# Galloping Gertie

bridge_name = Tacoma Narrows Bridge (Galloping Gertie)

caption = The first Tacoma Narrows Bridge undergoes twisting mode vibration before collapsing.
design = Suspension
mainspan = 2,800 ft (853 m)
length = 5,000 ft (1524 m)
below = 195 ft (59.4 m)
width =
clearance =
open = July 1 1940
closed = November 7 1940
coordinates = coord|47|16|00|N|122|33|00|W|display=title,inline

Galloping Gertie is the nickname given to the original Tacoma Narrows Bridge, which opened on July 1, 1940 and dramatically collapsed into Puget Sound on November 7 of the same year. The suspension bridge spanned the Tacoma Narrows strait between Tacoma and the Kitsap Peninsula in the same location as the current bridges. The bridge's collapse had a lasting effect on science and engineering. In many physics textbooks the event is presented as an example of elementary forced resonance with the wind providing an external periodic frequency that matched the natural structural frequency (even though its real cause of failure was aeroelastic flutter). Its failure also boosted research in the field of bridge aerodynamics/aeroelastics which have themselves influenced the designs of all the world's great long-span bridges built since 1940.

At the time of its construction (and destruction) Galloping Gertie was the third longest suspension bridge in the world, behind the Golden Gate Bridge and George Washington Bridge.

Design and construction

The desire for the construction of a bridge between Tacoma and the Kitsap peninsula dates back to 1889 with a Northern Pacific Railway proposal for a trestle, but concerted efforts began in the mid-1920s. The Tacoma Chamber of Commerce began campaigning and funding studies in 1923. Several noted bridge architects, including Joseph B. Strauss, who went on to be chief engineer of the Golden Gate Bridge, and David B. Steinman, builder of the Mackinac Bridge, were consulted. Steinman made several Chamber-funded visits culminating in a preliminary proposal presented in 1929 but by 1931 the Chamber decided to cancel the agreement on the grounds that Steinman was not sufficiently active in working to obtain financing. Another problem with financing the first bridge was buying out the ferry contract from a private firm running service on the Narrows at the time.

The road to Tacoma's doomed bridge continued in 1937, when the Washington State legislature created the Washington State Toll Bridge Authority and appropriated \$5,000 to study the request by Tacoma and Pierce County for a bridge over the Narrows.

From the start, financing was the issue: revenue from tolls would not be enough to cover construction costs, but there was strong support for a bridge from the U.S. Navy, which operated the Puget Sound Naval Shipyard in Bremerton, and from the U.S. Army, which ran McChord Field and Fort Lewis in Tacoma.

Washington State engineer Clark Eldridge came up with a preliminary tried-and-true conventional bridge design, and the Washington Toll Bridge Authority requested \$11 million from the federal Public Works Administration (PWA). Preliminary construction plans by the Washington Department of Highways had called for 25-foot-deep (7.6 m) girders to sit beneath the roadway and stiffen it.

But according to Eldridge, "eastern consulting engineers" petitioned the PWA and the Reconstruction Finance Corporation (RFC) to build the bridge for less. Eldridge meant by "eastern consulting engineers" the renewed New York bridge engineer Leon Moisseiff, designer and consultant engineer of the Golden Gate Bridge. Moisseiff proposed shallower supports &mdash; girders 8 feet (2.4 m) deep. His approach meant a slimmer, more elegant design and reduced construction costs than the one by the Washington Department of Highways. Moisseiff's design won out, inasmuch as the other proposal was considered to be too expensive. On June 23 1938, the PWA approved nearly \$6 million for the Tacoma Narrows Bridge. Another \$1.6 million was to be collected from tolls to cover the total \$8 million cost.

Following the design of Moisseiff, the bridge construction began on September 27, 1938. Its construction took only nineteen months, at a cost of \$6.4 million, which was financed by the grant from the PWA and a loan from the RFC. The Tacoma was, with a main span of 2800 feet (853 m), the third longest suspension bridge in the world at that time, after the George Washington Bridge in New York, and the Golden Gate Bridge in San Francisco [Henry Petroski. Engineers of Dreams: Great Bridge Builders and the Spanning of America. New York: Alfred A. Knopf, 1995.]

