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Tacoma Narrows Bridge (1940)
Encyclopedia
The 1940 Tacoma Narrows Bridge was the first incarnation of the Tacoma Narrows Bridge
, a suspension bridge
in the U.S.
state of Washington that spanned the Tacoma Narrows
strait of Puget Sound
between Tacoma
and the Kitsap Peninsula
. It opened to traffic on July 1, 1940, and dramatically collapsed
into Puget Sound on November 7 of the same year. At the time of its construction (and its destruction), the bridge was the third longest suspension bridge in the world in terms of main span length, behind the Golden Gate Bridge
and the George Washington Bridge
.
Construction on the bridge began in September 1938. From the time the deck was built, it began to move vertically in windy conditions, which led to construction workers giving the bridge the nickname Galloping Gertie. The motion was observed even when the bridge opened to the public. Several measures aimed at stopping the motion were ineffective, and the bridge's main span finally collapsed under 40 miles per hour (64.4 km/h) wind conditions the morning of November 7, 1940.
Following the collapse, the United States' involvement in World War II
delayed plans to replace the bridge. The portions of the bridge still standing after the collapse, including the towers and cables, were dismantled and sold as scrap metal. Nearly 10 years after the bridge collapsed, a new Tacoma Narrows Bridge
opened in the same location, using the original bridge's tower pedestals and cable anchorages. The portion of the bridge that fell into the water now serves as an artificial reef
.
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, though its actual cause of failure was aeroelastic flutter. Its failure also boosted research in the field of bridge aerodynamics-aeroelastics, the study of which has influenced the designs of all the world's great long-span bridges built since 1940.
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 engineers, including Joseph B. Strauss, who went on to be chief engineer of the Golden Gate Bridge
, and David B. Steinman
, who went on to design 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 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 of the bridge was a problem: revenue from the proposed tolls would not be enough to cover construction costs, but there was strong support for the 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
near Tacoma.
Washington State engineer Clark Eldridge
produced a preliminary tried-and-true conventional suspension 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 a set of 25-foot-deep (7.6 m) girder
s to sit beneath the roadway and stiffen it.
However, according to Eldridge, "Eastern consulting engineers" - by which Eldridge meant Leon Moisseiff
, the noted New York bridge engineer who served as designer and consultant engineer for the Golden Gate Bridge
- petitioned the PWA and the Reconstruction Finance Corporation
(RFC) to build the bridge for less. Moisseiff proposed shallower supports—girders 8 feet (2.4 m) deep. His approach meant a slimmer, more elegant design, and also reduced the construction costs as compared with the Highway Department's design. 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 estimated total $8 million cost.
Following Moisseiff's design, bridge construction began on September 27, 1938. 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 Narrows Bridge, with a main span of 2800 feet (853.4 m), was the third-longest suspension bridge in the world at that time, following the George Washington Bridge
between New Jersey
and New York City
, and the Golden Gate Bridge
, just north of San Francisco.
Moisseiff and Fred Lienhard, the latter a Port of New York Authority engineer, published a paper that was probably the most important theoretical advance in the bridge engineering field of the decade. Their theory of elastic distribution extended the deflection theory that was 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 argued for stiffening the bridge with a set of eight-foot-deep plate girders rather than the 25 feet (7.6 m)-deep trusses proposed by the Washington Toll Bridge Authority. This change was a substantial contributor to the difference in the projected costs of the designs.
Because planners expected fairly light traffic volumes, the bridge was designed with two lanes, and it was just 39 feet (11.9 m) wide. This was quite narrow, especially in comparison with its length. With only the 8 feet (2.4 m)-deep plate girders providing additional depth, the bridge's roadway section was also shallow.
The decision to use such shallow and narrow girders proved to be the original Tacoma Narrows Bridge's undoing. With such minimal girders, the deck of the bridge was insufficiently rigid and was easily moved about by winds; from the start, the bridge became infamous for its movement. A mild to moderate wind could cause alternate halves of the center span to visibly rise and fall several feet over four- to five-second intervals. This flexibility was experienced by the builders and workmen during construction, which led some of the workers to christen the bridge "Galloping Gertie." The nickname soon stuck, and even the public (when the toll
-paid traffic started) felt these motions on the day that the bridge opened on July 1, 1940.
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 bridge. Professor Farquharson and his students built a 1:200-scale model of the bridge and a 1:20-scale model of a section of the deck. The first studies concluded on November 2, 1940—five days before the bridge collapse on November 7. He proposed two solutions:
The first option was not favored because of its irreversible nature. The second option was the chosen one; but it was not carried out, because the bridge collapsed five days after the studies were concluded.
