Collapse of the Tacoma Narrows Bridge: A Case Study - The Constructor (2024)

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Construction of the first Tacoma Narrows Bridge started on November 23, 1938, and was opened to the public on July 1, 1940. It was constructed in Washington, US, to connect the cities of Seattle and Tacoma. The main span of the bridge was 853 m, connected with two glazing towers of 128 m height.

Despite the fact that, at that point, it was the third-longest suspension bridge in the world, the Tacoma Narrows Bridge was much flexible, smaller, and lighter than the other bridges which were constructed during that period.

The bridge easily accommodated two lanes for traffic movement with a sleek appearance. The bridge designer, Leon Moisseiff, wanted to give the bridge a sleek appearance without utilizing stiffening trusses. He replaced the stiffening trusses with plate girders of lesser weight that left the Tacoma Narrows Bridge with only 35% of the stiffness of the Golden Gate Bridge.

Also, the Tacoma Narrows Bridge had a 1/340 span-to-depth ratio, and its 1/75 width-to-span ratio was much less than the Golden Gate Bridge. These special attributes, combined with its very low damping ratio, initiated enormous vertical motions during moderate to low wind conditions.

For the first time, this type of design was called "Galloping Gertie" as the bridge exhibited heavy oscillations during construction. Vertical waves of up to 1.2-1.4 m double amplitude at up to 30 cycles per min were recorded. The lowest wind velocities (15-19 km/h) were able to generate 0.75 m double amplitude motion.

All the safety standards were followed during the design and construction of the Tacoma Narrows Bridge and its oscillations were considered to be falling within acceptable limits. However, the researchers proposed different methods to reduce its motion.

Hold-down ties were introduced and secured to solid square blocks of concrete buried in the slopes. These hold-down ties were proposed as temporary measures, and one of the holding ties broke seven days after installation. However, the broken tie was reinstalled within a few days. In addition, stayed cables and inclined cables were installed together with hold-down ties.

Inclined and stayed cables were connected to stiffening girder through main cables. Also, researchers suggested after conducting multiple wind tunnel tests that oscillation motion can be reduced by installing deflector vanes or fairings. These measures could have reduced the lift and oscillation. But, the failure of the bridge occurred before these solutions could be introduced.

1. Collapse of the Tacoma Narrows Bridge

On the night of 6^th November, a strong storm blew in the river where Tacoma Narrows Bridge was located. The next morning, the bridge authorities closed the bridge for traffic after noticing that the bridge was undergoing severe undulating motions. The cables on the west side of the bridge were broken and were swaying in the wind.

On 7^th November, the wind velocity had reached 68 km/h and the bridge was bending at 40 oscillations per minute. A highest oscillation amplitude of 1 m was observed. Unexpectedly, the center stayed cables broke and the bridge started bending violently in two parts. The edges of the deck moved more than 8 m vertically because the bridge had rotated to a maximum angle of 45⁰. Also, the motion exceeded the acceleration due to gravity at that time.

This was the highest wind velocity observed so far since the bridge had been built. Researchers already predicted that the bridge could swing in smaller nine to ten twisting waves. However, violent movement was noticed.

The movement was so dominating that the smaller waves became into two dominating torsional waves. These two waves caused the maximum rotation of the bridge up to 45⁰, which was not predicted earlier through the wind tunnel tests.

Firstly, the sidewalks and curbs of the bridge started to collapse with the crumbling of street-lights. After that, the main stiffening girder started to twist and indicated towards a collapse. Then, the main cables of the bridge broke and the whole section of the roadway dropped gradually into the river below.

Loud noises were heard by people living nearby, similar to gunfire. The mass of the hogging side spans dragged the towers 4 m toward the shore, and the crumbling bridge, at last, came to rest. Thus, the side spans dropped 20 m before coming back to a permanent sag of 10 m because it was no longer balanced by the main span.

2. Reasons Behind the Failure of the Tacoma Narrows Bridge

The main questions which can trouble a design engineer that, how could a bridge designed to withstand a wind velocity of 161 km/hr and a static horizontal wind pressure of 146 kg/m² collapsed under a wind velocity of less than half the design limit and less than one-sixth wind pressure limit.

The researchers predicted that the deflection theory was not enough, by itself, to safely design the Tacoma Narrows Bridge. Also, the dynamic effects of wind on the Tacoma Narrows Bridge were not accounted for in the design.

