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Bridge

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A bridge is a structure built to span physical obstacles such as rivers, lakes, roads, railways, ravines, or other geographic or artificial barriers. Its primary purpose is to provide passage over the obstacle, facilitating the movement of automobiles, trains, and pedestrians, but may also accommodate pipelines, utility lines, buildings, wildlife crossings, and even canals.

Bridges are classified into several structural types based on their design and construction. The principal styles include: arch, truss, beam, cantilever, suspension, and cable-stayed. Less common forms include: moveable bridges, double deck bridges, pontoon bridges, and military bridges. Bridges can also be categorized by their materials, which include wood, brick, stone, iron, steel, and concrete.

The history of bridge building reflects the evolution of engineering knowledge, materials, and construction techniques across different civilizations and eras. The greatest bridge builders of antiquity were the ancient Romans, who built numerous semicircular-arch bridges. The Renaissance in 1500s Europe brought a new emphasis on science and engineering leading to stronger bridges with longer spans. With the advent of the Industrial Revolution, iron became an important construction material for bridges. The abundance of inexpensive lumber in Canada and the United States caused timber bridges to be the most common type of bridge in those countries from the late 1700s to the late 1800s. In the late 1800s, concrete replaced stone and masonry as the primary material for bridge foundations. Steel became a common building material for bridges in the late 1800s, leading to suspension bridges and cable-stayed bridges that spanned long distances.

The designer of a bridge must address a wide range of functional, structural, environmental, and aesthetic requirements to ensure safety, efficiency, and durability. Fundamental requirements include structural strength, stability, and the capacity to provide safe passage for users. In addition to these core functions, designers must consider factors such as cost, aesthetics, expected lifespan, the time frame for construction, client or governmental preferences, and the experience and capabilities of the construction team. To address these complex demands, engineers employ methodologies such as Limit State Design, which ensures that bridges remain functional under both normal and extreme conditions. The finite element analysis analysis method enables detailed modeling of stresses and deformations within the structure.

History

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Antiquity

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A stone arch bridge passing over a river valley
The Pont du Gard aqueduct in France was built by the Roman Empire c. 40–60 AD, and is still standing.[1]

The earliest forms of bridges were simple structures used to cross swamps and creeks, consisting of stepping stones, wooden boardwalks, or logs.[2][a] Crude coffer dams and pilings – which are critical elements of bridge construction – were used in Switzerland in 4,000 BC to support houses built over water.[4]

Several corbel arch bridges were built c. 13th century BC by the Mycenaean Greece culture, including the Arkadiko Bridge, which is one of the oldest bridges still in use.[5] In the 7th century BC, the Neo-Assyrian Empire constructed stone aqueducts to carry the waters of one canal to the city.[6] One example across a small valley at Jerwan was 280 meters (920 ft) long and 20 meters (66 ft) wide, and utilized five corbelled arches.[6] In Babylonia in 626 BC, a bridge across the Euphrates was built with an estimated length of 120 to 200 meters (390 to 660 ft).[6]

In India, the Arthashastra treatise by Kautilya mentions the construction of dams and bridges.[7] Ancient China has a long history of bridge construction, including cantilever bridges[8] and large timber bridges, built during the Warring States period.[9]

The greatest bridge builders of antiquity were the ancient Romans.[10] The Romans built semicircular arch bridges and aqueducts – some of which still stand today – that could stand in conditions that would damage or destroy earlier designs.[10] An example is the Alcántara Bridge, built over the river Tagus, in Spain.[11] The Romans also used cement as a construction material, which could be poured into forms, and thus avoided the problem of variable strength found in natural stone. One type of cement, known as pozzolana, consisted of water, lime, sand, and volcanic rock.[12] The Roman's enormous Trajan's Bridge (105 AD) featured open-spandrel segmental arches in wooden construction.[13]

Middle Ages

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A bridge with buildings atop it, passing over a river
During the Middle Ages, bridge builders began employing flatter segmental arches – such as those seen in the Ponte Vecchio above – which allowed for longer spans compared to the previously used semicircular arches.[14]

The oldest surviving stone bridge in China is the Anji Bridge, built from 595 to 605 AD during the Sui dynasty. This bridge is also historically significant as it is the world's oldest open-spandrel stone segmental arch bridge.[15]

Rope bridges, a simple type of suspension bridge, were used by the Inca civilization in the Andes mountains of South America, prior to European colonization in the 16th century.[16] The Ashanti built bridges over streams and rivers.[17] They were constructed by pounding four large forked tree trunks into the stream bed, placing beams along these forked pillars, then positioning cross-beams that were finally covered with four to six inches of dirt.[18]

In Medieval Europe, bridge design capabilities declined after the fall of Rome, but revived in the High Middle Ages in France, England, and Italy with the construction of major bridges inspired by religious influences.[19] These included the Pont d'Avignon, bridges of the Durance river, the Old London Bridge, and the Ponte Vecchio in Florence.[20]

Modern era

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A wooden bridge, covered with a roof, passing over a river
The superstructure of the West Montrose Covered Bridge is made of wood.[21]

The Renaissance in 1500s Europe brought a new emphasis on science and engineering.[22] Figures such as Galileo Galilei, Fausto Veranzio, and Andrea Palladio (author of I quattro libri dell'architettura) wrote treatises that applied a rigorous, analytic approach to architecture and building.[22] New breakthroughs in bridge design and construction produced bridges such as Florence's Ponte Santa Trinita, Rialto Bridge in Venice, and Paris’ Pont Neuf.[23] A number of bridges, both for military and commercial purposes, were constructed in India by the Mughal administration in India.[24]

In the late 1700s, the design of arch bridges was revolutionized in Europe by Jean-Rodolphe Perronet and John Rennie who designed arches that were flatter than semi-circular Roman arches.[25] These flatter arches enabled longer spans, fewer piers, and required less material.[25] These designs were used for bridges such as Pont de la Concorde and New London Bridge.[25]

With the advent of the Industrial Revolution,[26] cast iron became an important construction material for bridges. Although cast iron was strong under compression, it was brittle, so it was supplanted by wrought iron – which was more ductile and better under tension.[27] An early iron bridge was built in Shropshire, England crossing the river Severn.[28]

The abundance of inexpensive lumber in Canada and the United States caused timber bridges to be the most common type of bridge in those countries from the late 1700s to the late 1800s.[29] Many of these timber bridges were covered bridges.[29] Rail bridges used timber to obtain long spans that utilized strong truss designs, and also tall trestle bridges that spanned deep ravines.[29]

A large suspension bridge, with large towers made of stone
The mass production of steel enabled the construction of large suspension bridges. The Brooklyn Bridge, built in the 1870s, was the first suspension bridge to use steel for its cables.[30]

The mass production of steel in the late 1800's provided a new material for bridges, enabling lighter, stronger truss bridges and cantilever bridges, and producing cables strong enough to make suspension bridges and cable-stayed bridges feasible.[31][b] Suspension bridges could span distances far longer than other bridge types – up to 2 kilometres (1.2 mi) – permitting transportation networks to cross deep waters that required ferries. The dynamic nature of suspension bridges requires special design considerations to safely carry rail traffic.[33]

