The 9/11 Forum

Hi all,

Just a quick question I thought of, had the point of impact been lets say 10 floors up, so very low on both buildings, when the collapse initiates, would the whole upper section crush itself top down? I would presume it would have enough structure above to activate an inverted pendulum effect. Can anyone add to what you feel may happen in this scenario?

Suggest changing the thread title to - Effect of lower impact location, or something.

Can you change the thread title? Would you shed some light on what you think might happen please?

Thanks

Illuminist14 wrote:Can you change the thread title?

Done. All you have to do s edit your initial post. I have limited mod status, so I've done it for you.

Would you shed some light on what you think might happen please ?

Who knows. Core columns significantly more substantial near the base, so perhaps "not a lot".

Ahh thank you. And thanks for the reply, Its a good point about the columns being stronger the lower down the building you go, there is more chance of tilting and then toppling of the upper section due to its large size, so for example when the tilt occurs (assuming this would happen as we see in reality) would the adjacent columns fail as they did in reality? I can just imagine the large top section toplling over, I cannot see the below 10 floors arresting the top section.

Columns are stronger at lower floors but not proportionately so as the loads increase toward the bottom. If you consider the FOS as a ratio of yield strength to actual load that likely is about the same... within the variations elsewhere in the structure. However... consider that 50% reserve strength of the columns at the base is likely to be 100 times the actual value of the 50% 100 stories up. But as the loads are 100 times greater... it may have negligible impact.

The core failure in the twins was the result of the CUMULATIVE loss of reserve strength or the dropping below FOS 1 of the entire core. When that occurs at any level the structure above cannot be supported and collapses down. The collapse progression is then determined by the collapsing mass meeting a threshold value to fracture each floor it falls upon. I am guessing it would take as little as 4 falling floor masses to kick off the ROOSD.

So Sander you think the whole structure would fail as it did in reality? If the scenario was the same apart from the impact point was at about 10 stories high?

Am I right in saying that, the potential energy that we know was more than enough to collapse the towers, would always stay the same? The PE would not increase?

Thanks

My very basic understanding is as follows, in order to increase the PE of the towers, you'd have to increase the mass or height?

Exactly. PE could be also increased by shifting the center of mass upward, with the existing total mass and height. That is, moving some of the office load to higher floors will increase the PE.

Ah thanks for clarifying. The collapse of WTC 2 was clocked at around 0.7G. Was this because there were decelerations, or because the PE was converted to KE partly, therefore not all the PE could be used to collapse the building at G?

Illuminist14 wrote:The collapse of WTC 2 was clocked at around 0.7G. Was this because there were decelerations, or because the PE was converted to KE partly, therefore not all the PE could be used to collapse the building at G?

All related; you've got the basic idea. Just some terminology...

Not deceleration as in terms of slowing down, rather not accelerating as much. If you start with the root concept, Force = Mass x Acceleration, you see that there must be a force additional to gravity which opposes the downward motion if acceleration is not freefall. There's not enough force to decelerate (continue indefinitely with deceleration and it will arrest, because 'deceleration' is slowing), but it prevents freefall - which occurs when there is no force opposing gravity.

The PE was only partly converted to KE because there was a resisting force acting on the upper body. By virtue of this force, acceleration is less than freefall. Going back to F=ma, and ignoring for a moment that the standard model for collapse has variable mass (accumulates during crushdown), think of the forces on the upper section. If gravity were the only force, the upper section would free fall, with the only force being mg.

But there's stuff in the way, and this provides an opposing force which retards the downward acceleration. So, there's a magnitude of force due to gravity, mg, and another force of opposite direction and some magnitude we'll call F'. With all the forces on the left side of the equation, it becomes mg - F' = ma, where a is the actual acceleration. This can be rearranged to read a = g - F'/m, which solves for acceleration.

(Note the direction of F' is accounted for by the negative sign in front; F' is the scalar magnitude. Down is also positive in this example.)

a = g - F'/m

If the magnitude of the resisting force is zero, like empty space, F' = 0 and the equation reduces to

a = g - (0)/m = g

or freefall. If the resisting force happens to be equal to the weight of the upper section (F' = mg), then

a = g - F'/m = g - (mg)/m = g - g = 0

or no acceleration at all. This doesn't mean stationary, it means constant velocity. If the original velocity is 0, then it's stationary and will remain so - this is support equal to load in the static case, like the building was for decades. If F' ever drops below mg - the load - the load will accelerate downward. If F' were to be 0.3 times the load, then the downward acceleration would be the 0.7g you're talking about.

Once an upper section is in motion, F' must exceed the load (mg) in order to decelerate the section. If F' eventually increased to be equal to mg during the collapse, there would be no acceleration, but the section would already be moving. This is the case of terminal velocity.

If F' eventually exceeds the load, for whatever reason (maybe because the bottom is a lot stronger proportionally), then deceleration occurs. The block slows down; acceleration is negative (upwards in our example). If it slows down enough, it will come to stop - arrest.

OWE,

What about the case of averaging? Let's say that you have motion of some object... such as the *collapse front*.. really a collection of objects as a descending destructive mass... and it accelerates, then meets resistance and acceleration is stopped or even slowed... then accelerates again... then is stopped or slowed and so forth many times. If you can't actually measure the movement on a fine enough scale the motion blends.

I use the analogy of a long drive where there are many accelerations and decelerations... some constant velocity and even no velocity... stop lights for example. The motion is *all over the place* but when you average the trip... it 40 mph and that's impossible because you had to at least accelerate to and then slow down.

I suspect we are using averages and that the floor masses slowed the acceleration and produced what APPEARS to be an average constant velocity... over the period of collapse.

Thanks for your detailed replies. I will try and understand them, thanks.

SanderO wrote:OWE,

What about the case of averaging? Let's say that you have motion of some object... such as the *collapse front*.. really a collection of objects as a descending destructive mass... and it accelerates, then meets resistance and acceleration is stopped or even slowed... then accelerates again... then is stopped or slowed and so forth many times. If you can't actually measure the movement on a fine enough scale the motion blends.

Exactly true.

I use the analogy of a long drive where there are many accelerations and decelerations... some constant velocity and even no velocity... stop lights for example. The motion is *all over the place* but when you average the trip... it 40 mph and that's impossible because you had to at least accelerate to and then slow down.

I suspect we are using averages and that the floor masses slowed the acceleration and produced what APPEARS to be an average constant velocity... over the period of collapse.

Agreed. How long does a collision between floor slabs take? Versus the time spent dropping?

For example, a slab/block simulation with perfect 1D collisions of rigid bodies and one virtual support per story has jolts! (And elastic snapback in this case!)

They're very short duration. You can see them at a frame rate of 500 samples per second:

(velocity vs time)



But you can't see them at 5 samples per second:



No explicit averaging and ZERO error, just very low resolution, which is an effective averaging. A short duration event not likely to be captured at a low frame rate and, if it is captured, it won't matter because the overall motion is freefall punctuated by a few jolts. Overlaying the two shows it's literally a game of connect-the-dots:




On the other hand...

Having thousands of micro-collisions, fractures, and deformational failure going on continuously - like a REAL collapse - can mechanically produce the same averaging effect. Only the idealized models have monolithic whams. The lens through which we see displacement in video is first smeared by plastic deformation and the many thousands of non-synchronous structural failures taking place every second, THEN comes the smearing effect of the data acquisition and processing. The last can include explicit averaging, of course.