The wind-induced collapse occurred on November 7, 1940, at 11:00 a.m. (Pacific time), because of a physical phenomenon known as aeroelastic flutter.
From the account of Leonard Coatsworth, a Tacoma News Tribune
editor who was the last person to drive on the bridge, he was driving with his dog, Tubby, over the bridge when the bridge started to vibrate violently. Coatsworth was forced to flee his car:
No human life was lost in the collapse of the bridge. Tubby, a black male cocker spaniel, was the only fatality of the Tacoma Narrows Bridge disaster; he was lost along with Coatsworth's car. Professor Farquharson and a news photographer attempted to rescue Tubby during a lull, 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. Coatsworth had been driving Tubby back to his daughter, who owned the dog. Coatsworth received US $450 for his car and $364.40 in reimbursement for the contents of his car, including Tubby.
, the director of the Guggenheim Aeronautical Laboratory
and a world-renowned aerodynamicist, was a member of the board of inquiry into the collapse. He reported that the State of Washington was unable to collect on one of the insurance policies for the bridge because its insurance agent had fraudulently pocketed the insurance premiums. The agent, Hallett R. French, who represented the Merchant's Fire Assurance Company, was charged and tried for 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 million structure's value. Most of these were collected without incident.
On November 28, 1940, the U.S. Navy's Hydrographic Office reported that the remains of the bridge were located at geographical coordinates 47°16′00"N 122°33′00"W, at a depth of 180 feet (55 meters).
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
. Elliot's original films of the construction and collapse of the bridge were shot on 16 mm Kodachrome film
, but most copies in circulation are in black and white because newsreels of the day copied the film onto 35 mm black-and-white stock.
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:
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 that are common for the area, and worse during severe winds. This vibration was transverse
, one-half of the central span rising while the other lowered. Drivers would see cars approaching from the other direction rise and fall, riding the violent energy wave through the bridge. However, at that time the mass of the bridge was considered to be 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 miles per hour (17.9 m/s). 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 center line 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; the composed system (bridge-fluid) therefore behaves as if it had an effective negative damping (or had positive feedback
), leading to an 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 stress. The wind speed that 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.
The bridge's spectacular destruction is often 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 Resnick et al. and Tipler et al. ) wrongly 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
(eq. 1)
where
, 
and 
stand for the mass
, damping coefficient and stiffness
of the linear system and
and 
represent the amplitude and the angular frequency of the exciting force. The solution of such ordinary differential equation
as a function of time
represents the displacement response of the system (given appropriate initial conditions). In the above system resonance happens when 
is approximately 
, i.e. 
is the natural (resonant) frequency of the system. The actual vibration analysis of a more complicated mechanical system—such as 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. 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
, and is given by
(eq. 2)
Here,
stands for the flow velocity, 
is a characteristic length of the bluff body and 
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,
was approximately 8 feet (2.4 m) and 
was 0.20.
It was thought that the Strouhal frequency was the same one of the natural vibration frequencies of the bridge i.e.
, 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 miles per hour (18.8 m/s) and the frequency of the destructive mode was 12 cycles/minute (0.2 Hz
). 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 be understood only 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.
is a source of misinformation: "The culprit in the Tacoma disaster was the Karman vortex Street."
However, the Federal Works Administration report of the investigation (of which von Kármán was part) concluded that
, steel from the bridge cables and the suspension span was sold as scrap metal to be melted down. The salvage operation cost the state more than was returned from the sale of the material, a net loss of over $350,000.
The cable anchorages, tower pedestals and most of the remaining substructure were relatively undamaged in the collapse, and were reused during construction of the replacement span that opened in 1950. The towers, which supported Gertie's main cables and road deck, suffered major damage at their bases from being deflected twelve feet towards shore as a result of the collapse of the mainspan and the sagging of the sidespans. They were dismantled, and the steel sent to recyclers.
, and these are listed on the National Register of Historic Places
with reference number 92001068.
, a leading bridge designer and member of the Federal Works Agency Commission investigating the collapse of the Tacoma Narrows Bridge, wrote:
The Bronx Whitestone Bridge
, which is of similar design to the 1940 Tacoma Narrows Bridge, was reinforced shortly after the collapse. Fourteen-foot-high (4.3 m) steel trusses were installed on both sides of the deck in 1943 to weigh down and stiffen the bridge in an effort to reduce oscillation. In 2003, the stiffening trusses were removed and aerodynamic fiberglass fairings were installed along both sides of the road deck.
Half a century later, the rebuilt bridge that was completed in 1950 was exceeding its traffic capacity, and a second, parallel suspension bridge was constructed to carry eastbound traffic. The suspension bridge that was completed in 1950 was reconfigured to solely carry westbound traffic. The new parallel bridge opened to traffic in July 2007.
