The Tacoma Narrows Bridge, built in 1940, was the first crossing across the Tacoma Narrows. This suspension bridge, located in the US state of Washington "Washington (state)"), spanned the Puget Sound in the Tacoma Narrows, between Tacoma and the Kitsap Peninsula. It opened to traffic on July 1, 1940 and collapsed dramatically on November 7 of the same year. At the time of its construction, it was the third-longest suspension bridge in the world in terms of main span length, behind only the Golden Gate Bridge and the George Washington Bridge.
Work on the bridge began in September 1938. From the time the deck was built "Deck (architecture)"), it began to move vertically on windy days, prompting construction workers to give the bridge the nickname Galloping Gertie. The movement could be seen even when the bridge opened to the public. Various measures intended to stop this movement were ineffective, and the main span of the bridge finally collapsed when a 40 mph (64 km/h) wind blew on the morning of November 7, 1940.
Following the collapse, United States involvement in World War II delayed plans to replace the bridge. The parts of the bridge still standing after the collapse, including the towers and cables, were dismantled and sold for scrap. Nearly 10 years after the sinking, a new Tacoma Narrows Bridge "Tacoma Bridge (1950)") opened at the same location, using the tower pedestals and cable anchors from the original bridge. The portion of the bridge that fell into the water now serves as an artificial reef.
The bridge collapse had a lasting effect on science and engineering. In many physics textbooks, the fact is presented as an example of elementary forced resonance. The bridge collapsed because moderate-speed winds produced aeroelastic flutter that matched the bridge's natural frequency. The collapse spurred research in aerodynamics and structural aeroelasticity, which has influenced the designs of all long-rear span bridges.
Design and construction
The desire to build a bridge between Tacoma and the Kitsap Peninsula dates back to 1889, when a proposal was made by the Northern Pacific Railroad to build a trestle bridge. However, the first truly concerted efforts began in the mid-1920s, when the Tacoma Chamber of Commerce began campaigning and funding studies on the future bridge in 1923.[2] Several prominent bridge consultants, including Joseph B. Strauss "Joseph Strauss (engineer)"), chief engineer of the Golden Gate Bridge, and David B. Steinman, who designed the Mackinac Bridge, were consulted. Steinman made several visits funded by the Chamber of Commerce, culminating in a preliminary proposal presented in 1929, but in 1931, it was decided to cancel the agreement, because Steinman was not active enough to obtain financing. Another problem with the financing of the first bridge was the purchase of the ferry contract from a private company that provided services in the strait at the time.
Broken straps
Introduction
The Tacoma Narrows Bridge, built in 1940, was the first crossing across the Tacoma Narrows. This suspension bridge, located in the US state of Washington "Washington (state)"), spanned the Puget Sound in the Tacoma Narrows, between Tacoma and the Kitsap Peninsula. It opened to traffic on July 1, 1940 and collapsed dramatically on November 7 of the same year. At the time of its construction, it was the third-longest suspension bridge in the world in terms of main span length, behind only the Golden Gate Bridge and the George Washington Bridge.
Work on the bridge began in September 1938. From the time the deck was built "Deck (architecture)"), it began to move vertically on windy days, prompting construction workers to give the bridge the nickname Galloping Gertie. The movement could be seen even when the bridge opened to the public. Various measures intended to stop this movement were ineffective, and the main span of the bridge finally collapsed when a 40 mph (64 km/h) wind blew on the morning of November 7, 1940.
Following the collapse, United States involvement in World War II delayed plans to replace the bridge. The parts of the bridge still standing after the collapse, including the towers and cables, were dismantled and sold for scrap. Nearly 10 years after the sinking, a new Tacoma Narrows Bridge "Tacoma Bridge (1950)") opened at the same location, using the tower pedestals and cable anchors from the original bridge. The portion of the bridge that fell into the water now serves as an artificial reef.
The bridge collapse had a lasting effect on science and engineering. In many physics textbooks, the fact is presented as an example of elementary forced resonance. The bridge collapsed because moderate-speed winds produced aeroelastic flutter that matched the bridge's natural frequency. The collapse spurred research in aerodynamics and structural aeroelasticity, which has influenced the designs of all long-rear span bridges.
Design and construction
The desire to build a bridge between Tacoma and the Kitsap Peninsula dates back to 1889, when a proposal was made by the Northern Pacific Railroad to build a trestle bridge. However, the first truly concerted efforts began in the mid-1920s, when the Tacoma Chamber of Commerce began campaigning and funding studies on the future bridge in 1923.[2] Several prominent bridge consultants, including Joseph B. Strauss "Joseph Strauss (engineer)"), chief engineer of the Golden Gate Bridge, and David B. Steinman, who designed the Mackinac Bridge, were consulted. Steinman made several visits funded by the Chamber of Commerce, culminating in a preliminary proposal presented in 1929, but in 1931, it was decided to cancel the agreement, because Steinman was not active enough to obtain financing. Another problem with the financing of the first bridge was the purchase of the ferry contract from a private company that provided services in the strait at the time.
The Washington State Legislature created the Washington State Toll Bridge Authority and appropriated $5,000 (equivalent to today's dollars) to study the request of Tacoma and Pierce County "Pierce County (Washington)") to build a bridge over the Straits.[3].
From the beginning, funding for the bridge was an issue: revenue from proposed tolls would not be enough to cover construction costs, but there was strong support for the bridge from the Navy, which operated the Puget Sound Naval Shipyard in Bremerton, and the Army, which operated Camp McChord and Fort Lewis ("Fort Lewis (Washington)") near Tacoma.
