch=726

This demonstrates that the CoS is a point around which all points in a rigid (!) plane rotate, once you subtract translations. It is essentially just a method to shift the coordinate system such that only rotations need to be described. This does not tell me much about the stresses, forces and deformations at any remote connection. In other words: I do not see how this concept applies to the problem at hand - how the girder end moves across its seat. Hulsey is not discussing that, or how, the WTC7 floor system

*rotates*.

I don't see an issue with performing sub simulations on particular areas.

So expressing motion relative to CoS is ... what? Optional? Or 100% the right thing to do? What did you really mean by "the right place" and "it is [the right place] 100%" when you asked and answered: "

*Is the centre of stiffness the right place to state the amount of movement due to expansion from ? I say it is. 100%.*" That sounded like "

*the one and only* right place to state the amount of movement". Now you say that not using CoS is okeydokey when focussing on particular areas

*such as the situation around column 79*.

Confusing.

But it would come down to how these are applied, and I see the CoS issue as relevant to that. IOW the building will expand wrt the CoS.

It's great that you "

*see*" that. Can you

*show* it also? I.e. explain

*why* the CoS issue is relevant?

Well they didn't mention their inputs either, but they surely had them.

They surely had inputs? Uhm yeah, d'uh. This doesn't address the question I asked, which was whether NIST made a conceptional mistake by not even mentioning CoS.

Do you claim that NIST did state, or compute, movement relative to CoS, but were silent about it, such that they did something right, only didn't talk about it?

Or do you assume they did not state anything relative to CoS? Then the question remains: Is that a fundamental mistake - or is CoS optional?

I suppose it depends how much you want to trust an agency that gets 11" confused with 1ft when it's written on a structural drawing bill of material right in front of them.

No, not at all. You are poisoning the well here without addressing the question.

No it wouldn't. We were checking the plausibility of NIST's hypothesis. Like with like. They were plain wrong. This has been proven for quite some time, but good to have that confirmed by the UAF study.

If their approach was wrong from the get go for not assessing movements relative to CoS, then repeating the same conceptual mistake is not likely to validly confirm or refute the result. It's a case of "Wrong with wrong" more than "Like with like" - and I guess my point was: Do you think today that your 2013ish analyses were even a valid approach

*at all*, given that you had no idea that stating movements relative to CoS would have been the 100% right thing to do?

What I am getting at of course is for you to realize that stating movements relative to CoS is not just only optional, it is indeed entirely irrelevant, unnecessary. It's a completely arbitrary point. It is just a matter of which orthogonal coordinate system you use - but

**all orthogonal coordinate systems are completely equivalent to one another**. Some are more practical than others, depending on the specific use they are put to. For example, if you want to know how a floor slab moves as a whole in a reaction to a lateral seismic force, CoS seems to be a useful coordinate system, as it can be shown that, as long as all connections hold and the slab does not deform laterally, all movements can be described as simple rotations. But we are in a different scenario, where in fact the slab deforms and we at least allow for connections to fail (that is indeed what we are after!) due to lateral forces of various magnitude going in all sorts of directions - it seems that the CoS coordinate is very ill defined in our case, and unpractical to describe what's going on at some remote connection. It seems a coordinate system local to Columns 79 is best suited to describe the motion of beams and girders near it.

The fact that a beam pinned at one end will expand away from the pinned end. Pin the opposite end instead and the direction in which it will expand axially reverses. Always expanding with respect to the stiffest point.

This explains why the expansion of a beam is best measured relative to a point a hundred yards away that may een be situated in the middle of a floor segment, away from any and all steel member? I think you just explained why Cos is a

**bad** choice of coordinate system!

A beam is connected on both of its end to other members. These other members, due to their own material and geometric properties, to being assembled into a larger framework (which may change over time as other connections fail), and due to current conditions (temperature!), at any one point in time have each a certain stiffness. All you need to describe the movement of

*that* particular beam is to look at what it is connected to, locally, and go from there.

ADD - how i am tending to think of it personally is this ( and this is my own personal way of thinking it out, so worth checking for error)

A 6 pointed star made up of I beams attached to a central hex shape. Heat it and the beams expand. They expand wrt the very centre of the hex shape.

If it is floating in free space. If the hexagon sits on the ground by one of its sides, the center will move up. That's called "boundary conditions", and I wonder at this point if we even know what Hulsey's boundary conditions are.

But that distiction, whether or not the center moves relative to the ground or any other [0,0] point is rather irrelevant if you want to figure out the stresses that arise in the connections in any one corner.

If you measure that from anywhere else you are on a bit steel that is moving, so dealing with 2 changes of position and not just one.

Yes. But remember: All orthogonal coordinate systems are completely equivalent to each other.

Now apply that to our column 79: In a local coordinate system pinned to column 79, only the girder moves. In a CoS-centered coordinate system, the column moves, and the girder moves.

Which one is better?

Apologies if that is maybe not the best way to think of it, or not the best way to explain it. But as I said, it's how I thought it through.

I should have added the "star" shape is lying flat on the ground and is entirely free.

Ah ok, there is your boundary condition.

Was WTC7 lying flat on the ground and being "entirely free"? I don't think so. The bottom ends of the columns were pinned to the foundations. I assume Hulsey modelled at least

*that* correctly. With differential heating, the floor slabs on all floors will experience differential expansion, and with this, their CoS will move relative to the ground, and relative to one another. They will also move relative to pretty much all columns and all beam ends. It is indeed very difficult to see what advantage such an unpredictably moving and almost impossibly to identify point would have as origin of your coordinate system.