Tacoma Narrows Suspension Bridge

Presented by:Muhammad Asad Hayat, 14-CE-148Civil Engineering Department, UET Taxila

Introduction• Tacoma Narrows Suspension Bridge was

constructed in the Washington D.C., a state in United States, that connected the Tacoma Narrows strait of Puget Sound (‘Sound’: narrow channel of the sea joining two larger bodies of water) between Tacoma and the Kitsap Peninsula.

• This bridge collapsed just four months after its construction.

• It was world’s 3rd longest suspension bridge in the world at the time of its failure.

Introduction (Contd…)• Total cost of bridge was 6.4 million U.S.D (105

million USD in 2012).• Total structure length was 5939 ft with 5000 ft

suspension span and it consisted of three spans, one central suspension span or deck and two short suspension spans one each side. Lengths of spans were as follows:

1. 1st Short Suspension Span (1100 ft)2. Central Span (2800 ft)3. 2nd Short Suspension Span (1100 ft)

Introduction (Contd…)• Center span (Height above water) = 195 ft• Width of roadway = 26 ft• Width of sidewalk (On each side) = 5 ft• Height of East Pier = 247 ft• Height of West Pier = 198 ft• Height, Towers above piers = 425 ft

Bridge Map

Main Cable Deck

Anchorage

Main Towers

1st Short Span 2nd Short Span

Center Span

Bridge at the time of its inauguration ceremony, 1940

E

W N

S

Need of Bridge• This bridge, constructed in two years, was designed

to join Tacoma and less-developed Kitsap Peninsula which could result in increase in development and population in both areas.

• Bridge also benefited the US Military (Air Force and Navy) connecting their air fields and ship yards.

• A road could be constructed to connect these two places, but it cost more money than to construct a bridge.

• Bridge was designed to hold 60,000 cars.

Historical Background and Funding

• Need of a bridge to connect two cities dates back to 1889 but concreted efforts began in 1920s.

• Initial design of bridge was given by Clark Eldridge in 1938 who was Washington State Engineer.

• Leon Moisseiff, New York bridge engineer who served as designer and consultant engineer for the Golden Gate Bridge - petitioned the PWA (Public Works Administration) and the RFC (Reconstruction Finance Corporation) to build the bridge for less. Moisseiff proposed shallower support which cost less. Moisseiff’s design won out.

Historical Background and Funding (Contd…)

Initial design of bridge by Eldridge, 23 May 1938 Safe Design ? Eldridge proposed truss deck for the bridge so that wind could easily pass through it.

BUT WHY?

FAILED!

Movements during Construction• A small movement in deck of bridge was noted

many times by workers even during the construction of the bridge when wind blew. A small vibration could be expected in a bridge but vibrations produced in this bridge were not normal.

• Engineers were aware that bridge was prone to motion.

• Retrofitting to design, as bridge construction progressed, by new ideas from engineers was also done.

Prevention of Movements• Retrofitting of bridge, to avoid the movements and

stiffen the bridge, as mentioned earlier was done by installing hydraulic jacks and tie down cables.

Tie-down cables

Failure• Analytical studies have shown that this bridge failed

due to winds running at 64 km/h velocity in the Eastern direction on 7th of November, 1940.

• In fact, “Tacoma Narrows was made with wind-resisting

plate girders rather than deep stiffening trusses.”• In design of bridge, aerodynamic forces were not

taken into account due to which winds running at 64km/h speed in one direction caused it to fail.

Failure (Contd…)

Twisting of deck of the bridge due to

wind action

Failure (Contd…)• Bridge was too skinny, fragile and flexible. It had

only two lanes, less mass.• The wind exerted a lot of pressure, assisted by more

and more severe aerodynamic forces, and made waves which caused the bridge to twist and collapse in water.

• During the collapse, the main suspension cables were thrown violently side to side, twisted, and tossed many feet into the air.

• On the north cable at mid span, where the support cable had loosened, it broke more than 350 wires.

Failure (Contd…)• Other wires were severely distorted. The main

cables were a total loss. Their only value was as scrap metal.

Ultimate Collapse Courtesy: Wikipedia

Failure (Contd…)

Bridge after failure (Center span crashed)

Torsional (Twisting) Movements at the time of failure

The nature and severity of the torsional movement is revealed in this image taken from the Tacoma end of the suspension span. When the twisting motion was at the maximum, elevation of the footpath at the right was 28 feet (9m) higher than the footpath at left side of the bridge.

Torsional (Twisting) Movements at the time of failure (Contd…)

Aerodynamic forces causing torsional movements

Damages to Side Spans• Side spans, which became unbalanced, were too

severely damaged.• Sag of approximately 45 feet appeared in both side

spans.

What does Physics say about failure?

• Vertical Oscillations or Torsional Movements, as mentioned earlier, were noted during construction of bridge.

• Aerodynamic flutter is regarded as major cause of failure.

• Resonance effect and vortex shedding also caused it to fail.