Washington State Engineer Clark Eldridge produced a pre-tested conventional suspension bridge design, and the Washington Toll Bridge Authority requested $11 million (equivalent to $220 million today) from the federal Public Works Administration (PWA). The Washington Department of Highways' preliminary construction plans had called for a 24-foot-deep "truss" framework, sufficiently rigid to support the roadway.
However, according to Eldridge, "consulting engineers from the East Coast" - a term referring to Leon Moisseiff, the famous New York bridge engineer who served as a designer and consultant for the Golden Gate Bridge - contacted the PWA and the Reconstruction Finance Corporation (RFC) to build the bridge at a lower cost. Moisseiff and Frederick Lienhard, the latter an engineer for what was then known as the Port of New York Authority, published a paper[4] that was probably the most important theoretical advance in the field of bridge engineering of the decade.[5] Their elastic distribution theory extended the "Arrow (engineering)" deflection theory originally devised by Austrian engineer Josef Melan") to determine horizontal bending under a static wind load. They showed that stiffness of the main cables (through the stays) would absorb up to half of the static pressure of the wind pushing a laterally suspended structure. This energy would then be transmitted to the anchors and towers. Using this theory, Moisseiff argued that it would be enough to use a 2.4 m deep box on the bridge, instead of the 7.6 m truss proposed by the Washington Toll Bridge Authority. This approach implied a more slender and elegant design, and also reduced. construction costs compared to the Highway Department's design proposed by Eldridge. Moisseiff's design prevailed, as the other proposal was considered too expensive. On June 23, 1938, the PWA approved nearly 6 million (equivalent to $130 million today) for the Tacoma Narrows Bridge. Another $1.6 million (35 million today) would be collected from tolls to cover the total estimated cost of $8 million. (173 million today).
Following Moisseiff's design, construction of the bridge began on September 27, 1938. Construction lasted only nineteen months, at a cost of 6.4 million (138.5 million today), which was financed by the PWA grant and a loan from the RFC.
The Tacoma Straits Bridge, with a main span of 2,800 feet (853.4 m), was the third-longest suspension bridge in the world at the time, after the George Washington Bridge between New Jersey and New York City, and the Golden Gate Bridge, which connects San Francisco "San Francisco (California)") with Marin County to the north.[6].
Because planners expected fairly light traffic volumes, the bridge was designed with two lanes, and was only 39 feet (11.9 m) wide, a fairly narrow deck especially compared to its length. With a box girder only 2.4 m deep, the bridge roadway section was also quite narrow.
The decision to use such a narrow, shallow box proved to be the undoing of the original Tacoma bridge. With this minimum caisson, the bridge deck was not rigid enough, being easily displaced by the wind. From the beginning, the bridge became famous for its movement. A light to moderate wind could cause the alternate halves of the center "Light (Engineering)" span to visibly rise and fall several feet at four to five second intervals. This flexibility of the bridge was experienced by the builders and by the workers during the work, which led to it being informally named "Galloping Gertie". The nickname soon caught on, and even the public (when toll traffic began) felt these unusual movements on the day the bridge opened on July 1, 1940.
Attempt to control structural vibration
Since the structure experienced considerable vertical oscillations while still under construction, several strategies were used to reduce the movement of the bridge. They included:[7].
• - Connection of the deck with tie cables, which were anchored to 50-ton concrete blocks on the coast. This measure proved ineffective, and the cables were cut shortly after installation.
• - Addition of a pair of oblique cables that connected the main cables to the bridge deck in the middle of the span. They remained in place until collapse, but were also ineffective in reducing oscillations.
• - Finally, the structure was equipped with hydraulic shock absorbers installed between the towers and the deck to cushion the longitudinal movement of the main section. However, the effectiveness of the hydraulic shock absorbers was negated because the joints of the box-girder units were damaged when the bridge was sandblasted before being painted.
The Washington Toll Bridge Authority hired Professor Frederick Burt Farquharson, an engineering professor at the University of Washington, to conduct wind tunnel testing and recommend solutions to reduce bridge sway. 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 were completed on November 2, 1940, five days before the bridge collapsed on November 7. He proposed two solutions:
• - Drill holes in the sides of the box beam and along the deck so that air flow could circulate through them (thus reducing lifting forces).
• - Give a more aerodynamic shape to the cross section of the deck by adding fairings or deflector plates along the deck, attached to the beam covering.
The first option was not favored due to its irreversible nature. The second option was chosen, but it was not carried out, because the bridge collapsed five days after the studies were completed.[5].
Collapse
The wind-induced collapse occurred on November 7, 1940, at approximately 11:00 a.m. m. (PST), and was caused by a physical phenomenon known as aeroelastic flutter.[1].
Leonard Coatsworth, an editor at Tacoma News Tribune, was the last person to drive a car over the bridge:
Tubby, Coatsworth's cocker spaniel, was the only victim of the Tacoma Narrows Bridge disaster; It was lost along with Coatsworth's car. Professor Farquharson[9] and a photojournalist[10] attempted to rescue Tubby during a break, 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 recovered.[11] Coatsworth was returning Tubby to his daughter, who was the dog's owner, that day. He received $450 for his car (equivalent to $9,787 today) and $364.40 ($7,925 today) in reimbursement for the contents of his car, including Tubby.[12].
Investigation
Contenido
Theodore von Kármán, director del Laboratorio Aeronáutico Guggenheim") y aerodinámico de renombre mundial, fue miembro de la junta de investigación sobre el colapso.[13] Informó que el estado de Washington no pudo cobrar una de las pólizas de seguro por el puente porque su agente de seguros se había embolsado fraudulentamente las primas de los seguros. El agente, Hallett R. French, que representó a la Compañía de Garantía de Incendios Mercantil, fue acusado y procesado por robo a gran escala por retener las primas por un valor de 800,000 dólares del seguro (equivalente a 17 millones en la actualidad).[14] Sin embargo, el puente estaba asegurado por muchas otras pólizas que cubrían el 80% del valor de la estructura de 5.2 millones (equivalente a 113 millones en la actualidad). La mayoría de estas pólizas se cobraron sin incidentes.[15].
