Bridges

SUMMARY: Bridges are subject to various complex forces, the distribution of which are determined by their structures.

Bridges are structures built to span a gap or a physical obstacle such as a road or body of water. The many forces acting on bridges make different designs variously suited to different conditions, uses, and building materials. The earliest bridges made by humans emulated naturally occurring bridges, like fallen trees that spanned rivers, and were improved upon by lashing logs into place, cutting planks to form a more even travel surface, and eventually building bridges out of stone. The mathematics of bridges was not well understood, and most improvements were achieved through trial and error. One of the most significant improvements was the advent of the arch bridge, introduced in Greece in 1300 BCE and used extensively by the Romans. Arch bridges use arch-shaped abutments, sometimes in a series, to distribute much of the bridge’s load into horizontal thrust the abutments can restrain—not only a major improvement over earlier designs, but a design well suited to the simple building materials of the time, as stone is strong in compression but weakly resists tension. As applied mathematics became more sophisticated, bridges were often objects of study.

Most bridges are built for functional purposes, but some of them are works of art, like the Golden Gate Bridge or the London Bridge. Mathematicians have long worked on various aspects related to the design and construction of bridges. For instance, Charles Hutton worked on equilibrium principles and Claude-Louis Navier developed a theory for suspension bridges. Applied mathematician P. Joseph McKenna analyzed bridge oscillations and differential equation models of the collapse of the Tacoma Narrows Bridge. The configuration of bridges in the East Prussian city of Königsberg (modern-day Kaliningrad, Russia) served as the subject of mathematical study for Leonhard Euler and is sometimes noted as the beginning of graph theory. The mathematician posed the problem of the seven bridges of Königsberg in a 1736 paper. The town of Königsberg contained an island with two branches of a river flowing around it. There were seven bridges spanning the river, and the question was whether a person could start at some point and follow a path that would cross each bridge exactly once and return to the starting point. Euler proved that there was no such path.

Types of Bridges

There are various types of bridges. Beam bridges consist of a horizontal beam with two supports called “piers” at the ends. Arch bridges are one of the oldest types of bridges and distribute the load of the bridge outward along the curve of the arch to the supports at the ends. Suspension bridges are light and strong and can span longer distances than any other type of bridge, but they are expensive to build. Large bundles of cables suspend the roadway from one end of the bridge to the other. Early Asian suspension bridges were suspended with bamboo cables. Cable-stayed bridges look like suspension bridges, but their cables are secured to towers that bear the load of the bridge. They cost less and their construction is faster than suspension bridges, since they need fewer cables and builders can use pre-cast concrete sections. Movable bridges can be occasionally levered for making way for ships or other kinds of traffic. Double-decked bridges have two levels and are used for multiple forms of traffic—subway, pedestrian, automobile, or bicycle.

Famous Bridges

Millau Bridge, France, is 1125 feet high—higher than the Eiffel Tower. Hangzhou Bay Bridge, China, is 22 miles long. The Rolling Bridge, England, is 39 feet long and rolls itself up until the two ends meet, using a hydraulic press. Tower Bridge, England, is a landmark of London and opens in the center, allowing ships to sail through. Ponte Vecchio, Italy, is considered by some to be the oldest stone arch bridge in Europe. Lake Pontchartrain Causeway, Louisiana, is 24 miles long. Vasco da Gama Bridge, Portugal, is 10.5 miles long. Confederation Bridge, Canada, is 8 miles long. Golden Gate Bridge, California, is one of the most famous symbols of San Francisco. Evergreen Point Floating Bridge, Washington, is a 1.5-mile-long floating bridge.

Bridge Collapses

Even as designs and materials advanced and safety inspection standards improved over the years, notable bridge collapses occurred around the world. These incidents have had varying causes, from age and loss of structural integrity to natural disasters, changes in transportation means and volume, damaging impacts, and construction errors. Japan's wooden Eitaibashi Bridge collapsed in the early 1800s under the weight of too may people, resulting in the deaths of more than one thousand. A similar scenario led to the collapse of a suspension bridge in Great Yarmouth, England, in the mid-1800s, and subsequently around seventy-nine deaths. Examples of natural causes included the 1850 collapse of France's Angers Bridge and the 1940 collapse of Washington's Tacoma Narrows Bridge due to high winds as well as the collapse of a railway bridge in 1953. The latter, which took place in New Zealand, involved a passenger train attempting to cross the bridge after a volcanic mudslide had recently compromised a portion of the bridge. While no people died in the case of the Tacoma Narrows Bridge collapse, those in France and New Zealand killed hundreds. In 1967, the failure, following investigation, of the Point Pleasant Bridge suspended over the Ohio River because of a weakness in an eyebar chain resulted in the deaths of forty-six people. In the twenty-first century, another major US bridge collapse drew media attention. With many pointing to a comparable disaster that had occurred in 1980 in which a significant portion of Florida's Sunshine Skyway bridge fell into Tampa Bay following a ship collision, killing thirty-five, in 2024 a cargo ship struck Maryland's Francis Scott Key Bridge, causing it to collapse. Though a distress signal meant that no traffic had been on the bridge at the time, it was believed that six construction crew members fell and died.

Bibliography

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