A Mechanical Engineer's take on the 9/11 WTC building collapses
This article was written by a friend of the show Mitch Stilborn. He's not generally a formal blogger or a writer but he was recently in a discussion with someone about the 9/11 WTC building collapses and wrote around 2200 words in response to some concerns that were raised. I asked him if I could post it to our website in the hopes that his take could help spread a bit more fact based information and dispel some myths about the buildings collapsing. This has been slightly edited (not much) to take it from a one on one conversational piece to a broader informational piece that is hopefully accessible to anyone who might want to read it. Thanks for taking the time to read it and feel free to comment or email firstname.lastname@example.org with any relevant points.
A Mechanical Engineer's Take on the 9/11 World Trade Center Collapses
by Mitch Stilborn
I'll try to keep these points as separate and clear as possible, to avoid accidentally muddying the waters. The points of concern seem to be 1) collapse speed and the visual lack of resistance, 2) the apparent homogeneity of the collapse (simultaneous yielding of multiple structural members), and 3) the temperature of the fires.
1) Speed of the collapse. This is a very, very reasonable question to raise. The manner in which the towers collapsed goes against our intuition; the total mass of the tower isn’t really changed much at all throughout the impact and subsequent fires, with the incoming mass of the planes and fuel being minuscule compared with the loads the towers’ structures were designed to support. Since it is dealt with in item 3, I’ll ignore for the moment the question of the impact of the fire and the collapse initiation event. A very important distinction to make when considering the speed of the tower collapse is the difference between a beam and a column. Most of the things we’re used to – particularly that we see fail – are beams. A good example of a beam is a bridge, a plank table-top, or a tree branch (cantilever beam). Beams tend to have a fair amount of flex to them, and when they fail it will be a steady, gradual flexing, with the load deflecting the beam beyond its elastic limit and pieces starting to crack, split, splinter, and finally fall. This is what we’re most used to, and what our minds likely expect when we see the towers fall; either a long steady jarring fall-stop-fall or something like a boulder bouncing down a hill. However, the structure of the towers – as with all tall buildings – is made up of columns. There are beams in between the columns, like the supports for the floor surface, but all of these transmit their loads back to the columns, which carry it down to the foundation. When columns fail, it is an altogether different affair. When a beam fails, the loading characteristic is unchanged; the amount of load it is carrying changes, but not the way it carries it. This is because a beam is kind of like a pendulum; it is inherently stable. A column, however, is inherently unstable; it is like a crutch or a pogo stick. If the load is applied incorrectly, it will suddenly flip the column over and fall down. This is for a load that is within its limits but is incorrectly applied (leading to the column falling over). However, the failure method exhibited in the tower collapses is not of a bearable load incorrectly applied, but rather that of a hugely excessive load applied more or less correctly (in the right direction). When a column is overloaded, the ends will tend to stay in their current spot but the middle of the column starts to bow outwards; once it starts to bow, it is over come because suddenly the load is creating a big bending force in the middle of the column. This is because at the middle of the column the material is no longer underneath the load but is suddenly off to the side. The column already wasn’t strong enough for the load when it was in line, and suddenly having a big bending moment added to it is suddenly WAY too much for the column to handle so it fails quickly and catastrophically. For a very rough analogy, think of your knees when you jump from a little too high; when you land your knees give out and you collapse to the ground with a ton of speed. If you’d jumped from a little lower and your knees had been able to stay straight you wouldn’t have crumpled to the ground at all, let alone at that sort of speed. The failure point of a column tends to be a very sudden, drastic change. You can see from this example as well, the sort of effect that a dynamic load has; you might be able to leg-press or squat 500lb slowly and with control but with just your own (say) 180lbs and a jump height of 6ft, suddenly they buckle. That’s what happened to the towers; the columns were designed to hold a static load of the floors above them, maybe like 1.5x or 2x the static load (called a safety factor), but that was nowhere near strong enough to support the dynamic load imparted to the lower columns by the upper floors suddenly dropping the 10ft (or whatever) when the fire-damaged floor gave out. And once the collapse started, it was inevitable to continue because of cascading failure; the first floor collapsed, the second floor couldn’t handle the loading after it had dropped 10ft and gained momentum, the third floor could handle the load even less after the ones above it had dropped the 20ft, 30ft, 40ft, etc.; getting worse and worse and worse all the way along. Columns are very rigid members, which means they can’t flex very much before they fail catastrophically, so they were not able to absorb the impact energy of the falling floors.
So in summary, the speed of the impact is explained by the failure mechanic of columns, and matches our observations of the collapse videos.