El 28 de noviembre de 1940, la Oficina Hidrográfica de la Marina informó que los restos del puente se encontraban en las coordenadas geográficas , a una profundidad de 180 pies (55 metros).
collapse movie
The bridge collapse was caught on film by Barney Elliott, owner of a local camera store. The film shows Leonard Coatsworth attempting to rescue his dog, unsuccessfully, and then abandoning the bridge. In 1998, the Library of Congress selected The Tacoma Narrows Bridge Collapse for preservation in the United States National Film Registry as being culturally, historically, or aesthetically significant. This footage is still shown to students of engineering, architecture, and physics as a cautionary tale.[16] Elliott'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 the newsreels of the day copied on 35 mm black and white film. Most copies in circulation also show the bridge swinging approximately 50% faster than real time, due to the assumption during conversion that the film had been shot at 24 frames per second rather than the 16 frames per second rate used during original filming.[17].
A second reel was located in February 2019, film taken by Arthur Leach from the Gig Harbor (west) side of the bridge, and one of the only known images of the collapse on that side. Leach was a civil engineer who served as a toll collector for the bridge, and is believed to have been the last person to cross the bridge heading west before its collapse, attempting to prevent further crossings from the west as the bridge began to collapse. Leach's footage (originally on film but later recorded on videotape by filming the projection) also includes Leach's comments at the time of the collapse.[18].
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 definitive conclusions, the commission explored three possible causes of the failure:.
• - Aerodynamic instability due to self-induced vibrations in the structure.
• - Eddy formations that may be periodic in nature.
• - Random effects of turbulence, which are random fluctuations in wind speed.
Cause of collapse
The original Tacoma Narrows Bridge was the first to be built with a carbon steel box anchored to concrete blocks; Previous designs typically had open trusses below the deck. This bridge was the first of its kind to use deep girders (pairs of double-T girders) to support the deck deck. With the previous designs, any wind simply passed through the frame, but in the new design the wind was deflected over and under the structure. Shortly after construction finished in late June (it opened to traffic on July 1, 1940), it was discovered that the bridge would sway and bend dangerously in relatively light wind conditions that are common in the area, and even worse during severe winds. This vibration was transverse, half of the central section rose while the other fell. Drivers would see cars approaching from the other direction rise and fall, riding the violent wave of energy across the bridge. However, at the time the mass of the bridge was considered sufficient to keep it structurally sound.
The collapse of the bridge occurred during a twisting mode never before experienced, with winds at a speed of 40 mph (64 km/h). This is the so-called torsional vibration mode (which is different from the transverse or longitudinal vibration mode), whereby when the left side of the road went down, the right side would go up and vice versa (i.e. the two halves of the bridge twisted in opposite directions), with the center line of the road still motionless. Two men tested this phenomenon by walking along the center line, unaffected by the flutter of the road rising and falling on either side. This vibration was caused by aeroelastic flapping.
Flutter is a physical phenomenon in which several degrees of freedom (Engineering Degree of Freedom) of a structure are coupled into an unstable oscillation driven by the wind. Finally, the amplitude of the motion produced by the flapping increased beyond the resistance of a vital part of the bridge, in this case, the suspension cables. Once several cables failed, the weight of the platform was transferred to adjacent cables which broke in turn until almost the entire central platform fell into the water below the span.
The spectacular destruction of the bridge is often used as an object lesson in the need to consider both aerodynamics and resonance effects ("Resonance (mechanical)") in civil and structural engineering. Billah and Scanlan (1991)[1] reported that, in fact, many physics textbooks (e.g., Resnick et al.[20] and Tipler et al.[21]) erroneously explain that the cause of the Tacoma Narrows Bridge failure was an externally forced mechanical resonance phenomenon. Resonance is the tendency of a system to oscillate at higher amplitudes at certain frequencies, known as the natural frequencies of the system. At these frequencies, even relatively small periodic driving forces can produce large amplitude vibrations, because the system stores energy. For example, a child using a swing realizes that if the impulses are properly timed, the swing can move with a very large amplitude. The driving force, in this case the child pushing the swing, exactly replaces the energy that the system loses if its frequency is equal to the natural frequency of the system.
Armistice Day Blizzard
The weather environment that caused the bridge to collapse also caused the Armistice Day Blizzard, which killed 145 people in the Midwest.
Fate of the collapsed superstructure
Los esfuerzos para salvar el puente comenzaron casi inmediatamente después de su colapso y continuaron hasta mayo de 1943.[27] Dos juntas de revisión, una nombrada por el Gobierno Federal y otra nombrada por el Estado de Washington, concluyeron que la reparación del puente era imposible, que habría que desmantelar todo el puente y construirse otra superestructura "Superestructura (ingeniería)") completamente nueva.[28] Dado que el acero era un producto especialmente valioso debido a la participación de los Estados Unidos en la Segunda Guerra Mundial, el acero de los cables del puente y de los tramos del tablero que se mantuvieron en suspensión se vendieron como chatarra para ser fundidos. La operación de rescate costó al estado más de lo que se obtuvo por la venta del material, una pérdida neta de más de 350.000 dólares (equivalentes a 6 millones en la actualidad).[27].
Los anclajes de los cables, los pedestales de las torres y la mayor parte de la subestructura restante no sufrieron daños en el colapso y se reutilizaron durante la construcción del nuevo puente que se abrió en 1950. Las torres, que soportaban los cables principales de Gertie y la cubierta de la carretera, sufrieron grandes daños en sus bases al quedar desviadas 3,7 m hacia la costa, como resultado del colapso del vano principal. Fueron desmanteladas, y el acero se recicló.
