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The next advance was the "method of sections" published in by A Ritter, a German engineer. Ritter simplified the calculations of forces by developing very simple formulae for determining the forces in the members intersected by a cross-section. The solution of bending in a cantilever was developed over a long period of time, starting with Galileo's famous illustration of the wooden beam, anchored in the ruinous masonry wall, holding a stone weight at its end. Although it was not entirely accurate, subsequent solutions were discussed in terms of Galileo's cantilever. C A Coulomb in France hypothesized in that the flexural stress in a cantilevered beam had a maximum value in compression on the bottom edge and a maximum value in tension on the top with a neutral axis somewhere between the two surfaces.

The Swiss mathematician Leonard Euler provided the solution to the elastic buckling of columns as early as Railroads, the transportation mode that revolutionized the 19th century, generated a bridge type that merits special attention.

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The limited traction of locomotives forced the railroad engineer to design the line with easy gradients. Viaducts and trestles were the engineering solution for maintaining a nearly straight and horizontal line where the depth and width of the valley or gorge rendered embankments impracticable. These massive, elevated structures were first built in Roman style of multiple-stone arches and piers.

Later, when wrought iron and steel became available, engineers built viaducts and trestles of great length and height on a series of truss spans or girders borne by individual framed towers composed of two or more bents braced together. Examples in Europe include the Viaduc de Barentine , constructed by British navvies under the direction of MacKenzie and Thomas Brassey in brick rather than stone, and the Viaduc de Saint-Chamas , both in France. Most notable of the early trestles was the Portage Viaduct in the USA , a remarkable timber structure designed by Silas Seymour, carrying the Erie Railroad over the Genessee River, ft 71m above the water and ft m long Figure It was destroyed by fire in , to be replaced in iron, and later in steel.

It served as the prototype for later ones, such as the Viaduc de la Bouble , a series of lattice girders on cast-iron towers flared at the bottom, built under the direction of Wilhelm Nordling. It was ft m long by ft 66m high on the Commentry-Gannett line in France. Dating from , it was a series of inclined cast-iron columns resting on stone pedestals connected at the top by cast-iron arches, the whole system braced by wrought-iron ties. Examples surviving today in North America include the Kinzua Viaduct on the former Erie Railroad in Pennsylvania Figure 15 , and the Lethbridge Viaduct on the Canadian Pacific in Alberta, composed of alternating 67ft 20m trestles and ft 30m girders, at ft m long the longest and heaviest in the world.

The Tunkhannock Viaduct , ft high 73m by ft long m , is the largest reinforced concrete-arch bridge in the world. Although suspension bridges had been known in China as early as BC, the first chain suspension bridge did not appear in Europe until , when the 70ft 21m span Winch Bridge was constructed over a chasm of the River Tees UK , with the flooring laid directly on two chains.

The span displayed all the essential elements of the modern suspension bridge: a level deck hung from a catenary system suspended over towers and anchored in the ground, and a truss-stiffened deck, resulting in a rigid bridge capable of supporting relatively heavy loads. The world's first wire-cable suspension bridge was a ft m temporary footbridge built in for the workers of wire manufacturers Josiah White and Erskine Hazard over the Schuylkill in Philadelphia.

The USA contributed little more until the middle of the century, but these inventions were immediately followed up in Europe. Its replacement still stands, probably the oldest wire-cable suspension bridge in the world, with its carefully replicated wooden stiffening truss and deck. From this developed the typical European standard - cables of parallel, thin wires, light decks stiffened by wooden trusses, piers and abutments sunk - using hydraulic cement - of which hundreds were built.

The British preferred to use chains of linked eyebars, and achieved spans of lightness and grace, all the more effective in contrast with the colossal masonry suspension towers. The United Kingdom's first large-scale suspension bridge was the Menai Bridge on the London to Holyhead road over the straits of the same name in North Wales Figure Travellers would board a ship at Holyhead for the final leg of the trip to Ireland.

It was designed by Thomas Telford and completed in , with an unprecedented span of ft m using wrought-iron eyebars, each bar being carefully tested before being pinned together and lifted into place. The roadway was only 24ft 7m wide and, without stiffening trusses, soon proved highly unstable in the wind.

The Menai bridge was twice rebuilt before the entire suspension system was replicated in steel in and the arched openings in the towers were widened. The oldest suspension bridge extant today is the Union Bridge over the River Tweed at Berwick UK , a chain-link bridge designed and erected by Captain Samuel Brown in , with a span of ft m. With the French declaring a moratorium on suspension-bridge construction following the collapse of the Basse-Chaine Bridge in , the creative edge passed back across the Atlantic, to be picked up by Charles Ellet and John Augustus Roebling in the USA.

After studying suspension bridges in France, Ellet returned with the technology and built a ft m bridge over the Ohio River at Wheeling, West Virginia, in , which was the longest in the world. Thanks to techniques developed by the Roeblings and used in the structure's rebuilding, following a storm that ripped the cables off their saddles, the bridge remains in service today. At mid-century, it was the only form capable of uniting the ft m gorge in a single span. This half-stereoscopic viewshows the massive stiffening trusses and the wire-cable stays that tied the deck superstructure to the walls of the gorge.

Eric DeLony Collection. Roebling had arrived in the USA ten years earlier and established a wire-rope factory in Saxonburg, Pennsylvania, which he later moved to Trenton, New Jersey. Educated in Europe, he would have been exposed to the concepts of wire-cable suspension bridge engineering of the French and Swiss.

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He and Ellet competed for primacy in suspension bridge design. Roebling won out when he took over design of the Niagara Suspension Bridge from Ellet, successfully completing it in Figure The inherent tendency of suspension bridges to sway and undulate in wavelike motions under repeated rhythmic loads such as marching soldiers or the wind was not completely understood by engineers until the s, following the collapse of the Tacoma Narrows Bridge "Galloping Gertie". Credit for designing the first suspension bridge rigid enough to withstand wind loads and the highly concentrated loadings of locomotives belongs to John Roebling.

