The influence of buckling

[chippy]

How many of you were aware of the fact that buckling was actually a major factor in the collapse of the World Trade Center? From a layman's point of view, you'll likely say "well duh, of course it buckled, that's how it fell on itself, silly!"

And this is why it's very dangerous to be a layman and try to hypothesize about what happened on 9/11.

Here. Educate yourselves.

(edit: there's some dumb rule that you can't post links until you've posted 15 times. So here is the Euler formula for buckling: P_cr = (pi^2 * E * I) / L^2, where P_cr is the amount of inward force a beam can endure before buckling, E is the modulus of elasticity (which varies for different materials), I is the moment of inertia which defines the geometry of the beam, and L is the length of the beam)

On the top you will find the Euler formula for buckling, which is a good approximation of the amount of force a beam can endure before it buckles. Notice the L^2 term on the bottom?

Now, consider the fact that when the airplanes hit the WTC, many floors of support were knocked out. These supports kept the lengths of the beams as small as possible to reduce the influence of buckling. But when these supports get knocked out, the beams increase in effective length. If a beam was 10 feet long for one floor and lost a few floors of support, its effective length may increase to 40 feet, meaning that there's 40 feet of beam between its upper and lower support. Remember L^2? If a beam's length increases by a factor of 4, then the amount of force a beam can support before it buckles reduces by a factor of 16.

SIXTEEN.

What if another floor was knocked out? That would decrease the amount of force a beam could support by a factor of 25! Once one beam fails, the building will topple in its direction, bringing extra momentum with it and initiating the pancake collapse of the towers.

Throw in a little heat from the fire that most definitely weakens the steel, and you shouldn't be surprised that the building would fall at all.

And please, stop arguing that the fire wasn't hot. If it wasn't hot, people wouldn't have chosen to jump down to the ground 100 stories, which is one of the most terrifying ways you can die.

 

[JamesB]

And please, stop arguing that the fire wasn't hot. If it wasn't hot, people wouldn't have chosen to jump down to the ground 100 stories, which is one of the most terrifying ways you can die.

Good post. It is hard to argue this point with the truthers though. I have even seen posts speculating that they were pushed by special forces operatives dropped by helicopters. When you have completely lost touch with reality, anything seems logical.

 

[jaydeehess]

Now what happens when a column buckles? It either bends over or snaps. In either case it, or debris from it, then impacts other columns with a horizontal velocity so even if an adjacent column was not buckling yet it now gets slapped on the side which just adds to buckling forces.

No matter though since many are the CT's that will state that the core of the WTC towers should have been able to stand on their own. Many will also state that the core columns took all of the gravity load and were in fact built to take 5 or more times the actual gravity load of the building.

Do I have to point out the problems with these statements?

 

[Unfit4Command]

Good post, I haven't heard of this formula till now.

I still can't believe that some members of the "Truth Movement" still think that buckling never even occured. This is one of those theories where the CTs are ignoring mountains of pictures proving them otherwise.

These are a few of my favorites:

 

[chippy]

Now what happens when a column buckles? It either bends over or snaps. In either case it, or debris from it, then impacts other columns with a horizontal velocity so even if an adjacent column was not buckling yet it now gets slapped on the side which just adds to buckling forces.

Right. Or they could fly straight outward, which explains why you can see beam components in...aw crap I can't post links yet! This rule is stupid. But you've seen the pictures. There are beams flying out horizontally, and the geniuses in the conspiracy department can't figure out why they could move horizontally if the building is falling vertically. When the beams buckle, they do snap out horizontally. I mean, if it's that hard to picture, find a stick in your backyard, press it down until it breaks, and see if it falls straight down or if it shoots out to the side first!

 

[R.Mackey]

Good post, and welcome, Chippy.

I've argued the beam equation before, but the bottom line is the Troothers are utterly immune to any kind of legitimate education. Which is why (like you, I suspect) I stopped talking to them entirely and focused on others who really want to learn.

Another point I often make, referencing the picture of the structure buckling, is that structural steel fails at about 3% strain. In other words, if you can see it bending, it's bad... really bad. The WTC collapses should surprise absolutely no one with any formal training whatsoever, unless one literally runs from the evidence.

Sadly, many people do.

 

[JamesB]

Good post, and welcome, Chippy.

Another point I often make, referencing the picture of the structure buckling, is that structural steel fails at about 3% strain. In other words, if you can see it bending, it's bad... really bad. The WTC collapses should surprise absolutely no one with any formal training whatsoever, unless one literally runs from the evidence.

Sadly, many people do.

LOL When I did my radio interview last week the host asked me about WTC7. I brought up the damage and fires and such and summarized it with, "Firefighters placed a transit on it, and discovered it was leaning. For a 47 story building, that's bad."

Great minds think alike I guess.

 

[Minadin]

Well, that really depends on what you mean by strain.

