**10. Cable-stayed bridges**

A cable-stayed bridge has one or more towers, from which straight cables carry the bridge deck as elastic supports. There is a clear analogy between the behaviour of backstays and cablestayed bridges. The first known analysis of this problem comes from 1823 and was performed by C.L. Navier, see [24]. Diagonal rods in Bollman trusses also bring to one's mind cable-stayed

**Figure 22.** Cable stayed bridges: (a) Strömsund Bridge (1956) (*photo by Lars Falkdalen Lindahl* [25]); (b) the tower of the Bratislava SNU bridge, 1972.

bridges. In 1873 in London, the Albert Bridge, designed by Ordish and Bazalgette, was constructed. The first modern cable-stayed bridge is the Strömsund Bridge in Sweden, designed by Franz Dischinger (1956), **Figure 22a**.

The deck is an orthotropic steel box of the aerofoil shape. The bridge was tested and approved

The First Bosphorus Bridge constructed in Istanbul in 1973 is a replica of this bridge. The main span—the distance between the towers—is 1074 m, **Figure 21**. When opened, it was the second

Currently, the construction works of the third Bosphorus bridge—Yavuz Sultan Selim Köprüsü —are underway, according to the design by Michel Virlogeux and Jean-François Klein. The

A cable-stayed bridge has one or more towers, from which straight cables carry the bridge deck as elastic supports. There is a clear analogy between the behaviour of backstays and cablestayed bridges. The first known analysis of this problem comes from 1823 and was performed by C.L. Navier, see [24]. Diagonal rods in Bollman trusses also bring to one's mind cable-stayed

**Figure 22.** Cable stayed bridges: (a) Strömsund Bridge (1956) (*photo by Lars Falkdalen Lindahl* [25]); (b) the tower of the

by the designers Freeman, Fox and Partners following wind tunnel tests.

**Figure 21.** First Bosphorus Bridge: (a) side view; (b) tower and aerodynamic low profile deck.

bridge has been designed as a hybrid structure.

**10. Cable-stayed bridges**

16 Structural Bridge Engineering

Bratislava SNU bridge, 1972.

bridge crossing between Europe and Asia constructed since 480 B.C.

Considering the development of the cable-stayed structure, one can specify the German period connected with German engineers F. Dischinger, U. Finsterwalder , F. Leonhardt, H. Homberg, H. Wittfoht, E. Jux and others. Naturally, cable-stayed bridges have been constructed everywhere. **Figure 22b** shows one on the most beautiful bridges of this kind, namely, the Bridge of the Slovak National Uprising in Bratislava, constructed in 1972. Another spectacular cablestayed bridge is the bridge located at the outlet of Lake Maracaibo, designed by R. Morandi and built in 1962, see [26].

**Figure 23.** Stayed cable bridges: (a) segmental assembling of the Nissibi Euphrates Bridge, 2015; (b) Norman Foster's Millau Bridge (*photo by A. Leniak‐Tomczyk, 2004*).

In the case of cable-stayed bridges at least two assembly technologies are available. The first one refers to a segmental bridge structure built in short sections. It is a very natural method of constructing such bridges. Successive segments are stabilised by attaching them to pylons by means of cables, **Figure 23a**. The other method consists in the incremental launching of a carrying-deck with the use of fixed and intermediate supports. After the launching, the bridge is rectified to its proper grade. An example here is the architecturally magnificent Millau Viaduct designed by M. Virlogeux and N. Foster (2004), **Figure 23b**.

**Figure 24.** Visible cables: (a) the Golden Horn Metro Bridge, 2014; (b) extradosed Viaducto de Teror, Gran Canaria, 2010.

Cable-stayed bridges are aesthetically challenging. To highlight their attractiveness appropriate lighting is required, **Figure 24a**. **Figure 24b** shows a bridge in the mountainous part of Gran Canaria where an austere structure matches an equally austere mountainous landscape. The whiteness of the bridge contrasts with the surroundings. The backstays are clearly visible paradoxically, thanks to cloudy weather. Very often backstays are not discernible at all and for this reason, at night special illumination is used.

In the family of cable-stayed bridges, a special group can be distinguished on constructional grounds, namely, *extradosed* bridges, **Figure 25b**. In this case, the inclination of cables measured from the deck level to the cables is significantly lower than Π/4. Projecting the normal force acting in the cable *N* onto horizontal and vertical directions we arrive at *NH*, *N*V components and, additionally, we obtain *NH* > *NV*. As a result there occurs a significant compression in the carrying-deck which in the extreme degree is manifested near the tower. The horizontal force can be used in the design as the force pre-stressing the deck longitudinally.

**Figure 25.** Badajoz, Spain: (a and b) views from the Roman Bridge.

During the design works and the construction of the Golden Horn Metro Bridge in Istanbul, there was an on-going global discussion about limiting the architectural dominance of a constructed bridge, see [27]. Despite the fact that the pylons demonstrated Ottoman features it was suggested that, with regard to the global cultural and architectural heritage of the area in the vicinity of Golden Horn, the bridge would constitute an extraneous dominant. The bridge was completed without any changes in 2015, see **Figure 24a**.