Tacoma Narrows Bridge
The Tacoma Narrows Bridge is a pair of twin suspension bridges in the U.S. state of Washington, which carry State Route 16 across the Tacoma Narrows strait of Puget Sound between Tacoma and the Kitsap Peninsula...
, a suspension bridge
Suspension bridge
A suspension bridge is a type of bridge in which the deck is hung below suspension cables on vertical suspenders. Outside Tibet and Bhutan, where the first examples of this type of bridge were built in the 15th century, this type of bridge dates from the early 19th century...
in the U.S.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
state of Washington that spanned the Tacoma Narrows
Tacoma Narrows
The Tacoma Narrows , a strait, is part of Puget Sound in the U.S. state of Washington. A navigable maritime waterway between glacial landforms, the Narrows separates the Kitsap Peninsula from the city of Tacoma....
strait of Puget Sound
Puget Sound
Puget Sound is a sound in the U.S. state of Washington. It is a complex estuarine system of interconnected marine waterways and basins, with one major and one minor connection to the Strait of Juan de Fuca and the Pacific Ocean — Admiralty Inlet being the major connection and...
between Tacoma
Tacoma, Washington
Tacoma is a mid-sized urban port city and the county seat of Pierce County, Washington, United States. The city is on Washington's Puget Sound, southwest of Seattle, northeast of the state capital, Olympia, and northwest of Mount Rainier National Park. The population was 198,397, according to...
and the Kitsap Peninsula
Kitsap Peninsula
The Kitsap Peninsula is an arm of land that is part of the larger Olympic Peninsula in Washington state that lies west of Seattle across Puget Sound. Hood Canal separates Kitsap Peninsula from the rest of the Olympic Peninsula...
. It opened to traffic on July 1, 1940, and dramatically collapsed
Structural failure
Structural failure refers to loss of the load-carrying capacity of a component or member within a structure or of the structure itself. Structural failure is initiated when the material is stressed to its strength limit, thus causing fracture or excessive deformations...
into Puget Sound on November 7 of the same year. At the time of its construction (and its destruction), the bridge was the third longest suspension bridge in the world in terms of main span length, behind the Golden Gate Bridge
Golden Gate Bridge
The Golden Gate Bridge is a suspension bridge spanning the Golden Gate, the opening of the San Francisco Bay into the Pacific Ocean. As part of both U.S. Route 101 and California State Route 1, the structure links the city of San Francisco, on the northern tip of the San Francisco Peninsula, to...
and the George Washington Bridge
George Washington Bridge
The George Washington Bridge is a suspension bridge spanning the Hudson River, connecting the Washington Heights neighborhood in the borough of Manhattan in New York City to Fort Lee, Bergen County, New Jersey. Interstate 95 and U.S. Route 1/9 cross the river via the bridge. U.S...
.
Construction on the bridge began in September 1938. From the time the deck was built, it began to move vertically in windy conditions, which led to construction workers giving the bridge the nickname Galloping Gertie. The motion was observed even when the bridge opened to the public. Several measures aimed at stopping the motion were ineffective, and the bridge's main span finally collapsed under 40 miles per hour (64.4 km/h) wind conditions the morning of November 7, 1940.
Following the collapse, the United States' involvement in World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
delayed plans to replace the bridge. The portions of the bridge still standing after the collapse, including the towers and cables, were dismantled and sold as scrap metal. Nearly 10 years after the bridge collapsed, a new Tacoma Narrows Bridge
Tacoma Narrows Bridge (1950)
The 1950 Tacoma Narrows Bridge is a suspension bridge in the U.S. state of Washington that carries the westbound lanes of Washington State Route 16 across the Tacoma Narrows strait, between the city of Tacoma and the Kitsap Peninsula...
opened in the same location, using the original bridge's tower pedestals and cable anchorages. The portion of the bridge that fell into the water now serves as an artificial reef
Artificial reef
An artificial reef is a human-made underwater structure, typically built to promote marine life in areas with a generally featureless bottom, control erosion, block ship passage, or improve surfing....
.
The bridge's collapse had a lasting effect on science and engineering. In many physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
textbooks, the event is presented as an example of elementary forced resonance
Mechanical resonance
Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies...
with the wind providing an external periodic frequency that matched the natural structural frequency, though its actual cause of failure was aeroelastic flutter. Its failure also boosted research in the field of bridge aerodynamics-aeroelastics, the study of which has influenced the designs of all the world's great long-span bridges built since 1940.