Concrete – which was originally used within the Roman Empire – was improved with the invention of portland cement in the early 1800s, and replaced stone and masonry as the primary material for bridge foundations. When iron or steel are embedded in the concrete, as in reinforced concrete or prestressed concrete, it is a strong, inexpensive material that can be used for horizontal elements of beam bridges and box girder bridges.[34]

Straight, diagonal cables – known as "stays" – can be used to directly connect the bridge deck to bridge towers.[35] Stays were used as supplemental supports in some suspension bridges in the 19th century – including the Brooklyn Bridge.[36] Cable-stayed bridges – which used cable-stays as the exclusive means of support – became a popular bridge design following World War II.[37][c]

Etymology

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The Oxford English Dictionary traces the origin of the word bridge to the Old English word brycg, of Germanic origin.[39] There is a possibility that the word can be traced farther back to Proto-Indo-European *bʰrēw-.[40]

Types

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Uses

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A bridge carrying canal with water, passing over a valley
The Magdeburg Water Bridge in Germany carries boats across a valley.[41]
A bridge, topped with soil and vegetation, passing over a highway
This wildlife crossing bridge is in Israel.[42]

Bridges perform a wide variety of functions. Until the 19th century, the most common use of bridges was to carry pedestrians, horses, and horse drawn carriages.[43] Aqueducts were developed early in human history, and carried water to towns and cities.[44] Following the invention of railways, many rail bridges were built; in England, the number of bridges doubled during the railway-building boom in the mid 1800s.[43] In the 20th century, the growth of motorway networks required the construction of vast numbers of bridges.[45]

Canal bridges are used in a canal system to carry a boats across a valley or ravine.[46]

Conservationists use wildlife overpasses to reduce habitat fragmentation and animal-vehicle collisions.[47] The first wildlife crossings were built in the 1950s, and these types of bridges are now used worldwide to protect both large and small wildlife.[48]

Some bridges accommodate uses other than transportation. Many historical bridges supported buildings, such as shrines, factories, shops, restaurants, and houses. Notable examples were the Old London Bridge and Ponte Vecchio.[49] In the modern era, bridge-restaurants can be found at some highway rest areas; these support a restaurant or shops directly above the highway and are accessible to drivers moving in both directions.[50] An example is Will Rogers Archway over the Oklahoma Turnpike.[51] The Nový Most bridge in Bratislava features a restaurant set atop its single tower.[52]

Basic types

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A huge steel bridge passing over a wide body of water
Many bridges combine two or more kinds of structures. The Forth Bridge, shown in the foreground, uses both trusses (left) and cantilevers (right).[53]

Bridges can be categorized by their structure (arch, truss, beam, suspension, etc) and their materials (stone, wood, iron, steel, concrete, etc). For example, a bridge could be identified as a timber truss bridge, or a reinforced concrete beam bridge, or a stone arch bridge.[54]

The basic bridge structures are arch, truss, cantilever, suspension, cable-stayed, and beam.[55] The choice of bridge structure to use in a particular situation is based on many factors, including aesthetics, environment, cost, and use.[56]

Many bridges are composed of multiple structures, for example, some Roman aqueducts contain dozens of adjacent arches. Long causeways over large lakes may be composed of hundreds of individual beam structures. Some bridges combine two kinds of structures, for example, it is common for large suspension bridges, such as the Verrazzano-Narrows Bridge, to have beam or truss elements in the approaches; and some large cantilever bridges, such as the Forth Bridge, use a truss segment in the middle to connect cantilevers on either side.[57]

Arch bridge

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Arch bridges consist of a curved arch, under compression, which supports the deck either above or below the arch.[58] The shape of the arch can be a semicircle, elliptical, a pointed arch, or a segment of a circle.[59] When the arch is semicircular, as used in Roman bridges, the force of the arch is directed vertically downward to the foundation.[60] When the arch is elliptical or a circular segment, the force is directed diagonally, and abutments are often required.[61] Deck arch bridges hold the deck above the arch; tied-arch bridges suspend the deck below the arch; and through-arch bridges position the deck through the middle of the arch.[62]

Truss bridge

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Through truss
Deck truss

A truss bridge is composed of multiple, connected triangular elements.[63][d] The set of triangles form a rigid whole, which rests on the foundation at both ends, applying a vertical force downward.[63] The deck can be carried on top of the truss ("deck truss") or at the bottom of the truss ("through truss").[64] Through trusses are useful when more clearance under the bridge is required; deck trusses permit oversized loads and do not interfere with overhead objects, such as electrical lines.[64] The individual bars can be made of iron or wood, but most modern truss bridges are made of steel.[65] The horizontal bars along the top are usually in compression, and the horizontal bars along the bottom are usually in tension.[63] Other bars in the truss may be in tension or compression, depending on the particular layout of the triangles.[66] Trusses typically have a span-to-depth ratio (the width of a structure divided by its height) of about 10 to 16, compared to beam bridges which typically have a ratio of about 20 to 30.[67] Trusses tend to be relatively stiff, and are commonly used for rail bridges which are required to carry very heavy loads.[67] In the modern era, truss bridges are generally not cost-effective for medium- or long-span bridges.[68]

Cantilever bridge

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Two cantilevers extending from anchorages
Balanced cantilever bridge

Cantilever bridges consist of one or more trusses, each supported at only one end.[69] Modern cantilever bridges are generally built from steel.[70] In Asia, cantilever bridges made of large rocks or timber were used to span small obstacles.[71] In the 1880s, some early cantilever bridges were built from wrought iron.[69] A basic cantilever bridge has two cantilevers, anchored at each end of the span, extending toward the center, and meeting in the center.[69] Some cantilever bridges have a small truss in the center, connecting the two cantilevers where they meet.[72] A balanced cantilever bridge consists of two connected cantilevers extending outward in opposite directions from a single central support.[73] The term "cantilever construction" is a method of building a bridge superstructure, which can be utilized for several types of bridges: arch, cable-stayed, as well as cantilever bridges. In this technique, construction begins at a support (such as a pier, abutment, or tower) and extends outwards across the obstacle, with no support from below.[74]

Suspension bridge

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Suspension bridges consist of two or more large cables, passing over one or more towers. The deck is suspended from the cables by large wires called hangers.[75] The earliest suspension bridges were made of ropes or vines.[76] In the early 1800s, the first modern suspension bridges – such as the Jacob's Creek Bridge – were chain bridges that used iron bars rather than bundled wires for the main cable.[77] When steel wire became widely available, hundreds of wires were strung between the towers and bundled to form large cables.[78] Each cable can weigh hundreds of tons.[78] When the bridge crosses a river, stringing hundreds of wires across the large span is a complex process.[78] Steel wire cables enabled suspension bridges to achieve spans 2 km long.[79] The cable of the bridge is in tension, and the towers are in compression.[75] The cable of a suspension bridge assumes the shape of a catenary when initially suspended between the bridge towers; however, once the uniform load of the bridge deck is applied, the cable adopts a parabolic shape.[80] Shorter towers require a smaller sag in the cable, which increases the tension in the cable, and thus requires stronger towers and anchorages.[75]

