Proceedings of the Institution of Civil Engineers View metadata, Bridgecitation Engineering and similar 163 papers at core.ac.uk brought to you by CORE June 2010 Issue BE2 Pages 67–78 provided by Spiral - Imperial College Digital Repository doi: 10.1680/bren.2010.163 .2.67 Paper 900033 Received 29/09/2009 Accepted 22/02/2010 Ana M. Ruiz-Teran Angel C. Aparicio Principal Lecturer in Professor in Bridge Keywords: Structural Engineering, Engineering, bridges/cables & tendons/viaducts School of Computing, Department of Information Technology Construction and Engineering, Engineering, Technical University of East University of Catalonia London, London, UK (UPC), Barcelona, Spain

Developments in under-deck and combined cable-stayed bridges

A. M. Ruiz-Teran MEng, PhD, CEng, MICE, MCICCP, FHEA and A. C. Aparicio MEng, PhD, MCICCP

Under-deck, cable-stayed bridges and combined cable- layouts that have been developed over the last three decades. In stayed bridges constitute two innovative bridge types that under-deck, cable-stayed bridges, the stay cables are located have been designed and built on relatively few occasions below the deck whereas in combined cable-stayed bridges the over the last 30 years, in most cases by renowned stay cables are located both above and below the deck. The structural engineers, such as Leonhardt, Schlaich, terms ‘under-deck cable-stayed bridges’ and ‘combined cable- Virlogeux, Manterola, Robertson and Cremer. In these stayed bridges’ were proposed by the authors during doctoral bridge types, the stay cables have unconventional layouts: studies (Ruiz-Teran, 2005) that investigated bridges with these either below the deck, in the case of under-deck cable- schemes (Figure 1). This work has produced numerous research stayed bridges, or above and below the deck, in the case outcomes (Ruiz-Teran and Aparicio, 2007a; 2007b; 2007c; of combined cable-stayed bridges. In this paper, a general 2008a; 2008b; 2008c; 2009a; 2009b), as a consequence of which and critical overview of the current state-of-the-art is the FIB Diploma 2009 for Research (Ruiz-Teran, 2010) was outlined, addressing issues related to proposals, built recently presented to the first author. However, the exciting and bridges and research. Significant attention is paid to their interesting history of the design, construction, and development highly efficient structural behaviour and unconventional of these bridges started to be written many years before, in the design criteria, both of which lead to a significant 1970s and 1980s, owing to the scholarship, intelligence, reduction in the amount of required materials, in resoluteness, and tenacity of two outstanding structural comparison with conventional bridges without stay engineers, namely Professor Fritz Leonhardt and Professor Jorg cables, and thus allow for sustainable design. Other Schlaich, who designed these bridge types for the first time. In advantages of these bridges, such as multiple addition, the contribution in the 1990s of other renowned construction possibilities, strong aesthetic characteristics structural engineers, such as Virlogeux, Manterola, Robertson and their broad range of potential applications, are also and Cremer, who designed several bridges with these forms, was stressed. critical for the development of these bridge types.

The aim of the present paper is to offer a general and critical 1. INTRODUCTION overview of the developments in under-deck and combined Civil engineering structures, and in particular bridge structures, cable-stayed bridges over the last 30 years in this special issue aim to be as light as possible (Schlaich and Bergermann, 2004) that is focused upon the recent advances in cable-supported in order to reduce the amount of materials required. This fact structures. has significant structural, construction, economic and sustain- ability implications. The best structural forms for achieving this 2. THE PRECURSOR UNDER-DECK aim are those that promote axial behaviour and reduce flexural SUSPENSION BRIDGES response. Cable-supported structures intrinsically promote the Under-deck suspension bridges appeared almost 150 years axial behaviour due to the lack of flexural stiffness of their before under-deck cable-stayed bridges. Robert Stevenson was cables. the first to publish a proposal for an under-deck suspension bridge with chains in 1821 (Peters, 1987) for the Cramond Suspension bridges, cable-stayed bridges, extra-dosed bridges, Bridge, over the Almond River, in Edinburgh. However, this and bow-strings are conventional types of cable-supported bridge was never constructed. The first under-deck suspension bridges. When referring to these types of bridges, the cables are bridges to be constructed were the Bergues Bridge (in 1834) and usually assumed to be located over the deck. However, this is not the Bel-Air Bridge at la Coulouvreniere (in 1837), with always the case. suspension systems made of chains and cables respectively (Peters, 1987). Both bridges were designed by Henri Dufour. The This paper is focused on two types of unconventional cable- reasons for locating the cables below rather than above the deck supported bridges, namely under-deck cable-stayed bridges and were: combined cable-stayed bridges. These are two innovative types of cable-stayed bridges with unconventional cable-staying (a) economic – saving the cost of the masonry towers;

Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio 67 One-span bridges Continuous bridges

Elimination of piers in viaducts

Two-span bridges

Three-span bridges

Figure 1. Schemes of cable-supported bridges studied by the authors

(b) structural – distributing the bearing cable system equally prestressing is required and, moreover, no prestressing can be along the transverse direction rather than concentrated in applied over the cables, since the action on the anchorages the sides, reducing the transverse bending and facilitating modifies the layout of the cable and the alignment of the deck, the anchorages of the cables; rather than the tension on the cables. (c) reduced maintenance – sheltering the cables from the rain and from vandalism; 3. HISTORICAL REVIEW OF UNDER-DECK AND (d) construction – providing a catwalk for construction and COMBINED CABLE-STAYED BRIDGES maintenance by means of the cables; and 3.1. Fritz Leonhardt’s invention: under-deck cable- (e) comfort for users – who were not aware of the suspension stayed bridges system that was very innovative and, consequently, a less Fritz Leonhardt was the first structural engineer to design an reliable type, at that time (Peters, 1987). under-deck cable-stayed bridge (Ruiz-Teran and Aparicio, 2007a); the Weitingen viaduct (Leonhardt, 1982) (Figure 2), over However, after the construction of these two bridges, this bridge the Neckar River, in Germany. Its construction was completed in type fell into oblivion and has only been recovered after the 1978. The proposal of this new bridge type arose in Leonhardt’s appearance of under-deck cable-stayed bridges a century later. mind as a consequence of trying to solve a complex engineering problem. The new highway from Stuttgart to Singen had to cross Under-deck suspension bridges can be considered the precursor over the 900 m wide Neckar valley with a height of 120 m of under-deck cable-stayed bridges. In fact, there are more above the river bed. The most appropriate solution was a viaduct similarities between under-deck suspension bridges and under- with main spans slightly larger than the central pier height. On deck cable-stayed bridges than between conventional (i.e. with this basis, a simple calculation, assuming end-spans of around the cables above the deck) suspension bridges and cable-stayed 80% of the length of the main spans, would provide five main bridges. When the cables of an under-deck suspension bridge spans of around 135 m and two shorter and well-balanced end- are self-anchored in the deck, it becomes a self-anchored under- spans. However, this proposal encountered significant difficul- deck suspension bridge. In addition, when the cables are ties in the design of the end piers of the viaduct, since the soil in prestressed, compensating the dead load and the superimposed the valley slopes suffered significant creeping. Leonhardt dead-load, the self-anchored under-deck suspension bridge addressed the problem by eliminating the end-piers of the becomes an under-deck cable-stayed bridge. The act of self- viaduct, replacing them by an under-deck cable-staying system anchoring the cables in the deck in an under-deck suspension (ASCE, 1978). The prestressed under-deck stay cables introduced bridge significantly changes its structural behaviour, promoting into the deck, by means of struts, an upward deviation force linear behaviour rather than geometrical non-linear behaviour equal to the vertical reaction that would have been provided by (Ruiz-Teran, 2005). When the decks are very slender, with a very the eliminated piers under the permanent loads of self-weight low flexural stiffness, both bridge types (the self-anchored and superimposed dead load. Nevertheless, he shifted the under-deck suspension bridge and the under-deck cable-stayed location of the struts closer to mid-span, making the initial end bridge) become the same bridge type. In this case, no spans longer than usual. This suggests that he could probably

