Tacoma Narrows Bridge

Tacoma Narrows Bridge
Facing west atop the Tacoma Narrows
Coordinates	47°16′05″N 122°33′02″W
Carries	State Route 16
Crosses	Tacoma Narrows
Locale	Tacoma to Gig Harbor, Washington
Characteristics
Design	Dual Suspension
Total length	5,979 ft (1822 m)
Longest span	2,800 ft (853 m)
Clearance below	187.5 ft (57.15 m)
History
Opened	October 14 1950 (westbound) July 15 2007 (eastbound)
Statistics
Toll	Eastbound only: $4.00 (cash/credit price), $2.75 (transponder price)
Location

The Tacoma Narrows Bridge is a pair of mile-long suspension bridges in the U.S. state of Washington, which carry State Route 16 across the Tacoma Narrows between Tacoma and the Kitsap Peninsula. The first bridge opened to traffic on July 1 1940 and became famous four months later for a dramatic wind-induced structural collapse that was caught on motion picture film. The original span's motion earned it the nickname Galloping Gertie.

The first replacement bridge opened October 14 1950, and a parallel bridge opened July 15 2007. The 1950 replacement bridge was sometimes referred to as "Sturdy Gertie".

Westbound bridge

The westbound bridge, in 1988, when it carried traffic in both directions

The current westbound bridge was designed and rebuilt with open trusses, stiffening struts and openings in the roadway to let wind through. It opened on October 14 1950, and is 5,979 feet (1822 m) long — 40 feet (12 m) longer than the first bridge, Galloping Gertie. Local residents nicknamed the new bridge Sturdy Gertie, as the oscillations that plagued the previous design had been eliminated. This bridge along with its new parallel eastbound bridge are currently the fifth-longest suspension bridges in the United States.

When built, the westbound bridge was the third-longest suspension bridge span in the world. Like other modern suspension bridges, the westbound bridge was built with steel plates that feature sharp entry edges rather than the flat plate sides used in the original Tacoma Narrows Bridge (see the suspension bridge article for an example).

The bridge was designed to handle 60,000 vehicles a day. It carried both westbound and eastbound traffic until the eastbound bridge opened on July 15, 2007.

Eastbound bridge

In 1998, voters in several Washington counties approved an advisory measure to create a second Narrows span. Construction of the new span, which carries eastbound traffic parallel to the current bridge, began on October 4 2002, and was completed in July 2007. The Washington State Department of Transportation collects a toll before entering the eastbound span, at $1.75 for Good to Go! account holders with in-vehicle transponders and a $3.00 toll for cash/credit card paying customers. The existing span has been toll-free since 1965. The new bridge marks the first installation of the new Good To Go! electronic toll collection system.

Starting on July 1 2008, the tolls for the eastbound span increased. The new toll is $2.75 for Good to Go! transponders, and $4.00 for cash- and credit-card-paying vehicles.

A group called NarrowsBridgeLights.org advocates illuminating both bridges with twinkling lights. The group recommends solar powered lighting, for both safety and beauty.

Galloping Gertie

First Tacoma Narrows Bridge
File:Image-Tacoma Narrows Bridge1.gif The first Tacoma Narrows Bridge undergoes twisting mode vibration before collapsing.
Coordinates	47°16′05″N 122°33′02″W
Characteristics
Design	Suspension
Total length	5,000 ft (1524 m)
Longest span	2,800 ft (853 m)
Clearance below	195 ft (59.4 m)
History
Opened	July 1 1940
Closed	November 7 1940
Location

Desire for a bridge at this location 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, builder of 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 toll bridge authority requested $11 million from the federal Public Works Administration (PWA). But, according to Eldridge, prominent Eastern-consulting engineers—led by New York engineer Leon Moisseiff—petitioned the PWA to build the bridge for less.

Preliminary construction plans had called for 25-foot-deep (7.6 m) girders to sit beneath the roadway and stiffen it. Moisseiff, a respected designer and consultant engineer of the famed Golden Gate Bridge, proposed shallower supports — girders 8 feet (2.4 m) deep. His approach meant a slimmer, more elegant design and reduced construction costs. Moisseiff's design won out. 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.

The decision to use the shallower girders proved to be the first bridge's undoing. With the 8-foot (2.42-meter) 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 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.

Collapse

The wind-induced collapse occurred on November 7 1940, at 11:00 AM (Pacific time), due partially 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:

Tacoma Narrows Bridge collapsing

Just as I drove past the towers, the bridge began to sway violently from side to side. Before I realized it, the tilt became so violent that I lost control of the car...I jammed on the brakes and got out, only to be thrown onto my face against the curb...Around me I could hear concrete cracking...The car itself began to slide from side to side of the roadway. On hands and knees most of the time, I crawled 500 yards [450 m] or more to the towers...My breath was coming in gasps; my knees were raw and bleeding, my hands bruised and swollen from gripping the concrete curb...Toward the last, I risked rising to my feet and running a few yards at a time...Safely back at the toll plaza, I saw the bridge in its final collapse and saw my car plunge into the Narrows.