Moisseiff and Fred Lienhard, a Port of New York Authority engineer, published a paper [Leon S. Moisseiff and Frederick Lienhard. "Suspension Bridges Under the Action of Lateral Forces", with discussion. Transactions of the American Society of Civil Engineers, No. 98, 1933, pp. 1080-1095, 1096-1141] that was probably, the most important theoretical advance in the bridge engineering field of the decadeRichard Scott. In the Wake of Tacoma: Suspension Bridges and the Quest for Aerodynamic Stability. American Society of Civil Engineers (June 1, 2001) ISBN-10: 0784405425 http://books.google.com/books?id=DnQOzYDJsm8C] . Their "theory of elastic distribution" extended the "deflection theory" originally devised by the austrian engineer Josef Melan, to horizontal bending under static wind load. They showed that the stiffness of the main cables (via the suspenders) would absorb up to one-half of the static wind pressure pushing a suspended structure laterally. This energy would then be transmitted to the anchorages and towers.

Using this theory, Moisseiff was able to justify stiffening the bridge with only eight-foot deep plate girders, instead of the 25-foot deep trusses proposed by the Department of Highways. This change was a substantial contributor to the difference in the projected costs of the designs.

The Tacoma was designed with two lanes inasmuch as it was expected a fairly light amount of traffic over the structure. In consequence, the bridge was only 39 ft (11.89 m) wide. This was quite narrow, especially in relation to its length. With only the 8 ft (2.44 m) deep plate girders providing additional depth, the bridge was also shallow.

The decision to use such shallow and narrow girders proved to be the first bridge's undoing. With such girders, the roadbed was insufficiently rigid and was easily moved about by winds. From the start, the bridge became notorious for its movement. A mild to moderate wind could cause alternate halves of the center span to visibly rise and fall several feet over 4- to 5-second intervals. This flexibility was experienced by the builders during construction, and by the drivers as soon as the bridge opened (under toll-paid traffic) in July 1, 1940. This led to the bridge being referred to as Galloping Gertie by the local residents, due to the apparent galloping motion felt by the drivers on the roadway.

Control of structural vibrations

As the structure experienced considerable vertical oscillations, several strategies were used to reduce the motion of the bridge. They included [Rita Robison. "Tacoma Narrows Bridge Collapse." In When Technology Fails, edited by Neil Schlager, 184-190. Detroit: Gale Research, 1994.] :

* attachment of tie-down cables to the plate girders, which were anchored to 50-ton concrete blocks on the shore. This measure proved ineffective as the cables snapped shortly after installation.
* addition of a pair of inclined cable stays that connected the main cables to the bridge deck at mid-span. These remained in place until the collapse, but were also ineffective at reducing the oscillations.
* finally, the structure was equipped with hydraulic buffers installed between the towers and the floor system of the deck to damp longitudinal motion of the main span. The effectiveness of the hydraulic dampers was, however, nullified because it was discovered that the seals of the unit were damaged when the bridge was sandblasted prior to being painted.

The Washington Toll Bridge Authority hired Professor Frederick Burt Farquharson, an engineering professor at the University of Washington, to make wind tunnel tests and recommend solutions in order to reduce the oscillations of the Tacoma. Prof. Farquharson and his students built a 1:200-full scale model of the bridge as well as a 1:20-scale model a section of the deck. The first studies concluded on November 2nd, 1940, that is five days before the bridge collapse on November 7th. He proposed two solutions:
* to drill some holes in the lateral girders and along the deck so that the air flow can circulate through them (in this way reducing lift forces) or,
* to give a more aerodynamic shape to the transversal section of the deck, by adding fairings or deflector vanes along the deck attached to the girder fascia. The first option was not favorable due to its irreversible nature. The second option was the chosen one, but it was not carried out because the bridge fell five days after the studies concluded.

Collapse

The wind-induced collapse occurred on November 7 1940, at 11:00 AM (Pacific time), due to a physical phenomenon known as aeroelastic flutter.

From the account of Leonard Coatsworth, a driver who narrowly managed to escape the bridge before the collapse:cquote|Just as I drove past the towers, the bridge began to sway violently from side to side. Before I realized it, the tilt became so violent that I lost control of the car...I jammed on the brakes and got out, only to be thrown onto my face against the curb...Around me I could hear concrete cracking...The car itself began to slide from side to side of the roadway.