The two decks, the upper for the railway and the lower for common road service, were separated by an 18ft 6m stiffening truss. In addition, the truss was braced with radiating cable stays inclined from the tops of the suspension towers and anchoring cables tying the deck to the sides of the gorge, arresting any tendency to lift under gusts of wind. Completed in , the plan involved two distinctive stone towers, four main cables, anchorages, diagonal stay cables, and four stiffening trusses separating the common roadway and trolley line from a pedestrian promenade. With a record-breaking span of ft m , the Brooklyn Bridge was designed by John Roebling, but it was built by his son and daughter-in-law after he died of blood poisoning following an accident while surveying the location of the Manhattan tower in which his foot was crushed.

Massive Egyptian towers, pierced by pointed Gothic arches, stand Diagonal stay cables give the bridge its distinctive appearance, but function to stiffen the deck. It took two years to lay up each of the four Two other Roebling suspension bridges survive, both recently rehabilitated. One spanning the Ohio River at Cincinnati was completed in Structural steel is stronger and more supple than cast or wrought iron, and allowed greater design flexibility. The last thirty years of the 19th century witnessed the phasing in of steel plates and rolled shapes, leading to the enormous production of steel trusses and plate-girder spans of ever-increasing lengths throughout the world.

Steel arches and cantilevers were favoured for long spans because they better withstood the impact, vibration, and concentrated loads of heavy rail traffic. The earliest known use of steel in bridge construction was the ft m suspension span across the Danube Canal near Vienna Austria , designed by Ignaz von Mitis. The steel eye-bar chains were forged from decarburized iron from Styria. Steel halved the weight of wrought iron, but remained prohibitively expensive for another forty years before steelmaking processes such as the Bessemer and the open-hearth were perfected it is uncertain whether the Styrian ironmasters created real steel or whether the decarburization was a mechanical process resulting in a surface-hardened steel, a kind of wrought iron rather than the mass steel that results from the Bessemer process.

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The first major bridge utilizing true steel was the Eads Bridge , the most graceful of the Mississippi River crossings in the USA, built by the Keystone Bridge Company, which subcontracted fabrication of the steel parts to the Butcher Steel Works and the iron parts to Carnegie-Kloman, both of Pittsburgh. Its ribbed, tubular steel arch spans of ft, ft, and ft m, m, and m and double-decked design shattered all engineering precedents for the time: the centre span was by far the longest arch.

Mathematical formulae for the design were developed by Charles Pfeiffer. The cantilever method of erection, devised by Colonel Henry Flad and used for the first time in the USA, eliminated the centring that would have been impossible in the wide, deep, and fast-flowing Mississippi. While recovering from illness in France, the designer James Buchanan Eads found the solution to sinking piers in deep water. He investigated a bridge under construction over the Allier at Vichy that used Cubitt and Wright's pneumatic caissons - floorless chambers filled with compressed air.

The first major bridge of steel in France was the Viaur Viaduct , a three-hinged steel arch of ft m flanked by ft 95m cantilevers. The crowning achievement of the material during the 19th century, however, was the mighty Forth Railway Bridge in Scotland Its design was motivated by the Tay Bridge disaster. About 54, tons of Siemens-Martin open-hearth steel were required for the ft m cantilever spans whose main compression struts of rolled steel plate were riveted into 12ft 4m diameter tubes.

Another authority on the effects of wind on structures was Gustav Eiffel, who conducted similar experiments in France prior to designing another of the world's great arch bridges, the ft m Garabit Viaduct in the windy valleys of the Massif Central, though he held to wrought iron, not being convinced of the efficacy of the new material. Steel arches of enormous span were built during the first few decades of the 20th century. One of the greatest is the Hell Gate Bridge in the USA , a two-hinged trussed arch, the top chord of which serves as part of a stiffening truss.

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The ft m arch, weighing 80, tons 81, tonnes , was the longest and heaviest steel arch in the world. The next was Bayonne Bridge , which remains one of the longest steel arches in the world today. It was built during the Depression by a team assembled under the direction of Swiss-born and educated engineer, Othmar Ammann, chief engineer of the Port Authority of New York, one of the remarkable public works organizations of the USA, if not the world.

Opening three weeks after the George Washington Bridge, then the longest suspension bridge in the world, this second record-breaking span was financed and built by the Port Authority simultaneously, the two projects forming one of the greatest public work endeavours since Roman times.

The Bayonne Bridge connects Bayonne New Jersey and Staten Island New York with a manganese-steel parabolic two-hinged arch of ft m span and ft 81m rise, the deck clearing high water by ft 46m. As in the Hell Gate, the arch's top chord acts as a stiffener, the bottom chord carrying the load. The Bayonne Bridge was designed to be 25ft 8m longer than the nearly identical Sydney Harbour Bridge in Australia, started five years earlier. Bridges in areas other than Europe and the USA should be investigated, as the colonial empires of several nations were at their peak during the autumn years of the 19th century.

In India, for example, the British built several long-span railway bridges, such as the Hooghly and the Sukkur bridges which exceeded ft m in span and are interesting because they were constructed using the simplest equipment and armies of unskilled labour. This structural form was mentioned in the previous section on steel bridges in the discussion of the Eads Bridge, where the erection of the arches employed principles of the cantilever, and the Forth Railway Bridge, perhaps the world's greatest cantilever.

A discussion of this type of bridge is warranted because of its engineering interest and because the form illustrates the outstanding application of iron and steel to bridge construction. Cantilevers were one of the first bridge types, many being built by the ancient cultures of China and India.