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 47°16′00″N 122°33′00″W, at a depth of 180 feet (55 m).

Film of collapse

Footage of the Tacoma Narrows bridge wobbling and eventually collapsing. (19.1 MB video, 2:30)

The final destruction 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.

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.

Remains of Galloping Gertie

The failure of the bridge occurred when a never-before-seen twisting mode occurred, from winds at a mild 40 MPH. This is called a torsional, rather than longitudinal, mode (see also torque) 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 due to aeroelastic flutter. Flutter occurs when a torsional disturbance in the structure increases the angle of attack of the bridge (that is, the angle between the wind and the bridge). The structure responds by twisting further. Eventually, the angle of attack increases to the point of stall, and the bridge begins to twist in the opposite direction. In the case of the Tacoma Narrows Bridge, this mode was negatively damped (or had positive feedback), meaning it increased in amplitude with each cycle because the wind pumped in more energy than the flexing of the structure dissipated. Eventually, the amplitude of the motion 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 was a first failure hypothesis, however failure was actually due to aeroelastic flutter

Vortex shedding and Von Kármán vortex street behind a circular cylinder. The first hypothesis of failure of the Tacoma Narrow Bridge was resonance, a myth that has been popularized by many physics textbooks. This is because it was thought that the Von Kármán vortex street frequency (the so called Strouhal number) was the same as the torsional natural vibration frequency. This resulted to be incorrect. Actual failure was due to aeroelastic flutter.

The bridge's spectacular destruction is often used as an object lesson in the necessity to consider both aerodynamics and resonance effects in civil and structural engineering. However the effect that caused the destruction of the bridge should not be confused with mechanical resonance (as from the periodic motion induced by a group of soldiers marching in step across a bridge). In the case of the Tacoma Narrows Bridge, there was no periodic disturbance. The wind was steady at 42 mph (67 km/h). The frequency of the destructive mode, 0.2 Hz, 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). The event can only be understood 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.

In 1943, New York City's similarly slim Bronx-Whitestone Bridge was retrofitted with a 14-foot-deep Warren truss and diagonal stays to reduce deck oscillations. The Warren Truss was removed in 2001 and replaced with hydraulic dampers and deck-edge fairings to maintain stability.

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 photographer, was driving with the dog over the bridge when it started to vibrate violently. Coatsworth was forced to flee his car, leaving Tubby behind. Professor Farquharson and a news photographer attempted to rescue Tubby, 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 only had three legs and was paralyzed.

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.

Plate structure in modern suspension bridges

The Yichang Bridge, a plate deck suspension bridge, over the Yangtze River in China

Modern design, analysis, materials, and construction methods have now permitted the use of plate structures in suspension bridges. Rather than using aerodynamically unstable flat vertical sides, the edges are now tapered (in cross section) to reduce vortex shedding and additional plate elements, forming a box beam that creates a structure sufficiently ridged against twisting to avoid the problems seen with the Tacoma Narrows bridge.

• 
  Remains of Galloping Gertie
• 
  New bridge sections used in construction of the new span.
• 
  A panorama of Tacoma Narrows Bridge in 2007.

External links

• Color video of the original bridge's construction and collapse
• Color video of the original bridge's construction and collapse with narration

• Physics behind the collapse of the bridge
• failurebydesign.info - physics presentation and resources
• Photos of the bridge and the new span under construction
• Tacoma Narrows Bridge (1940) at Structurae
• Tacoma Narrows Bridge (1950) at Structurae
• New Tacoma Narrows Bridge (2007) at Structurae

Historical

• History of the Tacoma Narrows Bridge
• University of Washington Libraries Digital Collection – Tacoma Narrows Bridge Collection More than 152 images and text documenting the infamous collapse in 1940 of the Tacoma Narrows Bridge. Also covers "Galloping Gertie's" creation, subsequent studies involving its aerodynamics, and finally the construction of a second bridge spanning the Narrows.
• The Tacoma Narrows Bridge Disaster, November 1940
• Images of failure
• Information and images of failure
• Firsthand account and images of the failure
• Official site of the Tacoma Narrows Bridge
• Timeline of the bridges
• Tacoma Narrows Bridge
• Suspended Animation - Failure Magazine (November 2000)
• Footage of the Tacoma Narrows bridge wobbling and eventually, collapsing, Stillman Fires Collection, in the Internet Archive.

Second span project

• Tacoma Narrows Bridge Project (WS DOT Web Page; information about the new bridge construction project)
• SR 16 - New Tacoma Narrows Bridge (computer projection of completed project)
• Puget Sound Transportation projects:Tacoma Narrows Bridge (unofficial site providing news, photos and information about the second span construction)
• Wind Tunnel Testing Summary from the National Research Council of Canada
• Wind Tunnel Testing Press Release from the National Research Council of Canada
• Tacoma Narrows Bridge Project (continuing coverage of bridge construction from The News Tribune)
• Bridge Workers are Walking Tall Above the Narrows Rob Carson (The News Tribune), Kitsap Sun, September 25 2005
• Wire by wire, Tacoma Narrows bridge is built Mike Lindblom, The Seattle Times, October 15 2005