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 RailwayNorthern Pacific Railway
The Northern Pacific Railway was a railway that operated in the west along the Canadian border of the United States. Construction began in 1870 and the main line opened all the way from the Great Lakes to the Pacific when former president Ulysses S. Grant drove in the final "golden spike" in...
proposal for a trestle
Trestle
A trestle is a rigid frame used as a support, especially referring to a bridge composed of a number of short spans supported by such frames. In the context of trestle bridges, each supporting frame is generally referred to as a bent...
, but concerted efforts began in the mid-1920s. The Tacoma Chamber of Commerce began campaigning and funding studies in 1923. Several noted bridge engineers, including Joseph B. Strauss, who went on to be chief engineer of the Golden Gate Bridge
Golden Gate Bridge
The Golden Gate Bridge is a suspension bridge spanning the Golden Gate, the opening of the San Francisco Bay into the Pacific Ocean. As part of both U.S. Route 101 and California State Route 1, the structure links the city of San Francisco, on the northern tip of the San Francisco Peninsula, to...
, and David B. Steinman
David B. Steinman
David Bernard Steinman was an American structural engineer. He was the designer of the Mackinac Bridge and many other notable bridges, and a published author. He grew up in New York City's lower Manhattan, and lived with the ambition of making his mark on the Brooklyn Bridge that he lived under...
, who went on to design the Mackinac Bridge
Mackinac Bridge
The Mackinac Bridge is a suspension bridge spanning the Straits of Mackinac to connect the non-contiguous Upper and Lower peninsulas of the U.S. state of Michigan. Opened in 1957, the bridge is the third longest in total suspension in the world and the longest suspension bridge between anchorages...
, 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 Washington State legislature created the Washington State Toll Bridge Authority
Washington Toll Bridge Authority
The Washington Toll Bridge Authority was created in 1937 by the Washington State Legislature, with a mandate to finance, construct and operate toll bridges....
and appropriated $5,000 to study the request by Tacoma and Pierce County
Pierce County, Washington
right|thumb|[[Tacoma, Washington|Tacoma]] - Seat of Pierce CountyPierce County is the second most populous county in the U.S. state of Washington. Formed out of Thurston County on December 22, 1852, by the legislature of Oregon Territory...
for a bridge over the Narrows.
From the start, financing of the bridge was a problem: revenue from the proposed tolls would not be enough to cover construction costs, but there was strong support for the bridge from the U.S. Navy, which operated the Puget Sound Naval Shipyard
Puget Sound Naval Shipyard
Puget Sound Naval Shipyard and Intermediate Maintenance Facility is a United States Navy shipyard covering 179 acres on Puget Sound at Bremerton, Washington...
in Bremerton
Bremerton, Washington
Bremerton is a city in Kitsap County, Washington, United States. The population was 38,790 at the 2011 State Estimate, making it the largest city on the Olympic Peninsula. Bremerton is home to Puget Sound Naval Shipyard and the Bremerton Annex of Naval Base Kitsap...
, and from the U.S. Army
United States Army
The United States Army is the main branch of the United States Armed Forces responsible for land-based military operations. It is the largest and oldest established branch of the U.S. military, and is one of seven U.S. uniformed services...
, which ran McChord Field and Fort Lewis
Fort Lewis
Joint Base Lewis-McChord is a United States military facility located south-southwest of Tacoma, Washington. The facility is under the jurisdiction of the United States Army Joint Base Garrison, Joint Base Lewis-McChord....
near Tacoma.
Washington State engineer Clark Eldridge
Clark Eldridge
Clark Eldridge was one of the engineers who designed the first Tacoma Narrows Bridge.In 1936, Eldridge joined the Washington State Highway Department. He designed two of the state's most colossal bridges, the Lake Washington Floating Bridge and the first Tacoma Narrows Bridge...
produced a preliminary tried-and-true conventional suspension bridge design, and the Washington Toll Bridge Authority
Washington Toll Bridge Authority
The Washington Toll Bridge Authority was created in 1937 by the Washington State Legislature, with a mandate to finance, construct and operate toll bridges....
requested $11 million from the Federal Public Works Administration
Public Works Administration
The Public Works Administration , part of the New Deal of 1933, was a large-scale public works construction agency in the United States headed by Secretary of the Interior Harold L. Ickes. It was created by the National Industrial Recovery Act in June 1933 in response to the Great Depression...
(PWA). Preliminary construction plans by the Washington Department of Highways had called for a set of 25-foot-deep (7.6 m) girder
Girder
A girder is a support beam used in construction. Girders often have an I-beam cross section for strength, but may also have a box shape, Z shape or other forms. Girder is the term used to denote the main horizontal support of a structure which supports smaller beams...
s to sit beneath the roadway and stiffen it.
