How does a cantilever bridge work
Cantilever bridges, tanner girders
A traditional cantilever bridge in Nepal. There are tree trunks with heavy stones on both sides of the bank
clamped and thus act as a cantilever. The gap between the cantilever arms is closed by boards.
© Robert Stutton 2009. All rights reserved, used under license.
|Sketch of a cantilever with a load|
by Galileo Galilei (1564-1642)
"Discorsi e Dimostrazioni Matematiche ..." (1638)
The archetype of a cantilever bridge is certainly almost as old as girder bridges or cable-braced bridge systems. Originally from Asia, it is still widespread today in countries such as Afghanistan, India and China. Between 1890 and 1930, this type of bridge even held the world record for the largest span.
In Asian mountain regions, simple cantilever bridges are often built as temporary structures that are swept away by the next flood and then rebuilt. The picture above shows such a structure in Nepal. Cantilever bridges are also called "cantilever bridges" or "Gerber girders". In the English-speaking world it is known as the "Cantilever Bridge".
What is a cantilever bridge?
Cantilever bridges are based on the principle of girder bridges, but allow larger spans. The span of a simple girder bridge is limited by the length of the existing components, e.g. the tree trunks or the wood made from them. Due to the cantilever design, a greater width can be achieved with the same components.
In general, a boom (or cantilever arm) is an elongated component that is clamped on one side and the other end protrudes freely into the room. In this respect, a crane or diving platform in a swimming pool can also be called a jib. A simple cantilever bridge consists of two cantilever arms that face each other at a certain distance and are usually connected to one another by a horizontal beam. Sometimes, however, the brackets are connected directly with a joint between them without a beam.
Cantilever bridges hardly played a role in Europe until the advent of the railroad. Bridges for pedestrians, wagons and mounts were built from Roman times to modern times either as wooden beam bridges or, in the more permanent version, as stone arch bridges. Suspension and cable-stayed bridges were added from around 1825, especially when larger spans had to be bridged. Chains or wire ropes were used for this, but this was only possible when iron could be produced in the appropriate quality and quantity.
The railway makes great demands on bridge construction
| The 'Wandipore Bridge' in the Kingdom of Bhutan |
Thomas Pope: "A Treatise on Bridge Architecture" (New York, 1811)
The progress in iron production also led to the invention and worldwide expansion of the railroad, the first real means of mass transport. Rail transport revolutionized the entire transport system and ultimately also the world economy. The world's first official railway line opened in England between Stockton and Darlington in 1825. Around 1830 there was a rail network in the whole of Europe with a total length of 24,500 km, but 50 years later it was over 283,000 km. The development in America was similar: around 1900 the route network had a length of 310,000 km.
It is difficult to imagine what this rapid development meant for bridge construction. Not only was the number of bridges to be built gigantic, but also the structural requirements and the required spans presented the engineers with major tasks.
Shortly before the beginning of the railway age, suspension bridges for road traffic were very successful. Thomas Telford completed the Menai Strait Bridge in 1826, which was then the largest bridge in the world with a main span of 177 m. It was replaced in 1849 by the Grand Pont Suspendu in Friborg / Switzerland, which already had a width of 273 m. Further suspension bridges with record spans followed, until 1889 with the Brooklyn Bridge in New York (486 m) a temporary high point was reached.
|The arms of the Firth of Forth Railway Bridge (1889) are being extended|
static reasons built in both directions at the same time
With the exception of the Brooklyn Bridge, none of these bridges were designed for the railroad, but for much lighter carriages, horse-drawn carts, oxcarts, etc. Of course, in the decades to come, many attempts were made to build suspension bridges for the railroad. In 1855, Johann A. Röbling completed the bridge over the Niagara River, which had separate lanes one above the other for wagons and for the railroad. Perhaps it was already the most successful suspension bridge for railways, because it existed until 1896. But then it was no longer capable of bearing the weight of the increasingly heavy and faster locomotives and had to be replaced by a steel arch bridge.
Another attempt to establish suspension bridges for the railroad was made by Friedrich Schnirch in Vienna in 1860. He had already built several chain bridges for road traffic before he completed the connecting railway bridge over the Danube Canal. Even in the run-up to the construction work, there had been a lot of criticism from specialist circles, and serious stability problems became apparent during the load test. The traffic on the bridge had to be regulated and reduced more and more over the years until it was finally removed in 1880.