Preservation of the collapsed road
Los restos submarinos de la cubierta de la calzada del antiguo puente colgante actúan como un gran arrecife artificial, y están listados en el Registro Nacional de Lugares Históricos con el número de referencia 92001068.[29][30].
In its main room, the Harbor History Museum displays information regarding the 1940 bridge, its collapse, and the two subsequent bridges.
A history lesson
Othmar Ammann, a prominent bridge designer and member of the Federal Works Agency Commission that investigated the collapse of the Tacoma Narrows Bridge, wrote:
After the incident, engineers took additional precautions to incorporate aerodynamics into their designs, and testing of designs in wind tunnels eventually became mandatory.[32].
The Bronx-Whitestone Bridge, which was similar in design to the 1940 Tacoma Bridge, was reinforced shortly after the collapse. In 1943, 14 ft (4.3 m) high steel beams were installed on both sides of the deck to reinforce and stiffen the bridge deck in an effort to reduce sway. In 2003, the reinforcing beams were removed and fiberglass aerodynamic fairings were installed along both sides of the road deck.
A key consequence was that suspension bridge decks reverted to heavier, deeper truss designs, including the Tacoma Bridge (1950), until the development in the 1960s of streamlined box-girder bridges, such as the Severn Bridge, reducing torsional forces on the deck and giving it the stiffness needed to endure them.
new bridge
Due to shortages of materials and labor as a result of the United States' involvement in World War II, it took 10 years before a new bridge "Tacoma Bridge (1950)") was opened to traffic, opening to traffic on October 14, 1950. At 5,979 feet (1,822.4 m) long, it is 40 feet (12.2 m) longer than the original bridge. It also has more lanes than the original bridge, which only had two lanes of traffic, plus shoulders on both sides.
Half a century later, the new bridge exceeded its traffic capacity, and a second parallel suspension bridge was built to carry eastbound traffic. The suspension bridge, which was completed in 1950, was reconfigured to carry westbound traffic only. The new parallel bridge opened to traffic in July 2007.
• - Tacoma Bridge (1950) "Tacoma Bridge (1950)").
• - Tacoma Narrows Bridge.
• - Millennium Bridge, London, initially unstable due to an engineering error.
• - Silver Bridge.
Related readings
• - "The Strangest, Most Spectacular Bridge Collapse (And How We Got It Wrong)" (December 2015). A detailed and in-depth research report on the complicated physics behind the collapse in simple terms, with videos, tables, graphs, diagrams, etc. By Alex Pasternack, Motherboard "Vice (magazine)").
• - Physics linked to the bridge collapse Archived April 8, 2011 at the Wayback Machine.
• - failurebydesign.info – Physical representation and resources.
• - Sudden lateral asymmetry and torsional oscillations in the original Tacoma suspension bridge, Joseph Malik, Journal of Sound and Vibration, Vol 332, Issue 15, 22 July 2013, p. 3772–3789. Full paid article, summary viewable for free.
• - Wikimedia Commons alberga una categoría multimedia sobre Puente de Tacoma "commons:Category:Tacoma Narrows Bridge (1940)").
• - Video en color de la construcción del puente original y colapso con narración.
• - Fotos del puente y del nuevo tramo en construcción.
• - Tacoma Narrows Bridge (1940) en Structurae.
Historical
• - 1940 Narrows Bridge Archived January 11, 2012 at the Wayback Machine. (1940 bridge construction) Washington State Department of Transportation.
• - History of the Tacoma Narrows Bridge Archived October 27, 2011 at the Wayback Machine.
• - University of Washington Libraries Digital Collection - Tacoma Narrows Bridge Collection More than 152 images and text documenting the 1940 collapse of the Tacoma Narrows Bridge. It also covers the creation of Galloping Gertie, subsequent studies related to its aerodynamics, and finally the construction of a second bridge spanning the Straits.
• - The Tacoma Straits Bridge disaster, November 1940.
• - Images of the collapse.
• - Information and images of the sinking.
• - Tacoma Narrows Bridge Official Site.
• - Chronology of the bridges Archived December 15, 2005 at the Wayback Machine.
• - Youtube video of similar deck swings on a new bridge in Volgograd in Russia.
The Washington State Legislature created the Washington State Toll Bridge Authority and appropriated $5,000 (equivalent to today's dollars) to study the request of Tacoma and Pierce County "Pierce County (Washington)") to build a bridge over the Straits.[3].
From the beginning, funding for the bridge was an issue: revenue from proposed tolls would not be enough to cover construction costs, but there was strong support for the bridge from the Navy, which operated the Puget Sound Naval Shipyard in Bremerton, and the Army, which operated Camp McChord and Fort Lewis ("Fort Lewis (Washington)") near Tacoma.
Washington State Engineer Clark Eldridge produced a pre-tested conventional suspension bridge design, and the Washington Toll Bridge Authority requested $11 million (equivalent to $220 million today) from the federal Public Works Administration (PWA). The Washington Department of Highways' preliminary construction plans had called for a 24-foot-deep "truss" framework, sufficiently rigid to support the roadway.