However, according to Eldridge, "Eastern consulting engineers" - by which Eldridge meant Leon Moisseiff
Leon Moisseiff
Leon S. Moisseiff was a leading suspension bridge engineer in the United States of America in the 1920s and 1930s. He was awarded The Franklin Institute's Louis E...
, the noted New York bridge engineer who served as designer and consultant engineer for the Golden Gate Bridge
Golden Gate Bridge
The Golden Gate Bridge is a suspension bridge spanning the Golden Gate, the opening of the San Francisco Bay into the Pacific Ocean. As part of both U.S. Route 101 and California State Route 1, the structure links the city of San Francisco, on the northern tip of the San Francisco Peninsula, to...
- petitioned the PWA and the Reconstruction Finance Corporation
Reconstruction Finance Corporation
The Reconstruction Finance Corporation was an independent agency of the United States government, established and chartered by the US Congress in 1932, Act of January 22, 1932, c. 8, 47 Stat. 5, during the administration of President Herbert Hoover. It was modeled after the War Finance Corporation...
(RFC) to build the bridge for less. Moisseiff proposed shallower supports—girders 8 feet (2.4 m) deep. His approach meant a slimmer, more elegant design, and also reduced the construction costs as compared with the Highway Department's design. 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 estimated total $8 million cost.
Following Moisseiff's design, bridge construction began on September 27, 1938. 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 Narrows Bridge, with a main span of 2800 feet (853.4 m), was the third-longest suspension bridge in the world at that time, following the George Washington Bridge
George Washington Bridge
The George Washington Bridge is a suspension bridge spanning the Hudson River, connecting the Washington Heights neighborhood in the borough of Manhattan in New York City to Fort Lee, Bergen County, New Jersey. Interstate 95 and U.S. Route 1/9 cross the river via the bridge. U.S...
between New Jersey
New Jersey
New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...
and New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
, and the Golden Gate Bridge
Golden Gate Bridge
The Golden Gate Bridge is a suspension bridge spanning the Golden Gate, the opening of the San Francisco Bay into the Pacific Ocean. As part of both U.S. Route 101 and California State Route 1, the structure links the city of San Francisco, on the northern tip of the San Francisco Peninsula, to...
, just north of San Francisco.
Moisseiff and Fred Lienhard, the latter a Port of New York Authority engineer, published a paper that was probably the most important theoretical advance in the bridge engineering field of the decade. Their theory of elastic distribution extended the deflection theory that was originally devised by the Austrian engineer Josef Melan
Josef Melan
Josef Melan was an Austrian engineer. He is regarded as one of the most important pioneers of reinforced concrete bridge-building at the end of the 19th century. Josef Melan is credited as the inventor of the Melan System, a method for the construction of reinforced bridges...
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 argued for stiffening the bridge with a set of eight-foot-deep plate girders rather than the 25 feet (7.6 m)-deep trusses proposed by the Washington Toll Bridge Authority. This change was a substantial contributor to the difference in the projected costs of the designs.
Because planners expected fairly light traffic volumes, the bridge was designed with two lanes, and it was just 39 feet (11.9 m) wide. This was quite narrow, especially in comparison with its length. With only the 8 feet (2.4 m)-deep plate girders providing additional depth, the bridge's roadway section was also shallow.
The decision to use such shallow and narrow girders proved to be the original Tacoma Narrows Bridge's undoing. With such minimal girders, the deck of the bridge was insufficiently rigid and was easily moved about by winds; from the start, the bridge became infamous for its movement. A mild to moderate wind could cause alternate halves of the center span to visibly rise and fall several feet over four- to five-second intervals. This flexibility was experienced by the builders and workmen during construction, which led some of the workers to christen the bridge "Galloping Gertie." The nickname soon stuck, and even the public (when the toll
Toll bridge
A toll bridge is a bridge over which traffic may pass upon payment of a toll, or fee.- History :The practice of collecting tolls on bridges probably harks back to the days of ferry crossings where people paid a fee to be ferried across stretches of water. As boats became impractical to carry large...
-paid traffic started) felt these motions on the day that the bridge opened on July 1, 1940.
Attempt to control structural vibration
Since the structure experienced considerable vertical oscillations while it was still under construction, several strategies were used to reduce the motion of the bridge. They included- 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 nullified, however, because the seals of the units were damaged when the bridge was sand-blasted before being painted.