On hands and knees most of the time, I crawled 500 yards [450 m] or more to the towers...My breath was coming in gasps; my knees were raw and bleeding, my hands bruised and swollen from gripping the concrete curb...Toward the last, I risked rising to my feet and running a few yards at a time...Safely back at the toll plaza, I saw the bridge in its final collapse and saw my car plunge into the Narrows. [cite web |url= http://www.wsdot.wa.gov/tnbhistory/people/eyewitness.htm|title= Tacoma Narrows Bridge: Eyewitness accounts of November 7, 1940|accessdate= 2008-08-17|author= Washington State Department of Transportation|authorlink= Washington State Department of Transportation|year= 2005]

No human life was lost in the collapse of the bridge, though Coatsworth's cocker spaniel named Tubby was lost along with his car in the collapse. Theodore von Kármán, director of the Guggenheim Aeronautical Laboratory and world-renowned aerodynamicist, was a member of the board of inquiry into the collapse. [cite book | last = Halacy, Jr. | first = D. S. | title = Father of Supersonic Flight: Theodor von Kármán | year = 1965 | pages = pp. 119-122] He reported that the State of Washington was unable to collect on one of the insurance policies for the bridge because its insurance agent fraudulently pocketed the insurance premiums. The agent, Hallett R. French who represented the Merchant's Fire Assurance Company, was charged with grand larceny for withholding the premiums for \$800,000 worth of insurance. The bridge, however, was insured by many other policies that covered 80% of the \$5.2&ndash;million structure's value. Most of these were collected without incident. [cite web | title = Tacoma Narrows Bridge | publisher = University of Washington Special Collections | url = http://www.lib.washington.edu/specialcoll/exhibits/tnb/page5.html | accessdate = 2006-11-13]

On November 28 1940, the U. S. Navy's Hydrographic Office reported that the remains of the bridge were located at geographical coordinates coord|47|16|00|N|122|33|00|W, at a depth of 180 feet (55 m).

Film of collapse

Infobox Film
name = Film of the 1940 Tacoma Narrows bridge collapse

image_size = 200px
caption = Footage of the Tacoma Narrows bridge wobbling and eventually collapsing. (19.1 MB video, 2:30)
director =
producer = Barney Elliott
writer =
narrator =
starring =
music =
cinematography =
editing =
distributor =
released =
runtime =
country =
language =
budget =
gross =
preceded_by =
followed_by =
website =
amg_id =
imdb_id =

The collapse of the bridge was recorded on film by Barney Elliott, owner of a local camera shop, and shows Leonard Coatsworth leaving the bridge after exiting his car. In 1998, "The Tacoma Narrows Bridge Collapse" was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant." This footage is still shown to engineering, architecture, and physics students as a cautionary tale. [cite web|quote="The effects of Galloping Gertie's fall lasted long after the catastrophe. Clark Eldridge, who accepted some of the blame for the bridge's failure, learned this first-hand. In late 1941 Eldridge was working for the U.S. Navy on Guam when the United States entered World War II. Soon, the Japanese captured Eldridge. He spent the remainder of the war (three years and nine months) in a prisoner of war camp in Japan. To his amazement, one day a Japanese officer, who had once been a student in America, recognized the bridge engineer. He walked up to Eldridge and said bluntly, 'Tacoma Bridge!'"|url=http://www.wsdot.wa.gov/TNBhistory/weirdfacts.htm#6|title=Weird Facts|work=Tacoma Narrows Bridge History|publisher=Washington State Department of Transportation] Elliot's original films of the construction and collapse of the bridge were shot on 16mm Kodachrome film, but most copies in circulation are in black and white because newsreels of the day copied the film onto 35mm black and white stock.

Commission of the Federal Works Agency

A commission formed by the Federal Works Agency studied the collapse of the bridge. It included Othmar Ammann and Theodore von Kármán. Without drawing any definitive conclusions, the commission explored three possible failure causes:
* aerodynamic instability by self-induced vibrations in the structure,
* eddy formations which might be periodic in nature and
* the random effects of turbulence, that is the random fluctuations in velocity and direction of the wind.

Cause of collapse

The bridge was solidly built, with girders of carbon steel anchored in huge blocks of concrete. Preceding designs typically had open lattice beam trusses underneath the roadbed. This bridge was the first of its type to employ plate girders (pairs of deep I beams) to support the roadbed. With the earlier designs any wind would simply pass through the truss, but in the new design the wind would be diverted above and below the structure. Shortly after construction finished at the end of June (opened to traffic on July 1 1940), it was discovered that the bridge would sway and buckle dangerously in relatively mild windy conditions for the area. This vibration was transverse, meaning the bridge buckled along its length, with the roadbed alternately raised and depressed in certain locations—one half of the central span would rise while the other lowered. Drivers would see cars approaching from the other direction disappear into valleys that dynamically appeared and disappeared. Because of this behavior, a local humorist gave the bridge the nickname Galloping Gertie. However, the mass of the bridge was considered sufficient to keep it structurally sound.