However, according to Eldridge, "consulting engineers from the East Coast" - a term referring to Leon Moisseiff, the famous New York bridge engineer who served as a designer and consultant for the Golden Gate Bridge - contacted the PWA and the Reconstruction Finance Corporation (RFC) to build the bridge at a lower cost. Moisseiff and Frederick Lienhard, the latter an engineer for what was then known as the Port of New York Authority, published a paper[4] that was probably the most important theoretical advance in the field of bridge engineering of the decade.[5] Their elastic distribution theory extended the "Arrow (engineering)" deflection theory originally devised by Austrian engineer Josef Melan") to determine horizontal bending under a static wind load. They showed that stiffness of the main cables (through the stays) would absorb up to half of the static pressure of the wind pushing a laterally suspended structure. This energy would then be transmitted to the anchors and towers. Using this theory, Moisseiff argued that it would be enough to use a 2.4 m deep box on the bridge, instead of the 7.6 m truss proposed by the Washington Toll Bridge Authority. This approach implied a more slender and elegant design, and also reduced. construction costs compared to the Highway Department's design proposed by Eldridge. Moisseiff's design prevailed, as the other proposal was considered too expensive. On June 23, 1938, the PWA approved nearly 6 million (equivalent to $130 million today) for the Tacoma Narrows Bridge. Another $1.6 million (35 million today) would be collected from tolls to cover the total estimated cost of $8 million. (173 million today).
Following Moisseiff's design, construction of the bridge began on September 27, 1938. Construction lasted only nineteen months, at a cost of 6.4 million (138.5 million today), which was financed by the PWA grant and a loan from the RFC.
The Tacoma Straits Bridge, with a main span of 2,800 feet (853.4 m), was the third-longest suspension bridge in the world at the time, after the George Washington Bridge between New Jersey and New York City, and the Golden Gate Bridge, which connects San Francisco "San Francisco (California)") with Marin County to the north.[6].
Because planners expected fairly light traffic volumes, the bridge was designed with two lanes, and was only 39 feet (11.9 m) wide, a fairly narrow deck especially compared to its length. With a box girder only 2.4 m deep, the bridge roadway section was also quite narrow.
The decision to use such a narrow, shallow box proved to be the undoing of the original Tacoma bridge. With this minimum caisson, the bridge deck was not rigid enough, being easily displaced by the wind. From the beginning, the bridge became famous for its movement. A light to moderate wind could cause the alternate halves of the center "Light (Engineering)" span to visibly rise and fall several feet at four to five second intervals. This flexibility of the bridge was experienced by the builders and by the workers during the work, which led to it being informally named "Galloping Gertie". The nickname soon caught on, and even the public (when toll traffic began) felt these unusual movements on the day the bridge opened on July 1, 1940.
Attempt to control structural vibration
Since the structure experienced considerable vertical oscillations while still under construction, several strategies were used to reduce the movement of the bridge. They included:[7].
• - Connection of the deck with tie cables, which were anchored to 50-ton concrete blocks on the coast. This measure proved ineffective, and the cables were cut shortly after installation.
• - Addition of a pair of oblique cables that connected the main cables to the bridge deck in the middle of the span. They remained in place until collapse, but were also ineffective in reducing oscillations.
• - Finally, the structure was equipped with hydraulic shock absorbers installed between the towers and the deck to cushion the longitudinal movement of the main section. However, the effectiveness of the hydraulic shock absorbers was negated because the joints of the box-girder units were damaged when the bridge was sandblasted before being painted.
The Washington Toll Bridge Authority hired Professor Frederick Burt Farquharson, an engineering professor at the University of Washington, to conduct wind tunnel testing and recommend solutions to reduce bridge sway. 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 were completed on November 2, 1940, five days before the bridge collapsed on November 7. He proposed two solutions:
• - Drill holes in the sides of the box beam and along the deck so that air flow could circulate through them (thus reducing lifting forces).
• - Give a more aerodynamic shape to the cross section of the deck by adding fairings or deflector plates along the deck, attached to the beam covering.
The first option was not favored due to its irreversible nature. The second option was chosen, but it was not carried out, because the bridge collapsed five days after the studies were completed.[5].
Collapse
The wind-induced collapse occurred on November 7, 1940, at approximately 11:00 a.m. m. (PST), and was caused by a physical phenomenon known as aeroelastic flutter.[1].
Leonard Coatsworth, an editor at Tacoma News Tribune, was the last person to drive a car over the bridge:
Tubby, Coatsworth's cocker spaniel, was the only victim of the Tacoma Narrows Bridge disaster; It was lost along with Coatsworth's car. Professor Farquharson[9] and a photojournalist[10] attempted to rescue Tubby during a break, 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 recovered.[11] Coatsworth was returning Tubby to his daughter, who was the dog's owner, that day. He received $450 for his car (equivalent to $9,787 today) and $364.40 ($7,925 today) in reimbursement for the contents of his car, including Tubby.[12].
Investigation
Contenido
Theodore von Kármán, director del Laboratorio Aeronáutico Guggenheim") y aerodinámico de renombre mundial, fue miembro de la junta de investigación sobre el colapso.[13] Informó que el estado de Washington no pudo cobrar una de las pólizas de seguro por el puente porque su agente de seguros se había embolsado fraudulentamente las primas de los seguros. El agente, Hallett R. French, que representó a la Compañía de Garantía de Incendios Mercantil, fue acusado y procesado por robo a gran escala por retener las primas por un valor de 800,000 dólares del seguro (equivalente a 17 millones en la actualidad).[14] Sin embargo, el puente estaba asegurado por muchas otras pólizas que cubrían el 80% del valor de la estructura de 5.2 millones (equivalente a 113 millones en la actualidad). La mayoría de estas pólizas se cobraron sin incidentes.[15].
