Simple Calculations of Strain Energy

[Heiwa]

It seems many JREF members have faint ideas what strain energy is. This may explain many misunderstandings of the WTC destructions.

So here we go:

From NIST report - NISTNCSTAR1-6D chapter 5.2 - we learn:

"The aircraft impacted the north wall of WTC 1 at 8:46 a.m. … between Floor 93 and Floor 98. … The subsequent fires weakened structural subsystems, including the core columns, floors and exterior walls. The core displaced downward … At 100 min (at 10:28:18), the north, east, and west walls at Floor 98 carried 7 percent, 35 percent and 30 percent more gravity load loads … and the south wall and the core carried about 7 percent and 20 percent less loads, respectively., … At 10.28 a.m., 102 min after the aircraft impact, WTC1 began to collapse. … The release of potential energy due to downward movement of the building mass above the buckled columns exceeded the strain energy that could be absorbed by the structure. Global collapse ensued."

From chapter 5.3 we learn:

"The aircraft … impacted the south wall of WTC 2 at 9.03 a.m. … between Floor 78 and Floor 84. … (9:59 am) … The release of potential energy due to downward movement of the building mass above the buckled columns exceeded the strain energy that could be absorbed by the structure. Global collapse ensued."

Note that the two Towers collapsed for exactly the same cause:

"The release of potential energy due to downward movement of the building mass above the buckled columns exceeded the strain energy that could be absorbed by the structure."

So what is the strain energy that could or could not be absorbed by the structure? Simply speaking it is the redundancy built into the structure, or the extra strength in it. If one structural part fails (no strength), its load is transmitted to other structural parts that carry it to prevent further failures. Some of these structural parts may also fail in the process of absorbing strain energy.

Let's assume that the total strain energy of WTC1 that can be absorbed is 10 000 units of strain energy. It is distributed all over the Tower and more at the bottom, where it is stronger. For simplicity let's assume that 1 000 units of strain energy was available in the structure above the floors of initial damage (buckled columns) and 9 000 units was located in the structure below (as the buckled columns divided the Tower 10/90).

When potential energy due to downward movement of the building mass above the buckled columns is released, it is evidently absorbed 50/50 by the structures above and below. It is in fact the structures adjacent to the initial failures that first absorb the energy released.

Say that 2 000 units of energy were released, when the columns buckled. It means that 1 000 units will be absorbed by the structure above and 1000 units by the structure below and that then the destruction is arrested due to lack of potential energy provided by gravity. No global collapse would have ensued.
What it actually means is that the structure above will be completely destroyed, as it could only absorb 1 000 units, when 8 000 units of strain energy still remains in the structure below.

If only 1 000 units of energy were released, when the columns buckled, then half the upper structure would remain, when the potential energy released had been absorbed. It would then rest on the top of structure below that had absorbed the other 500 units of energy released. No global collapse would have ensued.

So how much potential energy was actually released when the columns buckled? It would appear that it was about 1.22 Giga Joule [1] that actually corresponds to the energy content of only 41 kilograms of gas oil!

Now, does anybody believe that the total strain energy that could be absorbed by WTC1:s structure to prevent global collapse corresponded to only 41 kilograms of gas oil?

Evidently not! I have a feeling that NIST miscalculated the avaiable strain energy that could be absorbed in the structure by a factor of 1 000!

Only one, small mistake, can happen to anyone, small mistakes, but it is time to correct it.



Reference

[1] Help understanding the Destructions of the World Trade Center Twin Towers, by Anders Björkman, M.Sc., 2008 , http://heiwaco.tripod.com/nist.htm

 

[T.A.M.]

This topic belongs in the "Science Section" as I see no Conspiracy Theory in your opening diatribe/tutorial section.

Hopefully Newton's Bit or someone else will be along to address it for you before it is moved to the appropriate section.

