Myriad and Pgimeno, why do you think Bazant is showing how WTC1 and 2 data points match his crush down equation of motion originally derived in BV?
I think he did it to show that the original model makes adequate predictions.
Why does the model make adequate predictions? It could be because the assumptions made in the original model are actually accurate (that is, rubble did only impact on columns and every column experienced 3-hinge buckling), or it could be that the phenomenon being modeled is not very sensitive to the accuracy of those assumptions. Either way makes it an adequate model.
However, since it is obvious that three-hinge buckling of every column did not occur, the point I gather is the latter one: that the predicted collapse time is not very sensitive to the accuracy of the assumptions made about the exact mode of structural component failure (e.g. column buckling vs. column fracture vs. shearing of floor connections).
If your reasoning is correct, then the data points should descend faster than what you believe are equations of motion for an idealized case with assumptions most optimal for survival.
If my reasoning is correct that the collapse time is not sensitive to the assumptions made about the exact mode of structural component failure, then the collapse time should be sensitive to the assumptions made about the exact mode of structural component failure? I think not.
One could make an argument based on energy balance that the actual data should be faster, but to show it should be measurably faster given the errors of measurement and the range of uncertainty in the model input parameters (such as the actual masses of floors) would require a quantitative argument that I have not seen anyone make.
Do you really believe the BV equations of motion are intended to represent motion of the slowest possible descent of a building under conditions most optimal for survival?
Is he trying to match motion of real buildings of just derive a theoretical upper limit of the slowest possible descent?
First he derived a theoretical upper limit of the slowest possible descent, and then he pointed out that the predicted descent is not significantly slower than the actual measured collapse. This suggests that the collapse time is not sensitive to the assumptions made about the mode of structural component failure.
If I recall correctly, models have also been created assuming the fastest possible descent, in which the inertia of the floors in the lower structure is the only resistance mechanism (that is, the columns below each floor are assumed to break with zero energy absorption the moment the rubble mass from above touches that floor), and those models also make predictions of collapse times close to what was observed. Which is consistent with the above.
In summary: one paper shows the tower collapses even under best-case assumptions for collapse arrest; the other shows that the best-case assumptions don't make the model grossly inaccurate with respect to predicted collapse time. Two different conclusions that are entirely consistent with one another.
You appear to believe that if the model makes best-case assumptions then that
must make it grossly inaccurate with respect to the collapse times it predicts. That doesn't follow. Without a quantitative argument to that effect, any such belief on your part holds no significance.
Respectfully,
Myriad