Cable-stayed bridge

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Harp pattern, two towers
Fan pattern, single tower

Cable-stayed bridges are similar to suspension bridges, but the cables that support the deck connect directly to the towers.[81] Cable-stayed bridges offer some advantages over suspension bridges: anchorages are not needed, and constructing the deck can be readily accomplished by cantilevering outward from the towers.[81] The cables may be arranged in a fan pattern or a harp pattern.[82][e] Modern cable-stayed bridges became popular after WW II, when the design was used for many new bridges in Germany.[83] When evaluating the choice of suspension vs. cable-stayed structure for a given application, the suspension option generally uses more cable for a given span size, but provides a longer span (for comparable materials), and requires shorter towers (for a given span size).[84]

Beam bridge

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Beam bridges – including girder bridges – are simple structures consisting of one or more parallel, horizontal beams that span an obstacle. Beam bridges are the most common type of bridges for both railways and roadways.[85] Beam bridges are ideal for shorter spans (less than about 50 meters (160 ft)), but for longer spans, other structures, such as trusses, may be more efficient.[86] In many applications, beam bridges can be built rapidly and economically, because the individual beams can be produced offsite and transported to the bridge site.[85] Modern beam bridges are generally made of steel or reinforced concrete, although wood may be suitable for small beam bridges intended for light use.[85] Several different cross-sections may be utilized for beams, including I-beam (common for steel) or flat slabs (sometimes used with concrete).[85] Beams can traverse longer spans when they are designed as hollow box girders; bridges made of box girders are termed box girder bridges.[85] The vertical thickness of beam bridges is generally shallower than comparable deck truss bridges, permitting shorter and lower approach roads to cross an obstacle of a given height.[85] Several beam bridges can be chained together, with supports at each juncture, to form elevated highways or causeways.[85][f]

Other types

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Movable bridge

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A tall drawbridge, open, over a river
Tower Bridge in London is a moveable bridge of the bascule type.[88]

Moveable bridges are designed so that all or part of the bridge deck can be moved, usually to permit tall traffic – that would normally be obstructed by the bridge – to pass by.[89] Early moveable bridges include drawbridges that pivoted at one end, and required a large amount of work to raise; adding counterweights on the pivot side of the drawbridge – a bascule bridge – made raising and lowering easier and safer.[90] Swing bridges pivot horizontally around an anchor point on the bank of a canal, or sometimes from a pier in the middle of the water.[91] Lift bridges are raised vertically between two towers by cables passing over pulleys at the top of the towers.[92] In the modern era, designers sometimes create unusual moveable bridges with the intention of establishing signature bridges for a town or locality.[93] Examples include Puente de la Mujer swing bridge in Buenos Aires, Gateshead Millennium tilt bridge over the River Tyne, Hörn Bridge folding bridge in Germany, Erasmusbrug bascule in Rotterdam, and Limehouse Basin footbridge in London.[93]

Double-deck bridge

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A long, straight, flat bridge over a large body of water
The Padma Bridge in Bangladesh carries rail traffic on the lower deck and vehicular traffic on the upper deck.[94]

Double-deck bridges (also known as double-decked, or double-decker) carry two decks on top of each other. This technique may be used to increase the amount of traffic a bridge can carry, or to build in a location where space is limited.[95] Double-deck bridges permit two different kinds of traffic to be safely carried, by separating, for example, motor vehicles from pedestrians or railways.[95]

An early double-deck bridge was Niagara Falls Suspension Bridge, which carried rail on the upper deck, and carriages and pedestrians on the lower deck.[96] George Washington Bridge in New York carries 14 motor vehicle lanes (eight above, six below), and is the world's busiest bridge, carrying over 100 million vehicles annually.[97] Because of their ability to carry large amounts of motor vehicles, double-deck bridges are often found in large cities, such as Tsing Ma Bridge in Hong Kong,[98] San Francisco–Oakland Bay Bridge in California,[99] and Shimotsui-Seto Bridge in Japan.[100]

Long, multi-span bridge

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A large bridge, consisting of multiple tall sections, passing over a wide valley
The Millau Viaduct crosses the Tarn river valley in France.[101]

There are a variety of terms that describe long, multi-span bridges – such as raised bridge, viaduct, trestle, or causeway. The usage of the terms can overlap, but each has a specific focus.[102]

Viaducts (carrying vehicles) and aqueducts (carrying water) are bridges crossing a valley, supported by multiple arches or piers.[103] Romans built many aqueducts, some of which are still standing today.[104] Notable viaducts include Penponds Viaduct in England,[105] Garabit Viaduct in France,[106] Tunkhannock Viaduct in Pennsylvania,[107] and Millau Viaduct in France.[101]

A trestle is a bridge composed of a number of short spans supported by closely spaced supports, typically carrying a railway. A trestle is similar to a viaduct, but viaducts typically have taller piers and longer spans.[108]

A continuous truss bridge is a long, single truss that rests upon multiple supports, and experiences hogging stresses at the supports and sagging stresses between the supports.[109] A continuous truss bridge may use less material than a series of simple trusses because a continuous truss distributes live loads across all the spans (in contrast to a series of distinct trusses, where each truss must be capable of supporting the entire live load).[109][110]

A causeway is a raised road, usually built over a lake or other body of water.[111] Some causeways are bridges, such as the 38.4 km Lake Pontchartrain Causeway in Louisiana;[87] but many – such as the King Fahd Causeway in Saudi Arabia – are partially or entirely built on solid dirt or rock embankments. [112]

Pontoon bridge

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A concrete bridge over a large body of water
Floating concrete pontoons support the weight of the Nordhordland Bridge as it crosses a deep fjord in Norway.[113]

A pontoon bridge, also known as a floating bridge, uses floats or shallow-draft boats to support a continuous deck for pedestrian or vehicle travel over water.[114] Pontoon bridges are typically used where waters are too deep to build piers, or as a mechanism to implement a moveable swing bridge in a canal were boat traffic needs to pass by.[115]

Pontoon bridges were used in ancient China.[116] Duing the Second Persian invasion of Greece, Persian ruler Xerxes built a large pontoon bridge across the Hellespont, consisting of two parallel rows of 360 boats.[117]

Several pontoon bridges are in use in the modern world. Washington state in the U.S. has several, including Hood Canal Bridge.[118] In Norway, Nordhordland Bridge crosses a deep fjord by resting on floating concrete pontoons.[113] Many armies have pontoon bridges that can be rapidly deployed, including the PMP Floating Bridge, designed by the USSR.[119]

Portable military bridge

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A military vehicle carrying a bridge on its back, extending the bridge over a creek
This portable AM 50 bridge is being laid over a river in Slovakia.[120]