Short distances between bridges in cities contribute to amusing and sometimes even grotesque situations. Two gorgeous bridges in Sevilla can serve as an example. The Puente de la Barqueta is a tied-arch bridge designed by J. Arenas and J. Pantalerón. The other bridge is the cablestayed Puente del Alamillo designed by S. Calatrava. The construction of the both bridges was completed in 1992. They are located on a straight strip of the oxbow lake of the river Guadalquivir, 1 km apart. Their views overlap, which can be rather irritating.

It is quite a common case in highly urbanised areas and, actually, it occurs in every city on a big river. **Figure 25** shows two frames of a movie that is, so to speak, created in the head of a passer-by walking on the Roman Bridge over the Guadiana River in Badajoz. Depending on the spectator's mood and perception it can appear as chaos or an interesting coincidence.

Cable-stayed bridges are efficient in terms of bridge structure mechanics when placed between cantilever and suspension bridges. On this position, they also prove to be economic solutions. It means that they can be used in the area of small architecture, even if beam or plate bridges are cheaper and better, in a sense. Above all, the pylon, as an interesting dominant, contributes significantly to the attractiveness of a local landscape, see **Figure 26**.

Cable-stayed bridges are aesthetically challenging. To highlight their attractiveness appropriate lighting is required, **Figure 24a**. **Figure 24b** shows a bridge in the mountainous part of Gran Canaria where an austere structure matches an equally austere mountainous landscape. The whiteness of the bridge contrasts with the surroundings. The backstays are clearly visible paradoxically, thanks to cloudy weather. Very often backstays are not discernible at all and for

In the family of cable-stayed bridges, a special group can be distinguished on constructional grounds, namely, *extradosed* bridges, **Figure 25b**. In this case, the inclination of cables measured from the deck level to the cables is significantly lower than Π/4. Projecting the normal force acting in the cable *N* onto horizontal and vertical directions we arrive at *NH*, *N*V components and, additionally, we obtain *NH* > *NV*. As a result there occurs a significant compression in the carrying-deck which in the extreme degree is manifested near the tower. The horizontal force

During the design works and the construction of the Golden Horn Metro Bridge in Istanbul, there was an on-going global discussion about limiting the architectural dominance of a constructed bridge, see [27]. Despite the fact that the pylons demonstrated Ottoman features it was suggested that, with regard to the global cultural and architectural heritage of the area in the vicinity of Golden Horn, the bridge would constitute an extraneous dominant. The

Short distances between bridges in cities contribute to amusing and sometimes even grotesque situations. Two gorgeous bridges in Sevilla can serve as an example. The Puente de la Barqueta is a tied-arch bridge designed by J. Arenas and J. Pantalerón. The other bridge is the cablestayed Puente del Alamillo designed by S. Calatrava. The construction of the both bridges was completed in 1992. They are located on a straight strip of the oxbow lake of the river Guadal-

It is quite a common case in highly urbanised areas and, actually, it occurs in every city on a big river. **Figure 25** shows two frames of a movie that is, so to speak, created in the head of a passer-by walking on the Roman Bridge over the Guadiana River in Badajoz. Depending on the spectator's mood and perception it can appear as chaos or an interesting coincidence.

can be used in the design as the force pre-stressing the deck longitudinally.

this reason, at night special illumination is used.

18 Structural Bridge Engineering

**Figure 25.** Badajoz, Spain: (a and b) views from the Roman Bridge.

bridge was completed without any changes in 2015, see **Figure 24a**.

quivir, 1 km apart. Their views overlap, which can be rather irritating.

**Figure 26.** Architectural cable-stayed bridges: (a) the tram bridge in Bydgoszcz (*photo by courtesy of Gotowski Company*); (b) the bridge in Dźwirzyno over the Resko Channel (*photo by M. Delmaczyński*).

**Figure 26a** shows a tram bridge on the river Brda in Bydgoszcz, 75 m long. It was designed by K. Maciejewski and constructed in 2014. Among typical, ordinary urban buildings the short pylon is a moderate dominant contributing nevertheless to making the landscape more interesting when contrasted with the dynamics of the inclined pylon. Similar enhancement is visible in **Figure 26b**. The short pylon of a small, 51 m long bridge, located in the village of Dźwirzyno, is so different from the village buildings that it becomes a fascinating radical sculpture. It was designed by J. Siuda and M. Delmaczyński. After its construction in 2011, an increased demand for equally small but architecturally interesting bridges has been observed.

