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[NOTE: Because truthers and conspiracy theorists in general are unable to focus on one specific topic due to the fact that they are not able to substantiate their claims while doing so, I have decided to divide a few of the most important arguments regarding the conspiracy theory into their own threads, as to maintain focus on those particular topics. This way, I hope to get truthers to focus on one argument at a time and maybe actually extract some real discussion out of them instead of a complete avoidance of all of my rebuttals. Please don't take these threads as spamming, as it is necessary to address these issues and the conspiracy theory as a whole]
Can Fires Cause Buildings To Collapse?
This is the reasoning for how the building collapsed. What caused these failures? From wikipedia:
"Consistent with this theory, news footage shows cracking and bowing of the building's east wall immediately before the collapse, which began at the penthouse floors.[3] In video of the collapse, taken from the north by CBS News and other news media, the first visible sign of collapse is movement in the east penthouse 8.2 seconds before the north wall began to collapse, which took at least another 7 seconds.[3][43]
The working hypothesis, released in the June 2004 progress report and reiterated in a June 2007 status update, was that an initial failure in a critical column occurred below the 13th floor, caused by damage from fire and/or debris from the collapse of the two main towers. The collapse progressed vertically up to the east mechanical penthouse. The interior structure was unable to handle the redistributed load, resulting in horizontal progression of the failure across lower floors, particularly the 5th to 7th floors. This resulted in "a disproportionate collapse of the entire structure."[40][44][3]"
There is also photographic and video evidence to back up this explanation. For example, here is a photo of the 10-story gash in the south side of the building:
Here's some information on the structural strength of steel as a result of temperature. I'm going to make the presumption right here that, since I don't know the specific type of steel or specific type of beams/trusses used in WTC7, these results aren't going to be completely accurate.
Anyways, here's a graph I actually found on a 911 truth site which actually can be used against their own claims.
Source
As can be seen, even if the temperature is only 500 Fahrenheit, the strength of the steel is lowered by 40 percent. This alone could be used as proof or at least validation of the running hypothesis that fires within the building that were able to run rampant due to a malfunctioning sprinkler system and the inability of fire fighters to fight the fire due to low water pressure caused the building to collapse.
Now, they make numerous claims on this site that I'll address as well, for anyone ignorant enough to attempt to present them here (I realize that they are talking about the twin towers, but I've heard identical arguments used against the collapse of WTC7).
First, they cite the following from FEMA's World Trade Center Building Performance Study:
"In the mid-1990s British Steel and the Building Research Establishment performed a series of six experiments at Cardington to investigate the behavior of steel frame buildings. These experiments were conducted in a simulated, eight-story building. Secondary steel beams were not protected. Despite the temperature of the steel beams reaching 800-900° C (1,500-1,700° F) in three of the tests (well above the traditionally assumed critical temperature of 600° C (1,100° F), no collapse was observed in any of the six experiments)."
What isn't taken into consideration here is the fact that these results can vary drastically due to the design of the building. This can't apply to WTC7, for example, because of how the loads within the building were transferred to the outer load-bearing columns. Also, the buildings we are discussing were much taller than eight stories. So given the unique design and the height of the buildings, this is an ineligible criticism.
This is also why their following bullet ("If a steel structure does experience a collapse due to extreme temperatures, the collapse tends to remain localized to the area that experienced the high temperatures.") is false. The collapse of one column is localized to the area of that column and adjacent columns, which in turn causes those columns to buckle and collapse, which is localized in the area of those columns and their respective adjacent columns, etc... This is called a progressive collapse, and can happen seemingly instantaneously.
Here is some more accurate/professional/sourced data regarding the strength of steel related to temperature (ironically I found this data through a link from the truther website that I got the previous graph from):