The failure of the bridge occurred when a never-before-seen twisting mode occurred, from winds at a mild 40 MPH. This is a so-called torsional vibration mode (which is different from the transversal or longitudinal vibration mode), whereby when the left side of the roadway went down, the right side would rise, and vice-versa, with the centerline of the road remaining still. Specifically, it was the "second" torsional mode, in which the midpoint of the bridge remained motionless while the two halves of the bridge twisted in opposite directions. Two men proved this point by walking along the center line, unaffected by the flapping of the roadway rising and falling to each side. This vibration was caused by aeroelastic fluttering.

Fluttering is a physical phenomenon in which several degrees of freedom of a structure become coupled in an unstable oscillation driven by the wind. This movement inserts energy to the bridge during each cycle so that it neutralizes the natural damping of the structure, thus the composed system (bridge-fluid) behaves as if it had an effective negative damping (or had positive feedback), leading to a exponentially growing response; in other words, the oscillations increase in amplitude with each cycle because the wind pumps in more energy than the flexing of the structure can dissipate, and finally drives the bridge toward failure due to excessive deflection and stresses. The wind speed which causes the beginning of the fluttering phenomenon (when the effective damping becomes zero) is known as the flutter velocity. Fluttering occurs even in low velocity winds with steady flow. Hence, bridge design must ensure that flutter velocity will be higher than the maximum mean wind speed present at the site.

Eventually, the amplitude of the motion produced by the fluttering increased beyond the strength of a vital part, in this case the suspender cables. Once several cables failed, the weight of the deck transferred to the adjacent cables that broke in turn until almost all of the central deck fell into the water below the span.

Resonance hypothesis

[
Von Kármán vortex street behind a circular cylinder. The first hypothesis of failure of the Tacoma Narrow Bridge was resonance [cite news |first= |last= |authorlink= |coauthors= |title=Big Tacoma Bridge Crashes 190 Feet into Puget Sound. Narrows Span, Third Longest of Type in World, Collapses in Wind. 4 Escape Death. |url= |quote=Cracking in a forty-two-mile an hour wind, the \$6,400,000 Tacoma narrows Bridge collapsed with a roar today and plunged into the waters of Puget Sound, 190 feet below. |publisher=The New York Times |date=November 8 1940, Friday |accessdate=2007-07-21 ] . This is because it was thought that the Von Kármán vortex street frequency (the so called Strouhal frequency) was the same as the torsional natural vibration frequency. This resulted to be incorrect. Actual failure was due to aeroelastic fluttercite journal|last=Billah|first=K.|coauthors=R. Scanlan|year=1991|title=Resonance, Tacoma Narrows Bridge Failure, and Undergraduate Physics Textbooks|journal=American Journal of Physics|volume=59|issue=2|pages=118–124|url=http://www.ketchum.org/billah/Billah-Scanlan.pdf|format=PDF|doi=10.1119/1.16590] ]

Frequently, the bridge's spectacular destruction is used as an object lesson in the necessity to consider both aerodynamics and resonance effects in civil and structural engineering. Billah and Scanlan (1991) reported that in fact, many physics textbooks (for example Resnik et. al. Cite book | author=Halliday, David; Resnick, Robert; Walker, Jearl | authorlink= | coauthors= | title=Fundamentals of Physics, (Chapters 21- 44) | date= | publisher=John Wiley & Sons | location= | isbn=0-470-04474-8 | pages=] and Tipler et. al. Cite book | author=Tipler, Paul Allen; Mosca, Gene | authorlink= | coauthors= | title=Physics for Scientists and Engineers : Volume 1B: Oscillations and Waves; Thermodynamics (Physics for Scientists and Engineers) | date= | publisher=W. H. Freeman | location= | isbn=0-7167-0903-1 | pages=)] ) explain that the cause of the failure of the Tacoma Narrows bridge was mechanical resonance. Resonance is the tendency of a system to oscillate at maximum amplitude at certain frequencies, known as the system's "natural frequencies". At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system stores vibrational energy (for example a child using a swing realizes that if the pushes are properly timed, the swing can move with a very large amplitude. The driving force, in this case the agent pushing the swing, exactly replenishes the energy that the system loses if its frequency equals the natural frequency of the system).