68 Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio Figure 2. Weitingen viaduct (photograph courtesy of Holger Svensson of Leonhardt, Andra und Partner) have achieved this final solution with a compromise between In 1987, three footbridges of this type were constructed at the structural and aesthetic considerations (Ruiz-Teran and Gut Marienhof sewage treatment plant , near Munich (Holgate, Aparicio, 2007a). In addition, he designed the viaduct with a 1997; SBP, 2004). Schlaich was also encouraged by the fact that steel box girder with angled struts supporting the transverse Christian Menn had independently started research on this cantilever, a section that is not usually used for main spans of bridge type at the ETH in Zurich. this length due to the large cost of the stiffened top flange. He used it with the aim of reducing the cross-sectional area of the In 1987, Menn and Gauvreau began experimental research into stay cables by reducing the self-weight of the bridge, so that the structural behaviour of two-span continuous slabs with they could be located below the deck. The extra cost of the steel under-deck cable-staying systems with two struts (Menn and deck was justified on aesthetic and economic considerations, as Gauvreau, 1987). When the results were published in 1990 this design did not require the towers that a conventional cable- (Menn and Gauvreau, 1990) they found two great drawbacks in stayed bridge does (ENR, 1978). the structure that they had tested:

(a) a very small contribution of the stay cables under live load; 3.2. The contributions of Jorg Schlaich and Christian and Menn in the 1980s (b) a small capacity of the section over the intermediate support In 1982, Jorg Schlaich submitted a preliminary proposal for a for resisting hogging bending moments. new railway bridge in Munich, Germany, using an under-deck cable-staying system. At that time Schlaich was convinced that Their proposals for addressing these issues were, respectively: under-deck cable-staying systems were much more efficient than external prestressing, due to the higher eccentricity of the (a) replacing the prestressing steel by structural steel in order to tendons (Holgate, 1997). He demonstrated this idea in 1987, increase their axial stiffness; and when he designed the Kirchheim overpass, a portal frame with a (b) locate props between the bottom of the struts and the main span of 45 m, with a concrete slab of only 0?40 m depth intermediate pier. supported by under-deck stay-cables (Schlaich and Schober, 1994). However, the federal road authorities prevented the Menn and Gauvreau were therefore researching on intradosed construction of the initial proposal due to their concerns about bridges rather than on under-deck cable-stayed bridges. It is the accessibility and maintenance of the under-deck stay cables worth stressing that in both intradosed and extradosed bridges and the possible collapse of the bridge in the case of a vehicle the stay cables do not contribute significantly under traffic live collision. Schlaich had to present a final design in which the load. Despite the outcomes from their experimental work, Menn under-deck stay cables were replaced by internal prestressing by made a proposal for continuous bridges with main spans of considerably increasing the depth of the deck (Holgate, 1997). 36 m with under-deck cable-staying systems with two struts Subsequent research has demonstrated the large capacity of (Lemaitre and Kobler, 2005). Schlaich also followed the same under-deck cable-stayed bridges for overcoming the sudden approach for multi-span bridges, extrapolating the efficient breakage of several stay-cables without violating any ultimate under-deck cable-staying systems from single-span to contin- limit state (ULS) (Ruiz-Teran and Aparicio, 2009a). The concerns uous bridges, with the proposal in 1989 for Schornbachtal that emerged from the initial design were unfounded from a viaduct (Holgate, 1997). technical point of view. They were probably created as a consequence of the lack of understanding that great innovations The contemporary solution to the problem found by Menn and are usually accompanied by in their beginnings. Despite the Gauvreau is much simpler than the approach they suggested: to rejection, Schlaich took a giant step in the direction of designing provide eccentricity to the stay cables in the intermediate light structures by putting forward this proposal with a slender support, locating them above the deck, so that a large portion of deck (1/113). the bending moment due to traffic live load can be resisted by a

Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio 69 Figure 3. Obere Argen viaduct (photograph courtesy of Jorg Schlaich, copyright Elsner, Gert, Stuttgart)

couple with the stay cables working under tension and the deck (Schlaich, 1999). The configuration that he chose was the best working under compression. However, at that time, it was not for eliminating the end-piers in a viaduct by means of stay appreciated that multi-span continuous under-desk cable-stayed cables (Ruiz-Teran, 2005; Ruiz-Teran and Aparicio, 2008c). He bridges are inefficient. In fact, this modification to the stay- also chose a steel box-girder with angled struts supporting the cable layout would give rise to a new bridge: the combined transverse cantilever for the deck, as Leonhardt did (Schlaich, cable-stayed bridge. 1999).

3.3. Jorg Schlaich’s invention: combined cable- 3.4. The blossoming of the construction of under-deck stayed bridges and combined bridge types A major advance was again achieved by Schlaich through the Once these two steel bridges, Weitingen and Obere Argen design and construction of the Obere Argen viaduct (Figure 3), viaducts, with main spans larger than 200 m, had been completed in 1991. This was the first bridge using a combined successfully completed, many structural engineers paid atten- cable-staying system. Schlaich was asked to design a 730 m tion to these structural types. The deck slenderness achieved long viaduct, 45 m above the Obere Argen valley, for the A96 with both viaducts was not extremely high (1/43 and 1/69, highway in Germany (Cazet, 1992; WTB and Dywidag, 1991). respectively), but the structural system had been successfully On this occasion, he had to address a similar problem as tested on site. Leonhardt did a decade before, due to the creeping of the soil deposits in one of the valley slopes. He designed a viaduct with a In 1993, the Truc de la Fare fauna overpass (Figure 4), designed 258 m end-span with a combined cable-stayed system with by Michael Virlogeux, was completed. It was the first under- three struts, subdividing the span into six sections each 43 m deck cable-stayed bridge with a prestressed concrete deck. The long. This achievement was met after a thorough analysis of relatively low slenderness of the deck, for an under-deck cable- different conventional (such as arches, trusses and cable-stayed stayed bridge, equal to 1/33, was governed by the height of the bridges) and unconventional (such as under-deck cable-stayed parapets, which were incorporated into the section. In the bridges and combined cable-stayed bridges) bridge typologies conceptual design of this bridge, Virlogeux became aware of the

Figure 4. Truc de la Fare fauna overpass (photograph courtesy of Nicholas Janberg, www.structurae.de)