TAM

 

[GlennB]

Once again Heiwa - a building is not a unitary structure. The massive columns at the ground floor will not protect the thinner coumns (plus their bolts and welds) at the collapse zone.

Otherwise, you might as well include the entire planet in your "strain energy" calculations. The Earth is very big and strong, and WTC was embedded in it. Therefore no building can ever collapse

 

[Newtons Bit]

This topic belongs in the "Science Section" as I see no Conspiracy Theory in your opening diatribe/tutorial section.

Hopefully Newton's Bit or someone else will be along to address it for you before it is moved to the appropriate section.

TAM

I don't even need to. GlennB has pointed out the obvious before I could. I would also like to note that Heiwa NEVER calculates the strain capacity of a single floor. Perhaps this is because he knows it will fail?

 

[gumboot]

Yes, I'm a layman and even I saw the flaw in your reasoning immediately. Are you sure you're an engineer?

 

[Heiwa]

This topic belongs in the "Science Section" as I see no Conspiracy Theory in your opening diatribe/tutorial section.

Hopefully Newton's Bit or someone else will be along to address it for you before it is moved to the appropriate section.

TAM

As all conspiracy theories regarding the WTC:s destructions use strain energy as a vital ingredient, I think the topic belongs here.
You see, it is part of any conspiracy theory to use scientific terms incorrectly and/or in the wrong context, as demonstrated.

Nist does it quite cunningly (i.e. with intent): Nist says that energy X was released (no calculations) and that this energy X exceeded the strain energy Y that could be absorbed (no calculations) and that because X is bigger than Y "global collapse ensued".

Apart from neither calculating X nor Y (we don't know if X > Y), it is not explained why X > Y = global collapse. In my text books of structural analysis X > Y will only cause failures of various types of the structural parts involved and we are far, far away from any global collapse.

 

[A W Smith]

Heiwa,, When will you bring math to the argument? Show us your calculations for the strain energy reserve of the impact floors. Surely your correspondence school where you earned your degree taught you math

 

[pomeroo]

As all conspiracy theories regarding the WTC:s destructions use strain energy as a vital ingredient, I think the topic belongs here.
You see, it is part of any conspiracy theory to use scientific terms incorrectly and/or in the wrong context, as demonstrated.

Nist does it quite cunningly (i.e. with intent): Nist says that energy X was released (no calculations) and that this energy X exceeded the strain energy Y that could be absorbed (no calculations) and that because X is bigger than Y "global collapse ensued".

Apart from neither calculating X nor Y (we don't know if X > Y), it is not explained why X > Y = global collapse. In my text books of structural analysis X > Y will only cause failures of various types of the structural parts involved and we are far, far away from any global collapse.

A redundant demonstration of your total incompetence and inability to learn.

You FAIL again.

 

[Hellbound]

Heiwa:

You are negelcting some things, even if we take your view of how strain energy behaves.

First, let's consider your model. Your example was 2000 units, and those "destroyed" the top of the building. I have serious doubts that this is actually how strain energy works, mind you, but for the sake of argument I'll accept it provisionally.

So, you had 2000 units of energy that impacted, taking out 2000 strain units. You claim this would destroy, basically, the top 20% of the building.

Well, what happens to the rubble? What energy is imparted to shift the rubble off the rest of the building? That's what you are neglecting.

The strain energy is directly related to the construction methods and materials used in the building. As the entire WTC is a single structure, we can make the assumption that the materials and methods are the same throughout. This means that each unti of "strain energy" would be directly proportional to a unit of weight or mass.

So, when the top 20% of the building is destroyed, that's 4000 "strain energy mass equivalents" that are now impacting the next floor down. For arguments sake, I'll even let you state that 80% of the material is tossed outward and does not contribuite to downward momentum (actual values are less, but I'm giving you the most generous assumptions under your model). That still leaves 500 units for impact. Since each floor (assume 100 floors for simplicity, actual was 110 IIRC) is 1/100 of the building, each floor represents 100 "strain units". So, that 500 units destroys the next floor down as well as the four floors underneath, then would "stop".

