The 9/11 Forum

A structure such as a steel frame with moment connections if meant to have the axial loads distributed to the columns. When a structure tilts as a result of the loss of a significant number of columns and it remains supported at a line of columns which represent the "virtual hinge" those columns will see all the axial loads formerly carried by the full set of columns. The moment connections from the beams will see increases in loads and rotation. Depending on the safety factor of those connections, they will fail or support the unsupported "side" now performing as a cantilever. Considering that the lateral beams are not designed to perform as cantilevers an orthogonal lattice tilting steel frame with the loads of multiple stories is not likely to remain rigid very long with the connections failing at the lateral beam to column locations.

You raise some interest points. This one in particular:

SanderO wrote:When a structure tilts as a result of the loss of a significant number of columns and it remains supported at a line of columns which represent the "virtual hinge" those columns will see all the axial loads formerly carried by the full set of columns.

Of course this makes perfect sense and must be true in the static case. However, while a tilt is occurring and particularly while angular acceleration is happening, things might be a little different. Also, the failure of connections you note...

The moment connections from the beams will see increases in loads and rotation. Depending on the safety factor of those connections, they will fail or support the unsupported "side" now performing as a cantilever.

prevent moment applied to one side of the hinge from being transmitted to the other. Therefore, the existence of either accelerating tilt or deformation indicates unbalanced forces at play, and the conditions of static equilibrium don't apply - it is dynamics, however slowly it begins. As you say, the perimeter cannot act like a cantilever, so it bends. Because it yields against rotation, the corner may actually unload.

The difference between tilt and deformation is that the former will start at the boundary condition of the static case and evolve slowly (small angles at first) away from it as the hinge yields to rotation and subsequently resists the applied moment less and less as integrity is lost. Deformation, however, is a very broad category; what type of deformation, where and how? This makes a difference to the forces and torques applied to the hinge region over time. For example, if structural failure occurs on the south half of vertical members, causing a slump to that side, the net effect at the proposed hinge location at the wall will initially be tension, like this:



This is because there really is no hinge in this scenario, even though it may be tempting to place an effective hinge at the centerline. What's happening here is slumping (differential rotation) towards the south given a fully supported north half. Note that I'm not trying to portray my 2D uniform sheet as representative of the actual deformation in WTC1, simply suggesting analogous effect for analogous cause.

Casual inspection of videos led to the impression that there was a hinge on the north wall, despite the north wall being a particularly poor candidate with much of it gone. It's my premise that, by investigating this more closely, the motion can be accurately characterized. It looks like tilt at first glance but not on closer inspection. Some things indicate it cannot be tilt at all prior to global initiation.

achimspok has done a lot of work on this issue and I'll eventually compile some links here to posts. I want to do much the same thing but different approach.

For the structure to tilt a whole bunch of facade columns need to be pushed away, or buckled, not to mention a fair amount of core columns... while to begin the rotation a whole bunch of columns need to remain a bit to act as the hinge location. If the axis of rotation is perpendicular to one pair of facade those facades' columns would offer all sorts of resistance to the columns above them.

It seems to really get some rotation going you would need to remove most of the structure on the side opposite the hinge and all the columns aligned and perpendicular with the axis of rotation. I am thinking of felling a tree and notching the trunk so the upper fart has nothing to stop its rotation and the uncut side bends, stretches and then parts as the trunk rotates.

It the tree where hollow and were square to cut it down removing one side would not cause it to rotate. You would then have to attack the two sides adjoining the first removed side until all that was holding the hollow square tree was the remaining side and perhaps some of the two perpendicular which would get crushed as the top rotates and the last side acts as the hinge.

No?

Yeah, kind of makes you wonder why tilting is such a popular notion.

In the image above, it's pretty obvious that the simulated upper block is not nearly rigid, yet it's really strong. These elements are elastic over a wide range, they'll distort but won't fail as such. The purpose was to demonstrate the deformation associated with a particular kind of support loss, not at all realistic. With the south side "chopped and notched like a tree", it looks superficially like tilt from all angles, but the roofline corner above the hinge is subjected to a smaller tilt angle than the antenna.