70 Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio relevance of increasing the number of struts in order to increase prestressing (Gonzalez, 1997). This fact has been demonstrated the efficiency of the stay cables. In addition, he designed by subsequent research (Ruiz-Teran 2005; Ruiz-Teran and inclined struts aligned with the direction of the cable deviation Aparicio 2008a; 2008b). forces in order to avoid inducing bending moments in them. Moreover, Virlogeux clearly identified the different behaviour of Aurelio Muttoni, professor at the Swiss Federal Institute of the stay cables in comparison with design using external Technology in Lausanne, also paid attention to these cable- prestressing (Virlogeux et al., 1994). Subsequent research (Ruiz- staying systems (Muttoni, 2002). However, with his aim of both Teran and Aparicio, 2009a) demonstrated that deviators with increasing the efficiency of the cable-staying system and clamps would have provided additional resistance in the case of providing additional protection to the stay cables, his final a sudden breakage of a stay cable due to the collision of a heavy design was a similar, but different, bridge type. In his designs for vehicle exceeding the permitted clearance. In this latter case, a the Capriasca and the Bedretto Bridges (Muttoni, 1997) that were pin connection between the struts and the deck would have been completed in 1996, the under-deck cable-staying system was more effective by avoiding the introduction of bending replaced by prestressed concrete members. In addition, he moments in the slender deck (Ruiz-Teran and Aparicio, 2008a). replaced every strut by two struts in order to create a triangular cell with the deck. In 1994, the Osormort viaduct (Figure 5), designed by Javier Manterola, was completed (Lluch et al., 2001). It was the first In 1997, the Miho Museum footbridge, designed by Leslie continuous viaduct in which an under-deck cable-staying Robertson, was completed. This bridge was designed as a system with a single strut was implemented in all of the spans. It processional entrance to the Miho Museum in the remote and was a similar scheme to those proposed by Schlaich and Menn spectacular wooded valley of Shigaraki in Japan (Watanabe, years before. As could be expected, the large hogging bending 2002). In the authors’ opinion, the great achievement of this moments in the deck sections over the intermediate supports did bridge is how both the stay cables located above the deck and not allow a significant reduction in the deck depth. It was the transverse arch, in which the stay cables are anchored, frame designed with the usual slenderness of 1/25, but used a two- and bound the space of passage above the deck. This additional triangular-ribbed section that does not have a great hogging advantage from the aesthetic standpoint of the combined cable- bending moment resistance. Subsequent research (Ruiz-Teran stayed bridges has been highlighted in subsequent publications and Aparicio, 2008b) has demonstrated the low efficiency of the (Ruiz-Teran and Aparicio, 2008a; 2008b). under-deck cable-staying systems for continuous bridges. In fact, the implementation of under-deck cable-staying systems In 1998, six different bridges with under-deck and combined for continuous bridges with appropriate eccentricities from an cable-staying systems were completed (Table 1). The achieve- aesthetic standpoint (Ruiz-Teran and Aparicio, 2007b) leads to ments in the designs of Jumet footbridge, Tobu Recreation intradosed bridges rather than under-deck cable-stayed bridges. Resort footbridge and Glacis Bridge were remarkable. The Jumet This bridge was built following a span-by-span construction footbridge (Figure 6) was the first under-deck cable-stayed process using a self-launching gantry (Gonzalez, 1997). The bridge for which the depth/span ratio was reduced beyond 1/100 joints were located at a distance from the support section (Forno and Cremer, 2001; Ruiz-Teran and Aparicio, 2007a). The equivalent to 7?5% of the span length, rather than the usual Tobu Recreation Resort footbridge was the first under-deck 20%, as a consequence of the span subdivision achieved through cable-stayed bridge designed with multiple struts. Tsunomoto the under-deck cable-stayed system. In addition, Manterola and Ohnuma proposed a very appropriate tensioning procedure stressed the interest of under-deck cable-staying systems for for this bridge (Ruiz-Teran and Aparicio, 2007a; Tsunomoto and medium spans, owing to the large efficiency of the cable-staying Ohnuma, 2002). They designed pin connections between the systems that can be achieved using anchorages with conven- deck and all of the struts, with the exception of a fixed tional fatigue strength, similar to those used for external connection at mid-span. Prior to the prestressing of the stay

Figure 5. Osormort viaduct (photograph courtesy of Javier Manterola)

Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio 71 Year Structure Designer Status Country Material