Usually, the approach taken by those physics textbooks is to introduce a first order degree-of-freedom forced oscillator, defined by the second order differential equation

:$mddot\left\{x\right\}\left(t\right) + cdot\left\{x\right\}\left(t\right) + kx\left(t\right) = F cos \left(omega t\right)$ (eq. 1)

where $m$, $c$ and $k$ stand for the mass, damping coefficient and stiffness of the linear system and $F$ and $omega$ represent the amplitude and the angular frequency of the exciting force. The solution of such ordinary differential equation as a function of time $t$ represents the displacement response of the system (given appropriate initial conditions). In the above system resonance happens when $omega$ is approximately $omega_r = sqrt\left\{k/m\right\}$, i.e. $omega_r$ is the natural (resonant) frequency of the system. The actual vibration analysis of a more complicated mechanical system like an airplane, a building or a bridge is basically based on the linearization of the equation of motion for the system, which is basically a multidimensional version of equation (eq. 1). The analysis requires eigenvalue analysis and thereafter the natural frequencies of the structure are found, together with the so-called "degrees of freedom" of the system, which are a set of independent displacements and/or rotations that specify completely the displaced or deformed position and orientation of the body or system, i.e, the bridge moves as a (linear) combination of those basic deformed positions.

Each structure has natural frequencies. Now, for resonance to occur, it is necessary to have also periodicity in the excitation force. The most tempting candidate of the periodicity in the wind force was assumed to be the so-called vortex shedding. This is because bluff bodies (non-streamlined bodies), like bridge decks, in a fluid stream do shed wakes, whose characteristics depend on the size and shape of the body and the properties of the fluid. These wakes are accompanied by alternating low-pressure vortices on the downwind side of the body (the so-called Von Kármán vortex street). The body will in consequence try to move toward the low pressure zone, in an oscillating movement called vortex-induced vibration. Eventually, if the frequency of vortex shedding matches the resonance frequency of the structure, the structure will begin to resonate and the structure's movement can become self-sustaining.

The frequency of the vortices in the von Kármán vortex street is called the Strouhal frequency $f_s$, and is given by:$frac\left\{f_s D\right\}\left\{U\right\} = S$ (eq. 2)Here, $U$ stands for the flow velocity, $D$ is a characteristic length of the bluff body and $S$ is the dimensionless Strouhal number, which depends on the body in question. For Reynolds Numbers greater than 1000, the Strouhal number is approximately equal to 0.21. In the case of the Tacoma Narrows $D$ was approximately 8 ft. (2.44 m) and $S$ was 0.20.

It was thought that the Strouhal frequency was the same one of the natural vibration frequencies of the bridge i.e $2pi f_s = omega$, causing resonance and therefore vortex-induced vibration.

In the case of the Tacoma Narrows Bridge, there was no resonance. According to Professor Frederick Burt Farquharson, an engineering professor at the University of Washington and one of the main researchers about the cause of the bridge collapse, the wind was steady at 42 mph (67 km/h) and the frequency of the destructive mode was 12 cycles/minute (0.2 Hz) [F. B. Farquharson et. al. Aerodynamic stability of suspension bridges with special reference to the Tacoma Narrows Bridge. University of Washington Engineering Experimental Station, Seattle. Bulletin 116. Parts I to V. A series of reports issued since June 1949 to June 1954.] . This frequency, was neither a natural mode of the isolated structure nor the frequency of blunt-body vortex shedding of the bridge at that wind speed (which was approximately 1 Hz). It can be concluded therefore that the vortex shedding was not the cause of the bridge collapse. The event can only be understood while considering the coupled aerodynamic and structural system that requires rigorous mathematical analysis to reveal all the degrees of freedom of the particular structure and the set of design loads imposed.

