The Collapse of Tacoma Bridge

Faculty of Engineering, Technology & Built Environment

School of Architecture & Built Environment

JULY - NOV 2022

A CASE STUDY: THE COLLAPSE OF TACOMA BRIDGE (1940)

01. TheIntroduction

The incident of Tacoma Narrows bridge disaster that was happen in 1940 is still being the hot topic in the public eye recent days Clearly, in the most of the education about construction in building structure, this incident is presented as an example of failure in those relevant field of study. With these incident happened, people can treat it as a case study of suspension cable bridge and avoid on having similiar failure design in the future The Tacoma Narrows Bridge is a twinsuspension bridge which was built in Washington that connecting the mainland of Washington state with the Olympic Peninsula during 1930s and started opened to public travel on July 1st, 1940 The first cable suspension bridge of this kind was Tacoma Narrows Bridge, which also used a series of plate girders to support the roadbed. The Tacoma Narrows Bridge was well known as the third longest suspension bridge in the world at that time which covered about 5959 ft (1.8 km) For structural design part, a continuous steel grider that cover 450 ft approached on west side while for the east side consist of a 210ft long reinforced concrete frame. Two cable anchorages on the roadways, two on sidewalks and two on deep stiffening girders Also for the structural detail part, the suspension cable anchorages to the connection made by 20000 cubic yards of concrete, 2.7 lakh pounds of reinforcing steel and 6 lakh pounds of structural steel.

Engineer Clark Eldridge's initial plans for the bridge called for a standard suspension bridge with 25-foot-high trusses beneath the road to strengthen the building and lessen excessive swaying However, the $11 million suggested design was pricey. Soon then Leon Moisseiff is the one who designed the bridge which make it to be the most flexible ever constructed as he reduced the construction costs to $8 million by swapping the trusses for 8-foot-high plate girders, but offering much less resistance to bending and twisting, as a countermeasure He was born in Latvia in 1872, moved to New York at the age of 19. He was soon graduated from the Columbia University and became a young talented engineer in 1895. Moisseiff has the experience in helping dsign and build some of the world's largest suspension bridges before he was held to be the main designer of Tacoma Narrows Bridge. During the design development, Moisseiff and his New York City colleague Frederick Lienhard argued that the main cables would be sufficiently stiff to absorb enough static wind pressure to stabilise the structure because the aerodynamic forces acting on the bridge would only push it sideways rather than up and down. Deflection theory, which was created by Austrian civil engineers, served as the foundation for their argument

The very start construction of the Tacoma Narrows Bridge began in September 1938. Due to its long length, the bridge was considered a 'narrow bridge'. In 1940, a staggering $6 million was estimated to have been spent on the project overall. While the inflation was considered, it had a equivalent to almost $1 billion and all of the money used has just lasted for four months and seven days. At the time of the deck of the bridge was built it had began to move vertically in windy day conditions and that is why the bridge was nicknamed by the construction workers as "Galloping Gertie" The vertical motion that came from the bridge continued even after the bridge was finished constructed and opened to the public for usage, despite a number of dampening actions. There were several methods used to lessen the bouncing, including inclined cable stays that connected the main cables to the centre of the deck, tie-down cables that secured the plate girders to 50-ton concrete blocks, and hydraulic buffers to lessen the motion of the main span longitudinally (the cables soon snapped) None had a significant dampening impact In an effort to find a solution, Frederick Farquharson, an engineering professor from the University of Washington, was hired by the Washington Toll Bridge Authority to carry out wind tunnel tests. Despite being buffeted by winds of 50 mph throughout the month of October, Galloping Gertie had been surprisingly well-behaved. However, Farquharson observed that occasionally his models would twist, and he later told reporters, "We watched it and said that if that sort of motion ever occurred on the real bridge, it would be the end of the bridge."

On the morning of 1940 November 7, the bridge's main span ultimately collapsed in wind of 40 miles per hour (64 kilometres per hour), as the deck oscillated, it alternated between twisting and oscillations of increasing amplitude until it tore apart

Causes of the Collapse of Tacoma Bridge

Before going to the discussion about the causes of the collapse of Tacoma Narrows bridge, some other features about bridge to people should be discuss. A bridge is a classic example of a civil structure. As old as recoreded history itself, humans have always needed a way to travel from place to place without getting wet. And for a very long time, gravity was the only force that bridge designers had to deal with. In the face of gravity's pull toward the ground, how can we support the structure itself, in addition to all the people and vehicles that may pass through? This was the central question in bridge design. Additionally, since the majority of bridges are paid for by taxes, How can we make it happen cheaply and efficiently for the general public? About that, the suspension bridge is one of the lighter and more efficient shapes that bridge designs have evolved towards over time as a result of our growing structural engineering knowledge and capacity to produce better building materials.

A structure that primarily consists of a deck, two towers, two main cables, and connector rods that suspend the deck is referred to as a "suspension bridge." Suspension bridges' main benefit is their ability to span vast distances with just two towers, requiring less material and, more importantly, less money. Suspension bridges are known for their recognisable slender and graceful appearance thanks to the benefit of being able to span large distances with minimal material. But the same lack of material also makes the structure less rigid and stiff. A new force—the wind— began to influence bridge designs, whereas before they were typically so stiff that gravity was the only load that needed to be considered.