The Washington Toll Bridge Authority
Washington Toll Bridge Authority
The Washington Toll Bridge Authority was created in 1937 by the Washington State Legislature, with a mandate to finance, construct and operate toll bridges....
hired Professor Frederick Burt Farquharson, an engineering professor at the University of Washington
University of Washington
University of Washington is a public research university, founded in 1861 in Seattle, Washington, United States. The UW is the largest university in the Northwest and the oldest public university on the West Coast. The university has three campuses, with its largest campus in the University...
, to make wind-tunnel tests and recommend solutions in order to reduce the oscillations of the bridge. Professor Farquharson and his students built a 1:200-scale model of the bridge and a 1:20-scale model of a section of the deck. The first studies concluded on November 2, 1940—five days before the bridge collapse on November 7. He proposed two solutions:
- To drill some holes in the lateral girders and along the deck so that the air flow could circulate through them (in this way reducing lift forces).
- To give a more aerodynamic shape to the transverse section of the deck by adding fairings or deflector vanes along the deck, attached to the girder fascia.
The first option was not favored because of its irreversible nature. The second option was the chosen one; but it was not carried out, because the bridge collapsed five days after the studies were concluded.
Collapse
From the account of Leonard Coatsworth, a Tacoma News Tribune
Tacoma News Tribune
The News Tribune is a daily newspaper in Tacoma, Washington, in the United States.-History:It can trace its origins back to the founding of the weekly Tacoma Ledger by R.F. Radabaugh in 1880. The next year, H.C. Patrick founded The News, another weekly. Both papers became dailies in 1883. In 1898,...
editor who was the last person to drive on the bridge, he was driving with his dog, Tubby, over the bridge when the bridge started to vibrate violently. Coatsworth was forced to flee his car:
No human life was lost in the collapse of the bridge. Tubby, a black male cocker spaniel, was the only fatality of the Tacoma Narrows Bridge disaster; he was lost along with Coatsworth's car. Professor Farquharson and a news photographer attempted to rescue Tubby during a lull, 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. Coatsworth had been driving Tubby back to his daughter, who owned the dog. Coatsworth received US $450 for his car and $364.40 in reimbursement for the contents of his car, including Tubby.
Inquiry
Theodore von KármánTheodore von Karman
Theodore von Kármán was a Hungarian-American mathematician, aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization...
, the director of the Guggenheim Aeronautical Laboratory
Guggenheim Aeronautical Laboratory
The Guggenheim Aeronautical Laboratory at the California Institute of Technology , was a research institute created in 1926, at first specializing in aeronautics research. In 1930, Hungarian scientist Theodore von Kármán accepted the directorship of the lab and emigrated to the United States. Under...
and a world-renowned aerodynamicist, was a member of the board of inquiry into the collapse. He reported that the State of Washington was unable to collect on one of the insurance policies for the bridge because its insurance agent had fraudulently pocketed the insurance premiums. The agent, Hallett R. French, who represented the Merchant's Fire Assurance Company, was charged and tried for 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 million structure's value. Most of these were collected without incident.
On November 28, 1940, the U.S. Navy's Hydrographic Office reported that the remains of the bridge were located at geographical coordinates 47°16′00"N 122°33′00"W, at a depth of 180 feet (55 meters).
Film of collapse
The collapse of the bridge was recorded on film by Barney Elliott, owner of a local camera shop. The film 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 RegistryNational Film Registry
The National Film Registry is the United States National Film Preservation Board's selection of films for preservation in the Library of Congress. The Board, established by the National Film Preservation Act of 1988, was reauthorized by acts of Congress in 1992, 1996, 2005, and again in October 2008...
by the Library of Congress
Library of Congress
The Library of Congress is the research library of the United States Congress, de facto national library of the United States, and the oldest federal cultural institution in the United States. Located in three buildings in Washington, D.C., it is the largest library in the world by shelf space and...
as being culturally, historically, or aesthetically significant. This footage is still shown to engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, architecture
Architecture
Architecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...
, and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
students as a cautionary tale
Cautionary tale
A cautionary tale is a tale told in folklore, to warn its hearer of a danger. There are three essential parts to a cautionary tale, though they can be introduced in a large variety of ways. First, a taboo or prohibition is stated: some act, location, or thing is said to be dangerous. Then, the...
. Elliot's original films of the construction and collapse of the bridge were shot on 16 mm Kodachrome film
Kodachrome
Kodachrome is the trademarked brand name of a type of color reversal film that was manufactured by Eastman Kodak from 1935 to 2009.-Background:...
, but most copies in circulation are in black and white because newsreels of the day copied the film onto 35 mm black-and-white stock.