But wait, now you've added five more floors of debris...that's another 100 units, plus the 500 we had on top. There goes another 6 floors.

Ev en under your unrealistiic and simplistic model, global collapse is inevitiable. What you are failing to realize is that:

1. Strain cannot redistribute endlessly across the building structure, it is limited. Too much localized damage can overwhelm the capacity of the structural supports to "shift" the extra load.

2. The "destroyed" portion of the building, even if structurally disconnected, does not cease to exist or cease to have weight and mass. It is still as heavy as it was, and it must go somewhere. It contains and enormous amount of energy from gravitational potential, and that force is greatly multiplied by even a fall of 10 feet (one floor).

3. If a collapsing portion is enough to take out a single floor, it will continue to take out every floor under that one: it's mass grows as it falls (eac succedssive floor destroyed adds to the weight).

4. (This is key): Stronger structural elements may halt a collapse, but only if they are massively overbuilt. This is because the mass and weight will be unlikely to impact the designed load-bearing areas. If a floor is made with a 200% margin, for example (it's designed to hold twice the expected weight that it will be above that area), that 200% assumes the structure is intact, and the weight load is resting on the support columns and framework designed to carry it. When the weight is a shifting, incoherent mass of rubble, it will not be likely that every bit of it lands only on the designed support elements. And tyhis gets to the crux of why your model is wrong.

The strain energy only applies to the intact structure, resisting loads in the manner upon which it was designed to do so. If you were, for example, simply moving 1 ton weights onto a single floor, spreading them out evenly, then the strain energy would tell you how many you could get on a floor before it failed. The strain energy does not apply to loads that are not stressing the structure in it's designed manner. It's like the old trick of standing on a Coke can. If you are careful, you can set a soda can on the ground and stand on top of it without the can collapsing. The "strain energy" is greater than the force of your weight. However, if someone taps the side of the can with a pencil, it will immediately collapse. Likewise, once the loads are arriving on a structural area in a manner not consistent with the way those elements were designed, all bets are off. The weights and forces are acting at unpredictible poitns and angles.

 

[X]

As all conspiracy theories regarding the WTC:s destructions use strain energy as a vital ingredient, I think the topic belongs here.
You see, it is part of any conspiracy theory to use scientific terms incorrectly and/or in the wrong context, as demonstrated.

So now the theory involves, among everything else, corrupting specifici scientific terms.
How big is your theory going to get, before you admit it can't be amintained?

Nist does it quite cunningly (i.e. with intent): Nist says that energy X was released (no calculations) and that this energy X exceeded the strain energy Y that could be absorbed (no calculations) and that because X is bigger than Y "global collapse ensued".

Essentially, yes.

Apart from neither calculating X nor Y (we don't know if X > Y), it is not explained why X > Y = global collapse. In my text books of structural analysis X > Y will only cause failures of various types of the structural parts involved and we are far, far away from any global collapse.

My bolding.
You have just admitted that you do not understand why an input of energy greater then the amount of energy the building can physically sustain without failure leads to building failure.
Do you honeslty think that?
It's like saying you cannot comprehend why placing a 5 tonne load on a 3 tonne rated forklift will cause problems.
There's no point in making a discussion of this, because it is so blatantly rediculous.

 

[Heiwa]

Heiwa:

You are negelcting some things, even if we take your view of how strain energy behaves.

Well, what happens to the rubble? What energy is imparted to shift the rubble off the rest of the building? That's what you are neglecting.

So it is the rubble that destroys the building? Actually no free rubble should be produced in a gravity collapse! Let's take it once again:

The primary (load bearing) structure is only the vertical columns. Other structure is secondary (e.g. floors, spandrels, horizontal core beams) and they only carry local loads to or between the primary structural parts.

