Would the WTC Twin Towers have collapsed from fire alone, without plane impact?

[Pooua]

"Why both D Chandler and T Szamboti are wrong to expect a sudden jolt or significant deceleration"

AND the reason - yet again - in one sentence - "Because the Top Block did not drop to impact on the lower tower with columns in alignment"

AND I've already posted a pretty picture that is a large part of the necessary proof. Look and THINK:

Both Chandler and Szamboti expected the line of the perimeter - the yellow arrows - to hit its other part. Clearly it wasn't going anywhere near where the "Jolt" (Szamboti) OR "deceleration" (Chandler) would come from.

Did anybody do any kind of mathematical or experimental analysis to test how significant such a jolt would be? I don't deny that the columns were misaligned during the collapse, but I did my own back-of-envelope, first approximation calculations of the collapse of the Towers, as follows.

The force the section of the Towers that were above the damaged zone normally exerted on the section below the damaged zone can be approximated by taking the mass of those floors and multiplying it by gravitational acceleration. The entire building had a mass of about 450 x 10^6 kg, and about 10% of each Tower was above the impact zone, so I estimate about 45x10^6 kg of mass above the impact zone. This should be a conservative estimate; the real value probably is a bit larger, and would be different for each Tower.

F=ma = 45x10^6 kg * 9.8 m/s^2 ~= 441x10^6 Newtons

This is the gravity or static load that the portion of the Towers below the impact zones resisted from the portion above the impact zones on a normal day.

When the portion of the Towers above the impact zone began moving, they began moving pretty much as a rigid block, at least for a few meters, until they actually impacted the lower floors. Each floor was separated from the next by 3 or 4 meters. I don't know how fast they accelerated or what velocity they reached in this time, but I conservatively estimated 1/2 free fall acceleration for 3 meters, giving the falling section a velocity of 5.4 m/s by the time it reached the next lowest floor, using standard free fall velocity calculation.

The force the upper section was capable of generating on impact with the lower section would depend on the stopping distance or stopping time required to stop the falling mass. I'm assuming that the ultimate limit of stopping distance would be the distance the bolts holding each floor together could be distorted before shearing. If you wanted to assume that the columns were aligned, you would need to decide how far the columns could deflect before they broke. According to NIST's "Overview of the Structural Design of World Trade Center 1, 2, and 7 Buildings" (File Name 910105.pdf), "The typical bolt used in the simple shear connections was 22 mm (7/8 in) diameter ASTM A325... The bolt used for heavier brace and moment connections was a 25 mm (1 in) diameter ASTM A490." ("Overview of the Structural Design of World Trade Center 1, 2, and 7 Buildings." Unnumbered page; P 25 in the PDF.) I made several calculations using different values of stopping time (in the millisecond range) and stopping distances (in the millimeter range). An example calculation:

F=mgh/s

Where m is mass, g is gravitational acceleration, h is height of fall and s is the stopping distance.

Assuming the bolts could bring the falling upper section to a stop in 6 millimeters without shearing,

F= mgh/s = (45x10^6 kg * 4.9 m/s^2 * 3 m) / 6x10^-3 m = 110 x 10^9 N

The ratio of the impact force to the normal static load is

110x10^9 / 441 x 10^6 = 249

If, instead, the falling section fell at standard 1g, then the impact force becomes

(45x10^6 kg * 9.8 m/s^2 * 3 m) / 6x10^-3m = 221x10^9 N

and the ratio becomes 501 times the usual static load.

My results tell me that for the lower section to withstand the collapse of the falling material above them, they would have to have withstood about 250 times the static force they normally supported. As the bolts (and the rest of the building) would not be able to resist this much force, they would have broken before reaching that value. If the columns had been aligned and impacted straight on to each other, they would have to have deflected by a few meters without breaking to resist the force of the material falling on them.

As each floor broke apart, it would add to the falling mass of debris. Whatever wasn't ejected to the sides probably would contribute to the mass impacting the next floor, and all of it would continue accelerating, increasing the amount of force applied, until it reached equilibrium. Any jolt would have been momentary, lasting milliseconds, similar to the jolt or deceleration that a football player experiences when running through a paper banner. I don't believe you would notice very much! Just as you don't notice each detonation inside the piston chambers of a car revving its engine, you wouldn't notice the jolt as the falling section impacts the next floor.