Commission of the Federal Works Agency
A commission formed by the Federal Works AgencyFederal Works Agency
The Federal Works Agency was an independent agency of the Federal government of the United States which administered a number of public construction, building maintenance, and public works relief functions and laws from 1939 to 1949...
studied the collapse of the bridge. It included Othmar Ammann
Othmar Ammann
Othmar Hermann Ammann was a American structural engineer whose designs include the George Washington Bridge, Verrazano-Narrows Bridge, and Bayonne Bridge.-Biography:...
and Theodore von Kármán
Theodore von Karman
Theodore von Kármán was a Hungarian-American mathematician, aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization...
. Without drawing any definitive conclusions, the commission explored three possible failure causes:
- Aerodynamic instability by self-induced vibrations in the structure
- Eddy formations that might be periodic in nature
- Random effects of turbulence, that is the random fluctuations in velocity and direction of the wind.
Cause of the collapse
The original Tacoma Narrows Bridge was solidly built, with girders of carbon steelSteel
Steel is an alloy that consists mostly of iron and has a carbon content between 0.2% and 2.1% by weight, depending on the grade. Carbon is the most common alloying material for iron, but various other alloying elements are used, such as manganese, chromium, vanadium, and tungsten...
anchored in huge blocks of concrete
Concrete
Concrete is a composite construction material, composed of cement and other cementitious materials such as fly ash and slag cement, aggregate , water and chemical admixtures.The word concrete comes from the Latin word...
. 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
I-beam
-beams, also known as H-beams, W-beams , rolled steel joist , or double-T are beams with an - or H-shaped cross-section. The horizontal elements of the "" are flanges, while the vertical element is the web...
) 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 that are common for the area, and worse during severe winds. This vibration was transverse
Transverse wave
A transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer...
, one-half of the central span rising while the other lowered. Drivers would see cars approaching from the other direction rise and fall, riding the violent energy wave through the bridge. However, at that time the mass of the bridge was considered to be 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 miles per hour (17.9 m/s). This is a so-called torsional vibration mode (which is different from the transversal
Transverse mode
A transverse mode of a beam of electromagnetic radiation is a particular electromagnetic field pattern of radiation measured in a plane perpendicular to the propagation direction of the beam...
or longitudinal
Longitudinal mode
For the longitudinal mode of conduction of electric currents, see Common modeA longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive...
vibration mode), whereby when the left side of the roadway went down, the right side would rise, and vice versa, with the center line 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
Damping
In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator.In mechanics, friction is one such damping effect...
of the structure; the composed system (bridge-fluid) therefore behaves as if it had an effective negative damping (or had positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...
), leading to an 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 stress. The wind speed that 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
Aerodynamics
Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...
and resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
effects in civil
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...
and structural engineering
Structural engineering
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 specialty within civil engineering, but it can also be studied in its own right....
. Billah and Scanlan (1991) reported that in fact, many physics textbooks (for example Resnick et al. and Tipler et al. ) wrongly 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
(eq. 1)where
, and stand for the massMass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, damping coefficient and stiffness
Stiffness
Stiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body.-Calculations:...
of the linear system and
and represent the amplitude and the angular frequency of the exciting force. The solution of such ordinary differential equationOrdinary differential equation
In mathematics, an ordinary differential equation is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable....
as a function of time
represents the displacement response of the system (given appropriate initial conditions). In the above system resonance happens when is approximately , i.e. is the natural (resonant) frequency of the system. The actual vibration analysis of a more complicated mechanical system—such as 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. 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
Vortex shedding
Vortex shedding is an unsteady flow that takes place in special flow velocities . In this flow, vortices are created at the back of the body and detach periodically from either side of the body. See Von Kármán vortex street.Vortex shedding is caused when a fluid flows past a blunt object...
. 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
Von Kármán vortex street
A Kármán vortex street is a term in fluid dynamics for a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid over bluff bodies...
). The body will in consequence try to move toward the low-pressure zone, in an oscillating movement called vortex-induced vibration
Vortex Induced Vibration
In fluid dynamics, vortex-induced vibrations are motions induced on bodies interacting with an external fluid flow, produced by – or the motion producing – periodical irregularities on this flow.A classical example is the VIV of an underwater cylinder...
. 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
, and is given by (eq. 2)Here,
stands for the flow velocity, is a characteristic length of the bluff body and is the dimensionless Strouhal numberStrouhal number
In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. The parameter is named after Vincenc Strouhal, a Czech physicist who experimented in 1878 with wires experiencing vortex shedding and singing in the wind...
, 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,
was approximately 8 feet (2.4 m) and was 0.20.It was thought that the Strouhal frequency was the same one of the natural vibration frequencies of the bridge i.e.
, causing resonance and therefore vortex-induced vibrationVortex Induced Vibration
In fluid dynamics, vortex-induced vibrations are motions induced on bodies interacting with an external fluid flow, produced by – or the motion producing – periodical irregularities on this flow.A classical example is the VIV of an underwater cylinder...