Portable military bridges are an important type of equipment in the field of military engineering, and perform a variety of wartime roles, such as quickly erecting bridges in the midst of battle, and assembling large bridges behind front lines to facilitate resupply.[121][g]

Military bridges can be categorized as "wet" bridges that rest on pontoon floats, and "dry" bridges that rest on piers, river banks, or anchorages.[121] A crude mechanism to cross a small ravine is to place a fascine (a large bundle of pipes or logs) into the ravine to enable vehicles to drive across.[123]

Some military bridges, referred to as armoured vehicle-launched bridges (AVLB), are carried on purpose-built vehicles.[123] These vehicles typically have the same cross-country performance as a tank, and can carry a bridge to an obstacle and deploy ("launch") the bridge.[124] The UK Chieftain AVLB could launch a 23-meter (75 ft) bridge – capable of supporting 60 ton loads – in 3 minutes.[123]

Extradosed

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A concrete bridge over a river
The Shin Meisei bridge (foreground) in Japan is an example of an extradosed bridge.[125]

An extradosed bridge combines features of a box girder bridge and a cable-stayed bridge.[126] Visually, extradosed bridges can be distinguished from cable-stayed bridges because the tower height (above the deck) is less than 20% of the span width.[127][h] Extradosed bridges are suitable for applications where a box girder design would not provide sufficient clearance under the bridge; or where a cable-stayed design would produce towers that are too tall for the site.[129] Extradosed bridges tend to be more expensive than box girder bridges, but less expensive than cable-stayed bridges.[130]

The main girder rests on the towers; and – in most cases – no cables are attached to the deck near the towers.[131] Because of the relatively flat angle of the cables, the cables of an extradosed bridge compress the deck horizontally, performing a function comparable to prestressing wires that are used within concrete girders.[127]

Design

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Requirements

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A wide freeway, with many cars and signs
Many overpass bridges in the United States Interstate Highway System are concrete beam bridges, such as this one over Interstate 10 in California.

When designing a bridge to traverse a specific obstacle, the designer must identify a design that meets several requirements. The requirements may be categorized as engineering requirements and non-engineering requirements. Engineering requirements include safety, strength, lifespan, climate, traffic, the size and nature of the obstacle to be traversed, and clearance required for passage underneath.[132]

Non-engineering requirements include construction cost, maintenance cost, aesthetics, time available for construction, customer preference, and experience of the builders.[133] Other factors that may be weighed include impact to environment and wildlife; and the bridge's economic, social, and historic relationship to the local community.[134]

Several designs may meet the requirements. After considering all factors, the bridge designer – in consultation with the customer – will select a particular design.[135] The value engineering methodology can be used to select a final design from multiple alternatives.[136] This methodology evaluates candidate designs based on weighted scores assigned to several different criteria, such as: cost, service life, durability, availability of resources, ease of construction, construction time, and maintenance cost.[137]

Material

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An ornate bridge made of iron, passing over a small, lush valley
The Iron Bridge in Shropshire, England, completed in 1781, is the first major bridge made of entirely of cast iron.[28]
A construction site with a halfway built concrete structure
This concrete bridge support is being prepared for a concrete pour. The green reinforcing bars will be embedded inside the concrete after the concrete cures.[138]
The small circular holes in this box girder will hold prestressing cables, which run the length of the girder and keep the concrete in compression.[139]

Bridges are built from a wide variety of materials, including wood, brick, rope, stone, iron, steel, and concrete.[140] A bridge made from two or more distinct materials (such as steel and concrete) is known as a composite bridge.[141]

Wood is an inexpensive material that is rarely used for modern motor vehicle roads.[142] Wood is used in bridges primarily in a beam structure or truss structure, and is also used to build huge trestle bridges for railways.[143] When wood is used, it is often in the form of glued laminated timber.[142]

Masonry includes stone and brick, and is suitable only for elements of a bridge that are under compression, since masonry will crack if under tension. Therefore, masonry is limited to structures such as arches or foundations.[144] In the twentieth century, large masonry bridges  – although superseded by concrete in the West – continued to be built in China.[145]

Iron, including cast iron and wrought iron, was used extensively from the late 1700s to late 1800s, primarily for arch and truss structures. Iron is relatively brittle, and has been superseded by the much stronger steel for all but ornamental uses.[146]

Steel is one of the most common materials used in modern bridges.[147] Steel was made in small quantities in antiquity, but became widely available in the late 1800s following invention of new smelting processes by Henry Bessemer and William Siemens. Steel is especially useful for bridges, because it is strong in both compression and tension.[148] Steel is widely used for truss bridges and beam bridges, and steel wires are an essential component of virtually all suspension bridges and cable-stayed bridges.[149] Concrete bridges make extensive use of steel, because all concrete used in bridges contains steel reinforcing bars or steel prestressed cables.[150] Steel bridges are more expensive than comparable concrete bridges, but they are much lighter (for the same strength), faster to build, and offer more flexibility during construction and repair.[151]

Concrete is a strong and inexpensive material, but is brittle and can crack when in tension.[152] Concrete is useful for bridge elements that are in compression, such as foundations and arches.[153] Many roadway bridges are built entirely of concrete using a beam structure, often of the box girder variety.[153] Virtually all concrete used in bridges contains steel reinforcing bars, which greatly increase the strength.[138] Reinforcing bars are set inside the concrete form, and the concrete is poured into the form, and cures with the bars inside. If concrete is used in elements that experience tension – such as the lower region of a horizontal beam or slab – prestressed cables must be embedded within the concrete and tightened.[139] The prestressed cables can be pre-tensioned (stretched before – and while – the concrete cures); or post-tensioned (placed within tubes in the concrete, and tightened after the concrete cures).[154] The prestressed cables compress the concrete. When the beam is placed into the bridge and carries a load, the undesirable tension (produced by the tendency of the beam to sag) is counteracted by the compression from the prestressed cables.[154] Concrete beams can be precast offsite and transported to the bridge site, or cast in place.[155]

Analysis and engineering

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Load

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A very large suspension bridge passing over a large body of water
The San Francisco–Oakland Bay Bridge is designed to withstand severe earthquakes. The eastern span, shown above, is a self-anchored suspension bridge which can survive a once-in-1,500-year earthquake.[156]

A bridge design must accommodate all loads and forces that the bridge might experience. The totality of the forces that the bridge must tolerate is represented by the term structural load. The structural load is usually divided into three components: The dead load, which is the weight of the bridge itself;[i] the live load, which are the forces and vibrations caused by traffic passing over the bridge, including braking and acceleration; and the environmental load, which encompasses all forces applied by the bridge's surroundings, including wind, rain, snow, earthquakes, mudslides, water currents, flooding, soil subsidence, frost heaving, temperature fluctuations, and collisions (such as a ship striking the pier of a bridge).[158]