Aerodynamic Flutter in Bridge• Tendency to aerodynamic flutter is present in all

flexible structures i.e. bridges, jet planes, aeroplanes.

• It is possible only if structural and aerodynamic forces are running at same frequency.

• Majority of researchers consider aerodynamic flutter to be the main reason for the failure of bridge.

Understanding Aerodynamic Flutter• If a father is pushing his kid on swing then swing

would have a natural frequency. If swing would come back to him after every 4 seconds, then to maintain the motion of swing, father must push the swing each time (after every 4 seconds) known as external force applied with periodic frequency. If he is not able to do so, he will damp the motion.

• If external periodic frequency matches natural frequency, we get a resonance frequency. If this phenomenon remains for some time, it will, ultimately, cause amplitude to increase due to proper timing of force i.e. failure of plane wings, failure of deck of bridge.

Understanding Aerodynamic Flutter (Contd…)

Tendency of a flexible structure to aerodynamic flutter causing vibration in whole body.

Courtesy: Aerodynamic Flutter analysis of plane using ANSYS

Resonance• We know that resonance happens when: “Any system is vibrated at its natural frequency or

resonant frequency.”• Take example of a rope.

You can think of resonance as having the natural frequency of the system exactly in tune with your force.

Resonance effect on the bridges• In design of bridge, resonance phenomenon plays

an important role.• This is susceptibility or tendency of any structure to

respond at an increased amplitude when frequency of its oscillations meets its natural frequency.

• If it happens, severe vibrations are produced in the structure causing ultimate failure.

• Many factors are involved in vibrations of bridge i.e. vibrations due to traffic flow, heavy machinery, wind.

• One such affect was noted in Tacoma Narrows Bridge e.g. wind.

Resonance effect on the bridges (Contd…)

• If natural frequency of structure is achieved due to any factor, it will cause more vibrations and more storage of energy in the system. When this energy exceeds an object’s load limits, structure will lose its integrity.

• In case of Tacoma Narrows, when natural frequency met frequency of wind blowing, it caused denominator to be very small and therefore caused increase in amplitude.

windnatural

windnsoscillatio ff

F A

Nearly or completely equal to zero?

Vortex Shedding• It happens when winds hits a structure, then

vortices of fluid (air) are formed at certain frequency. When a vortex is formed on one side of body (Say A), it immediately increases pressure on side A causing decrease in velocity in side A and ultimately causing less pressure on other side (Say B) and more velocity.

• Due to these vortices, a fluctuating force on the body is induced which causes vibrations in the structure. If vibrations coincide with the natural frequency or resonance frequency of structure, they lead to failure.

Vortex Shedding (Contd…)

Imagine wind blowing from left on the cable cross-section.• Small vortex of low pressure• Move towards low pressure

Summary of Physics Analysis

Summarizing the whole analysis: “A small vibration produced, assisted by the more

and more wind caused the natural frequency of bridge to meet wind frequency which ultimately resulted in an increase in the bridge oscillations. Bridge oscillations increased with time and it ultimately failed.

Vortex shedding, resonance phenomenon and aerodynamic flutter were interlinked to each other in sense of natural frequency of the structure”.

Bridge (1950)• Soon after failure of bridge, it was expected to be

rebuilt with 1-1.5 years.• Due to WW-II, its construction delayed.• In 1950, new bridge was completed.• Second bridge had truss-girders which allowed to

wind to pass through bridge easily.• New bridge, being wide and thicker, had more

torsional stiffness than previous bridge.• Wind tunnel test were also performed prior to its

construction on small scale model.

Bridge (1950) (Contd…)

1950 Tacoma Narrows Bridge (1988)Courtesy: Wikipedia

Bridge (2007)• Due to high traffic flow, another bridge parallel to

1950 bridge was constructed to carry eastbound traffic.

Westbound Bridge (1950)

Eastbound Bridge (2007)

Twin Bridges of Tacoma

Major difference between the two (1940 & 1950)

• Following are some of differences between 1940 & 1950 suspension bridges:

1940 Bridge 1950 BridgeHad two lanes Has four lanes

Less stiff More stiff

Less weight More weight

Use of plate girders Use of trusses

Wind-disturbance No wind-disturbance

2.4m deep plate girders 10m deep stiff trusses

A Lesson for New Design• In modern suspension bridges construction, it is now

made mandatory to test the bridge model on small scale prior to start its construction.

• Science of aerodynamic flutter in bridges was born after the failure of Tacoma Narrows 1940.

• Effects of resonance on bridges and other flexible structures were studied thoroughly.

• Vortex shedding and its affects on the bridge were also taken into account.

• Wide use of open stiffening trusses to let wind pass through started.

A lesson for New Design (Contd…)

• Increase in the weight of bridge because:Vertical oscillations resistance Mass of bridge∝

• Increase in stiffness by using stiffening trusses and more depth of deck.

Thank YouAny Questions?