.
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 miles per hour (18.8 m/s) and the frequency of the destructive mode was 12 cycles/minute (0.2 Hz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
). This frequency was neither a natural mode of the isolated structure nor the frequency of blunt-body vortex shedding
Vortex shedding
Vortex shedding is an unsteady flow that takes place in special flow velocities . In this flow, vortices are created at the back of the body and detach periodically from either side of the body. See Von Kármán vortex street.Vortex shedding is caused when a fluid flows past a blunt object...
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 be understood only 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.
Origin of the confusion in failure modes
It is not clear what is the original source of the confusion . Billah and Scanlan cite that Lee Edson in his biography of Theodore von KármánTheodore von Karman
Theodore von Kármán was a Hungarian-American mathematician, aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization...
is a source of misinformation: "The culprit in the Tacoma disaster was the Karman vortex Street."
However, the Federal Works Administration report of the investigation (of which von Kármán was part) concluded that
Fate of the collapsed superstructure
Efforts to salvage the bridge began almost immediately after its collapse and continued into May 1943. 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 superstructure built. With steel being a valuable commodity because of the involvement of the United States in World War IIWorld War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, steel from the bridge cables and the suspension span was sold as scrap metal to be melted down. The salvage operation cost the state more than was returned from the sale of the material, a net loss of over $350,000.
The cable anchorages, tower pedestals and most of the remaining substructure were relatively undamaged in the collapse, and were reused during construction of the replacement span that opened in 1950. The towers, which supported Gertie's main cables and road deck, suffered major damage at their bases from being deflected twelve feet towards shore as a result of the collapse of the mainspan and the sagging of the sidespans. They were dismantled, and the steel sent to recyclers.
"Preservation" of the collapsed roadway
The underwater remains of the highway deck of the old suspension bridge act as a large artificial reefArtificial reef
An artificial reef is a human-made underwater structure, typically built to promote marine life in areas with a generally featureless bottom, control erosion, block ship passage, or improve surfing....
, and these are listed on the National Register of Historic Places
National Register of Historic Places
The National Register of Historic Places is the United States government's official list of districts, sites, buildings, structures, and objects deemed worthy of preservation...
with reference number 92001068.
A lesson for history
Othmar AmmannOthmar Ammann
Othmar Hermann Ammann was a American structural engineer whose designs include the George Washington Bridge, Verrazano-Narrows Bridge, and Bayonne Bridge.-Biography:...
, a leading bridge designer and member of the Federal Works Agency Commission investigating the collapse of the Tacoma Narrows Bridge, wrote:
The Bronx Whitestone Bridge
Bronx Whitestone Bridge
The Bronx–Whitestone Bridge is a suspension bridge in New York City that crosses the East River and connects the boroughs of Queens on Long Island and The Bronx via Interstate 678...
, which is of similar design to the 1940 Tacoma Narrows Bridge, was reinforced shortly after the collapse. Fourteen-foot-high (4.3 m) steel trusses were installed on both sides of the deck in 1943 to weigh down and stiffen the bridge in an effort to reduce oscillation. In 2003, the stiffening trusses were removed and aerodynamic fiberglass fairings were installed along both sides of the road deck.
Replacement bridge
Because of materials and labor shortages as a result of the involvement of the United States in World War II, it took 10 years before a replacement bridge was opened to traffic. This replacement bridge was opened to traffic on October 14, 1950, and is 5979 feet (1,822.4 m) long — 40 feet (12.2 m) longer than Galloping Gertie. The replacement bridge also has more lanes than the original bridge, which only had two traffic lanes, plus shoulders on both sides.Half a century later, the rebuilt bridge that was completed in 1950 was exceeding its traffic capacity, and a second, parallel suspension bridge was constructed to carry eastbound traffic. The suspension bridge that was completed in 1950 was reconfigured to solely carry westbound traffic. The new parallel bridge opened to traffic in July 2007.
External links
- Color video of the original bridge's construction and collapse with narration
- Physics behind the collapse of the bridge
- failurebydesign.info – physics presentation and resources
- Photos of the bridge and the new span under construction
Historical
- 1940 Narrows Bridge (1940 bridge construction) Washington Sate Department of Transportation
- History of the Tacoma Narrows Bridge
- 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.
- The Tacoma Narrows Bridge Disaster, November 1940
- Images of failure
- Information and images of failure
- Official site of the Tacoma Narrows Bridge
- Timeline of the bridges
- Tacoma Narrows Bridge
- Suspended Animation – Failure Magazine (November 2000)