El 28 de noviembre de 1940, la Oficina Hidrográfica de la Marina informó que los restos del puente se encontraban en las coordenadas geográficas , a una profundidad de 180 pies (55 metros).
collapse movie
The bridge collapse was caught on film by Barney Elliott, owner of a local camera store. The film shows Leonard Coatsworth attempting to rescue his dog, unsuccessfully, and then abandoning the bridge. In 1998, the Library of Congress selected The Tacoma Narrows Bridge Collapse for preservation in the United States National Film Registry as being culturally, historically, or aesthetically significant. This footage is still shown to students of engineering, architecture, and physics as a cautionary tale.[16] Elliott'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 the newsreels of the day copied on 35 mm black and white film. Most copies in circulation also show the bridge swinging approximately 50% faster than real time, due to the assumption during conversion that the film had been shot at 24 frames per second rather than the 16 frames per second rate used during original filming.[17].
A second reel was located in February 2019, film taken by Arthur Leach from the Gig Harbor (west) side of the bridge, and one of the only known images of the collapse on that side. Leach was a civil engineer who served as a toll collector for the bridge, and is believed to have been the last person to cross the bridge heading west before its collapse, attempting to prevent further crossings from the west as the bridge began to collapse. Leach's footage (originally on film but later recorded on videotape by filming the projection) also includes Leach's comments at the time of the collapse.[18].
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 definitive conclusions, the commission explored three possible causes of the failure:.
• - Aerodynamic instability due to self-induced vibrations in the structure.
• - Eddy formations that may be periodic in nature.
• - Random effects of turbulence, which are random fluctuations in wind speed.
Cause of collapse
The original Tacoma Narrows Bridge was the first to be built with a carbon steel box anchored to concrete blocks; Previous designs typically had open trusses below the deck. This bridge was the first of its kind to use deep girders (pairs of double-T girders) to support the deck deck. With the previous designs, any wind simply passed through the frame, but in the new design the wind was deflected over and under the structure. Shortly after construction finished in late June (it opened to traffic on July 1, 1940), it was discovered that the bridge would sway and bend dangerously in relatively light wind conditions that are common in the area, and even worse during severe winds. This vibration was transverse, half of the central section rose while the other fell. Drivers would see cars approaching from the other direction rise and fall, riding the violent wave of energy across the bridge. However, at the time the mass of the bridge was considered sufficient to keep it structurally sound.
The collapse of the bridge occurred during a twisting mode never before experienced, with winds at a speed of 40 mph (64 km/h). This is the so-called torsional vibration mode (which is different from the transverse or longitudinal vibration mode), whereby when the left side of the road went down, the right side would go up and vice versa (i.e. the two halves of the bridge twisted in opposite directions), with the center line of the road still motionless. Two men tested this phenomenon by walking along the center line, unaffected by the flutter of the road rising and falling on either side. This vibration was caused by aeroelastic flapping.
Flutter is a physical phenomenon in which several degrees of freedom (Engineering Degree of Freedom) of a structure are coupled into an unstable oscillation driven by the wind. Finally, the amplitude of the motion produced by the flapping increased beyond the resistance of a vital part of the bridge, in this case, the suspension cables. Once several cables failed, the weight of the platform was transferred to adjacent cables which broke in turn until almost the entire central platform fell into the water below the span.
The spectacular destruction of the bridge is often used as an object lesson in the need to consider both aerodynamics and resonance effects ("Resonance (mechanical)") in civil and structural engineering. Billah and Scanlan (1991)[1] reported that, in fact, many physics textbooks (e.g., Resnick et al.[20] and Tipler et al.[21]) erroneously explain that the cause of the Tacoma Narrows Bridge failure was an externally forced mechanical resonance phenomenon. Resonance is the tendency of a system to oscillate at higher amplitudes at certain frequencies, known as the natural frequencies of the system. At these frequencies, even relatively small periodic driving forces can produce large amplitude vibrations, because the system stores energy. For example, a child using a swing realizes that if the impulses are properly timed, the swing can move with a very large amplitude. The driving force, in this case the child pushing the swing, exactly replaces the energy that the system loses if its frequency is equal to the natural frequency of the system.
Armistice Day Blizzard
The weather environment that caused the bridge to collapse also caused the Armistice Day Blizzard, which killed 145 people in the Midwest.
Fate of the collapsed superstructure
Los esfuerzos para salvar el puente comenzaron casi inmediatamente después de su colapso y continuaron hasta mayo de 1943.[27] Dos juntas de revisión, una nombrada por el Gobierno Federal y otra nombrada por el Estado de Washington, concluyeron que la reparación del puente era imposible, que habría que desmantelar todo el puente y construirse otra superestructura "Superestructura (ingeniería)") completamente nueva.[28] Dado que el acero era un producto especialmente valioso debido a la participación de los Estados Unidos en la Segunda Guerra Mundial, el acero de los cables del puente y de los tramos del tablero que se mantuvieron en suspensión se vendieron como chatarra para ser fundidos. La operación de rescate costó al estado más de lo que se obtuvo por la venta del material, una pérdida neta de más de 350.000 dólares (equivalentes a 6 millones en la actualidad).[27].
Los anclajes de los cables, los pedestales de las torres y la mayor parte de la subestructura restante no sufrieron daños en el colapso y se reutilizaron durante la construcción del nuevo puente que se abrió en 1950. Las torres, que soportaban los cables principales de Gertie y la cubierta de la carretera, sufrieron grandes daños en sus bases al quedar desviadas 3,7 m hacia la costa, como resultado del colapso del vano principal. Fueron desmanteladas, y el acero se recicló.
Preservation of the collapsed road
Los restos submarinos de la cubierta de la calzada del antiguo puente colgante actúan como un gran arrecife artificial, y están listados en el Registro Nacional de Lugares Históricos con el número de referencia 92001068.[29][30].
In its main room, the Harbor History Museum displays information regarding the 1940 bridge, its collapse, and the two subsequent bridges.
A history lesson
Othmar Ammann, a prominent bridge designer and member of the Federal Works Agency Commission that investigated the collapse of the Tacoma Narrows Bridge, wrote:
After the incident, engineers took additional precautions to incorporate aerodynamics into their designs, and testing of designs in wind tunnels eventually became mandatory.[32].