Other people have also performed similar calculations, using different assumptions for the variables, but all of them concluding that the Towers could not possibly have withstood the force of impact of the falling material (and none of them assume the columns were aligned):

New Mexicans for Science and Reason, "How Does a Building Crush Itself?," By Dave Thomas
http://nmsr.org/nmsr911a.htm

"Static v. Dynamic Loading: Why the WTC Towers Fell So Fast"
https://burtonsys.com/staticvdyn/

"Why Did the World Trade Center Collapse? Science, Engineering, and Speculation"
http://www.tms.org/pubs/journals/jom/0112/eagar/eagar-0112.html

 

[econ41]

Some good thinking @Pooua - sadly a couple of your premises are not correct. We may need a few posts to identify and discuss the issues.

Let me start by identifying three key issues:

Did anybody do any kind of mathematical or experimental analysis to test how significant such a jolt would be? I don't deny that the columns were misaligned during the collapse, but I did my own back-of-envelope, first approximation calculations of the collapse of the Towers, as follows.

Yes. The issue has been extensively discussed. Because there were fundamental misunderstandings about the mechanism of collapse. The dominant presumption was that somehow the "Top Block" dropped to land on the lower tower resulting in a "jolt" of impact. The assumed scenario was that somehow broken top parts of columns in the Top Block fell to land on - in alignment with - their lower parts. Resulting in one big "Jolt". The misunderstanding arose because Bazant & Zhou were first to publish a paper explaining the collapse - the first version released 9/13 2001 - two days after the event. It was legitimately framed s a "limit case" and assumed "Top Block dropping to impact with columns aligned" because columns aligned is the best case scenario for survival - worst case for collapse. It was NOT intended as an explanation of what literally happened but most discussion assumed it was what actually happened. Debate and understanding was, for many years, dominated by those misunderstandings.

So that is the first issue and your analysis seems to follow that false trail.

The force the section of the Towers that were above the damaged zone normally exerted on the section below the damaged zone can be approximated by taking the mass of those floors and multiplying it by gravitational acceleration. The entire building had a mass of about 450 x 10^6 kg, and about 10% of each Tower was above the impact zone, so I estimate about 45x10^6 kg of mass above the impact zone. This should be a conservative estimate; the real value probably is a bit larger, and would be different for each Tower.

F=ma = 45x10^6 kg * 9.8 m/s^2 ~= 441x10^6 Newtons

This is the gravity or static load that the portion of the Towers below the impact zones resisted from the portion above the impact zones on a normal day.

No comment at this stage...
..BUT

When the portion of the Towers above the impact zone began moving, they began moving pretty much as a rigid block,...

Yes.

at least for a few meters,

No. Or, at least, the first motions were NOT "dropping". More discussion is needed.

until they actually impacted the lower floors.

No. The Top Block was always in contact with the lower tower EXCEPT for those columns sheared by aircraft impact. The columns were failing in axial compression overload because the Top Block was "pushing down on them".

Each floor was separated from the next by 3 or 4 meters. I don't know how fast they accelerated or what velocity they reached in this time, but I conservatively estimated 1/2 free fall acceleration for 3 meters, giving the falling section a velocity of 5.4 m/s by the time it reached the next lowest floor, using standard free fall velocity calculation.

.. and you are conflating - overlapping - the initiation stage and progression stage.

Let me not address the details at this preliminary stage of discussion. The problem is that the Twin Towers collapses involved four distinct stages. Two main ones viz "initiation" which resulted in Top Block starting to move bodily downwards and "progression" - the rapid descent to global collapse. Full explanation needs two further stages viz "transition" >> how "initiation" became "progression". And not needed at this stage of my comments but "early progression" involved an additional factor which we can discuss later.

The mechanisms for the two main stages were very different and your analysis conflates features from different scenarios.

A couple of examples:

The force the upper section was capable of generating on impact with the lower section would depend on the stopping distance or stopping time required to stop the falling mass.

It didn't "drop" through a gap >> explanation can await discussion.

I'm assuming that the ultimate limit of stopping distance would be the distance the bolts holding each floor together could be distorted before shearing.