Many of the load sources vary over time, such as vehicle traffic, wind, and earthquakes. The bridge designer must anticipate the maximum values that those loads may reach during the course of the bridge's lifespan.[157] For sporadic events like floods, earthquakes, collisions, and hurricanes, bridge designers must select a maximum severity that the design must accommodate.[159] The designer first selects a return period, which typically ranges from 100 to 2,500 years.[160] Longer return periods are used for bridges that are a critical part of the transportation infrastructure. For example, if the bridge is a key lifeline in case of emergencies, the designer may utilize relatively long return period, such as 2,000 years; in this example, the design must endure the strongest storm that is expected to happen once every 2,000 years.[161]

Stress and strain

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A computer screen running an app that is displaying engineering information
Software applications are used to evalute stress and strain.
A two-dimensional graph showing a curved line
Bridge engineers use stress-strain graphs to assist with the design process.[162]

The load forces acting on a bridge cause the components of the bridge to become stressed. Stress is a measure of the internal force experienced within a material. Strain is a measure of how much a bridge component bends, stretches, or twists in response to stress. Some strain (bending or twisting) may be acceptable in a bridge component if the material is elastic. For example, steel can tolerate some stretching or bending without failing. Other materials, such as concrete, are inelastic, and their change in shape when stressed is negligible (until the stress becomes excessive and the concrete fails).[162]

The bridge designer must calculate the maximum stress that each bridge component will experience, then select an appropriate design and size for the components to ensure they will safely tolerate the loads on the bridge.[163] Stresses are categorized based on the nature of the force that causes the stress, namely: compression, tension, shear, and torsion. Compression includes forces that compacts a component by pushing inward (for example, as felt by a bridge foundation when a heavy tower is resting on it). Tension is a stretching force experienced by a component when pulled (for example by the cables of a suspension bridge). Shear is a sliding force experienced by a component when two offset external forces are applied in opposite directions (for example, during an earthquake when the upper part of a structure is pulled north, and the lower part is pulled south). Torsion is a twisting force.[163]

Traffic

[edit]

An important component of the live load carried by a bridge is the vehicle and rail traffic the bridge is expected to carry.[164] In addition to the weight of the vehicle, other forces must be considered, including braking, acceleration, centrifugal forces, and resonant frequencies.[165] For roadways, the loads imposed by truck traffic far exceeds the loads imposed by passenger cars, and so the bridge design process focuses on trucks.[166]

The loads created by trains and vehicles can be determined by computer modelling, or by relying on data and algorithms contained in engineering specifications published by standards such as Eurocode or AASHTO bridge specifications.[164] In addition to algorithmic models contained in specifications, designers may determine traffic loads by utilizing data from real-world measurements on existing bridges that experience traffic comparable to that the proposed bridge will experience. Technologies such as weigh-in-motion (WIM) can produce accurate data without the guesswork inherent in an algorithmic model.[167]

Vibration and resonance

[edit]
The Tacoma Narrows Bridge collapsed shortly after opening in 1940 due to failure of the design to properly account for wind forces.[168]

Many loads imposed on a bridge, including winds and vehicular traffic, can cause a bridge to experience irregular or periodic forces, which may cause bridge components to vibrate or oscillate.[169] Many bridge components may have inherent resonant frequencies to which they are particularly susceptible, and vibrations near those frequencies can cause very large stresses.[170] The bridge design process must identify potential vibrations and oscillations, and address them with techniques to minimize vibration, such as adding components to dampen movement or stiffen the structure.[171]

Winds can produce a variety of forces on a bridge, including flutter and vortexes.[172] Considering wind forces during the design process is especially important for long, slender bridges (typically suspension or cable-stayed bridges).[173] Vibration and resonance concerns are especially important in longer bridges, but still must be accounted for in smaller bridges. The Eurocode guideline for bridge design specifies that vibration stress is due to moving vehicles should be accounted for by including an additional 10% to 70% of the vehicles' static load; the exact value depends on the span length, the number of traffic lanes, and the type of stress (bending moment or shear force).[174]

Neglecting to account for vibrations and oscillations can lead to bridge failure. The Angers Bridge collapsed in 1850, killing over 200 people, partly due to soldiers marching on the bridge in a manner that increased resonant oscillations.[175] The Tacoma Narrows Bridge collapsed in the 1940 in winds of 42 mph (68 km/h), even though the bridge was designed to withstand winds up to 128 mph (206 km/h). Investigations revealed that the designer failed to account for wind effects such as flutter and resonant vibrations.[168] The Golden Gate Bridge was damaged in 1951 due to wind forces, and as a result was reinforced in the 1950s with additional stiffening elements.[176]

Methodologies and tools

[edit]
A computer app displaying a bridge with engineering data
Engineers use finite element method software tools to evaluate a bridge design.[177]

The process used to design bridges uses structural analysis methods and techniques.[178] These methods divide the bridge into smaller components, and analyze the components individually, subject to certain constraints.[178] A proposed bridge design is then modeled with formulas or computer applications.[178] The models incorporate the loads and stresses the bridge will experience, as well as the bridge's structure and material. The models calculate the stresses in the bridge and provide data to the designer indicating whether the design meets the required design goals.[178]

Bridge design models include both mathematical models and numerical models.[178] The mathematical models that assess bridge loads and stresses are complex formulas that typically include differential equations. Solving these formulas directly is virtually impossible, so numerical models are used to provide approximate, but accurate, results.[178] The finite element method is the most common numerical model used to perform detailed analysis of stresses and loads of a bridge design.[179][j] The finite element method models a proposed bridge by dividing it into numerous small, interconnected pieces, and applying a computer algorithm to the pieces. The algorithm simulates the stresses on the bridge that are caused by the loads, and can iterate over time to simulate dynamic movements.[181]

A bridge designer evaluates the output of the models to determine if the design meets the design goals. Many criteria are evaluated when determining if a bridge design is sufficient, including deflection, cracking, fatigue, flexure, shear, torsion, buckling, settlement, bearing, and sliding.[182] The criteria, and their allowable values, are termed limit states. The set of limit states selected for a design are based on the bridge's structure and purpose.[183]

To ensure that a proposed bridge design is sufficiently strong to endure foreseeable stresses, many bridge designers use the Limit State Design methodology (known as Load and Resistance Factor Design in United States).[184] This methodology adds a margin of safety to the bridge design by incorporating safety factors into the design process.[185] The safety factors are applied two ways: (a) increasing the assumed loads and stresses the bridge will experience; and (b) decreasing the assumed strength of the bridge's structure.[186][k] The magnitude of the safety factors are based on several considerations, including the bridge's own dead weight; vehicle traffic; earthquakes; water or ice flows (from rivers or ocean currents) impacting the bridge foundations; rain, snow or ice on the bridge; winds; settling into the soil; and collisions (such as vehicles on the deck striking a bridge tower; or a ship striking a bridge foundation).[188]

Specifications and standards

[edit]