The Bronx-Whitestone Bridge, which was similar in design to the 1940 Tacoma Bridge, was reinforced shortly after the collapse. In 1943, 14 ft (4.3 m) high steel beams were installed on both sides of the deck to reinforce and stiffen the bridge deck in an effort to reduce sway. In 2003, the reinforcing beams were removed and fiberglass aerodynamic fairings were installed along both sides of the road deck.
A key consequence was that suspension bridge decks reverted to heavier, deeper truss designs, including the Tacoma Bridge (1950), until the development in the 1960s of streamlined box-girder bridges, such as the Severn Bridge, reducing torsional forces on the deck and giving it the stiffness needed to endure them.
new bridge
Due to shortages of materials and labor as a result of the United States' involvement in World War II, it took 10 years before a new bridge "Tacoma Bridge (1950)") was opened to traffic, opening to traffic on October 14, 1950. At 5,979 feet (1,822.4 m) long, it is 40 feet (12.2 m) longer than the original bridge. It also has more lanes than the original bridge, which only had two lanes of traffic, plus shoulders on both sides.
Half a century later, the new bridge exceeded its traffic capacity, and a second parallel suspension bridge was built to carry eastbound traffic. The suspension bridge, which was completed in 1950, was reconfigured to carry westbound traffic only. The new parallel bridge opened to traffic in July 2007.
• - Tacoma Bridge (1950) "Tacoma Bridge (1950)").
• - Tacoma Narrows Bridge.
• - Millennium Bridge, London, initially unstable due to an engineering error.
• - Silver Bridge.
Related readings
• - "The Strangest, Most Spectacular Bridge Collapse (And How We Got It Wrong)" (December 2015). A detailed and in-depth research report on the complicated physics behind the collapse in simple terms, with videos, tables, graphs, diagrams, etc. By Alex Pasternack, Motherboard "Vice (magazine)").
• - Physics linked to the bridge collapse Archived April 8, 2011 at the Wayback Machine.
• - failurebydesign.info – Physical representation and resources.
• - Sudden lateral asymmetry and torsional oscillations in the original Tacoma suspension bridge, Joseph Malik, Journal of Sound and Vibration, Vol 332, Issue 15, 22 July 2013, p. 3772–3789. Full paid article, summary viewable for free.
• - Wikimedia Commons alberga una categoría multimedia sobre Puente de Tacoma "commons:Category:Tacoma Narrows Bridge (1940)").
• - Video en color de la construcción del puente original y colapso con narración.
• - Fotos del puente y del nuevo tramo en construcción.
• - Tacoma Narrows Bridge (1940) en Structurae.
Historical
• - 1940 Narrows Bridge Archived January 11, 2012 at the Wayback Machine. (1940 bridge construction) Washington State Department of Transportation.
• - History of the Tacoma Narrows Bridge Archived October 27, 2011 at the Wayback Machine.
• - University of Washington Libraries Digital Collection - Tacoma Narrows Bridge Collection More than 152 images and text documenting the 1940 collapse of the Tacoma Narrows Bridge. It also covers the creation of Galloping Gertie, subsequent studies related to its aerodynamics, and finally the construction of a second bridge spanning the Straits.
• - The Tacoma Straits Bridge disaster, November 1940.
• - Images of the collapse.
• - Information and images of the sinking.
• - Tacoma Narrows Bridge Official Site.
• - Chronology of the bridges Archived December 15, 2005 at the Wayback Machine.
• - Youtube video of similar deck swings on a new bridge in Volgograd in Russia.
Typically, the approach taken by those physics textbooks is to introduce a first-order forced oscillator, defined by the second-order differential equation.
where y represent the mass, damping coefficient") and the stiffness of the linear system, and y represent the amplitude and angular frequency of the excitation force. The solution of said ordinary differential equation as a function of time represents the displacement response of the system (given the appropriate initial conditions). In the above system, resonance occurs when it is approx.
that is, it is the natural (resonant) frequency of the system. Actual vibration analysis of a more complicated mechanical system, such as an airplane, building, or bridge, is based on the linearization of the equation of motion for the system, which is a multidimensional version of the equation (eq. 1). Its study requires an analysis of eigenvalues and, subsequently, the natural frequencies of the structure are determined, along with the so-called fundamental modes of the system, which are a set of independent displacements and/or rotations that completely specify the position and orientation of the displacements or deformations. The body or system, i.e. the bridge, moves as a (linear) combination of those deformed basic positions.
Each structure has its own natural frequencies. For resonance to occur, it is also necessary to have periodicity in the excitation force. The most tempting candidate for periodicity in wind strength was supposed to be so-called vortex shedding. This is because non-aerodynamic bodies, such as the box of a bridge deck, in a stream of fluid form a wake "Wake (trace"), with a movement 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). Consequently, the body will try to move towards the low pressure zone, in an oscillating movement called vortex-induced vibration.
Eventually, if the vortex shedding frequency matches the natural frequency of the structure, it will begin to resonate and its motion can become self-sustaining.
The frequency of the vortices in the von Kármán vortex street is called the Strouhal frequency, and is given by.
Here, it represents the flow velocity, is a characteristic length of the 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 Tacoma, it was approximately 8 feet (2.4 m) and was worth 0.20.
It is thought that the Strouhal frequency was quite close to one of the natural vibration frequencies of the bridge, that is, it could generate a resonance phenomenon driven by vortex-induced vibration.