Note however that vortex-induced vibration is a far more complex process that involves both the external wind-initiated forces and internal self-excited forces that "lock-on" to the motion of the structure. During "lock-on", the wind forces drive the structure at or near one of its resonance frequencies, but as the amplitude increases this has the effect of changing the local fluid boundary conditions, so that this induces compensating, self-limiting forces, which restrict the motion to relatively benign amplitudes. This is clearly not a linear resonance phenomenon, even if the bluff body has itself linear behaviour, since the exciting force amplitude is a nonlinear force of the structural response [Billah, K.Y.R. and Scanlan, R. H. "Vortex-Induced Vibration and its Mathematical Modeling: A Bibliography", Report No.SM-89-1. Department of Civil Engineering. Princenton University. April 1989] .

Origin of the confusion

It is not clear which is the original source of the confusion. Billah and Scanlan cite that Lee Edson in his biography of Theodore von Kármán [Theodore von Karman with Lee Edson. The wind and Beyond.Theodore von Karman: Pioneer in Aviation and Pathfinder in Space. Little Brown and Company, Boston, 1963. Page 213] is a source of misinformation: cquote|"... the culprit in the Tacoma disaster was the Karman vortex Street"

Note however, that the Federal Works Administration report of the investigation (of which von Kármán was part of) concluded that cquote|... it is very improbable that the resonance with alternating vortices plays an important role in the oscillations of suspension bridges. First, it was found that there is no sharp correlation between wind velocity and oscillation frequency such as is required in case of resonance with vortices whose frequency depends on the wind velocity... [Steven Ross, et. al. "Tacoma Narrows 1940", in: "Construction disasters: design failures, causes, and prevention". McGraw Hill, p.p. 216-239, 1984]

Nowadays, even after half a century, it is common to find a wide range of rather weak descriptions, explanations, and speculations about the failure of the original Tacoma Narrows Bridge, in popular introductory physics and mathematical books for engineers.

Tubby the dog

Tubby, a black male cocker spaniel dog, was the only fatality of the Tacoma Narrows Bridge disaster. Leonard Coatsworth, a "Tacoma News Tribune" photographer, was driving with the dog over the bridge when it started to vibrate violently. Coatsworth was forced to flee his car, leaving Tubby behind. Professor Farquharson cite web|url=http://www.wsdot.wa.gov/TNBhistory/Connections/connections3.htm|title=Professor's Analysis|work=Tacoma Narrows Bridge History|publisher=WDOT] and a news photographer [ As told by Clarence C. Murton, head of the Seattle Post Intelligencer Art Dept at the time, and close collegaue of the photographer.] attempted to rescue Tubby, but the dog was too terrified to leave the car and bit one of the rescuers. Tubby died when the bridge fell, and neither his body nor the car were ever recovered.cite web|url=http://www.wsdot.wa.gov/TNBhistory/tubby.htm|title=Tubby Trivia|work=Tacoma Narrows Bridge History|publisher=Washington State Department of Transportation] Coatsworth had been driving Tubby back to his daughter, who owned the dog.

Coatsworth received US \$364.40 in reimbursement for the contents of his car, including Tubby. In 1975, Coatsworth's wife claimed that Tubby only had three legs and was paralyzed.

Fate

Efforts to salvage the bridge began almost immediately after its collapse and continued into May 1943. [http://www.wsdot.wa.gov/tnbhistory/Connections/connections4.htm#4 Tacoma Narrows Bridge Aftermath – A New Beginning: 1940 – 1950] ] Two review boards, one appointed by the federal government and one appointed by the state of Washington, concluded that repair of the bridge was impossible, and the entire bridge would have to be dismantled and an entirely new bridge built. [ [http://www.lib.washington.edu/specialcoll/exhibits/tnb/page5.html University of Washington Special Collections] ] With steel a valuable commodity due to the United States' participation in World War II, steel from the bridge cables and suspension span were sold as surplus. The salvage operation cost the state more than was returned from the sale of the material, a net loss of over \$350,000.

Preservation

The underwater remains of the bridge act as a large artificial reef, and are listed on the National Register of Historic Places with reference number 92001068.cite web|url=http://www.nr.nps.gov/|title=National Register Information System|date=2007-01-23|work=National Register of Historic Places|publisher=National Park Service] [cite web|url=http://www.wsdot.wa.gov/TNBhistory/|title=WSDOT - Tacoma Narrows Bridge: Extreme History|publisher=Washington State Department of Transportation|accessdate=2007-10-23]

