THE COLLAPSE OF THE TACOMA BRIDGE: The physics behind an engineering disaster
The collapse of Tacoma Narrows Bridge, a suspension bridge spanning the Tacoma Narrows Strait in Washington, is considered one of the most catastrophic engineering failures in history. The bridge was completed and opened to traffic on July 1st 1940, and collapsed after only four months on November 7th. The bridge experienced violent motion, oscillating vertically and twisting, for hours before crashing into the river below. Subsequent investigations showed that the design of the bridge had some major flaws which led to the buildup of “aerostatic flutter”. This dramatic disaster attracted wide attention at the time and has been one of the most interesting engineering case studies since.
The main considerations in the design of a bridge is its ability to counteract the force of gravity pulling it downwards while holding up all the vehicles and people passing over it, and how this can be done economically. Overtime this led to the development of the suspension bridge. A suspension bridge is essentially just a deck, two towers, two main cables, and connector rods which suspend the deck. This structure allows these bridges to span long distances with only two towers which reduces the amount of material required significantly and therefore costs while creating an elegant and graceful appearance. However, the lack of material also reduces stiffness and stability in the structure. With reduced rigidity, the effect of natural forces, like the wind, on the aerodynamics of the bridge now came into play, whereas before due to bridges’ stiffness the only force that had to be countered was gravity. The failure to recognise the effect of natural forces on the bridge was a fatal mistake and was the root cause in the collapse of the Tacoma
While designing the Tacoma bridge, in an effort to reduce costs even further, engineer Leon Moussaieff pushed the limits by making some critical changes in the design of the standard suspension bridge. He replaced the trusses (these are beneath the main deck and help to stiffen the deck which reduces the tendency of the roadway to sway and ripple) with 8-foot-high plate girders; he also exceeded the ratios of length and depth of the main deck. All these changes reduced costs to 7 million from the original 11 million, while producing an even slimmer and slender design. However, this meant the bridge was much more flexible and had a significantly lower resistance to bending and twisting — torsional forces.
During its construction, even in moderately windy conditions the flexibility in the bridge caused the deck to move up and down significantly. This prompted construction workers to nickname it “Galloping Gertie”. Alarmed by this undulating motion, engineers conducted experiments in wind tunnels and put several measures in place to reduce motion, but even these were not enough to counter the forces it faced on the day it collapsed.
On the morning of November 7, winds travelling at 40mph colliding with the bridge, developed a vertical motion in the bridge, although this was of a type of motion that had been previously observed, this time it was at a larger-than-usual amplitude. The excessive vertical motion of the bridge, however, wasn’t the main cause for the collapse. The bridge collapsed primarily due to a complex mechanism called aerostatic flutter; this is defined as “an unstable, self-excited structural oscillation where energy is extracted from the airstream by the motion of the structure”. Essentially, aerostatic flutter is a self-induced vibration within a structure, where the instability created can develop into very large and violent vibrations — which is what happened with the Tacoma bridge. The development of aerostatic flutter in the structure was due to a change from vertical to torsional movement. Multiple factors played a role in the sudden change in motion, which led to the bridges’ inevitable collapse. A crucial event, which directly led to torsional vibration, was the loosening of the north cable. This caused one of the main cables to become short on one side and long on the other; these unequal segments actually allowed the structure to twist which allowed the physical change from vertical to torsional movement.
Secondly, a phenomenon called “vortex shedding” occurred. A truss in the bridges structure allows the wind to flow through the bridge, however the Tacoma bridge was made with large steel plates a shown in the diagram below.
This led to unusual interactions with the wind. As the wind, which was travelling at a speed of 40mph hit the bridge it was forced to separate and move above and below the structure. Due to the flexibility of the bridge, this caused a little bit of twisting. This little bit of twisting led to a greater separation in the wind flow, which resulted in a vortex — “a swirling wind force”. This further lifted and twisted the bridge and twisted the bridge as shown in the diagram below:
The deck had a natural tendency to return to its previous position, however as it returned its speed and direction matched the force created by vortex shedding by the wind which further reinforced its motion. This instability caused the bridge to go straight into “torsional flutter”. This torque from the torsional movement acted on the bridge in such a way that it was always amplifying the current motion of that section of the bridge and causing the magnitudes of the oscillations to increase in size. In other words, the forces acting on the bridge were no longer caused by the wind, it was by the bridge decks own motion. This is referred to as “self-excited” motion; the bridge was inducing its own energy. The torsional flutter, as it increased, created too much stress on the cables and caused the bridge to collapse.
Currently, the remains of the Tacoma bridge form one of the largest man-made reefs at the bottom of the Puget Sound. A replacement bridge was built, that took into account all the lessons learnt from the collapse of this bridge. Although a catastrophic event, it has advanced our scientific methods greatly. Increasing research into bridge aerodynamics has allowed us to have a greater appreciation for the effects of natural forces on bridges which has resulted in the development of stronger and better bridges.
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