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Tacoma Narrows Bridge (1940)
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The original Tacoma Narrows Bridge opened on July 1, 1940 and dramatically collapsed into Puget Sound on November 7 of the same year. The suspension bridge spanned the Tacoma Narrows strait between Tacoma and the Kitsap Peninsula. Its replacement was opened in the same location in 1950, and a second, parallel bridge opened in 2007. The instability in winds earned the nickname Galloping Gertie.
The bridge's collapse had a lasting effect on science and engineering.
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The original Tacoma Narrows Bridge opened on July 1, 1940 and dramatically collapsed into Puget Sound on November 7 of the same year. The suspension bridge spanned the Tacoma Narrows strait between Tacoma and the Kitsap Peninsula. Its replacement was opened in the same location in 1950, and a second, parallel bridge opened in 2007. The instability in winds earned the nickname Galloping Gertie.
The bridge's collapse had a lasting effect on science and engineering. In many physics textbooks the event is presented as an example of elementary forced resonance with the wind providing an external periodic frequency that matched the natural structural frequency, even though its real cause of failure was aeroelastic flutter . Its failure also boosted research in the field of bridge aerodynamics/aeroelastics, the study of which has influenced the designs of all the world's great long-span bridges built since 1940.
At the time of its construction (and destruction) Galloping Gertie was the third longest suspension bridge in the world, behind the Golden Gate Bridge and George Washington Bridge.
Design and construction
The desire for the construction of a bridge between Tacoma and the Kitsap peninsula dates back to 1889 with a Northern Pacific Railway proposal for a trestle, but concerted efforts began in the mid-1920s. The Tacoma Chamber of Commerce began campaigning and funding studies in 1923. Several noted bridge architects, including Joseph B. Strauss, who went on to be chief engineer of the Golden Gate Bridge, and David B. Steinman, 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 road to Tacoma's doomed bridge continued in 1937, when the Washington State legislature created the Washington State Toll Bridge Authority and appropriated $5,000 to study the request by Tacoma and Pierce County for a bridge over the Narrows.
From the start, financing was the issue; revenue from tolls would not be enough to cover construction costs, but there was strong support for a bridge from the U.S. Navy, which operated the Puget Sound Naval Shipyard in Bremerton, and from the U.S. Army, which ran McChord Field and Fort Lewis in Tacoma.
Washington State engineer Clark Eldridge came up with a preliminary tried-and-true conventional bridge design, and the Washington Toll Bridge Authority requested $11 million from the federal Public Works Administration (PWA). Preliminary construction plans by the Washington Department of Highways had called for 25-foot-deep (7.6 m) girders to sit beneath the roadway and stiffen it.
But according to Eldridge, "eastern consulting engineers" petitioned the PWA and the Reconstruction Finance Corporation (RFC) to build the bridge for less. Eldridge meant by "eastern consulting engineers" the renowned New York bridge engineer Leon Moisseiff, designer and consultant engineer of the Golden Gate Bridge. Moisseiff proposed shallower supports — girders deep. His approach meant a slimmer, more elegant design and reduced construction costs compared to the Highway Department 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 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, with a main span of , was the third longest suspension bridge in the world at that time, after the George Washington Bridge in New York, and the Golden Gate Bridge in San Francisco
Moisseiff and Fred Lienhard, 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", originally devised by the Austrian engineer Josef Melan, to horizontal bending under static wind load. They showed that the stiffness of the main cables (via the suspenders) would absorb up to one-half of the static wind pressure pushing a suspended structure laterally. This energy would then be transmitted to the anchorages and towers.
Using this theory, Moisseiff was able to justify stiffening the bridge with only eight-foot deep plate girders, instead of the deep trusses proposed by the Department of Highways. 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 was only wide. This was quite narrow, especially in relation to its length. With only the deep plate girders providing additional depth, the bridge was also shallow.