2) The apparent simultaneousness of the collapse. Again, this is a very reasonable concern to have; the tower structure was made up of so many different pieces, with different column members and beam connection points, and it was made up of numerous elements like the welded-in corner gussets, attachment points, bolt plates, fasteners, etc. It seems impossible that they would all give way at the same time unless there was something placed there that made it all fail at the same time, like an explosive. This is a very reasonable concern, and the solution to it is very simple as well; one must remember to update the calculations with the new loads. When everything started out, there was say something like 300 structural members each holding 100,000lb for a total carried load of 30 million pounds (yes these numbers are just made up for argument’s sake). So it seems obvious that they couldn’t all fail; there are just so many of them and they are so strong with their total safe carrying capacity being like 45 million pounds (assuming that 1.5x factor mentioned in #1). However, one must only posit the failure of a couple of them in order to cause a collapse (the initial failure being covered in #3 below). The secret to this understanding is to update our calculation every time the loading changes. Initially the load is evenly-distributed between the members. Each member is carrying a load proportional to the total load and the area of the building loading it up (like 100sq-ft per column or something). When a member is too weak to carry its load, that load still has to go somewhere. For simplicity sake we’ll pretend that overloaded members fail completely (this is not how it happened but is useful for an analogy and the basic principle holds true in reality). So say there is a column that fails completely and there are 8 columns nearby. When it fails, this column’s 100,000lbs has to be transferred to those other 8 columns, which are now supporting 112,500lbs each (assuming the load is evenly distributed out to them). Now they are carrying 112,500lbs of their 150,000lb maximum. If another column within “range” of these columns fails it will transfer its load to them as well, but that’s assuming the same spacing and even load-transfer mechanics. If instead, say 3 columns next to each other all fail that load will spread to the columns closest to them (further away columns can’t do much to “help” carry this load because the load transferred through the structure to them is proportional to the rigidity of the beams/trusses connecting them and the rigidity of a beam is a function of the cube of its length. Which is a technical way to say that load doesn’t spread evenly. So these three columns all failing means there is 300sq-ft section of building that has to be spread out to other columns with the majority of the load going to the closest ones. Remembering that each column can only support 1.5x100sq-ft = 150sq-ft of building area, you can see how just a couple columns failing would cause another one to fail, which means there is now 400sq-ft of unsupported area, then 500, 600, etc. Remembering the speed of a column collapse discussed in #1 above, you can see how quickly the failure spreads. This rapid failure mechanic would make it seem like the whole thing just gave way all at once. Whether the bolts sheared off in a flange plate, or the weld at a corner cracked, or the column section simply buckled isn’t important to this analysis; so long as an element in one column failed, its loading had to then pass on to another member where it could cause the failure in its weakest link.
3) The temperature inside the buildings. There’s a big disclaimer here that I need to give; chemistry is outside of my area of expertise. Sure, I passed chemistry in university but I wouldn’t claim it as a strong point. However, I’ll try to answer this concern as best as I can. The way that I think about this issue is to remember that temperature is the average of the amount of heat in an object or given location. The amount of heat currently contained somewhere depends on two things (and we have to remember both) the amount of heat entering the system and the amount of heat leaving it. An important point of the equation is that the fires in the buildings did not have sufficient oxygen to burn completely (efficiently), so they wouldn’t be releasing as much heat as they would in an oxygen rich environment. So, a reasonable conclusion could be that the fires didn’t reach the textbook temperature for that of burning jet fuel. However, we have to remember to account for the heat leaving the system. The open-air combustion temperature for jet fuel means both that there is an open air environment to bring oxygen in but also that there is an open air environment for the heat to leave via convection of the huge updraft of hot air rushing away and heat radiating away like it does from a forge. But the fires weren’t in open air, so the heat that was generated – reduced as it was from a perfect-combustion perspective – stayed around, ratcheting the temperatures higher and higher. This is like the coals in a forge; the hottest ones aren’t at the top of the pile, because the heat those ones generate is lost to the atmosphere; the hottest coals are in the middle where the other coals act to insulate them and keep the heat trapped in. I see this every day in winter too; I heat my house with a wood stove, and it gets extremely hot inside despite, all things considered, very little air getting in; that’s because the heat generated stays inside the stove. Everyone is of course very familiar with how weak steel gets when it is heated. Even once it has cooled below a dull red it is still way easier to move than when it is fully cold and those beams and columns were designed based upon their strength when they were fully cold. They had fire protection sheathing around them, but that sheathing was designed to protect against heat only; it was probably something like welding blankets (I’m guessing). You can imagine how easily they could be stripped off by the impact of a 200,000lbs (or whatever) jet slamming into them going 500mph (or whatever). It’s important to note here as well that it is not just the yield strength of the steel that is affected by heat but also its Young’s modulus or modulus of elasticity. Basically as the steel got hotter it got softer (more elastic too). This is very important because the strength of a column (and of a beam) is dependent on that value, the Young’s modulus. So heating the steel is a double-whammy of softer and more plastic.