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 (about 2.3, it's hard to see with the motion blur). So about 1.77, a bit less than 2 due to the damping in the scale.

2 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.