Wednesday, December 17, 2008

The Physics behind Famous Bridge Collapses

The Physics behind Famous Bridge Collapses:

The history of bridge construction, both successful and unsuccessful, dates back thousands of years. In fact, both the Greek and Roman empires contributed greatly to the engineering of bridges and support systems. The people of this time not only guided us to understand the necessary materials for bridges, but more importantly the physics needed to keep a bridge up and sturdy. Since the time of the Greeks and Romans, many bridges have been built and many have fallen. However, only the spectacular and deadly bridge collapses are the ones we remember and the ones in which we point fingers. Just who is to blame for the collapse of the Tacoma Narrows, Schoharie Creek and Sliver Bridges, just to name a few?

In order to understand the engineering faults leading to bridge failure we must understand the forces (stresses) acting upon a bridge every time a car passes over. There are three main stresses in particular and six bridge designs that attempt to dissipate such stresses. These stresses include a tensile stress, better known as tension, a compressive stress and a shear stress.

Each stress is self explanatory; the tensile stress has a force at each end moving in opposite directions, thus pulling each way from the center creating tension.

The compressive stress consists of forces at each end of an object pushing toward the center creating compression.

Finally, the shear stress is forces acting in opposite directions along a parallel plane. The most common example of shear stress would be when earth’s plates move across one another creating an earthquake.

As the diagram above demonstrates, the existence of these stresses may wear on an object to the point of collapse. Here is where the job of the engineer becomes vital; he/she must create a support system which distributes, or spreads the forces along a wider area so that anticipated force/ stresses do not cause a collapse of the structure.
There are six designs which have been used to distribute loads on bridges historically: the beam, the cantilever, the arch, the suspension, the cable-strayed and the truss bridge. For the sake of discussing historical mishaps, we will only explore those designs that have specifically failed and why.

Tacoma Narrows Bridge Collapse

Perhaps the most memorable bridge collapse was the Tacoma Narrows Bridge on November 7, 1940. The bridge had only been operating for four months and even before its collapse was famous for its swaying and rippling. In fact the bridge obtained the nickname “Galloping Gertie” for its consistent galloping movement when weather was bad.

The Tacoma Narrows Bridge was one of three famous suspension bridges operating around that time. The others were the Golden Gate Bridge in San Francisco and New York’s George Washington Bridge, both of whom were larger than the Tacoma Narrows. The purpose of the suspension bridge was to carry rather large amounts of weight over large spans. The reason suspension bridges could carry such large loads was that it distributed the weight through several tension cables into the ground at several anchorage points.

As the diagram above shows, the cables were anchored at each end, and supported in the middle by several raised towers. This allowed for the tension in the cables due to the weight of the cars and road to be conveyed into the ground. The reason the Tacoma Narrows Bridge did not last is that engineers never considered aerodynamics and wind forces, which added both a compression and tension force to the bridge. Every time the wind blew at strong gusts the tension force of the cables would be overcome by compression, then back to tension causing galloping oscillations of the deck or road. It didn’t help that the engineers built the bridge so light either. Without the weight of the bridge to dapper the oscillations they could be very intense. The material holding the deck during these vigorous movements finally tensed to a point of collapse and the bridge went down.

The video link below shows the Tacoma Narrows Bridge as it “gallops” and eventually collapses:

Mianus Bridge Collapse

As you can see there is another video within this link lower on the page, describing the Mianus Bridge collapse of 1983. This bridge used a beam design with pins and hangars to restrict shearing. The beam design is different from other designs in that it endures all three stresses in a major way. As you see below the compression and tension stresses work along the center of each vertical post supporting the horizontal deck. When the stresses work their way to these posts the natural movement is for the posts to shear away from the horizontal deck.

The pin and hanger design below shows this point where two separate sections of the bridge are bolted so that if shearing in one direction takes place the other bolt will hold against the movement. The problem with the Mianus Bridge was that a lack of maintenance and repair allowed for one hanger to rust through forcing all stress on one side. This one side eventually gave out and the bridge collapsed killing 4 people.

I-35 W Minneapolis Bridge Collapse

The final bridge I will discuss was the most recent notable collapse of an American bridge. The I-35 bridge collapse in Minneapolis, Minnesota was a steel deck truss bridge which eroded due to corrosive salt chemicals. In almost all cases, bridges hold up to these chemical reactions, at least those built out of concrete. According to bridge engineer expert William Miller "concrete is a very forgiving material, and so it can stand up to a lot of cracking and wear. Steel on the other hand, cannot." . The steel reacted chemically with both the pavement and salt to erode the deck and eventually collapse. Since the bridge was a truss bridge there was nothing for the deck to fall upon other than the water below. This is because truss bridges use triangular looking shapes of steel supports above the bridge to distribute loads to the anchors on each side of the bridge. If the deck gives out in any way, the steel beams will not support the uneven loads, hence the collapse of this bridge. Below is a simple model of a truss bridge.

What is most interesting about the I-35 bridge is that it was deemed “structurally deficient” in 1990, yet was never scheduled to be repaired. It was however scheduled to be replaced in 2020, 13 deaths later!

Additional Famous Bridge Collapses in History

December 1876 Ashtabula River Bridge- 92 people killed (Truss)

November 1940 Tacoma Narrows Bridge- 0 people killed (Suspension)

December 1967 Silver Bridge- 46 people killed (Suspension)

June 1983 Mianus Bridge- 4 people killed

April 1987 Schoharie Creek Thruway Bridge- 10 people killed

Frommer, F. J. (2008). NTSB: Design Errors Factor in 2007 Bridge Collapse. Retrieved December 01, 2008 from Time, Inc., Time:​time/​business/​article/​0,8599,1858912,00.html.

Giancoli, D. C. (Ed.). (2005). Physics Principles with Applications Sixth Edition. Upper Saddle River, New Jersey 07458: Pearson Education, Inc.

Lemonick, M. D. (2007). Why Do Bridges Fall? Retrieved December 03, 2008 from Time, Inc., Time:​time/​nation/​article/​0,8599,1649423,00.html?cnn=yes.

Kwong, N. Physics of Bridges. Retrieved December 01, 2008 from None, Physics.ubc:​outreach/​phys420/​p420_04/​norman/​physics_of_bridges.ppt..

Nansi, B. (2005). Famous Bridge Collapses. Retrieved December 01, 2008 from Economic Research India Ltd., Project Monitor:​detailnews.asp?newsid=8976.

Engineering Disasters- Bridges. Retrieved December 01, 2008 from A&E Television Networks,​

Bridge Type- Truss. Retrieved December 03, 2008 from Matsuo Bridge Co., Ltd. , Matsuo Bridge:​english/​bridges/​basics/​truss.shtm.
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