psikeyhackr, the first link you provide concerning the calculation of the heat effects of the burning fuel is certainly far more detailed than the one I carried out. I acknowledge that I overestimated the fuel load of the aircraft, and that this lowers my estimate of temperature. I carried out a quickie calculation to demonstrate that the fire could have softened the steel enough to cause the collapse. So now let’s look more closely at the issue.
Let’s note that the two calculations make different estimates, that lean one way and the other. I estimated 5,000,000 kg of steel; they estimated 500,000 kg of steel—a difference of a factor of ten. I estimated 80,000 kg of fuel, they estimated 10,000 kg—a difference of a factor of eight. Of course, their lower estimate of the amount of fuel was based on the assumption that 10,000 kg of fuel were consumed in the initial fireball—and that none of the heat of the initial fireball remained in the building! That assumption of theirs immediately lowers the effective temperature by a factor of two.
The big difference in calculations, however, is their assumption that 1.4 million kg of concrete must also be heated to the same temperature as the steel. This assumption raises a great many questions, because the thermal conductivity of concrete is less than 1 W/mK. Depending upon the conformation of the concrete, much of it would have been insulated from the fire and would not have heated much.
But the real killer argument is that you don’t need to heat all the steel to the softening point—if just one section of steel softens, you can lose the entire structure. So instead of thinking in terms of a single mass of high-temperature material all at the same average temperature, we have to think in terms of hotter areas and cooler areas, and guarantee that none of the hotter areas exceed that critical temperature. By the way, I looked that up, and the building codes specify that structural steel be able to withstand temperatures up to 540C. Thus, if we can be certain that no portion of the structure exceeded 540C, then we can be certain that the structure would not have failed due to heating. But if the temperature at any point in the steel structure exceeded a mere 540C, then we have a reasonable basis for concluding that the steel at that location failed.
Let me also remind you of a basic point in mechanical engineering: the difference between force and torque. A standard rectilinear structure can withstand enormous amounts of force, but far less torque. That’s because the compression strength of materials is almost always much greater than the shear strength. Thus, a steel structure can withstand enormous vertical loads, but if that structure is bent even slightly, the gravitational load becomes a torque, and the strength of the structure depends upon the shear strength of the steel, not its compressive strength. Thus, a tall building must be strong enough to remain vertical in the strongest possible winds; if it flexes by more than some critical angle, it will collapse. That’s why even a slight weakening of a structural element can lead to collapse; if that structural element softens and sags, it pulls the rest of the structure and twists it—leading to catastrophic torque. Indeed, it is theoretically possible to bring a structure down without any steel softening. If the temperature of the structural steel on one side of the building is significantly higher than the temperature on the other side, then the hotter side will expand more from the heat, bending the building. It could bend the building past its critical angle, in which case the building would collapse. It all depends on the concentration and distribution of the heat in the structure.
Your central point seems to be summarized in this statement:
So how does a lighter portion overcome the inertia of the heavier portion to collapse in less than 18 seconds?
Perhaps you have forgotten the old story about Galileo dropping a lead shot and a cannonball from the top of the tower of Pisa and observing that the two hit the ground at the same time. Heavier objects fall just as fast as light ones. Yes, there was a diminution of speed arising from the collision of upper floors with lower floors. But that diminution of speed appears in the results as the fact that the building did NOT collapse at the speed of free fall—it took a few seconds longer. You seem to be flipping back and forth between arguing that the mass of the lower levels slowed the fall and that the structural strength of the building impeded the fall. Would you please make up your mind and argue these two issues separately? I have already given you the equations you need to carry out the calculation in the first case, and you have not reported any results. That says a lot.
I have lost patience with your confrontational style. It appears to me that you have no interest in discussing the physics of the collapse of the WTC buildings. Your primary interest appears to be in arguing. You have frequently indulged in denigratory comments. You seem to be more interested in proving that I am a dummy than in considering the physics of the WTC collapse. I will happily stipulate that I am in fact a dummy, but I have no interest in evaluating my intellectual strengths and weaknesses, nor do I care about your own. I have expended far too much time explaining in good faith the underlying physics, only to be countered with confrontational arguments made in bad faith. For this reason, I am terminating my participation in this discussion. I suggest that you take this matter up with Bryan. The two of you are well-suited to each other and I’m sure that you’ll have a delightful time communing in your preferred fashion.