This is a typical set of stress/strain graphs. If you're a freshman in an engineering curriculum you will recognize it right away. What this graph shows is the ultimate strength for ASTM A36 steel (a common structural steel). We can determine from this graph the yield strength of the steel. For example, at 600 Celsius the yield strength of this steel is about 20 kips per square inch (20,000 pounds per square inch) (the yield strength is the point where deformation goes from elastic to plastic, point 4 on this graph. Elastic deformation is basically the deformation of say a bar of steel where, when the load is removed, it will return to its original position, whereas plastic deformation is where it is permanently deformed. Because of this, steel design uses the yield point on top of a Factor of Safety to prevent any plastic deformation and/or buckling (failure)).
It's quite clear how significant of a role temperature plays in the yield strength of steel (and all materials). The increased temperatures caused one of the load-bearing columns to fail, which caused a progressive collapse. This is very basic structural engineering.
Since it's too late to edit my last post, I'd just like to clarify something. The first graph posted from the truther site is actually the Strength Reduction Factor vs. Temperature. Here is a graph from the same FEMA report that I got the second graph from:
This graph is used, then, to find the strength reduction factor given a temperature. You can then multiply the strength of the steel at room temperature by the strength reduction (retention) factor to get the strength at the temperature originally input.
The original stress/strain graph was labelled incorrectly as well; the first line should be at room temperature (20 C) and the second is at 200 C, as strength decreases with an increase in temperature.
Also, regarding the Alfred P. Murrah building: I haven't looked into how the building was designed, but from the photograph posted by Chanda (reposted below) I'm about 90% sure that it was designed using a mat foundation with the vertical columns seen in the photo bearing the load of the building.
As we can see, where these columns were compromised the building collapsed. This is completely clear by just looking at the above photo; you can basically trace an outline around where the collapse is based on the remaining columns.
So why didn't a progressive collapse occur in the Alfred P. Murrah building? Assuming that I am correct about the design, the loads were transferred much more evenly over the building, meaning that each column carried much less load. Designed even just based on a FS of 3 (the smallest commonly used Factor of Safety), the collapse of these columns then transferred much smaller loads to the remaining columns, which were able to handle the additional loads and thus prevented collapse anywhere where the columns weren't directly compromised.
UPDATE: Here (PDF) is a paper discussing the progressive collapse of the Alfred P. Murrah building which confirmed my earlier theory asserted based on the picture posted.
Even if it is true [that steel framed buildings have never collapsed due to fire] (which, of course, it isn't - PDF, and another; there are numerous more if you actually look for them), is completely irrelevant, given the fact that it is scientifically true.
I have yet to see any truther address the conclusion laid out in this post. If there is no response, then it is safe to say that they have no response.
Can Fires Cause Buildings To Collapse?
This is the reasoning for how the building collapsed. What caused these failures? From wikipedia:
"Consistent with this theory, news footage shows cracking and bowing of the building's east wall immediately before the collapse, which began at the penthouse floors.[3] In video of the collapse, taken from the north by CBS News and other news media, the first visible sign of collapse is movement in the east penthouse 8.2 seconds before the north wall began to collapse, which took at least another 7 seconds.[3][43]
The working hypothesis, released in the June 2004 progress report and reiterated in a June 2007 status update, was that an initial failure in a critical column occurred below the 13th floor, caused by damage from fire and/or debris from the collapse of the two main towers. The collapse progressed vertically up to the east mechanical penthouse. The interior structure was unable to handle the redistributed load, resulting in horizontal progression of the failure across lower floors, particularly the 5th to 7th floors. This resulted in "a disproportionate collapse of the entire structure."[40][44][3]"
There is also photographic and video evidence to back up this explanation. For example, here is a photo of the 10-story gash in the south side of the building:

