The textbooks written by David Halliday and Robert Resnick in the early 1960s enlivened the section on resonance with photographs of the Tacoma Narrows Bridge and concluded that the “wind produced a fluctuating resultant force in resonance … Additional details of the film and video analysis can be found in the November 2015 issue of the Physics Teacher, which also includes further description of the Armistice Day storm and the strong winds that earlier had caused the Tacoma Narrows Bridge to oscillate, twist, and collapse into the waters below. a reinforcing effect, opposite to damping). [6] Another $1.6 million ($29.1 million today) was to be collected from tolls to cover the estimated total $8 million cost ($145.3 million today). Selecting this option will search all publications across the Scitation platform, Selecting this option will search all publications for the Publisher/Society in context, The Journal of the Acoustical Society of America, Program in Structures and Mechanics, Princeton University, Princeton, New Jersey 08544, Department of Civil Engineering, The Johns Hopkins University, Baltimore, Maryland 21218. [39], Following the incident, engineers took extra caution to incorporate aerodynamics into their designs, and wind-tunnel testing of designs was eventually made mandatory.[40]. Selecting this option will search the current publication in context. Othmar H. Ammann, Theodore von Kármán and Glenn B. Woodruff. {\displaystyle \omega _{r}} The suspension bridge that was completed in 1950 was reconfigured to carry only westbound traffic. Here, U stands for the flow velocity, D is a characteristic length of the bluff body and S is the dimensionless Strouhal number, which depends on the body in question. ", However, the Federal Works Administration report of the investigation (of which von Kármán was part) concluded that, It is very improbable that the resonance with alternating vortices plays an important role in the oscillations of suspension bridges. [8] Using this theory, Moisseiff argued for stiffening the bridge with a set of eight-foot-deep (2.4 m) plate girders rather than the 25-foot-deep (7.6 m) trusses proposed by the Washington Toll Bridge Authority. Another problem with financing the first bridge was buying out the ferry contract from a private firm running services on the Narrows at the time. Construction began in September 1938. f [28] and Tipler et al. The bridge's main span finally collapsed in 40-mile-per-hour (64 km/h) winds on the morning of November 7, 1940, as the deck oscillated in an alternating twisting motion that gradually increased in amplitude until the deck tore apart. The film shows Leonard Coatsworth attempting to rescue his dog—without success—and then leaving the bridge. The solution of such ordinary differential equation as a function of time t represents the displacement response of the system (given appropriate initial conditions). This vibration was caused by aeroelastic fluttering. If one wishes to argue, however, that it was a case of externally forced linear resonance, the mathematical distinction ... is quite clear, self-exciting systems differing strongly enough from ordinary linear resonant ones.". They then state later in their paper "Could this be called a resonant phenomenon? The frequency seen in the videos is too high by 50%. where m, c and k stand for the mass, damping coefficient and stiffness of the linear system and F and ω represent the amplitude and the angular frequency of the exciting force. On 7 November 1940 the Tacoma Narrows Bridge in Washington State collapsed during a gale. [8] 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. If you need an account, please register here. [25] 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. [29]) wrongly explain that the cause of the failure of the Tacoma Narrows bridge was externally forced mechanical resonance. 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 (equivalent to $14.6 million today). 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. Plaut, R.H. (2008). The user's guide for the current American Association of Physics Teachers (AAPT) DVD states the bridge collapse "was not a case of resonance." Notably, in many. For example, a child using a swing realizes that if the pushes are properly timed, the swing can move with a very large amplitude. = Professor Farquharson[13] and a news photographer[14] attempted to rescue Tubby during a lull, but the dog was too terrified to leave the car and bit one of the rescuers. [21] 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 newsreels of the day copied the film onto 35 mm black-and-white stock. "Snap Loads and Torsional Oscillation of the original Tacoma Narrows Bridge". The remarkable oscillations of its long and slender center span in the months leading up to the catastrophe earned the bridge the moniker “Galloping Gertie.” The disaster is especially well known because of dramatic film footage taken the day of the collapse. With only the 8-foot-deep (2.4 m) plate girders providing additional depth, the bridge's roadway section was also shallow. Usually, the approach taken by those physics textbooks is to introduce a first order forced oscillator, defined by the second-order differential equation. A commission formed by the Federal Works Agency studied the collapse of the bridge. 2 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. f Othmar Ammann, a leading bridge designer and member of the Federal Works Agency Commission investigating the collapse of the Tacoma Narrows Bridge, wrote: The Tacoma Narrows bridge failure has given us invaluable information… It has shown [that] every new structure [that] projects into new fields of magnitude involves new problems for the solution of which neither theory nor practical experience furnish an adequate guide.

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