How did NIST calculate that the dynamic amplification factor for a suddenly applied load was 2 (FAQ 18)

[Shani]

Hi all,

I have been reading through some threads here for a while and the one thing i do not really understand is how NIST calculated the dynamic amplification factor.

They fully explain the static calculation but after watching the Mick West video below (that i really enjoy by the way) that crushed the can so would that be a dynamic amplification factor of 10 as the can could support 10x the static mass but was crushed by dropping it 2ft?


Source: https://www.youtube.com/watch?v=wZCFo3Lcbx8


If so when the top of WTC1 fell around 12ft ( it would be roughly double the velocity the hammer was going when can was hit) would that not be double the velocity of the hammer so 4x the dynamic amplification factor makig it 40 not 2?

Sorry if its a stupid question i just do not get how they calculated it as 2.

 

[Mick West]

Sorry if its a stupid question i just do not get how they calculated it as 2.

They didn't calculate it. It's the standard value from the scaling of force for a suddenly applied load, calculated decades earlier.

It's the theoretical maximum, and assumes an ideal undamped spring (which a building is not), so the real value will be less. You can see this experimentally here.

A weight, statically applied, is about 1.3 pounds. I raise it so it's still touching, but not loading, and release it. The peak weight (i.e., downward force) is somewhere over 2 pounds (about 2.3 pounds; it's hard to see with the motion blur). So about 1.77x, a bit less than 2x due to the damping in the scale.

2x is used conservatively large for safety reasons in design. But in this analysis, it's conservatively small. The weight of a falling floor is NOT suddenly applied from 0.0", it's falling. It's also not falling attached to a spring, or landing on a spring. The real forces involved are many times greater, and applied to floors that can't really deflect very much without failing.

The small 2x simply shows that global collapse was inevitable. The details of the collapse are more complicated.

 

[Shani]

2x is used conservatively large for safety reasons in design. But in this analysis, it's conservatively small. The weight of a falling floor is NOT suddenly applied from 0.0", it's falling. It's also not falling attached to a spring, or landing on a spring. The real forces involved are many times greater, and applied to floors that can't really deflect very much without failing.

Hi Mick,

Thank you for the detailed explanation it has certainly cleared up why that always confused me.

Also i would like to apologize to you and everybody else for failing to post a linked reference to some of the claims in my post, i have not felt qualified to comment on anything so have spent my time here just reading (although not always fully understanding) other peoples work.

I would edit my post to include where i got my information from but (again feeling a bit stupid) i cannot find the edit button.

So i will add them here and move them once i locate the edit function.

https://www.nist.gov/world-trade-center-investigation/study-faqs/wtc-towers-investigation#Results

This simplified and conservative analysis indicates that the floor connections could have carried only a maximum of about 11 additional floors if the load from these floors were applied statically. Even this number is (conservatively) high, since the load from above the collapsing floor is being applied suddenly. Since the dynamic amplification factor for a suddenly applied load is 2, an intact floor below the level of collapse initiation could not have supported more than six floors.

I got the floor height from here:

https://www.researchgate.net/public...WTC_North_Tower_using_computer_simulation#pf3

WTC1 consisted of 110 floors above ground with a roof height of 417 m and a ceiling height of 3.65
m for each occupied floor [10]

After reading through my post again i also made the claim that the upper section of WTC1 12ft and would have double the velocity of the hammer upon impact (I based this on the top section falling at 2/3g). I checked that claim and realised the roughly 2/3g is probably not correct for the initial part of the collapse, i am not sure exactly what it was as there seems to be a lot of differing opinions on that detail.