Many countries have standards organizations which publish documents that define acceptable bridge-building practices and designs. In Europe, the organization is the European Committee for Standardization, and the standards it publishes are the Eurocodes.[189] In the United States, the American Association of State Highway and Transportation Officials (AASHTO) publishes the AASHTO LRFD Bridge Design Specifications.[190] Canada's bridge standard is the Canadian Highway Bridge Design Code, developed by the non-profit CSA Group.[191]

Aesthetics

[edit]
A train moving atop a stone bridge in an attractive valley
The Brusio spiral viaduct is part of the Bernina railway in Switzerland, designated as a World Heritage Site.[192]

Many bridges are utilitarian in appearance, but in some cases, the appearance of the bridge can have great importance.[193] Bridges are typically more aesthetically pleasing if they are simple in shape, the deck is thinner in proportion to its span, the lines of the structure are continuous, and the shapes of the structural elements reflect the forces acting on them.[194]

The art historian Dan Cruickshank writes that bridges are regarded as objects of beauty by many people:[195]

Bridge construction remains... the most absolute expression of the beauty and excitement invoked by man-made constructions.... Bridges that are leaps of faith and imagination.... They are an act of creation that challenge the gods, works that possess the very power of nature itself. They are objects in which beauty is the direct result of functional excellence, conceptual elegance and boldness of design and construction.... A great bridge – one that defies and tames nature – becomes almost in itself a supreme work of nature. Bridges embody the essence of mankind’s structural ingenuity.... A great bridge has an emotional impact, it has a sublime quality and a heroic beauty that moves even those who are not accustomed to having their senses inflamed by the visual arts.[195]

Construction

[edit]

Elements

[edit]
A schematic diagram identifying the various parts of a fictional bridge
Schematic diagram showing some structural elements of a bridge. 1 Approach, 2 Arch, 3 Truss, 4 Abutments, 5 Bearings, 6 Deck, 7 Pier Cap, 8 Pier, 9 Pilings, 10 Footing, 11 Caisson, 12 Subsoil.[196]

The elements of a bridge are generally divided into the superstructure and the substructure.[197] The superstructure consists of most of the visible parts of a bridge, including the horizontal span, deck, wearing surface (e.g. the asphalt on top surface of the deck), trusses, arches, towers, cables, beams, and girders.[198] The substructure consists of the lower portions of the bridge which support the superstructure, including the footings,[l] abutments, piers, pilings, anchorages, and bearings.[200]

Substructure

[edit]
Two schematic diagrams showing how force is transmitted in a flat bridge compared to an arched bridge
Beam bridges (left) direct force vertically into the abutments; some arch bridges (right) direct forces diagonally. 1 Deck, 2 Abutments, 3 Subsoil, 4 Load on bridge, 5 Force from abutment into subsoil.[61]

Construction of all bridge types begins by creating the substructure. The first elements built are the footings and abutments, which are large blocks of reinforced concrete, entirely or partially buried underground, which support the entire weight of the bridge, and transfer the weight to the subsoil.[201] Based on their height-to-width ratio, footings are categorized as: shallow (height is less than width) or deep (height is greater than width).[202] If the subsoil cannot support the load placed on the footings, pilings must first be driven below the footings: pilings are long structures – made of wood, steel, or concrete – placed vertically below footings.[201] Some pilings reach down and rest on bedrock; others rely on friction to prevent the footing from sinking lower.[41]

Abutments are at the ends of a bridge span, where it reaches the subsoil.[203] They direct the weight into the subsoil, either vertically or diagonally.[61] Abutments may also act as retaining walls, keeping the subsoil under the approach road from eroding.[203]

After the concrete abutments and footings have been created, the piers and pier caps, if any, are built to complete the substructure.[204][m] Suspension bridges usually require anchorages, which are large reinforced concrete blocks solidly anchored into the earth – they must be exceptionally heavy and tied into the subsoil because they must withstand the lateral pull of the large cables that hold the entire deck and live load.[206][n]

Building supports in water

[edit]
A large concrete structure in the middle of a river, kept dry by a steel wall surrounding it
This bridge pier is being built within a cofferdam (the rusted, vertical steel walls).
A schematic diagram showing the cross section of a structure used to excavate bridge foundations under water
To build a bridge pier in water, caissons may be used to hold workers and machinery during excavation.[208]

When bridge supports (piers or towers) are built in a river, lake, or ocean, caissons are often used to provide a workspace while constructing the submerged portion of the supports. A caisson is a large, watertight, hollow structure, open on the bottom. It is usually sunk to the bottom of the water and workers can work inside, preparing the ground for the footings When excavation is complete, a caisson is typically filled with concrete to create all or part of the footing.[208]

Air pressure inside a caisson must be kept high to prevent water from seeping in.[208] Workers, if they do not properly decompress when exiting the caisson, can get decompression sickness.[209] Early bridge builders did not understand decompression, and deaths were common: thirteen workers died from decompression sickness when building the Eads Bridge (completed in 1874).[209]

An alternative to a caisson is a cofferdam, which is a temporary dam surrounding the support location, open on top, where workers may work while constructing the footings.[210]

Bearings

[edit]
Two cylinders of steel, supporting a large steel bridge, and resting on a concrete support
Two types of bridge bearings are used in this application: a hinge bearing above a pair of roller bearings.

Bearings are often placed between the superstructure and the substructure at the points of contact. Bearings are mechanical devices that enable small movements – which may result from thermal expansion and contraction, material creep, or minor seismic events. Without bearings, the bridge may be damaged when movements occur. Bearings can be selected to permit small rotational or slipping movements in a specific direction, without permitting movements in other directions. Types of bearings used on bridges include hinge bearings, roller bearings, rocker bearings, sliding bearings, spring bearings, and elastomeric bearings.[211]

Superstructure

[edit]
A bridge being constructed, with two large cranes on top
Gantries are one technique used to gradually assemble a bridge deck.[212]
A large concrete arch bridge being constructed
The deck of this arch bridge is being horizontally pushed onto the substructure with jacks.[213]
A huge wooden arch structure, over which an arch bridge is being built
This temporary falsework will be removed after an arch is built over it.[214]

After the substructure is complete, the superstructure is built, resting on the substructure.