The decision to use such shallow and narrow girders proved to be the first bridge's undoing. With such girders, the roadbed was insufficiently rigid and was easily moved about by winds. From the start, the bridge became notorious for its movement. A mild to moderate wind could cause alternate halves of the center span to visibly rise and fall several feet over 4- to 5-second intervals. This flexibility was experienced by the builders during construction, and by the drivers as soon as the bridge opened (under toll-paid traffic) on July 1, 1940. This led to the bridge being referred to as Galloping Gertie by the local residents, due to the apparent galloping motion felt by the drivers on the roadway.
Control of structural vibrations
As the structure experienced considerable vertical oscillations, several strategies were used to reduce the motion of the bridge. They included:
- attachment of tie-down cables to the plate girders, which were anchored to 50-ton concrete blocks on the shore. This measure proved ineffective as the cables snapped shortly after installation.
- addition of a pair of inclined cable stays that connected the main cables to the bridge deck at mid-span. These remained in place until the collapse, but were also ineffective at reducing the oscillations.
- finally, the structure was equipped with hydraulic buffers installed between the towers and the floor system of the deck to damp longitudinal motion of the main span. The effectiveness of the hydraulic dampers was, however, nullified because it was discovered that the seals of the unit were damaged when the bridge was sandblasted prior to being painted.
The Washington Toll Bridge Authority hired Professor Frederick Burt Farquharson, an engineering professor at the University of Washington, to make wind tunnel tests and recommend solutions in order to reduce the oscillations of the Tacoma. Prof. Farquharson and his students built a 1:200-full scale model of the bridge as well as a 1:20-scale model 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 can circulate through them (in this way reducing lift forces) or,
- to give a more aerodynamic shape to the transversal section of the deck, by adding fairings or deflector vanes along the deck attached to the girder fascia.
The first option was not favorable due to its irreversible nature. The second option was the chosen one, but it was not carried out because the bridge fell five days after the studies concluded.
Collapse
The wind-induced collapse occurred on November 7, 1940, at 11:00 am (Pacific time), due to a physical phenomenon known as aeroelastic flutter.
From the account of Leonard Coatsworth, a driver who narrowly managed to escape the bridge before the collapse:
No human life was lost in the collapse of the bridge, though Coatsworth's cocker spaniel named Tubby was lost along with his car in the collapse. Theodore von Kármán, director of the Guggenheim Aeronautical Laboratory and world-renowned aerodynamicist, was a member of the board of inquiry into the collapse. He reported that the State of Washington was unable to collect on one of the insurance policies for the bridge because its insurance agent fraudulently pocketed the insurance premiums. The agent, Hallett R. French who represented the Merchant's Fire Assurance Company, was charged with grand larceny for withholding the premiums for $800,000 worth of insurance. The bridge, however, was insured by many other policies that covered 80% of the $5.2–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 , at a depth of 180 feet (55 m).
Film of collapse
The collapse of the bridge was recorded on film by Barney Elliott, owner of a local camera shop, and shows Leonard Coatsworth leaving the bridge after exiting his car. In 1998, The Tacoma Narrows Bridge Collapse was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant." This footage is still shown to engineering, architecture, and physics students as a cautionary tale. Elliot's original films of the construction and collapse of the bridge were shot on 16mm Kodachrome film, but most copies in circulation are in black and white because newsreels of the day copied the film onto 35mm black and white stock.
Commission of the Federal Works Agency
A commission formed by the Federal Works Agency studied the collapse of the bridge. It included Othmar Ammann and Theodore von Kármán. Without drawing any definitive conclusions, the commission explored three possible failure causes:
- aerodynamic instability by self-induced vibrations in the structure,
- eddy formations which might be periodic in nature and
- the random effects of turbulence, that is the random fluctuations in velocity and direction of the wind.