In the case of the Tacoma bridge, this does not appear to have been the cause of the catastrophic damage. According to Frederick Burt Farquharson, an engineering professor at the University of Washington and one of the main investigators of the causes of the bridge collapse, the wind was sustained, reached 42 miles per hour (68 km/h) and the frequency of the destructive mode was 12 cycles/minute (0.2 Hz).[22] This frequency also did not coincide with a natural mode of the isolated structure, with nor the frequency of a vortex of a non-aerodynamic body facing a wind with the recorded speed (which should be approximately 1 Hz). Therefore, the vortex effect of the airflow around the box girder was not the cause of the bridge collapse. Collapse can be understood only if the coupling of the aerodynamic and structural system is considered, which requires rigorous mathematical analysis to reveal all the degrees of freedom of the particular structure and the set of loads considered in its design.
Even so, it should be noted that vortex-induced vibration is a much more complex process, involving both the initial external forces generated by the wind and the internal reactive forces that limit the movement of the structure. If wind forces act on the structure bringing its mode of oscillation closer to one of its natural frequencies, when the amplitude increases this has the effect of changing the local boundary conditions of the air flow, so that forces are induced that tend to compensate for the increased oscillation by themselves, restricting the movement to relatively benign amplitudes. This is a clearly non-linear resonance phenomenon, even if the body opposite the wind has linear aerodynamic behavior, given that the amplitude of the induced structural response forces also does not have linear behavior.[23].
Billah and Scanlan concluded that Lee Edson, in his biography of Theodore von Kármán,[24] is the source of the subsequent misinformation: "The culprit of the Tacoma disaster was von Kármán's vortex street."[23].
However, the Federal Works Administration investigation report (in which von Kármán participated) concluded that:.
A group of physicists pointed out "the amplification of wind-induced torsional oscillation" as a phenomenon distinct from resonance:
Even so, in a way the debate is due to the lack of a precise and generally accepted definition of the concept of resonance. Billah and Scanlan provide the following definition of resonance:.
Later they asked in their article:
Typically, the approach taken by those physics textbooks is to introduce a first-order forced oscillator, defined by the second-order differential equation.
where y represent the mass, damping coefficient") and the stiffness of the linear system, and y represent the amplitude and angular frequency of the excitation force. The solution of said ordinary differential equation as a function of time represents the displacement response of the system (given the appropriate initial conditions). In the above system, resonance occurs when it is approx.
that is, it is the natural (resonant) frequency of the system. Actual vibration analysis of a more complicated mechanical system, such as an airplane, building, or bridge, is based on the linearization of the equation of motion for the system, which is a multidimensional version of the equation (eq. 1). Its study requires an analysis of eigenvalues and, subsequently, the natural frequencies of the structure are determined, along with the so-called fundamental modes of the system, which are a set of independent displacements and/or rotations that completely specify the position and orientation of the displacements or deformations. The body or system, i.e. the bridge, moves as a (linear) combination of those deformed basic positions.
Each structure has its own natural frequencies. For resonance to occur, it is also necessary to have periodicity in the excitation force. The most tempting candidate for periodicity in wind strength was supposed to be so-called vortex shedding. This is because non-aerodynamic bodies, such as the box of a bridge deck, in a stream of fluid form a wake "Wake (trace"), with a movement 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). Consequently, the body will try to move towards the low pressure zone, in an oscillating movement called vortex-induced vibration.
Eventually, if the vortex shedding frequency matches the natural frequency of the structure, it will begin to resonate and its motion can become self-sustaining.
The frequency of the vortices in the von Kármán vortex street is called the Strouhal frequency, and is given by.
Here, it represents the flow velocity, is a characteristic length of the 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 Tacoma, it was approximately 8 feet (2.4 m) and was worth 0.20.
It is thought that the Strouhal frequency was quite close to one of the natural vibration frequencies of the bridge, that is, it could generate a resonance phenomenon driven by vortex-induced vibration.
In the case of the Tacoma bridge, this does not appear to have been the cause of the catastrophic damage. According to Frederick Burt Farquharson, an engineering professor at the University of Washington and one of the main investigators of the causes of the bridge collapse, the wind was sustained, reached 42 miles per hour (68 km/h) and the frequency of the destructive mode was 12 cycles/minute (0.2 Hz).[22] This frequency also did not coincide with a natural mode of the isolated structure, with nor the frequency of a vortex of a non-aerodynamic body facing a wind with the recorded speed (which should be approximately 1 Hz). Therefore, the vortex effect of the airflow around the box girder was not the cause of the bridge collapse. Collapse can be understood only if the coupling of the aerodynamic and structural system is considered, which requires rigorous mathematical analysis to reveal all the degrees of freedom of the particular structure and the set of loads considered in its design.
Even so, it should be noted that vortex-induced vibration is a much more complex process, involving both the initial external forces generated by the wind and the internal reactive forces that limit the movement of the structure. If wind forces act on the structure bringing its mode of oscillation closer to one of its natural frequencies, when the amplitude increases this has the effect of changing the local boundary conditions of the air flow, so that forces are induced that tend to compensate for the increased oscillation by themselves, restricting the movement to relatively benign amplitudes. This is a clearly non-linear resonance phenomenon, even if the body opposite the wind has linear aerodynamic behavior, given that the amplitude of the induced structural response forces also does not have linear behavior.[23].
Billah and Scanlan concluded that Lee Edson, in his biography of Theodore von Kármán,[24] is the source of the subsequent misinformation: "The culprit of the Tacoma disaster was von Kármán's vortex street."[23].
However, the Federal Works Administration investigation report (in which von Kármán participated) concluded that:.
A group of physicists pointed out "the amplification of wind-induced torsional oscillation" as a phenomenon distinct from resonance:
Even so, in a way the debate is due to the lack of a precise and generally accepted definition of the concept of resonance. Billah and Scanlan provide the following definition of resonance:.