GregoryUrich
Graduate Poster
- Joined
- May 16, 2007
- Messages
- 1,316
Introduction:
Many have theorized that the fall time of WTC7 can only be explained by controlled demolition. The fall time indicates there was very little resistance to collapse. This analysis looks at some energy issues in that context to try and quantify the resistance.
Method:
My approach was to use the top 47 floors of WTC1 because the mass and column cross sections are known and the floor area and height was roughly equivalent. Dr. Greening has suggested that the mass was much higher (180,000 tonnes; PE = 166 GJ), but I reject this because NCSTAR1-1 gives thinner (2.5 in) normal concrete floors and WTC7 didn't need the strength of the lower half of WTC1 either for gravity or wind. Making a building 80% heavier than necessary would not be economical.
I used a bottom-up collapse. I have used Dr. Frank Legge's fall time adjusted for perpective (based on informal input from Dr. Greg Jenkins) which comes out around 6.4-6.5 seconds and I use 6.5 seconds. This is the fall time from the point the roof started to move, indicating global failure. Obviously there were localized failures prior to that (i.e. the penthouses).
I have used linear scaling of the energy loss based on an input which I adjusted iteratively until the required falltime was achieved. This results in a decreasing rate of accelleration. It could be scaled differently of course but my scaling is roughly in line with the relative strength of the structure. Legge arrived at a constant accelleration but the perpective issues will probably change that conclusion when the details are worked out.
I have estimated the energy required for expulsion of air in the following manner. For each 1m increment from the center, I calculated the mass and required acceleration to move the mass to the perimeter, based on the time for the particular floor to collapse. Then I figured out the final velocities and summed the KEs. This is a lower bound as aperature affects will increase amount of energy required. In WTC1, the aperature is never larger than 38% of the facade area due to the external columns and spandrels. Actually, I only calculated the bounds and used a linear interpolation between the bounds which reduces the total somewhat.
Results:
The total mass of the building is calculated to be 103,000 tonnes (roughly 36% of WTC1) with a total PE of 97 GJ. The resistance energy is calculated to be 14 GJ. The energy required to expel air from the building in a progressive bottom up collapse is 28.6 GJ. If a constant acceleration is assumed (supported by Legge's work), then the energy dissipated by resistance is: 1-(6/6.5)^2 ~ 14.8%.
Spread sheets:
Energy
Air expulsion
Discussion:
The "resistance" energy turns out to be less than the energy for air expulsion in a progressive collapse may indicate that the mass assumptions are incorrect or more likely the the collapse was not entirely "progressive" in terms of one floor at a time. Keep in mind that this is NOT a general energy issue as there was more than sufficient PE to destroy the building. However, even using Dr. Greenings PE there is no energy left for plastic buckling, concrete comminution or adiabatic heating.
Conclusion:
While this does not prove controlled demolition, it does raise the question of how, at the point when the structure could no longer hold up the building (weight slightly greater than strength), the resistance of the structure suddenly became zero. In this context some mechanism of assisted collapse is a reasonable line of inquiry.
Many have theorized that the fall time of WTC7 can only be explained by controlled demolition. The fall time indicates there was very little resistance to collapse. This analysis looks at some energy issues in that context to try and quantify the resistance.
Method:
My approach was to use the top 47 floors of WTC1 because the mass and column cross sections are known and the floor area and height was roughly equivalent. Dr. Greening has suggested that the mass was much higher (180,000 tonnes; PE = 166 GJ), but I reject this because NCSTAR1-1 gives thinner (2.5 in) normal concrete floors and WTC7 didn't need the strength of the lower half of WTC1 either for gravity or wind. Making a building 80% heavier than necessary would not be economical.
I used a bottom-up collapse. I have used Dr. Frank Legge's fall time adjusted for perpective (based on informal input from Dr. Greg Jenkins) which comes out around 6.4-6.5 seconds and I use 6.5 seconds. This is the fall time from the point the roof started to move, indicating global failure. Obviously there were localized failures prior to that (i.e. the penthouses).
I have used linear scaling of the energy loss based on an input which I adjusted iteratively until the required falltime was achieved. This results in a decreasing rate of accelleration. It could be scaled differently of course but my scaling is roughly in line with the relative strength of the structure. Legge arrived at a constant accelleration but the perpective issues will probably change that conclusion when the details are worked out.
I have estimated the energy required for expulsion of air in the following manner. For each 1m increment from the center, I calculated the mass and required acceleration to move the mass to the perimeter, based on the time for the particular floor to collapse. Then I figured out the final velocities and summed the KEs. This is a lower bound as aperature affects will increase amount of energy required. In WTC1, the aperature is never larger than 38% of the facade area due to the external columns and spandrels. Actually, I only calculated the bounds and used a linear interpolation between the bounds which reduces the total somewhat.
Results:
The total mass of the building is calculated to be 103,000 tonnes (roughly 36% of WTC1) with a total PE of 97 GJ. The resistance energy is calculated to be 14 GJ. The energy required to expel air from the building in a progressive bottom up collapse is 28.6 GJ. If a constant acceleration is assumed (supported by Legge's work), then the energy dissipated by resistance is: 1-(6/6.5)^2 ~ 14.8%.
Spread sheets:
Energy
Air expulsion
Discussion:
The "resistance" energy turns out to be less than the energy for air expulsion in a progressive collapse may indicate that the mass assumptions are incorrect or more likely the the collapse was not entirely "progressive" in terms of one floor at a time. Keep in mind that this is NOT a general energy issue as there was more than sufficient PE to destroy the building. However, even using Dr. Greenings PE there is no energy left for plastic buckling, concrete comminution or adiabatic heating.
Conclusion:
While this does not prove controlled demolition, it does raise the question of how, at the point when the structure could no longer hold up the building (weight slightly greater than strength), the resistance of the structure suddenly became zero. In this context some mechanism of assisted collapse is a reasonable line of inquiry.
Last edited:
