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# Equation: Formula for Calculating a Skycraper’s Sway: (and 9-11 results)

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posted on Dec, 8 2010 @ 12:11 PM

A skyscraper is a giant tuning fork. Give one a good knock — like with an earthquake or a heavy gust of wind — and it’ll start vibrating at its own natural resonance frequency (about seven octaves below the lowest notes on a piano). If you’re on the top floor of, say, the 1,667-foot-tall Taipei 101, you could find yourself swaying back and forth abruptly, a total of up to 2 feet within five seconds. Highly barfogenic.

So Taipei 101’s designers hung a pendulum inside the building — in this case, they used an equation like the one below to determine that the megastructure needed a 730-ton weight with giant shock absorbers bolted to its bottom.

Source: www.wired.com...

Now, the reason I say good luck. At the source article one can find the definition of the equation letter/symbols.
Reading the short article, it seemed all fine and dandy for me.

However, the last time I put something about buildings related to 9-11, a heated debate developed and a lot of it surrounded the content of the building materials etc. I witnessed some of the best debating/side pulling stuff I have ever witness here on ATS (for me). All very intertesting.

So, I see this and I look it over and then, the novice in me in the area of building/structures asks: Was this equation utilized in any of the calulations performed in the Twin Towers investigation to take into account any Sway Factor from the wind occurring at that time?

Or maybe some other equation that is used for the same calulating. Thanks
edit on 12/8/2010 by anon72 because: (no reason given)

posted on Dec, 8 2010 @ 12:48 PM

Originally posted by anon72

Source: www.wired.com...
I think that's an oversimplified equation, the real world analyses the designers do is probably much more involved, and these days it might even use finite element analysis.

So, I see this and I look it over and then, the novice in me in the area of building/structures asks: Was this equation utilized in any of the calulations performed in the Twin Towers investigation to take into account any Sway Factor from the wind occurring at that time?
I think the equation is way too simple for the twin towers too. They installed about 10,000 visco-elastic dampers between support columns and floor trusses throughout the building and I'm not sure such a simple equation accurately represents such a complex interaction of so many components.

science.howstuffworks.com...

The WTC crew ran extensive tests to find out just how much sway they could allow without disturbing the building occupants. They put structural models in wind tunnels and even lured unsuspecting test subjects to movable rooms hooked up to heavy hydraulics.

In the end, they designed the towers so they could sway about 3 feet in either direction. To minimize the sway sensation, they installed about 10,000 visco-elastic dampers between support columns and floor trusses throughout the building. The special visco-elastic material in these dampers could move somewhat, but it would snap back to its original shape. In other words, it could give a little and then return to its initial position, absorbing much of the shock of the building's swaying motion.
Even when the planes hit, I doubt the buildings swayed much more than 3 feet, if that, did they? So apparently the dampening system worked.

posted on Dec, 8 2010 @ 01:53 PM

Even when the planes hit, I doubt the buildings swayed much more than 3 feet, if that

What if the building was already in a sway at the time of impact-say 2 feet sway. The planes hitting it and the resulting damage may have all factored into a building that was in the process of self correcting-or rather didn't have a change to begin the self-correcting.

All resulting in the building suffering a weight re-distribution that resindated over a period of time. All factors coming together at the same time-adding to what the fires had done to the structure.

posted on Dec, 8 2010 @ 02:23 PM

Originally posted by anon72
What if the building was already in a sway at the time of impact-say 2 feet sway. The planes hitting it and the resulting damage may have all factored into a building that was in the process of self correcting-or rather didn't have a change to begin the self-correcting... Thanks for the links.
You're welcome.

If I'm not mistaken, the 3 foot sway was designed to occur during hurricane-force winds of 225 km/hr, and I'm guesstimating that a 2 foot sway would require gale force winds. I'm not aware of any winds of that magnitude when the planes hit so I suspect a 2 foot sway prior to when the planes hit is unlikely. I couldn't confirm the "normal" sway but I'm guessing maybe no more than 1 foot and probably 6-8" was "normal", but if anyone's got better data they can share it.

www2.matse.psu.edu...

Look at page 24 of this, talking about all the different vibrational modes they calculated:

wtc.nist.gov...

Since that shows two vibrational modes for the N-S direction, that one equation won't work with a single set of values. This illustrates the vibrational complexity is greater than the simple equation suggests, there are at least 6 modes of vibration listed for each tower.

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