Introduction

     The Tacoma Narrows Bridge, located in the Puget Sound was completed on July 1st, 1940. At the time of completion it was the third longest suspension span bridge in the world. The first plans for the bridge were created in 1889 by The Northern Pacific Railway, for a trestle bridge, however the plan did not come to fruition (1). In 1923, the Washington state government began funding and planning for the bridge to finally be built. Joseph B. Strauss (Chief Engineer of the Golden Gate Bridge) and David B. Steinman were chosen to design the bridge (2).

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     The Tacoma Narrows Bridge was given the nickname "Galloping Gertie" by construction workers due to the way the bridge would sway back and forth during sustained winds (3). 

     The bridge lasted only about 4 months, until it collapsed on November 7th, 1940. The day of the collapse there was sustained winds of 35mph. These winds caused the suspension bridge to oscillate back and forth, snapping each one of the steel support lines one by one. There was no direct human error involved, it was more of a lack of understanding in the field of harmonics and oscillations. Fortunately, there were no human fatalities (1).

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Engineering Perspective

     In the simple free body diagram drawn below, it can be shown how the wind creates an oscillation of movement within the bridge.

     The collapse of the Tacoma Narrows Bridge has been one of the most studied bridge collapses in history, serving as a teaching point for oscillationsLinks to an external site. and resonance frequenciesLinks to an external site. within structures. The design of the bridge allowed for oscillations to build within the structure due to the force of the wind. This is turn created a vibrational force within the structure, eventually reaching resonance frequency. Ultimately, it was a vibrational force that caused the demise of the Tacoma Narrows Bridge. A sustained wind of 35mph was deemed to be the root cause of these forces. Shown below is a harmonic equation used for analysis of structures (4).

When w=k, the problem

 x''(t) + k2 x(t) = cos(k t)

has the special solution x(t) = t sin(k t)/(2k).

     Before the collapse of the Tacoma Narrows Bridge, there was not a whole lot of vibrational force analysis within structures. It was a known topic, however the applications of it within design were not well defined. As stated earlier, this disaster became a famous case analysis for this exact problem. With the right equations laid out, it is easy to see how the oscillation started, grew, and eventually caused a failure within the structure. During the construction of the bridge, designers and workers noticed the strange sway in the wind and tried to add preventative measures. Concrete supported, steel reinforcement cables were installed on either end, however those quickly failed (1).

Lessons Learned

       The most important lesson learned after the Tacoma Narrows Bridge collapse was that odd combinations of natural factors can result in resonance frequencies within structures. This specific disaster has been one of the most common case studies in structural analysis, specifically involving oscillations and resonance frequencies. All modern designs now include resonance frequency calculations, from both natural and manmade causes.

     The biggest lesson that I took away from this disaster is that no matter how obscure a disaster sounds, you must plan for it. Brainstorming odd scenarios and planning for them, may be what sets your design apart from the others. I also learned that the most notorious disasters all boil down to the impacts of the fundamental laws of physics. When looking at any disaster, the root cause can be proven with physics and a solution can be made with physics.       

     The design process for suspension bridges was forever changed after this incident. A newer high strength tension cable system was adopted, transferring loads in a way that prevents oscillations.

Resources

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Resource #7Links to an external site.