Advantages and disadvantages of continuous beams
|The Lansdowne Bridge in Sukkur / Pakistan still exists today. At Her Completion (1889)|
Sukkur was still part of the British Indian Crown Colony. The state of Pakistan only came into being in 1947. Also
this bridge has been criticized for its design, which meets purely static requirements.
The first large European railway bridges were girder bridges with still relatively small individual spans and correspondingly many pillars. They were initially built as box-shaped hollow girders (Britannia Bridge / 1850) or as lattice girders (Dirschauer Weichsel Bridge / 1857). After initial experience with parallel-belt girders, all possible truss shapes were tried out: parabolic or arched, curved upwards or downwards, lens or fish belly beams, trapezoidal beams, etc.
In the second half of the 19th century, however, the spans that could be achieved were still quite small and usually did not exceed 100 m. For example, when it was completed, the bridge on the Tay was the longest bridge in the world at 3,264 m, but its largest individual spans only had a span of 75 m. One of the longest railway truss bridges of its time was the Lekbrücke in Culemborg in the Netherlands (1868), but with its span of 155 m it was already an exception.
Multi-span bridges had to be built for larger obstacles, although there are various options for this in terms of statics. Either you place a short single girder between two pillars, or you run a long beam as a so-called continuous girder over the entire length of the bridge.
| Variants of the multi-span beam support.|
The circular interruptions in the beam represent joints.
© Bernd Nebel
Continuous girders are usually more economical than individual girders, among other things because they can be erected from an abutment using the push-pull method. However, continuous beams also have a serious disadvantage: they are statically indeterminate. A statically indeterminate system can be imagined as follows: Imagine a beam that is carried by three people, one of which is significantly smaller than the other two. As a result, the entire load is distributed to the taller people, while the smaller one hardly has to carry anything.
A continuous beam has a similar effect if the bearing foundations are set differently. As a result, the system is statically indeterminate and the load distribution on the pillars would be uneven, which would ultimately result in damage to the structure. At the time of the first joint supports, this theoretical approach was applied to every material, including iron and steel. It was only through the development of the theory of plasticity around 1913 that it was recognized that steel can deform under load after a certain period of time. Of course, this process only takes place within narrow limits due to shifts in the crystal structure of the metal. Since the setting of a pillar also takes place within a certain time frame, a steel girder can adapt to minor differences in support heights in the mm or cm range without damage.
Heinrich Gerber and the tanner bearer
In around 1864 the engineer Heinrich Gerber (1832-1912), who was born in Hof, was looking for a way to combine the advantages of continuous beams with those of single-span beams. Before that, there had already been theoretical approaches by August Ritter and Claus Köpcke, which, however, did not lead to any significant success in practice. It was Gerber who invented a system of cantilever arms and suspension brackets that are connected to one another by joints. Since no bending moment can occur in a joint, there is always a statically determined system, even if there should be differences in settlement.
| The road bridge over the Main near Haßfurt (1864/38 m).|
Heinrich Gerber's first modern cantilever bridge
Gerber had his invention patented in 1866 after building the road bridge over the Main near Haßfurth using this system two years earlier. Although it was the world's first modern cantilever bridge made of steel, it initially went largely unnoticed by experts. It was not until the World Exhibition of 1873 in Vienna that the Deutsche Bauzeitung dealt with this bridge. However, her judgment was not particularly flattering, because she criticized the "adventurous, ugly appearance of the bridge". Many a cantilever bridge had to live with such criticism in the following decades, especially if it was designed from a purely static point of view. Gerber was evidently aware of the aesthetic flaws of the first cantilever bridges, as he mostly worked with an architect on later projects.
Towards the end of the 19th century, more and more cantilever bridges were built and the term "tanner girders" gradually gained acceptance in German-speaking countries. However, the sole authorship of German engineers for the articulated supports was disputed, in particular from the British side. Especially in connection with the construction of the Forth Bridge, it was pointed out that the engineers John Fowler and Daniel Kinnear Clark had already published corresponding ideas around 1850. The dispute remained at an academic level, however, because all publications were also published in the respective foreign countries. At that time, it would have been possible for both sides to find out about relevant publications.
