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Steel Collapse Energy Ratio Calculation

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I'm new here and I have an important and hopefully
easy structural engineering question.

What is the easiest way to calculate the energy ratio
Wg/Wp ?
The formula comes from Bazant&Zhou 2001.

I have recently read an article by structural engineer
Dr. Abolhassan Astaneh-Asl
which describes that the WTC twin towers may have
collapsed due to architectural flaws.

This is in contradiction of the NIST report which is
the motivation for my question. I have calculated the
energy ratio myself and I find it to be MUCH LOWER
than the one mentioned in the NIST report.

However, the calculations for this important energy
ratio are nowhere to be found. Not in the NIST report
and not in the orinal Bazant paper nor in a more
recent paper june 2006 which agains states the energy
ratio is 8.4.

This ratio of 8.4 seems to be calculated for damaged
storeys whereas NIST and others seem to mistakenly
assume it applies to intact storeys.

So I have been trying to track down this calculation
and understand the root of this confusion.

In NCSTAR 1-6 chapter 9 NIST refers to a paper by
Bazant that quotes an energy ratio of 8.4 in favor of
collapse (Wg/Wp) implying that the potential energy
released for each storey would exceed the energy
required to crush it.

In NCSTAR 1-6 chapter 8 there are DCRs for the columns
of the 95th storey before impact. Averaging the values
for all of the columns, the implied safetyFactor is 4.

The energy ratio I come up with from my simplfied
formula is:

energyReleased = m*g*h
energyAbsorbed =

(The areaUnderLoadProfile of Bazant 2001 Fig. 5d is
therefore the energyReleased is LOWER than the
energyAbsorbed by a factor of
1/(safetyFactor*areaUnderLoadProfile )= 1/(4 * 35%) =

I will not be surprised to see energy ratios greater
than 1 if the safetyfactor or loadprofile that I have
used are incorrect.

However, an energy ratio of 8 seems absurd.

Can anyone provide some clarification for how to
calculate the energy ratio?

Dom Dudz

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