Beam bridge construction
[edit]

Beam bridge superstructures may be fabricated off-site (common for steel beams) or cast-in-place (for many concrete beams).[215] The beams may be laid across the piers by a crane or gantry.[216] If the span crosses a deep ravine, a technique known as launching may be used: the full span (beams and deck) are assembled on the approach road, then pushed horizontally across the obstacle.[213][o]

Arch bridge construction
[edit]

Arch bridge superstructure construction methods depend on the material. Concrete or stone arches use a temporary wood structure known as falsework or centering to support the arch while it is built.[214] Some steel arch bridges are constructed without falsework: both sides are built in a cantilever fashion from the abutments, and when they reach the middle, they are jacked slightly apart for the final section to be inserted.[217]

Cantilever bridge construction
[edit]

Cantilever bridge superstructures are usually built incrementally by proceeding outward from anchorages or piers. Most cantilever superstructures can be built without temporary support piers, as the bridge can support itself as it extends outward. A similar process is used for both steel or concrete cantilevers: prefabricated sections may be positioned at ground (or water) level and hoisted into place with a gantry; or may be transported horizontally along the previously completed portion of the cantilever. Concrete cantilevers require steel prestressing cables to be inserted through tubes inside each section as they are added, and tightened to put the concrete into compression.[218]

Cable-stayed bridge construction
[edit]

Cable-stayed bridge superstructures begin by building one or more towers, which rest directly on footings that are part of the substructure. The deck is constructed in pieces beginning at the tower(s) and moving outward. As each piece of the deck is added, it is connected to towers with steel cables, and the cables are tightened to take the load of the deck. The deck proceeds outwards in both directions at the same rate, to ensure the forces applied to the tower are balanced. If the deck is made of concrete, steel prestressing cables are inserted through tubes inside each deck section, and tightened to put the concrete into compression.[219]

Suspension bridge construction
[edit]

Suspension bridge superstructures begin with construction of with the towers. The towers may be steel or concrete, and rest directly on the footings. To build the large cables, a large pulley is hauled back and forth across the span, stringing multiple wires between the anchorages in each pass.[p] After hundreds of journeys, the wires are bundled together to form the cables. The cables are securely fastened to the anchorages at both ends. Vertical wires called hangers are suspended from the cables, and the deck is then attached to the hangers in small sections.[221]

Protection

[edit]
A thick, old wire cable, with paint that is partially worn off
Paint can be used to reduce deterioration of steel components. Steel bridges need to be repainted periodically, as seen in this wire hanger from the Golden Gate Bridge, which is painted international orange.[222]

To achieve a longer lifespan, a bridge should be protected from deterioration by incorporating certain features into the design. Bridges can deteriorate due to a variety of causes, including rust, corrosion, chemical actions, and mechanical abrasion. Deterioration is sometimes visible as rust on steel components, or cracks and spalling on concrete.[223]

The deterioration can be slowed – thus prolonging the life of the bridge – by various measures, primarily aimed at excluding water and oxygen from the bridge elements.[224] Techniques to prevent water-based damage include drainage systems, waterproofing membranes (such as polymer films), and eliminating expansion joints.[225][q]

Concrete bridge elements can be protected with waterproof seals and coatings.[227] Reinforcing steel within concrete can be protected by using high-quality concrete and increasing the thickness of the concrete surrounding the steel.[228] Steel elements of a bridge can be protected by paints or by galvanizing with zinc.[229] Paint can be avoided entirely for steel members by using certain steel alloys, such as stainless steel or weathering steel (a steel alloy that eliminates the need for paint, by forming a protective outer layer of rust).[230]

Bridge scour is a potentially serious problem when bridge footings are located in water. Currents in the water can cause the sand and rocks around and below the footings to wash-away over time. This effect can be mitigated by placing a cofferdam around the footings, or surrounding the footings with rip-rap.[231]

Operations

[edit]

Maintenance, inspection, and monitoring

[edit]
A large block of concrete, partially crumbling, with internal steel bars exposed
This pier of a bridge in Germany is degrading, and the internal steel reinforcing bars are exposed and rusting.

Bridge maintenance encompasses the activities that ensure a bridge remains open to traffic, avoids safety incidents, and achieves its intended lifespan.[232] Maintenance responsibilities include planning, budgeting, and prioritizing all monitoring and inspection tasks.[232] Bridge designers use Life-Cycle Cost Analysis (LCCA) methodologies to estimate the maintenance costs of a bridge throughout its lifetime.[233] Annual maintenance costs increase as the bridge ages and degrades.[234]

An important part of maintenance is inspecting for damage or degradation, and taking steps to mitigate any issues detected. Degradation can come from a variety of sources: expansion/contraction from freeze/thaw cycles, rain and snow, oxidation of steel, saltwater spray, carbonation of concrete, vehicular traffic, corrosion, mechanical abrasion, poor bridge design, and improper repair procedures.[235]

A variety of inspection techniques can be utilized to measure degradation of bridge elements. Destructive testing removes material samples from the bridge – such as cores drilled from concrete, or fragments from broken steel wires – to a laboratory. In the laboratory, the samples are analyzed using microscopes, sonic devices, or X-ray diffraction.[236]

Non-destructive testing that can be performed on a bridge in situ include hammer strike tests, ultrasonic pulse velocity tests, seismic tomography, and ground penetrating radar. Magnetometers can be used to detect the location of reinforcing steel within concrete. Various electrical tests such as permeability and resistance can give insight into the condition of surface concrete.[237] X-rays can be passed through concrete to obtain data about concrete density and condition.[238] Videography using slender probes can be used where access is available.[239]

During bridge construction, permanent sensors may be placed within bridge elements at critical locations, and may be measured at any time to obtain data about stresses and chemical degradation in hard-to-reach locations.[240] Many long-span bridges are now routinely monitored with a range of sensors, including strain transducers, Sodar, accelerometers, tiltmeters, and GPS.[241]

A tall bridge covered in temporary scaffolding
Scaffolding is erected under the Sitterviadukt rail bridge in Switzerland while maintenance on the deck truss is performed.[242]

To evaluate the condition of large steel cables, as used in suspension bridges or cable-stayed bridges, electrical coils are moved along the cable, measuring the induction of the cable, which can reveal corrosion issues.[243]

Structural evaluation tests can be conducted which measure deflections in bridge elements when test loads are placed in certain points. Sensitive instruments measure how much the bridge elements bend or twist, and the results can reveal if the element is not performing within expected limits. Another test involves jacking the bridge deck off its supports slightly, and measuring the force required. Cables can be evaluated by vibrating them and measuring their dynamic response.[244]

Detailed measurements of the external surface of a bridge can be recorded using Lidar technology. Comparing measurements taken at multiple points in time can reveal long-term changes.[245]

Failures

[edit]

Bridge failures are of special importance to structural engineers, because the analyses of the failures provide lessons learned that serve to improve design and construction processes.[246] Before the advent of bridge engineering procedures based on rigorous, scientific principles, bridges frequently failed. Failures were most common in the mid 1800s, when the rapidly expanding railway networks were building hundreds of new bridges every year around the globe.[247] In the United States, 25% of all bridges failed during the 1870s.[248] A notable disaster was the 1876 Ashtabula River railroad disaster, in which a railway bridge failed, resulting in over 80 deaths.[247] Over time, bridge failures led to improvements in bridge design, construction, and maintenance practices.[249]

A broken bridge and a large ship; the ship has struck the bridge
This bridge in Baltimore collapsed after a powerless containership collided with it.[251]
A broken bridge, which has fallen into the water over which it used to pass
The Nanfang'ao Bridge in Taiwan collapsed because of excessive corrosion that went undetected.[250]

In culture

[edit]
The cover of a book, which has an illustration of a monk standing before a mountain and a bridge
The Pulitzer Prize winning novel The Bridge of San Luis Rey revolves around a bridge failure that killed five people.[253]

