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When the Tacoma Narrows Bridge over Puget Sound in the state of Washington famously collapsed on November 7, 1940, it was captured on film for posterity. The footage became the basis for a textbook example of resonance, which is a standard topic in high school physics. But that classic explanation is incorrect.
Initial designs for the bridge by engineer Clark Eldridge were for a typical suspension bridge with 25-foot-high trusses under the road to stiffen the bridge and keep it from swaying too much. But the $11 million proposed design was costly. Engineer Leon Moisseiff — who consulted on the Golden Gate Bridge in San Francisco — countered with a novel and aesthetically pleasing design that replaced the trusses with 8-foot-high plate girders, lowering the construction costs to $8 million but providing much less resistance to bending and twisting.
Moisseiff and his New York City colleague, Frederick Lienhard, argued that the main cables would be sufficiently stiff to absorb enough static wind pressure to stabilize the structure, because the aerodynamic forces acting on the bridge would push it only sideways, rather than up and down. Their argument was based upon deflection theory, which was developed by Austrian civil engineers.
That cheaper, slimmer, and more elegant design won out, and construction began on September 27, 1938. There were problems even while the bridge was still being constructed, with the deck moving up and down vertically significantly in even moderately windy conditions. It prompted construction workers to dub the bridge “Galloping Gertie,” inspired by a popular saloon song. When the bridge opened on July 1, 1940, the public experienced the vibrations firsthand.
Several attempts were made to reduce the bouncing: tie-down cables anchoring the plate girders to 50-ton concrete blocks (the cables soon snapped); the addition of inclined cable stays connecting the main cables to the middle of the deck; and hydraulic buffers to dampen the main span’s longitudinal motion. None had much of a dampening effect. So the Washington Toll Bridge Authority brought in a University of Washington engineering professor named Frederick Farquharson to conduct wind tunnel studies in hopes of finding a solution.
Galloping Gertie had been surprisingly well-behaved throughout October, despite being blasted by 50 mph winds. But Farquharson noticed that occasionally his models would show a twisting motion, and later told reporters, “We watched it and said that if that sort of motion ever occurred on the real bridge, it would be the end of the bridge.”
Farquharson was standing on the Tacoma Narrows Bridge on the morning of November 7, and noted that problematic twisting motion of the bridge — rather than the typical bouncing — with growing alarm. Half an hour earlier, officials had closed it to traffic, but Tacoma News Tribune reporter Leonard Coatsworth had made it onto the bridge just before then; but when he was halfway across, an especially big bounce toppled his car onto its side. He jumped out and managed to crawl, bruised and bleeding, on his hands and knees to the safety of the towers, as six lamp posts snapped off and the steel coverings on the cables produced a metallic wail. The big steel cables snapped around 11 a.m., followed by a rumbling roar as 600 feet of the roadway crumbled into the water below. Finally, the entire center span cracked, leaving just the two towers standing.
The days that followed revealed a struggle to explain why the bridge collapsed. A New York Times article attributed it to the phenomenon of resonance: “Time successive taps correctly and soon the pendulum swings with its maximum amplitude. So with this bridge.” And when educator Franklin Miller distributed the footage of the collapse for classroom use in 1962, one of the captions erroneously mentioned “resonance vibration” as the cause. (The footage itself also proved to be misleading, thanks to errors converting the early film reels into other formats with different frames-per-second rates.)
That explanation stuck for decades, even though the Federal Works Administration concluded that resonance was an “improbable” explanation. Farquharson confirmed as much in his own report a decade later. The true culprit was the twisting motion he had observed both in his early models and on bridge itself the day of the collapse.
For more detail, below is a section from the State of Washington Department of Transportation (DOT) undated online report on the cause of the Tacoma Narrows Bridge collapse:
… The primary explanation of Galloping Gertie's failure is described as "torsional flutter." It will help to break this complicated series of events into several stages.
Here is a summary of the key points in the explanation.
When the bridge movement changed from vertical to torsional oscillation, the structure absorbed more wind energy. The bridge deck's twisting motion began to control the wind vortex so the two were synchronized. The structure's twisting movements became self-generating. In other words, the forces acting on the bridge were no longer caused by wind. The bridge deck's own motion produced the forces. Engineers call this "self-excited" motion.
It was critical that the two types of instability, vortex shedding and torsional flutter, both occurred at relatively low wind speeds. Usually, vortex shedding occurs at relatively low wind speeds, like 25 to 35 mph, and torsional flutter at high wind speeds, like 100 mph. Because of Gertie's design, and relatively weak resistance to torsional forces, from the vortex shedding instability the bridge went right into "torsional flutter."
Now the bridge was beyond its natural ability to "damp out" the motion. Once the twisting movements began, they controlled the vortex forces. The torsional motion began small and built upon its own self-induced energy.
In other words, Galloping Gertie's twisting induced more twisting, then greater and greater twisting. This increased beyond the bridge structure strength to resist. Failure resulted.
19th century bridge designers had learned painful lessons from numerous bridge collapses, but 20th-century designers did not heed them. Again, quoting the Washington State DOT report:
Early suspension-bridge failures resulted from light spans with very flexible decks that were vulnerable to wind (aerodynamic) forces. In the late 19th century engineers moved toward very stiff and heavy suspension bridges. John Roebling consciously designed the 1883 Brooklyn Bridge so that it would be stable against the stresses of wind. In the early 20th century, however, says David P. Billington, Roebling's “historical perspective seemed to have been replaced by a visual preference unrelated to structural engineering.
Just four months after Galloping Gertie failed, a professor of civil engineering at Columbia University, J. K. Finch, published an article in Engineering News-Record that summarized over a century of suspension bridge failures. Finch declared, ‘These long-forgotten difficulties with early suspension bridges clearly show that while to modern engineers, the gyrations of the Tacoma bridge constituted something entirely new and strange, they were not new — they had simply been forgotten.’ … An entire generation of suspension-bridge designer-engineers forgot the lessons of the 19th century. The last major suspension-bridge failure had happened five decades earlier, when the Niagara-Clifton Bridge fell in 1889. And, in the 1930s, aerodynamic forces were not well understood at all.
The remains of the original Tacoma Narrows Bridge deck are still on the bottom of Puget Sound, forming an artificial reef, and its side spans were melted down for steel during World War II. Eventually state authorities approved a replacement bridge, completed in 1950 and dubbed ‘Sturdy Gertie.’ This time the design used 33-foot trusses to stiffen the bridge, as well as wind grates and hydraulic shock absorbers. A second bridge was added in 2007.
1. Washington State Department of Transportation, Tacoma Narrows Bridge: Lessons from the Failure of a Great Machine, Why Did Galloping Gertie Collapse? Available at wsdot.wa.gov/TNBhistory/Machine/machine3.htm#6
Billah, K. and Scanlan, R. "Resonance, Tacoma Narrows Bridge Failure, and Undergraduate Physics Textbooks," American Journal of Physics 59 (1991): 118–124.
Green, D. and Unruh, W. G. “The Failure of the Tacoma Bridge: A physical model,” American Journal of Physics 74 (2006): 706.
Olson, Donald W.; Wolf, Steven F.; Hook, Joseph M. (2015) "The Tacoma Narrows Bridge collapse on film and video," Physics Today 68 (11): 64–65.
Pasternak, Alex. “The Strangest, Most Spectacular Bridge Collapse (And How We Got It Wrong)," Motherboard, December 2015.
Photo: Washington Department of Transportation
The collapse of the Tacoma Narrows Bridge was driven by wind-generated vortices that reinforced the twisting motion of the bridge deck until it failed.
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