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9/11 Remembering World trade centers

Today, exactly 13 years ago, two planes crashed in the two towers of the World trade center. WTC1 and WTC2. This attack of terrorists is one of the most dangerous attack of all time. Being a structural engineer it is of prime importance to study such a case. A flight, Boeing 767, very small and tiny in front of the tall towers was the reason behind the collapse of the structure.Let us study some important aspects behind the collapse, like the time difference between the collapse of two towers, collapse type and structural failures.

1. Structural Design

To understand the failure of any structure in a better sense, it is first important to study the structural integrity and the behavior of the structure itself. You can only know how the column or a beam will fail when you load it and understand it's deformation patter as well as it's load path. Similarly it is important to study the structural design or the structural system of the two towers of world trade center to understand their failure pattern.

As shown in picture above, the building was made using a concept called framed tube and a shear core. A framed tube is a tube made by placing a closely spaced columns at the periphery of the building which are located very close to each other. This concept was very widely used during that time as it provided a large open space between the core and the building edge where people can easily design the layout of their office. But the disadvantage of this system is that you end up with large beams spanning between the core and exterior columns or trusses resting on the core and exterior columns. In WTC, engineers used trusses to make the floor lighter and as we all know a truss can span more distance much more efficiently. 


The above image shows how the trusses spanned in the building. This completely acts like a one way slab, which means, if you lose one support the failure of the floor begins.


The above image shows how closely the exterior columns are located in the building and the shear chore made up of steel columns. Somebody might give a thought that how can such a stiff system collapse because of a plane that looked so small in front of this.


The above image shows the schematic diagram of the floor truss used in the floors of world trade center. 

From all the above images, one thing is definitely clear, the person who designed this was definitely a genius. He saved a lot of material by designing lighter floor system which in turn reduced the size of columns, which reduced the dead load of the over all structure. Apart from that the structural system that is used was the best known system in 1950's to design such tall buildings. Now that is what we call something remarkable. But wait, they failed..!! So we as a engineers should learn why did they fail.


2. The Attack

The two towers were attacked at different times by two flights at different time interval. The north tower or the 1 world trade center was hit by the plane at 8:46 A.M while the second tower was struck at around 9:03. The picture below shows the location at which both the towers were hit.

The above picture clearly shows that the first tower was hit quite high as compared to the second one. This will have impact on the time within which the tower was hit by the plane to the time of it's collapse or we can say the period of it's instability. 

The above picture shows much clear view of the trajectory which a particular flight followed and on which face did it hit the tower. But what happened to the building immediately after the strike? Well, the flights sheared of the column, passed through the floor, damaged the core and the stairwells, a blast occurred simultaneously, and a wave traveled through the building from top to bottom and again bottom to top. You can now imagine the amount of local damage that a flight full with tones of fuel can do. Let me show you some of the important pictures showing the damage done to the towers.

 




 The pictures above show the immense amount of energy that a flight was carrying because of it's velocity as well as burning fuel. It literally sheared of the columns for more than two floors. But how do we know about the damage of the core? Well, we know because all the people who were located above the point of damage were not able to access any fire stairs because they were collapsed. So the damage did reach the shear core of the building. Apart from that the floors near to the collapse were completely damaged. So technically this was just the local damage on the building. But you can see the extent of the damage.


3. The Collapse

So now let us discuss on why did they collapse..!! Let me give you a simple example before moving any further. Take a column that you have designed for say load P. Let it be a two story tall columns connected by beams at both the floors. So now if you are a really good engineer then you might have designed it for 1.2 times the load P that is acting. But now suppose something wrong happens and the beam at the 1st floor collapses, which means that you just lost the point of fixity for the column and this means that the critical buckling load has been reduced to 1/4th of the original value.

Take another example. Don't fail the beam but increase the load to 1.2P and also increase the temperature of the steel. We know that the stress capacity of steel reduces as the temperature increases. Let us say that you heat it up to 500 degree C. But at this temperature the material strength reduces to 85% of it's original value. So this may also cause the failure of the column.

Now consider two floors located above one another. One floor collapses on the floor below. What happens to the bottom floor? Thee are chances that it may collapse and the chance of collapse depends on the connectivity of the floor with other structural members.

I think the above two example might have helped you in visualizing the collapse of the building. Let me mention the points which were actually the main reason behind kicking the collapse.
  • At the location of jet strike majority of the columns on one face, many core columns, as well as side faced and back faced columns suffered from damage as shown in pictures above and majority of them were sheared off. 
  • This discontinuity in columns will cause the load present in the above stories of the building to find an alternative load path to travel to the ground which causes an increase in stresses in the neighboring columns.
  • Apart from this many floors suffered from heavy damage which cause the loss of connection between the column and floor and so the effective length of the columns increase and along with that the stresses in the columns too. 
  • Along with the the fire raised the temperature inside the building which resulted in loss of stress of the structural members of the building.
  • The damaged floor and debris started falling on the floor below which increases the load on the subsequent floor. 
  • The heat reduced the stiffness of the floor which caused the floor to sag and pulled the columns inwards
  • Now consider the P-Delta effect on columns loaded with such a tremendous amount of load. They will surely buckle and start failing because of such critical points.
  • Once the collapse initiates, it is almost impossible to stop it, because the failed floor will fall on the bottom floor which will not resist the load and eventually pull the column inwards and the impacts of the loads above will eventually cause the failure.
  • This type of collapse is known as pancake collapse, it is like stacking of floors on the top of each other while they are collapsing. 
I know I haven't provided any equations or mathematical formulation to prove this, but if you are interested in that then many papers are available online supporting this particular claim. I know that this not as simple as I said over here. It is much more complicated and includes failure analysis of the structure at different time steps but this is a blog where I can put up generalized situations and not every mathematical equation. I hope that now I made clear that why did they collapse. But there is one more critical point that we need to see in this event. Why the second tower took less than an hour to collapse while the first one took more than 100 minutes.

Look at the above image again. Left one is tower 2 and the right one is tower 1. Can you see the difference in the location of attack? Yes, the second tower was hit lower as compared to the first tower. So the structural members located at failure zone were in higher loads and higher load potential as compared to the first tower. So definitely the second tower should collapse in a much shorter time. Now ideally you will say that if you hit the plane at the base, then it should collapse almost immediately. But no, the plane will be destroyed and there will be some non structural damage to the building because near the base, the building is so strong that it will not fail. In 1993 a bombing took place at the base of WTC but nothing happened to the building apart from some damage in the slab.


4. Conclusion

The conclusion from today's discussion is that the building design was really good, there was no fault in that, but we came to know one important thing. To resist such kind of local failures you need to increase the robustness of your building, that is increase the indeterminacy of the structure. Any structure above a particular amount of local failure is susceptible to global collapse. As a structural engineer you need to make sure that the occupants get enough time to evacuate the building. At last the choice lay in the hands of a contractor or a the builder or the investor or the owner. If s/he can spend more they can definitely get a better design, but being an engineer it is our duty to design it to an optimum level and not over-design it.

P.S: This was a very simplified version of the collapse. But to trigger such collapse there might be more than 1000 hidden parameters which we cannot see at this stage. It can be a failure of a single joint that might be critical or the failure of all the members simultaneously. It can be anything, but apparently these were the important reasons behind the collapse of the structure.

Thank you 

Have a good day ahead.