Initiation is the alleged buckling (failures) of all primary structure, i.e. all the columns, in an initiation zone. This results in release of potential energy.

(Some sources talk about free fall of weights and impacts but such events are not seen on any videos, etc).

Structural failures of primary structure result in release of potential energy because the structure carries gravity loads. Some of this potential energy is immediately consumed to develop the failures further, e.g. buckle, bend, rip apart, etc, the structural parts involved.

If only buckling or bending occur, the parts involved are still connected. No rubble is produced. Ripping apart is the ultimate stage of a local failure, i.e. the parts become disconnected. Still no rubble.

In WTC1 after initiation (and prior destruction of the Tower itself) all columns were apparently ripped apart in the initiation zone.

The probability that these primary structural parts, i.e. the columns, will contact again is nil.

Thus the original interface between the top parts and the bottom parts (the columns) after initiation is permanently broken.

This means, of course, that the primary structure, the columns, of both top and bottom parts, after initiation and the serious failures associated with it will only contact secondary structure or nothing at all, e.g. upper/lower wall columns are displaced outside the structure below/above in open air and cannot produce further failures.

A new interface is developed. This Nist & Co carefully avoid to mention.

After initiation the interface thus changes - upper/lower columns (previously attached to one another) are now resting on secondary structure, mainly floors or the floors are resting on the columns.

The resulting, further structural failures can then only be of one type, i.e. the wall columns slices apart the next floors above/below and the core columns punches big holes in the next floors above/below. In the latter case horizontal core beams may slice apart the first floor above/below or at least shear off from the floors.

Only secondary structures, mainly floors, are now failing at one edge in the top and bottom structures and hinge down around the other edge.

No rubble is produced!

The end result of these local failures of secondary structure is further described at http://heiwaco.tripod.com/nist3.htm ; more upper part floors hinge down and become entangled inside the structure below and the further damaged floors there, and in the worst case two walls of the upper block are sheared off and drops to the ground.

One thing should be clear. Any potential energy released will cause as much local structural damage/failures of secondary structure above the initiation zone as below it. Nist & Co carefully avoid to mention this obvious fact.

If enough energy is released, two walls of the upper block should have sheared off completely and dropped down to the ground in one big piece.

Sooner or later the local failures up top would have been arrested; when all energy released is consumed in local failures, friction, deflection of damaged parts and shifted loads, etc. The primary structure, the columns, of the part below the initiation zone are not really damaged! The remaining primary structure of the upper part, i.e. its columns, will be resting inside the structure below and will not really be damaged. Very little rubble is produced.

It is called collapse arrest. Happens all the time.

A final remark regarding "rubble" should also be clear. There is not really any rubble produced! The secondary structure floors of both upper and lower parts, the only structure affected after initiation, have just been sliced or punched apart and have hinged down around the unaffected edges and are loaded on top of each other. No rubble is really produced and definitely no rubble that can free fall producing more energy, etc.

Evidently the above described, new interface after initiation and associated structural failures of secondary structural parts are not what we see on any videos of the destruction. What we see can only be some exotic CD.

 

[Smackety]

...horizontal core beams...

WTF?

 

[Alferd_Packer]

The resulting, further structural failures can then only be of one type, i.e. the wall columns slices apart the next floors above/below and the core columns punches big holes in the next floors above/below. In the latter case horizontal core beams may slice apart the first floor above/below or at least shear off from the floors.

WTF?

Yes, there were beams connecting the columns in the core areas, but to claim that these beams "may slice apart the first floor above/below." is stupid.

 

[Hellbound]

Heiwa:

Use Debris instead of rubble, if you like. But in any case, that's irrelevant. My primary point is that the mass that has failed is hitting the structure below in palces that it was not designed to support weight. From your own post:

After initiation the interface thus changes - upper/lower columns (previously attached to one another) are now resting on secondary structure, mainly floors or the floors are resting on the columns.