If there were elements which could fracture or otherwise fail, the area in red would be toast. While the simulation has reached a new stable equilibrium, this state would evolve with rapid lateral fracture towards the hinge if allowed to fail. It would never have developed the degree of strain seen above with a peak capacity of only 2 or 3 times normal demand. The "tilt" angle prior to a total failure would be small.

Enhanced simulations are in work. I hope anyone reading understands why I chose to skip over the analytical aspect and go straight to simulation. Torque = (Moment of Inertia) x (Angular Acceleration). For a rigid rectangle rotating about a corner under gravity and simple retarding force, not too bad, even when the corner is allowed to translate horizontally. Also not too useful. Some ardor, not much reward. I've already breezed by that in every way with the most trivial of simulations.

Still, I'm very clear that these are in no way representative of the tower.

SanderO:

For the structure to tilt a whole bunch of facade columns need to be pushed away, or buckled, not to mention a fair amount of core columns... while to begin the rotation a whole bunch of columns need to remain a bit to act as the hinge location.

Exactly. One side buckles while the other side bends. For WTC1 there is no evidence of this happening.

RIgid tilting is popular because the powers that be claim that such tilting existed in WTC1.

In reality it seems the top part of the building slouched slightly before collectively falling. That slouching looks like tilting if you don't look too carefully.

And this discussion returns me to the antenna. On the antenna thread I started it was stated that the antenna did not drop into the core but dropped over the side. DId the roof and hat truss tilt sufficiently to move the CG of the antenna enough for it to rip itself from its "moorings" and continue to fall over the side (south) or did it remain secured to the hat truss and the whole bit tilted right over?

Is there any theory proposed about the mechanism associated with the tilting over the side antenna... or is this not been worked out you?

Your approach is of a 2-D perimeter face? It's a 2-D grid, like a grid body comprised of small connections between adjacent points?

Great stuff. What is the plan for tweaking this into a simplified WTC model?

It's my opinion that most all discussion about hinges and tilting to this point have been too clumsy. Too many global assumptions. Your system has no global assumptions, and that is good. It may be the beginning of the first really good study on the subject we have seen.


Even in it's current form it is similar to the east or west perimeter of WTC1. It's just a grid, or a sheet.

It would be interesting to apply the same 2-D grid to a cross-section through the center of a tower. The OOS regions would have a modified grid to match their characteristics.

One of the strange things about early WTC1 movement is how a south perimeter failure could rip down the core with very little tilt. There is about 65 ft of OOS that has no vertical supports, so how south wall failure could translate so quickly into total core failure is one of the great mysteries of our times.

The truth being, my friends, there are no rigid blocks, only rigid minds.



It's a bit of an insane idea, that the "upper block" would "tilt rigidly".

65 ft of OOS between core and perimeter, obviously two distinct groups of columns (core and perimeter) with large distances between them relative to the total width of the structure...

A giant measuring stick in the form of the antenna firmly attached to the top of the core....

It is more natural to talk in terms of deformity, and specifically convex or concave roofline deformity or the deformation of a perimeter sheet, than of rigid tilt.


It's interesting to think about how that ridiculous idea entered the debate. From where?


The physics and geometry used in WTC research is so bad, really. So 18th century, with blocks and magic "zone B" and rigid tilts and a bunch of absurd over-simplifications.

I think the trick for us is to rise above the 18th century mindset and try to solve real problems like this one, maybe for the first time.

Thanks, Major_Tom.

Major_Tom wrote:Your approach is of a 2-D perimeter face? It's a 2-D grid, like a grid body comprised of small connections between adjacent points?

Yes, there is a grid of mass points. There are many ways to construct a grid; mass points versus bodies, translation and/or rotational springs, or finite element areas. For now it will be 2D. I can do 3D, but want to start simple in order to abstract certain features along the way.

What is the plan for tweaking this into a simplified WTC model?

The first step is a finer grid. Nothing special about that, except this is a research program and making large structures by hand can be pretty mind-numbing. Therefore I'm scripting the creation of large grids and auxiliary components, a side job that's taking a little time but well worth it. Once the larger grid is in place, there will be a lot more necessary complexity added.