A lesson for history

Othmar Ammann, leading bridge designer and member of the Federal Works Agency Commission investigating the collapse of the Tacoma Narrows Bridge wrote:

cquote|... the Tacoma Narrows bridge failure has given us invaluable information ... It has shown [that] every new structure which projects into new fields of magnitude involves new problems for the solution of which neither theory nor practical experience furnish an adequate guide. It is then that we must rely largely on judgement and if, as a result, errors or failures occur, we must accept them as a price for human progress. [Othmar H. Ammann, Theodore von Kármán and Glenn B. Woodruff. The Failure of the Tacoma Narrows Bridge, a report to the administrator. Report ot the Federal Works Agency, Washingthon, 1941]

New bridges

In the same location where Galloping Gertie collapsed, two newer Tacoma Narrows Bridges were constructed. The first one (now called the Tacoma Westbound bridge), was open to the public on October 14 1950, and is 5,979 feet (1822 m) long &mdash; 40 feet (12 m) longer than Galloping Gertie. The second one, or Tacoma Eastbound Bridge was opened in July 2007.

References in popular culture

Canadian rock group, The Tragically Hip made a reference to the collapse of the bridge in their song "Vaccination Scar".

References

* [http://www.youtube.com/watch?v=AsCBK-fRNRk Color video of the original bridge's construction and collapse]
* [http://www.youtube.com/watch?v=3mclp9QmCGs Color video of the original bridge's construction and collapse with narration]
* [http://www.lightandmatter.com/html_books/3vw/ch02/ch02.html Physics behind the collapse of the bridge]
* [http://failurebydesign.info failurebydesign.info] - physics presentation and resources
* [http://www.citynoise.org/article/5410 Photos of the bridge and the new span under construction]
*Structurae|id=s0000074|title=Tacoma Narrows Bridge (1940)

Historical

* [http://www.lib.washington.edu/specialcoll/exhibits/tnb/ History of the Tacoma Narrows Bridge]
* [http://content.lib.washington.edu/farquharsonweb/index.html University of Washington Libraries Digital Collection – Tacoma Narrows Bridge Collection] More than 152 images and text documenting the infamous collapse in 1940 of the Tacoma Narrows Bridge. Also covers "Galloping Gertie's" creation, subsequent studies involving its aerodynamics, and finally the construction of a second bridge spanning the Narrows.
* [http://www.enm.bris.ac.uk/research/nonlinear/tacoma/tacoma.html The Tacoma Narrows Bridge Disaster, November 1940]
* [http://www.ketchum.org/bridgecollapse.html Images of failure]
* [http://www.civeng.carleton.ca/Exhibits/Tacoma_Narrows/ Information and images of failure]
* [http://www.camerashoptacoma.com/ Firsthand account and images of the failure]
* [http://www.wsdot.wa.gov/TNBhistory/ Official site of the Tacoma Narrows Bridge]
* [http://www.wsdot.wa.gov/TNBhistory/spanning_time.htm Timeline of the bridges]
* [http://www.nwrain.net/~newtsuit/recoveries/narrows/narrows.htm Tacoma Narrows Bridge]
* [http://www.failuremag.com/arch_science_tacomanarrows.html Suspended Animation ] - Failure Magazine (November 2000)
* [http://www.archive.org/details/Pa2096Tacoma "Footage of the Tacoma Narrows bridge wobbling and eventually, collapsing", Stillman Fires Collection, in the Internet Archive.]

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• Puente de Tacoma Narrows — Saltar a navegación, búsqueda El Puente de Tacoma Narrows es un puente colgante de 1600 metros de longitud con una distancia entre soportes de 850 m (el tercero más grande del mundo en la época en que fue construido).[1] El puente es… …   Wikipedia Español

• Flutter (electronics and communication) — In the field of electronics and communication, flutter is the rapid variation of signal parameters, such as amplitude, phase, and frequency. Examples of electronic flutter are:*Rapid variations in received signal levels, such as variations that… …   Wikipedia

• Resonance — This article is about resonance in physics. For other uses, see Resonance (disambiguation). Resonant redirects here. For the phonological term, see Sonorant. Increase of amplitude as damping decreases and frequency approaches resonant frequency… …   Wikipedia

• Structural engineering — is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a speciality within civil engineering, but it can also be studied in its own right. [cite… …   Wikipedia

• Suspension bridge — This article is concerned with a particular type of suspension bridge, the suspended deck type.:For an index to the several types see suspension bridge types.:For the Gladiators event, see Suspension Bridge (Gladiators). A suspension bridge is a… …   Wikipedia