Friday, May 26, 2017

Resonant Frequency Didn't Kill 'Galloping Gertie'

Science Busts the Biggest Myth Ever About Why Bridges Collapse

Forbes  May 24, 2017  Ethan Siegel, Contributor

Photolibrarian / flickr

A wine glass, stimulated by a continued sound at just the right pitch/frequency, will vibrate at such a frequency that the internal stresses will destroy it.

The collapse of the Tacoma Narrows Bridge on the morning of November 7, 1940, is the most iconic example of a spectacular bridge failure in modern times. As the third largest suspension bridge in the world, behind only the George Washington and Golden Gate bridges, it connected Tacoma to the entire Kitsap Peninsula in Puget Sound, and opened to the public on July 1st, 1940. Just four months later, under the right wind conditions, the bridge was driven at its resonant frequency, causing it to oscillate and twist uncontrollably. After undulating for over an hour, the middle section collapsed, and the bridge was destroyed. It was a testimony to the power of resonance, and has been used as a classic example in physics and engineering classes across the country ever since. Unfortunately, the story is a complete myth.

Published on Nov 13, 2015
1 min. 6 sec.  Made using footage in the public domain. Music: "Galloping Gertie" by Sam Fonteyn

Every physical system or object has a frequency that's naturally inherent to it: its resonant frequency. A swing, for example, has a certain frequency you can drive it at; as a child you learn to pump yourself in time with the swing. Pump too slowly or too quickly, and you'll never build up speed, but if you pump at just the right rate, you can swing as high as your muscles will take you. 

Resonant frequencies can also be disastrous if you build up too much vibrational energy in a system that can't handle it, which is how sound alone at just the right pitch is capable of causing a wine glass to shatter.

Marty33 of YouTube

A wine glass, stimulated by a continued sound at just the right pitch/frequency, will vibrate at such a frequency that the internal stresses will destroy it.

It makes sense, looking at what happened to the bridge, that resonance would be the culprit. And that's the easiest pitfall in science: when you come up with an explanation that's simple, compelling, and appears obvious. Because in this case, it's completely wrong. You can calculate what the resonant frequency of the bridge would be, and there was nothing driving at that frequency. All you had was a sustained, strong wind. In fact, the bridge itself wasn't undulating at its resonant frequency at all!

But the story of what was actually happening was fascinating, and holds lessons — lessons we haven't necessarily heeded — for all the bridges we've built ever since.

Leonard G. of English Wikipedia
Capilano bridge in Vancouver, Canada, is one of the world's largest pedestrian suspension bridges. If you walk across it, you'll leave disoriented from the undulations.

Whenever you have an object suspended between two points, it's free to move, vibrate, oscillate, etc. It has its own response to outside stimuli, just like a guitar string vibrates in response to outside excitations. That's what the bridge did most of the time: simply vibrated up-and-down as cars passed over it, as the wind blew, etc. It did what any suspension bridge would do, only slightly more severely due to the cost-saving measures implemented in its construction. Structures like bridges are particularly good at shedding this kind of energy, so that, on its own, posed no danger of collapse.

Bernard J. Feldman, The Physics Teacher, v. 41, 92 (Feb. 2003)

As a steady wind passes over a solid object, it creates vortices, which can then alter the motion of the remaining object if sustained for long enough.

But as the wind passed over the bridge on November 7th, a stronger, more sustained wind than it had ever experienced before, causing vortices to form as the steady wind passed over the bridge. In small doses, this wouldn't pose much of a problem, but take a look at the effects of these vortices on a structure in the video below.

51 sec.  Uploaded on Sep 29, 2011
This is 2D CFD simulation of the flutter phenomenon of Tacoma Narrow Bridge 1940 (TNB). If you are impatient, please go to the end of this video directly. TNB is famous for its sad collapse due to its H type configuration which has a very poor aerodynamic performance. You will see from the simulation how flutter happens almost suddenly. All the parameters are chosen as those are in real world. Please keep in mind, that this is just an effort to simulate the aeroelastic instability in free vibration, no grid convergence, no turb modeling etc. have been investigated so far. However the blockage ratio is small enough (1%), and the solver is ready to extend to parallel, 3D LES based simulations.

Over time, they cause a aerodynamic phenomenon known as "flutter," where the extremities in the direction of the wind get an extra rocking motion to them. This causes the outer portions to move perpendicular to the wind direction, but out-of-phase from the overall up-and-down motion of the bridge. This phenomenon of flutter has been known to be disastrous for aircraft, but it was never seen in a bridge before. At least, not to this extent.

Netherlands Aerospace Center / NLR
Under the effects of flutter, aircraft wings can bend or even break off entirely. This has let to the demise of a number of pilots and numerous plane crashes over the years.

When the flutter effect began, one of the steel suspension cables supporting the bridge snapped, removing the last major obstacle to this fluttering motion. That was when the additional undulations, where the two sides of the bridge rocked back-and-forth in harmony with one another, began in earnest. With the sustained, strong winds, the continued vortices, and no ability to dissipate those forces, the bridge's rocking continued unabated, and even intensified. The last humans on the bridge, the photographers, fled the scene.

University of Washington Tacoma Narrows Bridge historical archives
Photographer Howard Clifford flees the Tacoma Narrows Bridge at approximately 10:45 AM on November 7th, just minutes before the central section collapsed.

But it wasn't resonance that brought the bridge down, but rather the self-induced rocking! Without an ability to dissipate its energy, it just kept twisting back-and-forth, and as the twisting continued, it continued to take damage, just as twisting a solid object back-and-forth will weaken it, eventually leading to it breaking. It didn't take any fancy resonance to bring the bridge down, just a lack of foresight of all the effects that would be at play, cheap construction techniques, and a failure to calculate all the relevant forces.

Public domain image, from the Seattle Post-Intelligencer, 1940
A large section of the concrete roadway in the center span of the new Tacoma (Wash.) Narrows bridge hurtled into Puget Sound, Nov. 07, 1940.

This wasn't a total failure, however. The engineers who investigated its collapsed began to understand the phenomenon quickly; within 10 years, they had a new sub-field of science to call their own: bridge aerodynamics-aeroelastics. The phenomenon of flutter is now well-understood, but it has to be remembered in order to be effective. The two bridges currently spanning the Tacoma Narrows' previous path have shorn up those flaws, but London's Millennium Bridge and Russia's Volgograd Bridge have both had "flutter"-related flaws exposed in the 21st century.

Don't blame resonance for the most famous bridge-collapse of all. The true cause is much scarier, and could affect hundreds of bridges across the world if we ever forget to account for, and mitigate, the fluttering effects that brought this one down.

Astrophysicist and author Ethan Siegel is the founder and primary writer of Starts With A Bang! Check out his first book, Beyond The Galaxy, and look for his second, Treknology, this October!

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