Next, there will be supports instead of magic forces. A combination of brittle rotational and translational springs which can be finely tuned to the desired capacity distribution across the width. These will be capable of mimicking failure in compression, tension and rotation. There can be an initial defect, presumably leading to a catastrophic failure as load is redistributed. Various distributions of capacity can be explored.

Pretty much alongside of this will come non-uniform distribution of mass and capacity. This will require a bit more thought, though. There's no reason not to try for some accuracy in this, but the caveat will always remain that 2D is not going to represent 3D well at all in this case. 2D implies translational symmetry in and out of the viewing plane, i.e. a building stretching to +/- infinity in and out of the screen, with that same cross-section. What I'm striving for is a crude "X-ray" projection of mass density and strength which account for the skeleton of core/perimeter/hat and the utter lack of vertical support in the open floor space. Not sure yet the best approach.

The finite element sheets are very nice far from the failure point but, ultimately, that's what's more interesting and useful. However, the chance of a realistic simulation of failure sequence in this environment is nil, and would never be an objective. It's best to stay crude and in the domain of basic principle where the applicability is more sound. Having failure propagate across the perimeter face is something that can possibly be modeled, as well as seeing trends in surface and corner motion as a result. Think of it as extending the rigid kinematic approximation done by achimspok.

It's my opinion that most all discussion about hinges and tilting to this point have been too clumsy. Too many global assumptions. Your system has no global assumptions, and that is good. It may be the beginning of the first really good study on the subject we have seen.

Analysis gets ugly quickly for even the simplest of systems. Deformation is a terrible wildcard; at least with a decent simulation, you can identify the primary characteristics of a modest system and know that, if the model has correspondence in any aspect, that aspect may be considered a candidate in actual initiation.

Of course, the question naturally arises: is it possible to at least partially reverse engineer the failure sequence from feature motion? It hasn't been presented in this thread yet, but other work (including by you) seems to strongly contradict rigid body tilt, to the point where it's not even a useful approximation. The work of checking multiple angles to determine 3D motion has been also been done by others but that's on the list for later, too. Right now, I want to compare the differential motion predicted by various modes of flexure in advance of trying to see into which class observations fit.

Even in it's current form it is similar to the east or west perimeter of WTC1. It's just a grid, or a sheet.

Yes, the intention at this time is interpreting it as a 2D representation of a block, but it can be set up as just a perimeter sheet, too. One of the runs I did showed a pattern of stress propagating across the face in a manner similar to what was seen on the north face of WTC2. I'm waiting to get the more complex sims in place to look at that some more. Again, beware, no out-of-plane deformation in 2D. That will have wait for 3D.

It would be interesting to apply the same 2-D grid to a cross-section through the center of a tower. The OOS regions would have a modified grid to match their characteristics.

Yes, exactly what I have in mind. It's even possible to use truss assemblies for floors, and loose office loading mass (which can acquire angular momentum, too) later on. The next approximation I'm shooting for, though, is an FEA sheet to represent the top nine stories or so, then a grid of frangible connections through six stories of failure zone, then another FEA grid for three stories of intact bottom block which will be fixed on the lower edge. Uniform mass and capacity, then a more accurate heterogeneous distribution culled from femr2's mass table and the floor plans.

Lots o work.

One of the strange things about early WTC1 movement is how a south perimeter failure could rip down the core with very little tilt. There is about 65 ft of OOS that has no vertical supports, so how south wall failure could translate so quickly into total core failure is one of the great mysteries of our times.

Good question.

Major_Tom wrote:The truth being, my friends, there are no rigid blocks, only rigid minds.

What I thought was very interesting was the extent some individuals have gone to recently in trying to deny evidence against rigidity. In one case, it was posited that the reaction force from tilting would displace the hinge far enough in the opposite direction to effectively leave the roofline in the same location! Another was the paradoxical suggestion that rigidity was maintained by way of a moving hinge - an extreme form of deformation if there ever was one!

!!!

Why are some people so desperate to cling to rigid tilt in the face of contrary evidence?

It's a bit of an insane idea, that the "upper block" would "tilt rigidly".

That's a funny thing. If you ask some of these same people whether they think the block was perfectly rigid, they'd say no. It's more a matter of certain types of deformation, like core slump, being verboten.

It is more natural to talk in terms of deformity, and specifically convex or concave roofline deformity or the deformation of a perimeter sheet, than of rigid tilt.

