Failure in engineering structures and parts is largely due to the design level. This can arise as a result of the failure to understand the relationship of force between the system and its components and the environment in which it is to be implemented. The climate here applies to other components or structures to which it is attached, or also to the geographical setting of prevailing weather conditions. Failure to understand these requirements contributes to high-level fatal disasters such as those encountered in the Tacoma Narrows Bridge. The main span of Tacoma Narrows Bridge collapsed as a result of aeroelastic flutter caused by wind at 42 mph. in relation to vibrations principles, the occurrence was an equivalent of an elementary forced resonance, with the wind providing an external periodic frequency equal to the natural structural frequency of the bridge.
Every system has a natural fundamental vibration frequency.If forces are exerted on that system at the right frequency and phase, then sympathetic vibrations can be excited.Oscillating forces at the right frequency and phase can cause sympathetic vibrations of catastrophic proportions.The forces applied to the bridge by the wind were applied at a natural frequency of the bridge.Thus, the amplitude of the bridge’s oscillations increased until the steel and concrete could no longer stand the stress.
However, the resonant frequency could only cause such damage if certain considerations were not put in place during design and hence the construction stage. It is very improbable that resonance with alternating vortices plays an important role in the oscillations of suspension bridges. First, it was found that there is no sharp correlation between wind velocity and oscillation frequency such as is required in case of resonance with vortices whose frequency depends on the wind velocity.
Secondly, there is no evidence for the formation of alternating vortices at a cross-section similar to that used in the Tacoma Bridge, at least as long as the structure is not oscillating. It seems that it is correct to say that the vortex formation and frequency are determined by the oscillation of the structure than that the oscillatory motion is induced by the vortex formation. (Ammann, O .H., T.Von Karman, and G .B.Woodruff .“The Failure of the Tacoma Narrows Bridge.” Report to the Federal Works Agency.Washington, DC (March 28, 1941)).
The design error occurred in the specification in general proportions of the bridge and the type of stiffening girders and floor. The ratio of the width of the bridge to the length of the main span was so much smaller and the vertical stiffness was so much less than those of standard specifications. The bridge was a long, narrow, shallow, and therefore a very flexible structure standing in a wind ridden valley. “Its stiffening support was a solid girder, which, combined with a solid floor, produced a cross-section peculiarly vulnerable to aerodynamic effects.” Source: Gies, Joseph. Bridges and Men.Garden City, NY: Doubleday, 1963. These led to a reduction in the capacity of load that the bridge could carry and also lowered the aerodynamic resistance of the bridge span to a value that could not resist the effect of resonant frequency balance brought by the wind.
The magnitude of the oscillations depends on the structure shape, natural frequency, and damping. While all winds have fluctuations in their wind speeds, these tend to be random in phase and variable in frequency. The forces exerted on the bridge are up-and-down forces, transverse to the direction of the wind.The wind was blowing across the bridge from one side to the other, and the forces on the bridge were acting up and down.
An explanation for these oscillating vertical forces lies in the concept of vortex shedding.When a wind that exceeds a minimum speed blows around any object, vortices will be formed on the back side of that object. The oscillations are caused by the periodic shedding of vortices on the leeward side of the structure, a vortex being shed first from the upper section and then the lower section.
As the wind increases in speed, the vortices form on alternate sides of the down-wind side of the object, break loose, and flow downstream.At the time a vortex breaks loose from the backside of the object, a transverse force is exerted on the object.The frequency of these fluctuating eddies is about 20 percent of the ratio of the velocity of the wind to the width of the object.These lateral forces can be as much as twice as large as the drag forces. The design did not provide for structures such as holes and curved outriggers for distributing the wind force.
To conclude, the collapse of the Tacoma Narrows Bridge was basically brought by an engineering design error that was further implemented during bridge construction.The original design called for stiffening the suspended structure with trusses. However, a cheaper stiffening was adopted using 8-foot tall girders running the length of the bridge on each side rendering the stiffening inadequate.The collapse theory of aerodynamic stability of suspension bridges had not yet been adequately worked out, and wind-tunnel facilities were not installed for testing. Reliability and catastrophic stability of the bridge were therefore questionable.It, therefore, implies that the dimensions of the bridge rendered it unable to withstand and dissipate the drag forces of the wind, rendering the bridge flexible and subject to damage.
Blillah, K.; R. Scanlan (1991). “Resonance, Tacoma Narrows Bridge Failure, and Undergraduate Physics Textbooks”. American Journal of Physics. 59 (2): 118-124.
Holstine, Craig E. (2005). Spanning Washington: historic highway bridges of the Evergreen State. Washington University Press. pp. 61-62.
Schagler, N. (1995). Failed Technology: True Stories of Technological Disasters. New York: UXL. ISBN 978-0-8103-9796-5.