Cause of collapse
The bridge was solidly built, with girders of carbon steel anchored in huge blocks of concrete. Preceding designs typically had open lattice beam trusses underneath the roadbed. This bridge was the first of its type to employ plate girders (pairs of deep I beams) to support the roadbed. With the earlier designs any wind would simply pass through the truss, but in the new design the wind would be diverted above and below the structure. Shortly after construction finished at the end of June (opened to traffic on July 1, 1940), it was discovered that the bridge would sway and buckle dangerously in relatively mild windy conditions for the area. This vibration was transverse, meaning the bridge buckled along its length, with the roadbed alternately raised and depressed in certain locations—one half of the central span would rise while the other lowered. Drivers would see cars approaching from the other direction disappear into valleys that dynamically appeared and disappeared. Because of this behavior, a local humorist gave the bridge the nickname Galloping Gertie. However, the mass of the bridge was considered sufficient to keep it structurally sound.
The failure of the bridge occurred when a never-before-seen twisting mode occurred, from winds at a mild . This is a so-called torsional vibration mode (which is different from the transversal or longitudinal vibration mode), whereby when the left side of the roadway went down, the right side would rise, and vice versa, with the centerline of the road remaining still. Specifically, it was the second torsional mode, in which the midpoint of the bridge remained motionless while the two halves of the bridge twisted in opposite directions. Two men proved this point by walking along the center line, unaffected by the flapping of the roadway rising and falling to each side. This vibration was caused by aeroelastic fluttering.
Fluttering is a physical phenomenon in which several degrees of freedom of a structure become coupled in an unstable oscillation driven by the wind. This movement inserts energy to the bridge during each cycle so that it neutralizes the natural damping of the structure; the composed system (bridge-fluid) therefore behaves as if it had an effective negative damping (or had positive feedback), leading to a exponentially growing response. In other words, the oscillations increase in amplitude with each cycle because the wind pumps in more energy than the flexing of the structure can dissipate, and finally drives the bridge toward failure due to excessive deflection and stresses. The wind speed 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
Frequently, the bridge's spectacular destruction is used as an object lesson in the necessity to consider both aerodynamics and resonance effects in civil and structural engineering. Billah and Scanlan (1991) reported that in fact, many physics textbooks (for example Resnik et al. and Tipler et al. ) 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 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 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.
Origin of the confusion
It is not clear which is the original source of the confusion. Billah and Scanlan cite that Lee Edson in his biography of Theodore von Kármán is a source of misinformation:
However, the Federal Works Administration report of the investigation (of which von Kármán was part) concluded that
Nowadays, even after half a century, it is common to find a wide range of rather weak descriptions, explanations, and speculations about the failure of the original Tacoma Narrows Bridge, in popular introductory physics and mathematical books for engineers.
Tubby the dog
Tubby, a black male cocker spaniel dog, was the only fatality of the Tacoma Narrows Bridge disaster. Leonard Coatsworth, a Tacoma News Tribune editor, was driving with the dog over the bridge when the bridge started to vibrate violently. Coatsworth was forced to flee his car, leaving Tubby behind. 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 $364.40 in reimbursement for the contents of his car, including Tubby. In 1975, Coatsworth's wife claimed that Tubby had only three legs and was paralyzed.
Fate
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 built. With steel a valuable commodity due to the United States' participation in World War II, steel from the bridge cables and suspension span were sold as surplus. The salvage operation cost the state more than was returned from the sale of the material, a net loss of over $350,000.
Preservation
The underwater remains of the bridge act as a large artificial reef, and are listed on the National Register of Historic Places with reference number 92001068.
A lesson for history
Othmar Ammann, leading bridge designer and member of the Federal Works Agency Commission investigating the collapse of the Tacoma Narrows Bridge, wrote:
New bridges
Due to materials shortages as a result of the United States' participation in World War II, it took 10 years to replace Galloping Gertie. Its replacement opened to the public on October 14, 1950, and is long — longer than Galloping Gertie.
50 years later, the 1950 bridge was deemed to be exceeding its capacity, and a second, parallel suspension bridge was constructed to carry eastbound traffic, while the 1950 bridge was reconfigured to carry westbound traffic. The new bridge opened in July 2007.
See also
External links
- - physics presentation and resources
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Historical
- 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.
- - Failure Magazine (November 2000)
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