Here's some information on the structural strength of steel as a result of temperature. I'm going to make the presumption right here that, since I don't know the specific type of steel or specific type of beams/trusses used in WTC7, these results aren't going to be completely accurate.
Anyways, here's a graph I actually found on a 911 truth site which actually can be used against their own claims.

Source
As can be seen, even if the temperature is only 500 Fahrenheit, the strength of the steel is lowered by 40 percent. This alone could be used as proof or at least validation of the running hypothesis that fires within the building that were able to run rampant due to a malfunctioning sprinkler system and the inability of fire fighters to fight the fire due to low water pressure caused the building to collapse.
Now, they make numerous claims on this site that I'll address as well, for anyone ignorant enough to attempt to present them here (I realize that they are talking about the twin towers, but I've heard identical arguments used against the collapse of WTC7).
First, they cite the following from FEMA's World Trade Center Building Performance Study:
"In the mid-1990s British Steel and the Building Research Establishment performed a series of six experiments at Cardington to investigate the behavior of steel frame buildings. These experiments were conducted in a simulated, eight-story building. Secondary steel beams were not protected. Despite the temperature of the steel beams reaching 800-900° C (1,500-1,700° F) in three of the tests (well above the traditionally assumed critical temperature of 600° C (1,100° F), no collapse was observed in any of the six experiments)."
What isn't taken into consideration here is the fact that these results can vary drastically due to the design of the building. This can't apply to WTC7, for example, because of how the loads within the building were transferred to the outer load-bearing columns. Also, the buildings we are discussing were much taller than eight stories. So given the unique design and the height of the buildings, this is an ineligible criticism.
Buildings are generally engineered to a Factor of Safety of 3, sometimes 4 and (rarely) 5. This means that they are engineered to hold 3/4/5 times the allowable load (q all = q ult / FS). Since the load was distributed evenly over these outer columns, when one of these columns fails it will cause the shifting load to redistribute to adjacent columns, which would exceed the designed load (using the FS). This would in turn cause those columns to collapse, and so on until the entire structure has been demolished.* High-rise buildings are over-engineered to have strength many times greater than would needed to survive the most extreme conditions anticipated. It may take well over a ten-fold reduction in strength to cause a structural failure.
This is also why their following bullet ("If a steel structure does experience a collapse due to extreme temperatures, the collapse tends to remain localized to the area that experienced the high temperatures.") is false. The collapse of one column is localized to the area of that column and adjacent columns, which in turn causes those columns to buckle and collapse, which is localized in the area of those columns and their respective adjacent columns, etc... This is called a progressive collapse, and can happen seemingly instantaneously.
Here is some more accurate/professional/sourced data regarding the strength of steel related to temperature (ironically I found this data through a link from the truther website that I got the previous graph from):

This is a typical set of stress/strain graphs. If you're a freshman in an engineering curriculum you will recognize it right away. What this graph shows is the ultimate strength for ASTM A36 steel (a common structural steel). We can determine from this graph the yield strength of the steel. For example, at 600 Celsius the yield strength of this steel is about 20 kips per square inch (20,000 pounds per square inch) (the yield strength is the point where deformation goes from elastic to plastic, point 4 on this graph. Elastic deformation is basically the deformation of say a bar of steel where, when the load is removed, it will return to its original position, whereas plastic deformation is where it is permanently deformed. Because of this, steel design uses the yield point on top of a Factor of Safety to prevent any plastic deformation and/or buckling (failure)).
It's quite clear how significant of a role temperature plays in the yield strength of steel (and all materials). The increased temperatures caused one of the load-bearing columns to fail, which caused a progressive collapse. This is very basic structural engineering.
Since it's too late to edit my last post, I'd just like to clarify something. The first graph posted from the truther site is actually the Strength Reduction Factor vs. Temperature. Here is a graph from the same FEMA report that I got the second graph from:

This graph is used, then, to find the strength reduction factor given a temperature. You can then multiply the strength of the steel at room temperature by the strength reduction (retention) factor to get the strength at the temperature originally input.
The original stress/strain graph was labelled incorrectly as well; the first line should be at room temperature (20 C) and the second is at 200 C, as strength decreases with an increase in temperature.
Also, regarding the Alfred P. Murrah building: I haven't looked into how the building was designed, but from the photograph posted by Chanda (reposted below) I'm about 90% sure that it was designed using a mat foundation with the vertical columns seen in the photo bearing the load of the building.

As we can see, where these columns were compromised the building collapsed. This is completely clear by just looking at the above photo; you can basically trace an outline around where the collapse is based on the remaining columns.
So why didn't a progressive collapse occur in the Alfred P. Murrah building? Assuming that I am correct about the design, the loads were transferred much more evenly over the building, meaning that each column carried much less load. Designed even just based on a FS of 3 (the smallest commonly used Factor of Safety), the collapse of these columns then transferred much smaller loads to the remaining columns, which were able to handle the additional loads and thus prevented collapse anywhere where the columns weren't directly compromised.
UPDATE: Here (PDF) is a paper discussing the progressive collapse of the Alfred P. Murrah building which confirmed my earlier theory asserted based on the picture posted.
Even if it is true [that steel framed buildings have never collapsed due to fire] (which, of course, it isn't - PDF, and another; there are numerous more if you actually look for them), is completely irrelevant, given the fact that it is scientifically true.
I have yet to see any truther address the conclusion laid out in this post. If there is no response, then it is safe to say that they have no response.