Talking back to the Tacoma Narrows Bridge, a significant barrier to financing the bridge's construction was the need for an innovative design, which was pursued by the state. Instead of the initially recommended trusses, the bridge stiffened the deck with two thin plate girders, giving it the recognisable steel ribbon appearance across Puget Sound. Unfortunately, the analogy went further than it first appeared. The bridge was obviously too flexible even during construction, even in moderate winds. Then four months after the bridge was opened, the bridge suffered collapsed in dramatic fashion by a wind of about 42 miles per hour. A three-dimensional scaled model at a 1:200 scale was constructed following the incident for wind tunnel tests and to clearly understand the cause of failure. The experiments gave rise to a new theory: oscillations caused by the wind. The bridge's shape was unstable from an aerodynamic perspective in the transverse direction. The vertical girders of the H-shape enabled flow separation, which resulted in the generation of vortices that matched the oscillation's phase. The energy produced by these vortices was sufficient to move the girders from their place. The issue that led to the collapse of the Tacoma Narrows Bridge was not a brand-new issue; rather, it was an unidentified issue. Increasing the dead load, adding dampers, stiffening trusses, or using guy cables are just a few design strategies that can be used to account for increased stiffness brought on by wind action. These elements, however, were not initially taken into account and were added to forensics much later.

A crucial event happened on the morning of November 7, 1940, just after 10 a.m The north cable's mid-span cable band fell [and slid along the bridge]. The cable was able to divide into two different segments as a result. This influenced the bridge deck's transition from vertical (up-anddown) movement to torsional (twisting) movement "Vortex shedding" was another factor in the bridge deck's torsional motion. In the Narrows Bridge, vortex shedding happened as follows, in brief: The 8-foot solid plate girder that supports Galloping Gertie's deck was struck by the wind as it split apart Due to steel's inherent elasticity and ability to change shape under extreme stress, a small amount of twisting occurred in the bridge deck. Also, The wind flow separation increased as a result of the twisted bridge deck. This generated a vortex, or swirling wind force, which raised and bent the deck even higher Moreover, This lifting and twisting was resisted by the deck structure. It had a tendency to go back to where it had been. Its return's direction and speed matched the lifting force It moved "in phase" with the vortex, to put it another way. The wind later accentuated that motion A "lock-on" event was the result of this

The bridge structure absorbed more wind energy when the movement changed from vertical oscillation to torsional oscillation The wind vortex started to be controlled by the bridge deck's twisting motion, and soon the two were coordinated. The twisting motions of the structure became self-generating. In other words, the wind was no longer the source of the forces acting on the bridge The forces were generated by the motion of the bridge deck. Engineers refer to this motion as "self-excited." The fact that both torsional flutter and vortex shedding occurred at relatively low wind speeds was crucial. Typically, torsional flutter takes place at high wind speeds, such as 100 mph, while vortex shedding happens at relatively low wind speeds, such as 25 to 35 mph. The bridge immediately entered "torsional flutter" due to the design of Gertie and its relatively low resistance to torsional forces caused by the vortex shedding instability. The bridge's natural ability to "damp out" the motion was now exhausted. They were able to manage the vortex forces once the twisting movements started. The torsional motion started out slowly and grew as a result of its own internal energy. To put it another way, Galloping Gertie's twisting caused additional twisting, which led to increasing amounts of twisting. The strength of the bridge structure was unable to withstand the increase then failure followed.

Resonance is a periodic force synchronises with a system's inherent frequency in this phenomenon The standard illustration is a swing. Because the energy is stored when resonance occurs, small periodic driving forces, such as pushing someone in a swing, can eventually add up to large oscillations The periodic driving force for wind-induced motion is caused by a phenomenon known as vortex shedding. When vortices form on the backside of a blunt object, the fluid flowing past it oscillates. Even small amounts of wind can cause significant oscillations when the frequency of these alternating zones of low pressure is close to the natural frequency of the structure. For this reason, some chimneys have helical vanes installed in order to generate turbulence and disperse the vortices. The Tacoma Narrows Bridge did experience resonance from the vortex shedding on the day it failed This is evident in the vertical undulations that made the bridge famous. But the failure wasn't due to this resonance. A distinct oscillation started 45 minutes prior to failure.

The bridge is seen oscillating in a torsional motion rather than a vertical one in the historical footage just before failure. Although the cause of this shift in oscillation is still up for debate, one of the most compelling hypotheses relates to the bridge's aerodynamics. The Tacoma Narrows Bridge's shape and the big steel plates on either side resulted in some peculiar wind interactions, as opposed to a truss through which wind can flow. Any twist in the bridge produced vortices or regions of low pressure in specific places, which served to amplify the motion. When the bridge reached its original position, its momentum caused it to twist in the opposite direction so that the wind could catch it and keep twisting it. Aeroelastic flutter is the technical term for this occurrence. The same causes cause a strap or piece of paper to vibrate in the wind. Because the bridge's naturally unstable aerodynamic shape causes periodic forces to be self-induced, resonance from vortex shedding's mechanism is completely different from this one. The suspension cables underwent too much stress as a result of this torsional flutter, and the bridge collapsed.