Middle-aged fitness fanatics don't mix with skyscrapers, according to the "tentative" conclusions of an investigation into the strange shaking that brought about the evacuation of the 39-story Techno Mart in northeastern Seoul on July 5. After the original panic, the building’s owner, Prime Development, had speculated that “loud …
Narrows bridge was not felled by resonance.
This has been a common misstatement, even in engineering text books, as to the reason the bridge failed.
According to the Washington State DOT, it was caused by aerodynamics:
(1) The principal cause of the 1940 Narrows Bridge's failure was its "excessive flexibility;"
(2) the solid plate girder and deck acted like an aerofoil, creating "drag" and "lift;"
(3) aerodynamic forces were little understood, and engineers needed to test suspension bridge designs using models in a wind tunnel.
The primary explanation of Galloping Gertie's failure is described as "torsional flutter." It will help to break this complicated series of events into several stages.
Here is a summary of the key points in the explanation.
1. In general, the 1940 Narrows Bridge had relatively little resistance to torsional (twisting) forces. That was because it had such a large depth-to-width ratio, 1 to 72. Gertie's long, narrow, and shallow stiffening girder made the structure extremely flexible.
2. On the morning of November 7, 1940 shortly after 10 a.m., a critical event occurred. The cable band at mid-span on the north cable slipped. This allowed the cable to separate into two unequal segments. That contributed to the change from vertical (up-and-down) to torsional (twisting) movement of the bridge deck.
3. Also contributing to the torsional motion of the bridge deck was "vortex shedding." In brief, vortex shedding occurred in the Narrows Bridge as follows:
(1) Wind separated as it struck the side of Galloping Gertie's deck, the 8-foot solid plate girder. A small amount twisting occurred in the bridge deck, because even steel is elastic and changes form under high stress.
(2) The twisting bridge deck caused the wind flow separation to increase. This formed a vortex, or swirling wind force, which further lifted and twisted the deck.
(3) The deck structure resisted this lifting and twisting. It had a natural tendency to return to its previous position. As it returned, its speed and direction matched the lifting force. In other words, it moved " in phase" with the vortex. Then, the wind reinforced that motion. This produced a "lock-on" event.
4. But, the external force of the wind alone was not sufficient to cause the severe twisting that led the Narrows Bridge to fail.
5. Now the deck movement went into "torsional flutter."
"Torsional flutter" is a complex mechanism. "Flutter" is a self-induced harmonic vibration pattern. This instability can grow to very large vibrations.
When the bridge movement changed from vertical to torsional oscillation, the structure absorbed more wind energy. The bridge deck's twisting motion began to control the wind vortex so the two were synchronized. The structure's twisting movements became self-generating. In other words, the forces acting on the bridge were no longer caused by wind. The bridge deck's own motion produced the forces. Engineers call this "self-excited" motion.
It was critical that the two types of instability, vortex shedding and torsional flutter, both occurred at relatively low wind speeds. Usually, vortex shedding occurs at relatively low wind speeds, like 25 to 35 mph, and torsional flutter at high wind speeds, like 100 mph. Because of Gertie's design, and relatively weak resistance to torsional forces, from the vortex shedding instability the bridge went right into "torsional flutter."
Now the bridge was beyond its natural ability to "damp out" the motion. Once the twisting movements began, they controlled the vortex forces. The torsional motion began small and built upon its own self-induced energy.
In other words, Galloping Gertie's twisting induced more twisting, then greater and greater twisting.
This increased beyond the bridge structure's strength to resist. Failure resulted.
Sounds like resonance to me.
What? What a load of crap!
The energy came from the wind. Without resonance the motion could not have reached destructive levels.
Thank you for a detailed technical explanation...
but I think I can see a couple of key phrases:
'it moved " in phase" with the vortex. Then, the wind reinforced that motion.'
'"Flutter" is a self-induced harmonic vibration pattern. This instability can grow to very large vibrations.'
So, you're saying it was aerodynamics and resonance (albeit several specific forms of resonance). Why are you saying blaming resonance on a windy day is a misstatement?
flutter == resonance
Flutter is a form of resonance. Can we move along now?
Still resonance though to my mind...
Flutter is surely basically a species of resonance phenomenum. Unless you're using resonance as a technical term with a more limited meaning than its normal english one. If so that's a usage I haven't come across.
Aeroelastic flutter != resonance
Judging by the technical nature of his post he probably is using resonance in the technical sense. Resonance is not simply positive feedback. Resonance occurs when the external forcing frequency approaches the mechanical natural frequency of the system. So, obviously a periodic forcing at the correct frequency is a pre-requisite (this is quite different from simply 'positive feedback' or 'self reinforcing').
You are correct, Sir!
"Aeroelastic flutter != resonance"
Having listened to my father, an aeronautical and mechanical engineer with more doctorates than thumbs, go mildly insane whenever the Tacoma Narrows incident is brought up and mis-expained, I've had the concept of aeroelastic flutter pounded home ad nauseum.
Unless the wind itself was 'pulsing,' resonance - as a technical term - does not enter into it.
The wind started the motion and the structure clearly resonated. Combination of wind and resonance.
"how do you ‘simulate’ an exercise which itself is a simulation of tae kwon do combined with boxing?"
I'm guessing in a half-arsed, poorly executed, non-committal sort of way similar to doing .... okay, right. I accept your point.
"El Reg: how do you ‘simulate’ an exercise which itself is a simulation of tae kwon do combined with boxing?)"
Very easy, I can show you via a simulation.
Anyway, I'll add "danger of house collapsing" to the list of excuses to cite to the wife for not doing any exercises.
Bruce: you might want to register an ISBN number for your comment.
It was the Ants that done it
The boffins had failed to spot the hammock on the roof garden.
http://www.youtube.com/watch?v=ihUJUNL1jyI at about 2 mins
So you mean from here?
Don't worry, not many people know you can link a specific time in a YouTube video.
Failing to learn the lesson of history
Sign on the Albert Bridge in London (and probably in the past on others)
"Marching Troops must break step".
Are we all in "harmony" now?
Ever since the Tacoma Narrows Bridge shook apart
every engineer has carefully studied the effect of as many modes of resonance as possible in the bridges they design.
so why the fuck did we let a poxy architect design the millenium bridge?
Maybe Nikola Tesla was down in the basement with a hammer, tapping away steadily on the steel beams.
Sounds like a dodgy building they got there.
I thought it was the dog's fault?
The only victim of the Tacoma Narrows disaster was the photographer's dog. I just assumed everybody knew to blame it for the problem...
This has already been done.
8th August 1992 the Metropolitan Police contacted the British Geological Survey suspecting there was an eathquake in London as a number of blocks of flats in the Frinsbury area were shaking and needed to be evacuated.
The BGS concluded the the the Audience at the Madness gig in Frinsbury Park were jumping up and down at the resonant frequency of the blocks of flats.
I used to work on the 5th floor with a guy that probably weighed about 500 pounds.
When he walked in certain areas of the floor it would start oscillating like a swell on the ocean.
The motion caused several employees to feel motion sickness. This was a modern high rise building.
It was scary, he was a great guy, I'm glad he took a job elsewhere.
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