Most steel structures are over-designed by about 1.5x. Meaning that the actual live+dead load is 2/3 of what the members can take. So, if it's taking 103% of what it should, it would not be a big deal.

At 3% deflection you can visibly see it bend and that is indeed very bad. We normally design buildings first for the structural strength and then doublecheck it for deflection. A deflection of more an 1/4 inch or so for a floor is VERY noticeable and will cause people to feel unsafe even if it isn't structurally true. So oftentimes a structure will be even more oversized for just that reason.

Any time steel visibly bends in a building it is not good. In the WTC, there were so many different ways that the steel could bend, for so many reasons, that it is almost suprising that it did not fail earlier. In truth, the collapse was caused in part by the steel failing in a couple of different ways. One added to the other.

 

[uk_dave]

It's also worth remembering that whilst steel does have some flexibility, the materials used to make it look pretty such as plaster or marble are very rigid and prone to cracking at the slightest movement.

So when the woowoos get all incredulaous that marble panels had been destroyed in the foyer after the plane impact they are failing to take into account that these panels are just thin slabs of material held in place with either a mechanical fixing or adhesive and they don't take kindly to the type of movement the tower would experience by having a plane slammed into it.

But then, there are many things that the woowoos fail to take into account in their fantasies

 

[Magic 8 Ball]

Did they jump?

If it wasn't hot, people wouldn't have chosen to jump down to the ground 100 stories.

Chosen to jump?
I perfer "the heat forced them out."
I don't want to be anal, but your statement does seem to imply suicide (even though I know that's not intended). I heard people say "they jumped" a number of times and I believe it is only because the reporters covering the event, were saying it. I watched 9/11 live on TV and never once thought anyone was jumping. I couln't tell if someone was making a conscious effort to jump or there was another force at hand. I always figured that the pressure coming from the heat pushed them out of the building. I am no expert in fire, but I have seen and felt heat that can push things away involintarily.

 

[uk_dave]

I seem to recall seeing video of one guy trying to climb down, presumeably to the storey below..... it doesn't bear thinking about.

 

[JanH]

Good post, chippy.

UK Dave: When some stupid social anthropologist imported 9-11 woo to Norway I was compelled to make myself more familiar with the evidence. I spent weeks studying documents, videos, pictures and virtually relived the whole monstrosity again (I was actually on a plane in the vicinity of Afghani airspace when this happened in 2001!). It was emotionally draining, to put it mildly, and this greatly increased my disdain for all the sloppy and dishonest woo tactics. It's a dirty job, but somebody has to do it...

 

[Bell]

I seem to recall seeing video of one guy trying to climb down, presumeably to the storey below..... it doesn't bear thinking about.

That was shown in NG's Inside 9/11. Very sad to see that man fall

About the buckling, I posted a link to this video a few times before. It clearly shows the buckling ocuring at the south tower.

 

[Bell]

Chosen to jump?
I perfer "the heat forced them out."
I don't want to be anal, but your statement does seem to imply suicide (even though I know that's not intended). I heard people say "they jumped" a number of times and I believe it is only because the reporters covering the event, were saying it. I watched 9/11 live on TV and never once thought anyone was jumping. I couln't tell if someone was making a conscious effort to jump or there was another force at hand. I always figured that the pressure coming from the heat pushed them out of the building. I am no expert in fire, but I have seen and felt heat that can push things away involintarily.

I prefer to use the term 'fall' since that doesn't imply the people made the choice consiously.

A very simple experiment to experience what heat can do, is to turn on an oven, say 200 degrees celcius, and then stick your hand in it. You will automaticaly withdraw your hand. I'm not sure if that's what you meant by 'heat pushing things away' or if you mean physically pushing away?

 

[Bell]

Right. Or they could fly straight outward, which explains why you can see beam components in...aw crap I can't post links yet! This rule is stupid. But you've seen the pictures. There are beams flying out horizontally, and the geniuses in the conspiracy department can't figure out why they could move horizontally if the building is falling vertically. When the beams buckle, they do snap out horizontally. I mean, if it's that hard to picture, find a stick in your backyard, press it down until it breaks, and see if it falls straight down or if it shoots out to the side first!

Those 'beams' would be the aluminum panels that covered the outside of the towers.

 

[jaydeehess]

People indeed "chose" to exit the building but there were not many "choices" one could make.

Obviously if there were any other way out they would have chosen to make use of it.

Instead, the people who jumped were either exposed to unbearable heat and the only way to stop that pain was to exit the building through a window, or they were subject to choking, acrid, smoke that made the eyes, throat and lungs feel like they were burning, makes one cough uncontrollably, makes you dizzy and is generally a living hell from which the only respite is , again, exiting the building via the window. They would indeed know that this is suicide but in such cases when the pain is so great people will choose relief in the form of death. These are instances in which the person requires escape or rescue not in 30 minutes, not in 5 minutes not in 30 seconds but simply cannot bear up any longer. It is torturous, literraly!

