Failure Analaysis

   Fracture Mechanics

   Failure as a Design      Criterion

 Structural Failures
 ::  Unforeseen Loads & Consequences
- Tacoma Narrows Bridge
- Comet Airliner
 Human System Interaction  Failures
 ::  Flawed Decision Making
 :: Flawed Safety culture
 Failure of Design Management
 ::  Visionary Management Style
 ::  Inaccurate Assessment of Market Needs


Tacoma Narrows is the single point in the 20 000 square mile Puget Sound where the Washington mainland and the Olympic Peninsula are close (Map). Work on a suspension bridge began in early 1939 and it was opened on 1 July 1940 at a cost of $6.4 million (Bridge Plan). The suspension bridge section was 5 000 feet long, giving the bridge the third longest suspension span in the world at that time. Its design represented the pinnacle of suspension bridge lightness, grace and flexibility – obtained using shallow plate girders instead of the traditional deep stiffening trusses (this change was justified because only automobile traffic would be carried by the bridge). These desirable architectural features led to its collapse after only 4 months of operation, due to undesirable aerodynamic phenomena in low wind velocities.

The roadbed experienced vertical oscillations even during construction, which were unsteady in nature and might occur under low velocity winds (4 mph), but not under stronger breezes. Hydraulic buffers were installed at the towers and tie down cables were added to the side spans – these were not successful in controlling the oscillations. The bridge became known as ‘Galloping Gertie’ and attracted significant public attention for sensation seekers – hence the bridge was much photographed.

In the early morning of Thursday November 7 1940 the centre span was undulating 3-5 feet in winds of 35-46 mph (Twist). The bridge was closed at 10h00. Shortly afterwards the motion changed from rhythmic rising and falling to 2 wave twisting (Twist2), which grew stronger with each cycle – 5-28 foot undulations causing 45° tilts to the roadbed. (Video Clip)

At about 10h30 a centre span floor panel dropped into the water 195 feet below (First Drop). At 11h02 a 600 foot section of the western end of the span flipped over and plunged into the water (600' piece). The twisting continued and at 11h09 the remaining centre sections ripped free and fell into the Sound (Missing Section). The 1 100 foot side spans settled down to a 30 foot sag.

The bridge sections on the floor of the Puget Sound are the largest man-made structure ever lost at sea (Sonar Scan).

Technological Outcome:
Wind tunnel testing of 3-d scale model showed the same failure mode and proved the validity of similitude between model and prototype replacement bridge. Prototype was modified considerably to achieve stability – open steel grid slots between traffic lanes, greater depth of stiffening truss to span (1940 Roadway; 1950 Roadway), double laterals, hydraulic damping devices etc. Aerodynamic considerations were taken into account in the design of all extant and future bridges.

Causes:
  1. Designer ignored, or was unaware of the volume of evidence for wind-induced vibration of bridges (stemming back to 1818) – Ignorance of previous problems/failures. The designer extended the slender span concept too far, despite notable gaps in understanding of aerodynamic loading, to a depth-to-span ratio of 1:350 (twice that of the Golden Gate bridge with a span of 4200 feet).
  2. Designer also used a new deflection theory method of calculating stresses, whereby shear and bending loads are partly carried in the cables, rather than relying on stiffening trusses. Vertical and torsional rigidity of the bridge were much higher than contemporary bridges (Vertical Rigidity; Torsional Rigidity), and the bridge relied on the dead load for its rigidity with little inherent structural damping.
Commission of enquiry into the failure determined that the bridge was correctly designed in terms of ‘failure’ criteria, i.e. stresses exceeded the yield strength of the steel and the tensile strength of the concrete roadway. Theories proposed to account for the failure over the intervening 60 years include:
  • Periodic wind gusting ‘in tune’ with a natural frequency of the bridge – this requires precise pressure variation which is unlikely to happen in turbulent wind flow
  • Von Karman vortex shedding off the blunt body – if the frequency of vortex shedding matches a natural frequency of the structure, the driving force for vortex formation feeds off the motion of the structure. The frequency in a 42 mph wind is 1 Hz, while measurements of the bridge twist recorded a frequency of 0.2 Hz.
  • Self-excitation – here the driving force for oscillation is a function of bridge twist and rate of change of twist and involves interaction between structure and wind. Hence the wind provided the power and the motion supplied the power-tapping mechanism. Essentially, the bridge experienced flutter which excited torsional response modes, to which the structure had little resistance.
Design Failure:
This last theory appears to be correct, and hence failure of the bridge arose from the introduction of a new failure mode through the streamlining and slender shape of the bridge.

References:
  1. http://www.nwrain.com/~newtsuit/recoveries/narrows/narrows.htm
  2. http://maclab.alfred.edu/students/robinmr/link.html
  3. http://www.me.utexas.edu/~uer/papers/paper_jk.html

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Structural Failures | Human System Interaction Failures | Failure of Design Management

Failure Analysis  -  Fracture Mechanics  -  Failure As A Design Criterion