Bridges occur extensively in art, legend, and literature, often employed in a metaphorical manner.[254] In Norse mythology, the home of the gods – Asgard – is connected to the earth by Bifröst, a rainbow bridge.[255] Many bridges in Europe are named "Devil's Bridge", and sometimes have folkloric stories that explain why the bridge is associated with the devil.[256] There are many stories, mostly apocryphal, relating bridges to Christian saints.[257] Stories and poems often employ a bridge as a metaphor of the human lifespan, or human experiences.[258] Bridges are often the setting for pageants, celebrations, and processions.[259]

Bridges are often venerated as symbols of humankind's heroism and accomplishments.[260] The inspirational nature of bridges has led them to be featured in the works of poets, painters and writers.[261] Bridges feature prominently in paintings – often in the background – as in the Mona Lisa.[262] Authors have used bridges as the centerpiece of novels, such as The Bridge on the Drina by Ivo Andrić, and Thornton Wilder's The Bridge of San Luis Rey.[253]

Signature bridges

[edit]
A large bridge, and about thirty large, colorful balloons in the sky above the bridge
The Clifton Suspension Bridge is a landmark associated with the city of Bristol in England.[263]

Many bridges – known as signature bridges – are strongly identified with a particular city or country.[264] In some cases they are deliberately built with an especially magnificent design, to serve as a landmark or icon.[265] The art historian Dan Cruickshank writes: "I am ... enthralled by [the] ability [of bridges] to transform a place a community and amazed by the way a bold bridge can make its mark on the landscape and in men’s minds, capture the imagination, engender pride and sense of identity and define a time and place."[195]

Large suspension bridges, in particular, are often regarded as iconic landmarks that symbolize the cities in which they are located. Notable examples include the Brooklyn Bridge in New York; the Golden Gate Bridge in San Francisco; the Clifton Suspension Bridge in Bristol; and the Széchenyi Chain Bridge in Budapest.[263]

Numismatics

[edit]
A colorful 500 euro bank note illustrated with a bridge and a map of Europe
The 500 euro banknote displays a cable-stayed bridge.[266]

Bridges appear on a variety of coins and banknotes. A prominent use of bridges is on euro banknotes. In 1996, the European Commission held a competition to select art for the euro banknotes. Robert Kalina, an Austrian designer, won with a set of illustrations of bridges. Bridges were chosen because they symbolize links between states in the union and with the future. The designs were supposed to be devoid of any identifiable characteristics, so as to not show favoritism to specific countries. The initial designs by Kalina were discovered to be of specific bridges, including the Rialto and the Pont de Neuilly, and were subsequently changed to be more generic. Each banknote depicts a bridge design representative of a certain architectural era: €5 Classical, €10 Romanesque, €20 Gothic, €50 Renaissance, €100 Baroque and Rococo, €200 19th century (iron and glass), and €500 20th century.[266]

References

[edit]

Footnotes

[edit]
  1. ^ Examples of early stepping stone bridges include the Sweet Track and the Post Track in England, approximately 6,000 years old.[3]
  2. ^ Long before the steel era, people made suspension bridges from vines or ropes. Iron was used in a few early suspension bridges in the form of iron rods or chains (rather than steel wires or cables).[32]
  3. ^ An early cable-stayed bridge was the 1955 Strömsund Bridge in Norway.[38]
  4. ^ A truss can be considered as a deep beam, where numerous triangular holes have been cut into the beam to reduce the weight.[63]
  5. ^ The Severins Bridge was first cable-stayed bridge that arranged its cables in a fan pattern, rather than the usual harp pattern.[38]
  6. ^ Notable bridges consisting of hundreds of beam bridge elements include Hangzhou Bay Bridge and Lake Pontchartrain Causeway.[87]
  7. ^ An example of a portable military bridge is the Bailey bridge.[122]
  8. ^ Another definition of an extradosed bridge is one where the "stiffness ratio" (load carried by stay cables divided by total vertical load) is less than 30%.[128]
  9. ^ The dead load also includes any permanent fixtures on the bridge, such as light poles, traffic signage, and guardrails;[157]
  10. ^ An alternative to the finite element method is the simpler, but less powerful, finite strip method.[180]
  11. ^ The strength of a bridge component is referred to as "resistance" in the context of LRFD.[187]
  12. ^ The term "foundation" is sometimes used to represent footings, but in most contexts it means all or most of the substructure.[199]
  13. ^ A pier cap is a block of concrete at the top of a pier, upon which rests the deck.[205]
  14. ^ Self-anchored suspension bridges do not require anchorages.[207]
  15. ^ Incremental launching may be employed for several types of bridges: beam bridges, deck arch bridges, and cable-stay bridges with short spans. In all cases, the substructure is completed first, then the deck is pushed horizontally across the top of the substructure.[213]
  16. ^ Spinning the wires took 209 days for the George Washington Bridge.[220]
  17. ^ Expansion joints relieve stress due to thermal expansion and contraction, but permit water to seep into vulnerable bridge elements, which can lead to corrosion and degradation. Integral bridge concepts are an alternative to expansion joints.[226]

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Sources

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Books

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  • Abdunur, Charles (2000). "Inspection, Monitoring, and Assessment". In Ryall, Michael (ed.). The Manual of Bridge Engineering. Thomas Telford. pp. 883–942. ISBN 0727727745. Retrieved 1 September 2025.
  • Birnstiel, Charles (2000). "Moveable Bridges". In Ryall, Michael (ed.). The Manual of Bridge Engineering. Thomas Telford. pp. 663–698. ISBN 0727727745. Retrieved 1 September 2025.
  • Jones, Vardiman (2000). "Suspension Bridges". In Ryall, Michael (ed.). The Manual of Bridge Engineering. Thomas Telford. pp. 595–662. ISBN 0727727745. Retrieved 1 September 2025.
  • Mulheron, Mike (2000). "Protection". In Ryall, Michael (ed.). The Manual of Bridge Engineering. Thomas Telford. pp. 805–848. ISBN 0727727745. Retrieved 1 September 2025.
  • Shanmugam, N. E. (2000). "Structural Analysis". In Ryall, Michael (ed.). The Manual of Bridge Engineering. Thomas Telford. pp. 95–224. ISBN 0727727745. Retrieved 1 September 2025.
  • Vassie, Perry (2000). "Bridge Management". In Ryall, Michael (ed.). The Manual of Bridge Engineering. Thomas Telford. pp. 849–882. ISBN 0727727745. Retrieved 1 September 2025.

Journals and websites

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Unknown author

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  • "Bridge". Oxford English Dictionary. Oxford University Press. Retrieved 11 September 2025.
  • "Bridge Layer AM-50". Ministry of Defence and Armed Services of the Czech Republic. Retrieved 17 September 2025.
  • "Causeway". Merriam-Webster Dictionary. Merriam-Webster. 12 September 2025. Retrieved 16 September 2025.

Further reading

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