**Figure 27.** Arch bridge erection by cable-stayed supports at sunset, Estremadura, 2015.

The cable-stayed technology has been used as a temporary support for arch bridge scaffolding for many years. These are transitional arrangements and images but ones that are truly charming thanks to the additional spaciousness they create. Sometimes, as shown in **Figure 27**, an austere surrealist image is obtained. This short-lived aesthetic form refers directly to the art of performance as it disappears the moment the arch is built.

**Figure 28.** Katehaki footbridge, Athens, 2004: (a–c) different views of the bridge.

A separate place in architecture and structural engineering belongs to Santiago Calatrava, although in this paper he is mentioned only briefly. Calatrava, in the architectural millieu's opinion, is a creator of gigantic forms—spatial sculptures which enhance the landscapes of various cities around the world. As a bridge constructor, he broke a mental barrier existing in the area of bridge design where bridges were designed for bending as a dominant mechanical state. In the case of pedestrian footbridges he constructed bridges where carrying elements are screwed together. Due to this, the mental barrier has been broken.

Examples of gigantic sculptures in urban areas include the following bridges: the Puente del Alamillo in Sevilla, 1992, the Puente De La Mujer in Buenos Aires, 2001 and the Sundial near Redding, California, 2004. The Jerusalem Chords Bridge, however similar, is new concept. These bridges are purely white, the pylons are inclined by approx. 50° and they resemble each other, as images, to a high degree. However, the structural engineering of each of the bridges is different. The Alamino is a road bridge with a beam load-bearing structure identical to the one of the arch bridge Puente Lusitania in Mérida. The rest are pedestrian footbridges with screwed load-bearing structures. The Puente de la Mujer is a moveable bridge with a rotary movement about the vertical axis on the support with a pylon. The Sundial has a truss loadcarrying structure. As demonstrated, each of these bridges is different and only for architects their images are identical.

austere surrealist image is obtained. This short-lived aesthetic form refers directly to the art of

performance as it disappears the moment the arch is built.

20 Structural Bridge Engineering

**Figure 28.** Katehaki footbridge, Athens, 2004: (a–c) different views of the bridge.

screwed together. Due to this, the mental barrier has been broken.

A separate place in architecture and structural engineering belongs to Santiago Calatrava, although in this paper he is mentioned only briefly. Calatrava, in the architectural millieu's opinion, is a creator of gigantic forms—spatial sculptures which enhance the landscapes of various cities around the world. As a bridge constructor, he broke a mental barrier existing in the area of bridge design where bridges were designed for bending as a dominant mechanical state. In the case of pedestrian footbridges he constructed bridges where carrying elements are

Examples of gigantic sculptures in urban areas include the following bridges: the Puente del Alamillo in Sevilla, 1992, the Puente De La Mujer in Buenos Aires, 2001 and the Sundial near Redding, California, 2004. The Jerusalem Chords Bridge, however similar, is new concept. These bridges are purely white, the pylons are inclined by approx. 50° and they resemble each other, as images, to a high degree. However, the structural engineering of each of the bridges is different. The Alamino is a road bridge with a beam load-bearing structure identical to the one of the arch bridge Puente Lusitania in Mérida. The rest are pedestrian footbridges with screwed load-bearing structures. The Puente de la Mujer is a moveable bridge with a rotary In the author's opinion, the most interesting is the Katehaki Footbridge in Athens, 2004, **Figure 28**. The footbridge is never entirely visible and therefore mysterious—making one yearn for more. The pylon is slightly bent as a result of which it loses the original but at the same time primitive form of an opened set square and becomes similar to boats crossing the Mediterranean Sea. The footbridge is literally squeezed between uninteresting street buildings of Athens. A crossing passer-by who reaches one of its ends can look into the windows of the buildings located only 10 m away. The footbridge is in the middle of street traffic. The lack of space and the constant flow of passing vehicles contribute to the dynamics of the structure which, thanks to its white and slender elegance, floats above crowded streets of Athens.

The Millennium Bridge in London is a hybrid of two static schemes. There are deck segments supported by cables (*vide* the ribbon scheme) and at the same time the deck is suspended on the same cables as in the case of the suspension bridge. **Figure 29**.

**Figure 29.** Millennium Bridge in London: (a) view of the bridge; (b) support detail.

The history of the bridge opening is a typical English story, i.e., starting from a total failure and ending in full glory, see, e.g., [28]. The bridge was conceived as an interesting design, quite innovative.

The opening day had been expected for a long time. Finally, on 10 June 2000, thousands (ca. 5000) of people were waiting to enter the bridge and walk to other side. At this moment, the new bridge entered into a state of unpleasant complex horizontal and vertical vibrations. It turned out that despite the use of advanced computational techniques and the designers' experience, the bridge demonstrated dynamical over-sensitiveness. The new bridge was closed on 12 June of the second millennium. Soon after, a diagnosing research was conducted which pinpointed the cause of the dynamic instability of the bridge. On its basis, it was decided to install a system of dampers which changed the dynamic response of the bridge. Two years later, the Millennium Footbridge was reopened and has been working properly ever since.