If the heat were physically pushing them out in the form of causing the atmosphere in the room to flow outward fast enough to compel them out then the heat would incinerate them before they exited the building.

 

[jaydeehess]

Those 'beams' would be the aluminum panels that covered the outside of the towers.

[qimg]http://media.washingtonpost.com/wp-srv/photo/attack/images/newyork/10pm/ny_4.jpg[/qimg]

In the bottom left of the photo though we do see a perimeter column 'tree'.

Besides the buckling forces there is another horizontal force. All the material that is coming down within the footprint of the towers does what? It hits the remaining tower. It then must pile up but can only do so before it slides off the side. Before it does so though, if the perimeter column tree is still fastened to the remaining tower it is now being hit at the fastening level, by the debris that is pileing up. Take an empty milk carton and start filling it with sand. You will notice the sides bowing outward due to the pressure of the sand piling up inside. You can fill the carton all the way to the top and it will survive with little problem. Now do this again except pour the sand in from a height of 5 feet above the carton and mix in rocks about half the size of your thumb. The carton will explode long before you fill it. Why? The pressure is building much faster than the carton can distribute it and besides simply flowing to the sides the sand/pebble mix is retaining some of the velocity it had gained in falling so it hits the sides harder than in the first slow fill, the pebbles also concentrate momentum more than the first sand only fill so forces are very assymetric on the carton.

Such forces acted on the perimeter columns in the WTC and imparted sometimes large horizontal velocities on them. Near the top of the collapse this would mean that those perimeter column sections had more time to travel horizontally while they fell. Further down the mass of debris would tend to knock out the perimter column sections sooner and thus they would have less horizontal velocity(the mass is piling up faster and thus the momentum transfer takes place over a shorter time period but less momentum is transfered)

 

[JamesB]

In the bottom left of the photo though we do see a perimeter column 'tree'.

Besides the buckling forces there is another horizontal force. All the material that is coming down within the footprint of the towers does what? It hits the remaining tower. It then must pile up but can only do so before it slides off the side. Before it does so though, if the perimeter column tree is still fastened to the remaining tower it is now being hit at the fastening level, by the debris that is pileing up. Take an empty milk carton and start filling it with sand. You will notice the sides bowing outward due to the pressure of the sand piling up inside. You can fill the carton all the way to the top and it will survive with little problem. Now do this again except pour the sand in from a height of 5 feet above the carton and mix in rocks about half the size of your thumb. The carton will explode long before you fill it. Why? The pressure is building much faster than the carton can distribute it and besides simply flowing to the sides the sand/pebble mix is retaining some of the velocity it had gained in falling so it hits the sides harder than in the first slow fill, the pebbles also concentrate momentum more than the first sand only fill so forces are very assymetric on the carton.

Such forces acted on the perimeter columns in the WTC and imparted sometimes large horizontal velocities on them. Near the top of the collapse this would mean that those perimeter column sections had more time to travel horizontally while they fell. Further down the mass of debris would tend to knock out the perimter column sections sooner and thus they would have less horizontal velocity(the mass is piling up faster and thus the momentum transfer takes place over a shorter time period but less momentum is transfered)

Bah! A milk carton would only behave like that if it were hit with a Star Wars death ray!

 

[T.A.M.]

Chosen to jump?
I perfer "the heat forced them out."
I don't want to be anal, but your statement does seem to imply suicide (even though I know that's not intended). I heard people say "they jumped" a number of times and I believe it is only because the reporters covering the event, were saying it. I watched 9/11 live on TV and never once thought anyone was jumping. I couln't tell if someone was making a conscious effort to jump or there was another force at hand. I always figured that the pressure coming from the heat pushed them out of the building. I am no expert in fire, but I have seen and felt heat that can push things away involintarily.

I disagree...to an extent. I think that the heat, and the thought of burning to death, perhaps a more horrible and time involving death, was the more horrendous of the options. It is absolutely horrible to think, but I believe many of them were left with death by burning, and death by plummetting to the earth below, and most took what they felt would be the quickest, painless death. Most would have lost their breath, passed out, and been unconcious before they even reached the ground, so death would have been instant, and virtually painless. the other option would have been much longer, and painful...IMO.

TAM

 

[The Almond]

Nice analysis Chippy, it's always great to have a math/science type around to kick a few equations around. When I was back at Clemson, I was on a radio show where a caller made the, "The fires weren't hot enough" argument and I used the thermal expansion and hooke's law to prove that a temperature change of 500 degrees centigrade would result in a 174 psi stress over the entire beam.

The caller challenged me saying that steel failed at 36,000psi and that little stress couldn't hurt anything. I then proceeded to demonstrate that a distributed load of 174psi over 210 feet on an 8 inch beam was the equivalent of 3,000,000 pounds of load at one point on the beam. The caller hung up.

The point is that you can't always use mathematics to prove your point. For people to accept math, they have to demand that their argument be mathematically and scientifically valid. That's something conspiracy theorists simply don't do.