Of course, even with the failure method you describe...when those upper floors fail they are coming down on the lower structure.

I'd also like to know how you reconcile these two statements:

The resulting, further structural failures can then only be of one type, i.e. the wall columns slices apart the next floors above/below and the core columns punches big holes in the next floors above/below.

No rubble is produced!

Also, yo simply assert these two key points, rather than giving any evidence for them:

Sooner or later the local failures up top would have been arrested; when all energy released is consumed in local failures, friction, deflection of damaged parts and shifted loads, etc.

and

It is called collapse arrest. Happens all the time.

The collapse arrest, specifically, interests me. Can you shoe me another case where a high-rise building failed at about 80% to 90% of it's height, and then arrested the collapse? It's a serious question.

Finally, you post this:

The remaining primary structure of the upper part, i.e. its columns, will be resting inside the structure below and will not really be damaged.

I don't think you understand load bearing structures. The columns are NOT independent entities. They do not stand alone, with only vertical forces as the forces to consider. In fact, your point about strain energy being distributed leads into this. Although I believe your model to be incorrect, it is true to an extint. Buildings are designed to be able to "shift" load to other columns and support members when one area fails. That is done through the horizontal and diagonal cross-bracing between columns. If that fails, then each primary column suddenly must support it's load independently. Take a simple example:


The horizontal and diagonal cross-braces hold the primary columns in place (so the load pushes agains tthe length of the column) and help the columsn redistribute weight to each other should one become heavily loaded or fail.

What would happen to the above structure if Weight, instead of falling on the tops of the primary supports, fell at the spot marked B? Or C? What if it fell onto all the cross members?

 

[Heiwa]

Yes, there were beams connecting the columns in the core areas, but to claim that these beams "may slice apart the first floor above/below." is stupid.

Stupid? The bolted connections between any floor/horizontal core beam should shear off when the beams were displaced, as the core columns supporting the beam were displaced, i.e. the floors are sliced off the beams. Weakest parts. No rubble produced. Except some sheared off bolts.

But let's assume the core beams do not slice apart the floors' connections to the beams! Collapse arrest will occur much earlier.

If anybody is stupid, it is Nist. It should analyse in detail the local failures after initiation. Be professional. Do a proper job. That's all I ask for. Not mess up the investigation witn nonsense.

 

[Heiwa]

Heiwa:

Use Debris instead of rubble, if you like. But in any case, that's irrelevant. My primary point is that the mass that has failed is hitting the structure below in palces that it was not designed to support weight.

No mass has failed, primary structural parts have failed and contact secondary structural parts. The latter fails.

 

[Heiwa]

Heiwa:

Of course, even with the failure method you describe...when those upper floors fail they are coming down on the lower structure.

The floors in the upper and lower parts fail only at the side, where they are sliced of by the columns (and core beams). So the floors are still connected on the the other side ... an hinge down on floors below. No rubble is produced.

 

[BenBurch]

Collapse proceeded from the walls not the core!

In fact, in the second collapse, much of the core STOOD on its own for several minutes after all of the walls and floors had fallen.

The core of the towers was practically a second building within the first and meant to support only the service core including the elevators and plumbing and stairs. It did not contribute to the strength of the outer building in a serious way, and in fact depended upon that outer building for lateral bracing.

That you propose such things shows only that you do not understand the theory of the building as it stood, and therefore cannot hope to understand how it failed.

Please study some before you make a fool of yourself again. OK?

-Ben

 

[Heiwa]

Heiwa:

I'd also like to know how you reconcile these two statements:

Rubble is only produced when a structural part is cut in more than one location. No secondary structural parts in WTC1 can be cut in more than one location after initiation. These failed parts will still be connected to other primary structure. No rubble.

 

[Heiwa]

Heiwa:


Also, yo simply assert these two key points, rather than giving any evidence for them:

and

Study the reference [4] at http://heiwaco.tripod.com/nist3.htm