1978 U Weitingen viaduct Fritz Leonhardt Built Germany Steel 1987 U Kirchheim overpass Schlaich, Berermann und Proposal Germany PC Partner U Gut Marienhof footbridge Schlaich, Berermann und Built Germany Steel Partner U Under-deck cable-stayed viaduct Christian Menn Proposal Switzerland ? 1989 U Schornbachtal viaduct Schlaich, Berermann und Proposal Germany ? Partner U Kampfelbach viaduct Schlaich, Berermann und Proposal Germany ? Partner 1991 C Obere Argen viaduct Schlaich, Berermann und Built Germany Steel Partner U Vinalopo Bridge Esteyco SA Proposal Spain PC 1993 U Truc de la Fare overpass Michael Virlogeux Built France PC 1994 U Millau viaduct Francis Soler Proposal France ? U Millau viaduct – Proposal France ? 1995 U Osormort viaduct Javier Manterola Built Spain PC 1997 C Miho Museum footbridge Leslie E. Robertson Built Japan Steel 1998 U Jumet footbridge Jean Marie Cremer Built Belgium Steel U Losa of the Obispo Bridge Jose´ Ramo´n Atienza Built Spain Composite U Tobu Recreation Resort foot- Toyo Ito & Associates Built Japan PC bridge U Glacis Bridge Schlaich, Berermann und Built Germany PC Partner C Wacshhaussteg footbridge Schlaich, Berermann und Built Germany Steel Partner C Hiyoshi footbridge Simura & Tanase Built Japan Steel 1999 U Weil am Rheim viewpoint Schlaich, Berermann und Built Germany Steel Partner C Ayumi Bridge CTI Engineering Built Japan PC 2000 U Takehana Bridge – Built Japan PC 2001 U Morino-Wakuwaku-Hashi foot- Yosuki Kojima Built Japan PC bridge C Torizaki River Park footbridge Civil Eng. Services Built Japan PC 2002 U Numedalslagen footbridge Kristoffer Apeland Built Norway Timber 2003 C Montabaur footbridge Ludwig Mu¨ller Offenburg Built Germany Steel U Haute Provence glass footbridge Johaness Liess Built France Structural glass U Chicago Michigan Avenue Apple Dewhurst MacFarlane & Built USA Structural glass store footbridge Partners, Inc. & A. Epstein and Sons Int. U Nishisonogi Bridge Kazumi Terada and Takuya Built Japan Composite Fujimoto 2004 U Meaux viaduct Michael Placidi Built France Composite U Spinningfields Bridge Whitbybird Proposal UK Aluminium 2006 U Barajas Airport Terminal 4 – Built Spain Steel footbridge U Seiryuu footbridge Asahi Development Built Japan PC Consultants Ltd & Oriental Construction Co. Ltd U Fureai footbridge Taiyo Consultants Co. Ltd Built Japan PC and Oriental Construction Co. Ltd 2007 U University Limerick Living Bridge Ove Arup and Partners Built Ireland Steel

Table 1. Summary of proposals and built under-deck cable (U) and combined (C) cable-stayed bridges in chronological order according to year of completion

cables, the struts were located in a certain position that was cables were prestressed by means of temporary vertical tensor determined so that the struts were located in the appropriate cables anchored in the riverbed so that the deformations were final position after the elongation of the stay cables due to their minimised during construction (Schlaich and Werwigk, 2001). prestressing. In addition, they highlighted the relevance of the vibrations due to live load that governed the depth of the deck 3.5. Recent developments in research on under-deck and (Tsunomoto and Ohnuma, 2002). The Glacis Bridge was combined bridge types designed by Schlaich with a portal frame configuration, similar Following the construction of the bridges just mentioned, to that proposed for Kirchheim overpass. In this case, despite the several researchers from different universities started to pay length of the main span, doubling that at Kirchheim, the attention to these bridge types. In most of the cases, these bridge construction was successfully completed. Moreover, the Danube types were not the focus of the study, but they were considered. Bridge was spanned without using temporary falsework, as the In 1998, Ziyaeifar et al. (1998), from Chiba University in Japan, under-deck stay-cables were used as bearing cables. These proposed to use the under-deck stay cables as bearing cables