The Public Works Administration (PWA) created a board of engineers to investigate the incident. The following points describe the findings of the PWA report:

1. The bridge was well planned and designed. In spite of the fact that it could safely resist all the static loads, the wind load caused extraordinary undulations, leading to the failure of the bridge.
2. The designers of the bridge made efforts to control the oscillation amplitude of the bridge.
3. No one thought that the Tacoma Narrows Bridge's excellent flexibility, combined with its inability to assimilate dynamic loads, would make the severe motions that would ultimately wreck the bridge.
4. Vertical motions of the bridge were caused only due to wind load and caused negligible damage to the structural parts.
5. The collapse of the cables on the north side caused the catastrophic torsional movement of the bridge. These cables were connected to the center ties, thus the center span twisted with higher angular movement. Due to the twisting movements, shear stresses developed throughout the span of the bridge and these stresses led to the failure of the main span.
6. The bridge was designed for static and dynamic loads using the same method. However, the rigidity against static and dynamic loads couldn't be found using the same method.

The PWA finally inferred that the Tacoma Narrows Bridge failed due to its extraordinary flexibility, lightness, and narrowness. These characteristics helped the wind force, which occurred on the failure day, to cause the torsional motions that led to the collapse of the bridge.

The PWA stated that the wind loads initiated the oscillatory motion, which moved toward the characteristic frequencies of the structure, developing the resonance (the cycle by which the recurrence of an object matches its regular recurrence, causing a sensational expansion in amplitude). This hypothesis clarified why the low-speed wind 68 km/h caused the tremendous oscillatory motions and decimation of the Tacoma Narrows Bridge.

The PWA's hypothesis, in any case, isn't the only clarification. Numerous researchers accepted that this clarification disregards the significant inquiry concerning how wind, arbitrary in nature, could produce a periodic impulse.

One clarification proposed by researcher Von Karman credited the movement of the bridge to the development of air vortices. These air vortices developed a wake zone, also known as Von Karman's zone. This wake zone strengthened the oscillatory motions, in the end causing the failure of the bridge.

The problem with this hypothesis is that the determined recurrence of a vortex brought about by a 68 km/h wind is 1 Hz, though the recurrence of the torsional oscillatory motions of the bridge estimated by bridge authorities was 0.2 Hz.

Another clarification, given by researcher Scanlan, suggest that vortex shedding phenomenon related to the Von Karman's zone was occurring, however, recommends that it didn't influence the motion of the bridge.

Another sort of vortex, one related to the structural oscillation itself, was developed, with a similar recurrence as the bridge. The resonance between the bridge and these vortices caused unreasonable movement, decimating the Tacoma Narrows Bridge.

In spite of the fact that these three hypotheses are in contrast to what precisely caused the torsional motions of the bridge but they all agree that the extraordinary flexibility, lightness, and narrowness of the Tacoma Narrows Bridge permitted these motions to develop until they obliterated it. A contributing variable may have been slippage of a band that held the cables.

For quite a long time, the movements of the bridge had been even and roadway was in a flat position. The light posts on the walkways remained in the vertical plane of the cables even as they rose, fell, and bent.

However, on 7^th November, a band of cable slipped out of the spot at mid-length, and the movements became lopsided, similar to a plane banking in various directions. Due to the torsional movements, the metal fatigue occurred and the hangers broke like paper clips that had been bowed time and again.

3. Solutions to Prevent the Collapse of the Tacoma Narrows Bridge

The Tacoma Narrows Bridge failure illustrated the structural designers and the world about the significance of damping, necessity of rigidity in the vertical direction, and resistance to torsion in suspension bridges. When the danger of twisting was acknowledged, there were numerous ways that the tragedy of the Tacoma Narrows Bridge might have been averted. The adoption of the following changes may have prevented the collapse of the Tacoma Narrows Bridge:

1. If the open stiffening trusses could have been used in the place of plate girders, the wind would have passed freely through the bridge and the collapse of the bridge could have been avoided.
2. Adopting a higher width/span ratio would have increased the stiffness of the bridge.
3. By increasing the weight of the bridge, natural frequency of the bridge could have been increased.
4. By improving the damping ratio of the bridge, oscillatory motions could have been absorbed and the movements could have been restricted.
5. Use of dynamic damper could have restricted the motion of the bridge.
6. Increasing the depth of plate girders could have provided greater stiffness against the torsional motion.
7. Streamlining the deck of the bridge could have reduced the formation of wake zone due to wind forces.

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