The Tacoma Narrows Bridge, which collapsed on November 7, 1940, in winds of only 40mph, gained the attention of the entire scientific community. The stability of a suspension bridge is paramount; consequently engineers must scrutinize every aspect of a bridge design. One of the most important considerations in bridge design is aerodynamic force, which, even when very small, can have great effects on a suspended structure. This article presents some of the design characteristics of bridges, a short history of the Tacoma Narrows, and explores what can be done in bridge design to prevent unnecessary undulation, damage, and total collapse.
There are 144 suspension bridges in the United States. When designing suspension bridges, engineers face many natural problems. The wind does not initially seem able to move structures as massive as bridges; however, the summation of small forces that the wind exerts can result in displacements by inducing resonant effects in the span. Suspension bridge engineers need to take these effects into account because the added effects of wind shear can result in disaster.
At a basic level, all suspension bridges are similar. They are usually composed of two or three towers built on solid ground at each end of the span and two main cables attached to these towers. From these large cables hang many smaller cables, where the roadway or deck rests. However, bridges are not limited to these components. Suspension bridges need stiffening to assist with efficient weight distribution. If the roadway were simply hanging from the main cables a large, heavy-loaded truck passing over the bridge would exert all its weight on the cables immediately around it. This would compromise the integrity of the structure, placing too much weight on a single hanging cable, and stressing the roadway. This CAN result in cracking and bending. However, regardless of the location of the load on the bridge, stiffening prevents the bridge from bending and allows for better distribution of weight over more cables and a larger section of the roadway. At the end of each main cable is a huge concrete structure, called a "cable stay." The cable stay is firmly implanted into the ground, where each cable is securely fastened into the concrete, and can then transfer the huge load of the bridge into the ground. Thus, the part of the bridge that now bears the weight is shifted from the roadway and hanging cables to the main towers and cable stays.
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There are two primary design elements that are used to stiffen the bridges: plate girders and trusses. Plate girders line the bridge like a wall, giving it lateral stiffness. They are essentially large, flat pieces of steel that effectively "box" the bridge span, adding stiffness to the roadway. Two positive characteristics of plate girders are cost effectiveness and ease of maintenance. They are effective in the displacing of vertical movements, but do not resist the undulating horizontal movements efficiently. Additionally, plate girders do not allow air to flow through the bridge. A bridge with plate girders is simply a big wall hanging in the air, and when air is forced up against the sides of the bridge the air starts swirling over and under the structure, exerting forces on the top and bottom of the span. This causes the bridge to roll and twist. The wakes that form when the air swirls around the bridge are called vortices and are periodic in nature. The repeated force of the wind swirling around the bridge deck can be compared to someone pushing a child on a swing, where you repeatedly exert a small force on the child, but after a few cycles this small force can have a large effect on the motion of the person.
Trusses consist of metal beams arranged in a series of triangular patterns pointing up and down along the sides of and under the roadway. An increased complexity of trusses leads to an increase in design costs and an increase in the difficulty in terms of installation. Trusses are the stronger of the two designs; this is because trusses are attached at several angles, instead of simply being a single, large sheet like a girder. Trusses provide support for the span throughout a larger range of motions, ultimately offering greater stability than plate girders.
Another factor that bridge designers have to deal with when building the bridge is the length-to-depth ratio. Engineers have settled on the ratio 150 feet long to 1 foot deep in order for a bridge to be safe. An example of a bridge with a low length-to-depth ratio is the Williamsburg Bridge in New York, with a ratio of just 40:1. A huge weight and large stiffening trusses also aid this bridge. Even in large storms with high winds, this structure has never been affected with any undulating motion of its deck. These effects still have to be taken into account. On the other extreme, we have the Tacoma Narrows Bridge, which had a ratio of 350:1. This bridge, with its flat plate girders, low weight, and high length-to-depth ratio, was in danger of succumbing to wind shears. The engineers did not foresee the severity of this potential problem, which became apparent when the bridge swayed violently in even small breezes.
Design and History of the Tacoma Narrows
The Tacoma Narrows Bridge, which is one of the most recognizable names in bridges, along with the Golden Gate in San Francisco, met its fate due to several serious design flaws. In the four months that the bridge stood, it became a tourist attraction. People came from all around the country to drive across the undulating span. The bridge became affectionately known as "Galloping Gertie" soon after its opening.
The Tacoma Narrows was a disaster from the start; it had a main span of 2,800 feet, and was only 39 feet wide. This made the bridge extremely light, around 5,700 pounds per linear foot. Other suspension bridges of the time were over 30,000 pounds per linear foot. With a large mass, a bridge has a very high resonant frequency, and this takes a very strong wind to produce vortices with this frequency. Also, the extra mass contributes to dampen the wind's motion, since there is simply more weight to push around. However, what eventually led to the bridge's demise was a combination of low weight, large length-to-depth ratio, and poorly designed girders that did not take into account the effects that the wind can have on such a structure. On Nov 7, 1940, the bridge finally came to a crashing halt, its main span collapsing into the river below, in winds of only 40 mph. The Tacoma Narrows Bridge was eventually reconstructed, and was greatly over-engineered this time. Instead of the plate girders, the designers used trusses, and at 33 feet deep, the length-to-depth ratio decreased to a very safe 85:1. The span was also widened by 20 feet, wind grates were installed between the lanes, and oil-filled hydraulic dampening mechanisms were installed at the towers. It has since never had any problems with the wind.
By applying engineering methods such as plate girders and trusses, engineers are now able to build larger and more stable suspension bridges. As technology advances so will the design of bridges. The enhancement of bridge design will ensure that collapses, such as that of the Tacoma Narrows Bridge, will remain an event of the past.
-  Y. Billah and R. Scanlan. 1991. "Resonance and the Tacoma Narrows Bridge Failure." American Journal of Physics, vol. 59, no.2 (February), pp. 118-123.
-  Editorial Staff. 1990. "Professors Spread the Truth About Gertie", Civil Engineering (December), pp. 19-20.
-  I. Peterson. 1990. "Rock and Roll Bridge", Science New, vol. 137 (November), pp. 344-346.
-  Doug Smith. "Tacoma Narrows Bridge Failure". 29 March 1974. <http://www. civeng.Carleton.ca/Exhibits/Tacoma Narrows/Dsmith/photos.html>.