It is.

It's interesting to think about how that ridiculous idea entered the debate. From where?

I don't know. I picked the idea up by osmosis. It just seemed to come into being. I do understand the impression, it does look that way on first (and even subsequent) inspections, but I'm not sure at what point it became a sacred cow, or why.

The physics and geometry used in WTC research is so bad, really. So 18th century, with blocks and magic "zone B" and rigid tilts and a bunch of absurd over-simplifications.

I think the trick for us is to rise above the 18th century mindset and try to solve real problems like this one, maybe for the first time.

It's a long, hard road when it's not your day job, but yep, it might happen.

I should mention that I've done a pretty extensive set of validations on the program itself, both as pure testing and in the course of working on other problems. Some of the testing results led the author to make changes in the program, so it was not lightweight validation. At this point, I'm fairly well acquainted with the program's comfort zone and trust it to produce valid physical behavior in the demonstrations I present. The actual trustworthiness and degree of applicability to anything is up to the reader.

Again, the lack of an analytical treatment for a rectangle rotating about a corner is no loss for the time being, the sim does it and a lot more just fine. Soon, though, I want to go over the rigid body geometry and Sauret perspective correction as a parallel effort. The femr2 and achimspok datasets do not appear to represent rigid tilt in any plane. Hopefully the sims will present a set of alternative deformation categories from which to choose a best fit. In this, a 2D diagonal slice NW-SE may suffice.

SanderO wrote:DId the roof and hat truss tilt sufficiently to move the CG of the antenna enough for it to rip itself from its "moorings" and continue to fall over the side (south) or did it remain secured to the hat truss and the whole bit tilted right over?

I don't know the answer to this. I believe some here are inclined towards an early breaking point, and I think I agree. There is a profound whack after a short descent. It is also possible from one angle to see the antenna appear to tilt back back towards its original orientation. This is quite an abrupt angular acceleration and might well be expected to snap the antenna somewhere.

Independently, I think some of the upper block went over the side; when and how much...?

Is there any theory proposed about the mechanism associated with the tilting over the side antenna... or is this not been worked out you?

Directed at Major_Tom?

OneWhiteEye wrote:It's more a matter of certain types of deformation, like core slump, being verboten.

Or perhaps the amount of deformation is the problem. Has anyone addressed the concept of the upper block falling apart in place?

From the moment I read the discussion about the collapse I saw people analyze what happened in reductionist metaphors - the smaller weaker upper block and the strong lower block. Gage made a model and dropped a card board box which was supposed to represent the top block falling at free fall.

People went off about the impossibility of the weaker and light mass of the upper block crushing the stronger mass of the lower block and all those really strong box columns down there.

There were many physics papers written by people such as Bazant which engaged this reductionist block metaphor to reduce the collapse to a Newtonian physics exercise.

My hair was on fire as I could not understand how these structures could be treated a homogenous blocks. First they were made from tens of thousands of structural elements with unique structural performance characteristics. Second there were even more connections / joints between these discrete elements and finally these blocks were 98% air by volume.

The analysis of what happens needs to look at the stress and interactions of forces in thousands of connections which in the course of the destruction were subjected to all sorts of loading conditions which were not present in the static condition.

The floor system clearly was not able to support the dynamic loading that ensued as floors broke free or broke apart and dropped. The destruction of the floor system removed the lateral support between the facade structure and the perimeter core structure. The floor system also likely added horizontal impulse to both the core perimeter and the facade as it came apart.

When I think of a block I think of a glass "cube" dropping to the ground and shattering. When I think of a building collapse I think of a lego set constructed into some tall structure coming apart into a pile or legos.

Thinking of the collapse of the towers as a blocks is a fool's exercise. It simply does not represent the reality. It reduces a complex system to a overly simplified cartoon. It confuses the forest as the trees in it. When we study the forest or an eco system we see how the micro influences the macro and we study the micro to understand the macro.

When we engineer a structure we work on the micro level... beam by beam, column by column, connection by connection, bolt by bolt, weld by weld. The towers may have represented over 200,000 tons of steel but this hardly describes their complexity.

Whoever uses the notion of blocks... should be sent to the corner for eternity.