Probably not the case - the "initiation stage" was dominated by a cascading failure of columns losing the ability to carry vertical loads in axial compression. Shearing of bolts or similar was a main feature of the progression stage.

If you wanted to assume that the columns were aligned,

They weren't - and understanding why is a big part of understanding the whole collapse mechanism.

My results tell me that for the lower section to withstand the collapse of the falling material above them, they would have to have withstood about 250 times the static force they normally supported. As the bolts (and the rest of the building) would not be able to resist this much force, they would have broken before reaching that value. If the columns had been aligned and impacted straight on to each other, they would have to have deflected by a few meters without breaking to resist the force of the material falling on them.

As each floor broke apart, it would add to the falling mass of debris. Whatever wasn't ejected to the sides probably would contribute to the mass impacting the next floor, and all of it would continue accelerating, increasing the amount of force applied, until it reached equilibrium. Any jolt would have been momentary, lasting milliseconds, similar to the jolt or deceleration that a football player experiences when running through a paper banner. I don't believe you would notice very much! Just as you don't notice each detonation inside the piston chambers of a car revving its engine, you wouldn't notice the jolt as the falling section impacts the next floor.

<< some good points - I'll reserve comments at this stage.

Other people have also performed similar calculations, using different assumptions for the variables, but all of them concluding that the Towers could not possibly have withstood the force of impact of the falling material (and none of them assume the columns were aligned):

Actually that is not true. Most debunkers accept Bazant & Verdure's "Crush Down/Crush Up" hypothesis without question. And it is premised on "columns aligned" which didn't happen.

New Mexicans for Science and Reason, "How Does a Building Crush Itself?," By Dave Thomas
http://nmsr.org/nmsr911a.htm

I'm familiar with Dave Thomas' work.

Clearly we have some points for discussion and clarification.

 

[Abdullah]

Thermal expansion could maybe knock out some vital core columns.

This is the tower under maximum designed wind loads, from NCSTAR 1-5A

Notice how the maximum interstiry drift is around 0.5%. This corresponds to around 2cm for a typical floor. And notice how the core columns are in average almost 80% capacity.

The core is 40m in the long axis and 20m in the short.

From NCSTAR 1-6C

Which means that at a temperature of 200°C, the core tries to expand 8cm on the long axis and 4cm on the short. Corresponding to an attempted push out of 4cm (more than 2× the design drift) at the ends of the core, where the largest columns are.

 

[econ41]

Thermal expansion could maybe knock out some vital core columns.

Your argument is premised on NIST's interpretation of the actual event.

This is the tower under maximum designed wind loads, from NCSTAR 1-5A

Notice how the maximum interstiry drift is around 0.5%. This corresponds to around 2cm for a typical floor. And notice how the core columns are in average almost 80% capacity.

The core is 40m in the long axis and 20m in the short.

From NCSTAR 1-6C

.. the fires NIST estimates for the Real event.

The Topic of this thread is: "Would the WTC Twin Towers have collapsed from fire alone, without plane impact?"

This raises two questions:
1) How could fires of the intensity of the real event happen without the plane impact compacting the office contents fuel; without aviation fuel accelerant, without insulation stripping OR destruction of sprinklers?

2) And wouldn't "active fire fighting" have been started? << No active fire fighting was one of the bigger factors allowing the real event fires to cause collapse.

Which means that at a temperature of 200°C, the core tries to expand 8cm on the long axis and 4cm on the short. Corresponding to an attempted push out of 4cm (more than 2× the design drift) at the ends of the core, where the largest columns are.

Actually, this is a secondary factor - bypassed by my first question. BUT "an attempted push out of 4cm". How much would that outwards thrust have bent the columns - if any? And would the actual bending be sufficient to de-stabilise the column(s)?

I OPed this thread for reasons I gave in the OP.

In subsequent posts, I firmed up my answer to affirm that the WTC Twin Towers could not have been caused to collapse by fires without aircraft impact. Because the scale and intensity of the actual 9/11 fires resulted from aircraft impact. And couldn't be deliberately caused without the plane impact.

Do you disagree with my reasoning?
If so - for what reasons? and
What is the relevance of your beam expansion hypothesis to either scenario discussed in this thread?