The great age of the truss cantilever bridges
|The Viaduc de Viaur (1902/220 m) in central France is a good example of one|
Cantilever bridge without Gerber girders. The two cantilevers are through in the middle
a pressure joint connected to each other and additionally secured against tensile forces.
Cantilever bridges opened up new possibilities for overcoming large obstacles, especially for the railways. The system's final breakthrough was achieved by the construction of the Firth of Forth railway bridge in Scotland, whose span of 521 m when completed was even greater than that of any other bridge in the world. Due to its overall length and the more than necessary load-bearing capacity, it appears extremely bulky and massive. But it should too, because after the disaster on the Tay there was an urgent need to restore confidence in the railroad to the people of northern Great Britain.
The construction of the Firth of Forth Bridge was a national challenge, both in terms of the manpower to be provided and the material required. Not everywhere in the world have such an effort been made to build a single bridge. An increase seemed hardly possible, and in fact the span of the Firth of Forth Bridge was exceeded only once by a cantilever bridge.
The bridge over the St. Lawrence River in Quebec / Canada is the largest cantilever bridge in the world with a span of 549 m. Due to several accidents and delays in its construction, however, it already marks the approaching end of the large truss cantilever bridges. After an almost complete collapse in August 1907, when the hinge bracket was attached on September 12, 1916, there was a second accident with many deaths. By the time the bridge was finally opened to rail traffic in 1919, the automobile was already well advanced. As early as 1951, one of the two tracks was removed to make room for the new means of transport. In 1970 a second bridge - this time a suspension bridge - had to be built just for road traffic in their immediate vicinity.
Cantilever bridges today
|The Howrah Bridge in Kolkota (former Calcutta) / India |
© U.A. Satish
After all, various factors were responsible for the decline in boom design. The problems with the construction of the bridge over the St. Lawrence River had certainly been observed very closely by the experts. The better control of statically indeterminate systems through the development of plasticity theory has already been mentioned. But there were other reasons as well.
Individual traffic by car became more and more important and led to a decline in rail traffic. For most road bridges, however, other systems such as suspension and cable-stayed bridges were also sufficiently stable. In addition, the first reinforced concrete bridges were built around 1890, which could be built in a more economical and faster way than truss bridges. The sometimes monstrous cantilever bridges no longer corresponded to the taste of the time and were increasingly perceived as "unaesthetic".
One of the last large trusses is the Howrah Bridge over the Hoogly River in Kolkota / India. It was built between 1937 and 1943 by the English colonial administration, and is now one of the busiest bridges in the world. It was still completely riveted, although welding has already been carried out elsewhere. Its span is 457 m and its articulated beam has a length of 166 m. It was also originally built for the railroad, but is now only used by motor vehicles and countless pedestrians and cyclists.
| Two options for training |
of joints in a concrete bridge
© Bernd Nebel
The German bridge builder Fritz Leonhardt judged in his book "Bridges, Aesthetics and Design": "With trusses, deterrent bridges have already been built with a confusing disorder of the rods. In my opinion, the first Hooghly River Bridge in Calcutta is one of the ugliest bridges that thousands of people and vehicles have to use every day."
In America, some large trusses were built beyond the middle of the 20th century, such as the Commodore Bary Bridge over the Delaware or the Mississippi Bridge in Greater New Orleans. But then the era of steel truss bridges slowly came to an end in this part of the world as well. Despite the material and time savings through the welding technology, they had simply become too expensive compared to reinforced concrete and prestressed concrete bridges.
From around 1930, cantilever bridges were increasingly built from reinforced concrete and a few decades later also as solid steel girders. As a rule, the cantilever girders are erected in the open front structure, while the suspension girder is used as a prefabricated component, as is the case with the truss bridges. Because of the advantageous construction, solid steel girders are sometimes made like cantilever bridges, but welded in the joints after assembly, so that ultimately one has a continuous girder. In concrete tanner girders, the design of the joints is particularly important so that damage in this sensitive area is permanently avoided.
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