Case Study Mechanical Engineering (Politeknik)

Case Study

TACOMA NARROWS BRIDGE

Introduction :  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.

Problem Statement :

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.

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. Rigidity; Torsional Rigidity), and the bridge relied on the dead load for its rigidity with little inherent structural damping.

3.       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:

Theory :

1.       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

2.       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.

3.       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.

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