72 Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio Figure 6. Jumet footbridge (photograph courtesy of Jean Marie Cremer) during construction, as Schlaich had done before. In the same fact can also be re-interpreted in terms of efficiency. Combined year, Umezu et al. (1998), members of a research partnership cable-stayed bridges are more efficient because they require half between Sumitomo Construction and Nihon University in Japan, the eccentricity in under-deck cable-stayed bridges for achiev- presented a preliminary theoretical study about the transition ing the same load-carrying capacity, and consequently they are from external prestressing to combined stay cables. In the more appropriate for continuous bridges. laboratories at ETH Zurich, Switzerland in 1998, Fu¨rst and Marti (1999) tested four different simply-supported prestressed con- In 2005, Ruiz-Teran submitted her PhD dissertation (Ruiz-Teran, crete trusses, with two triangle cells as struts, similar to those 2005) concerning the structural behaviour and design criteria of designed by Muttoni. They found that these schemes had a unconventional cable-stayed bridges, including under-deck and significant non-linear behaviour, as was expected, due to the combined cable-staying bridges. Ruiz-Teran and Aparicio have significant loss of axial stiffness in the tension member after outlined the state-of-art of these structural types (Ruiz-Teran cracking. One year later, Laffanchi completed his PhD thesis and Aparicio, 2007a), identified the parameters governing their (Laffanchi, 1999), supervised by Professor Marti, on graphical structural response (Ruiz-Teran and Aparicio, 2007b), studied analysis for curved bridges, including under-deck cable-stayed their structural behaviour and proposed design criteria for both bridges. In 2004, Ploch completed his PhD thesis (Ploch, 2004), single-span (Ruiz-Teran and Aparicio, 2008a) and multi-span that was supervised by Professor Kurt Schafer, at ILEK, in (Ruiz-Teran and Aparicio, 2008b) bridges with these structural Stuttgart, Germany, on reliability of prestressed structures, types, studied their response under the accidental breakage of including under-deck cable-stayed bridges. The main outcome stay cables (Ruiz-Teran and Aparicio, 2009a), proposed uncon- of this research was the proposal of independent load factors for ventional cable-stayed layouts for either eliminating piers in the prestressing of stay cables. This approach was used by the viaducts or allowing an unbalanced distribution of spans (Ruiz- first author in her PhD thesis (Ruiz-Teran and Aparicio, 2005). In Teran and Aparicio, 2008c), and proposed appropriate method- 2005, Aravinthan et al. (2005), from the University of Southern ologies for the analysis of the dynamic response under either the Queensland in Australia and Saitama University in Japan, breakage of stay cables (Ruiz-Teran and Aparicio, 2007c) or the published their experimental work on three different uncon- transit of traffic live load (Ruiz-Teran and Aparicio, 2009b), ventional schemes: a single-span under-deck cable-stayed since traditional procedures were demonstrated to be inap- beam, a two-span under-deck cable-stayed beam, and a two- propriate. span combined cable-stayed beam. This research was conceived as an extension of external prestressing and consequently the 3.6. Recent developments in design design criteria was different to those required for under-deck Over the past ten years, in parallel with the aforementioned and combined cable-stayed bridges. Nevertheless, for the under- research developments, many bridges of these types had been deck cable-stayed two-span beam, they reported both a constructed (Table 1). Whereas under-deck and combined cable- redistribution of 50% in the hogging bending moment over the staying systems were initially used in steel decks and rapidly intermediate support and ‘a premature crushing of concrete near implemented in prestressed-concrete (PC) and composite (steel the centre support’. They obviously faced the same problem that and concrete) decks, these schemes have recently been used in Menn and Gauvreau found 15 years earlier. However, these decks made up from a larger range of materials, such as timber authors did not identify the lower efficiency of under-deck (Numedalslagen footbridge), galvanised steel (Montabaur foot- cable-staying systems in continuous beams. They also reported bridge), aluminium (Spinningfields footbridge) and structural similar load capacity in continuous beams with under-deck and glass (Haute Provence footbridge and Chicago Michigan Avenue combined layouts when these were vertically translated. This Apple store footbridge). The last bridge catalogued by the

Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio 73 authors is the living bridge at the University of Limerick 4.3. High efficiency under traffic live load (Brownlie and Lavery, 2008), which was completed in 2007 in In order to design cable-staying systems that are efficient under Ireland. It is the first multi-span under-deck cable-stayed bridge live load it is necessary: with independent spans. This system is one of the schemes that have been recommended by the authors for multi-span bridges (a) to design stay cable layouts with large eccentricities at the (Ruiz-Teran and Aparicio, 2008b), as the lack of continuity critical sections of the deck, locating them beyond the side eliminates the problems reported by Menn and Gauvreau (1990). of the deck in which tensile stresses are introduced due to the existing bending moments, and All of these bridges have now become less unconventional for (b) to design the bridge with a small relative rigidity of the deck structural engineers. A proof of this assertion is the fact that to the cable-staying system. they have been included in recent overviews of cable-stayed bridges (Strasky, 2005). The satisfaction of both conditions leads to cable-stayed bridges that resist the traffic live load mainly by axial response rather than by flexural response. The bending moment envelopes due 4. MAIN FEATURES to traffic load (Figures 7(e) and 7(f)) are significantly different to those in conventional bridges without stay cables. High 4.1. High efficiency of the cable-staying systems efficiencies (b~0:9) can be easily achieved in these types of The efficiency of the cable staying system (Ruiz-Teran and bridges. Aparicio, 2007b) can be measured through a parameter b that 2 represents the fraction of the external isostatic moment (qL /8 4.4. High sensitivity to vibrations due to traffic live load due to a uniform-distributed load q and QL/4 due to a point load The reduction of the flexural response allows a large reduction Q, in a beam of length L) that is resisted by means of the stay in the deck depth that leads to a significant increase of the cables working in tension. The efficiency of the cable-staying accelerations in the deck due to the transit of heavy vehicles system is inversely proportional to the relative rigidity of the (Figure 7(g)). In fact, the depth of the deck in road bridges with deck to the cable-staying system (Ruiz-Teran and Aparicio, these structural types with short and medium spans is governed 2007b), x, that is given by by the serviceability limit state (SLS) of vibrations. This SLS   must be verified following an acceleration-based approach, EI L I L ~ S z S since the traditional deflection-based approach considered by 1 x 2 gI ,n 2 gA ,n ESCASCL L AL L many codes leads either to unsafe design or to overdesign (Ruiz- Teran and Aparicio, 2009b). For example, the maximum vertical

where E and ESC are the Young’s modulii of the deck and of the accelerations in the under-deck cable-staying road bridge 2 stay cables, respectively, A and ASC are the cross-sectional area included in Figure 7 are equal to 0?41 m/s , which is 14 times of the deck and of the stay cables respectively, I is the moment larger than that in a road bridge with the same length without

of inertia of the deck, LS is the length of the strut at mid-span stay cables.

section, n is the number of struts. gI and gA are two functions that are defined on the basis of the geometry of the cable- 4.5. Sustainable design due to small amount of

staying system and are inversely proportional to LS/L and n. The conventional materials smaller the relative rigidity of the deck to the cable-staying The reduction of the flexural response leads to a significant system, the larger the efficiency of the cable-staying system. reduction in the amount of materials required for the deck, in comparison with conventional bridges without stay cables. These new structural types are therefore compliant with 4.2. Span subdivision sustainable design considerations. For single-span bridges with The span subdivision (Ruiz-Teran and Aparicio, 2008a; 2008b) prestressed concrete decks and main spans of 80 m, the depth of is easily achieved in these bridges by prestressing the stay cables the deck is reduced to 20% (with slenderness equal to 1/80), the in such a way that the vertical components of either the anchor self weight to 30% and the amount of active steel to 30% (Ruiz- forces of the stay cables in the deck, or the cable deviation forces Teran and Aparicio, 2008a). For continuous bridges with introduced into the deck by means of the struts, are equal to the prestressed concrete decks and spans of 80 m, the depth of the vertical reactions in a continuous beam with supports in the deck is reduced to 25% (with slenderness equal to 1/100), the sections of the deck in which either the stay cables are anchored self weight to 60% and the active steel to 40% (Ruiz-Teran and or to which the struts are connected (Figure 7(c)). The larger the Aparicio, 2008b). efficiency of the cable-staying system, the smaller the compo- nent of the stay cable loads in permanent state due to the active 4.6. Great construction possibilities prestressing of the cables, and the larger the component These structural types offer a wide range of possibilities from the attributable to the passive response due to the self-weight and point of view of construction. In fact, the use of these bridge the superimposed dead load. In addition, the smaller the flexural types would allow the extension of the span range of certain stiffness of the deck, the larger the efficiency of the cable- construction methods, such as construction by means of staying system, the smaller the losses in the cables and longitudinal precast prestressed elements (with joints over the consequently the smaller the redistribution of internal forces struts, and assembled on site) (Ruiz-Teran and Aparicio, 2008a) due to time-dependent effects. In under-deck and combined and the construction of viaducts by means of self-launching cable-stayed bridges, the span subdivision is almost maintained gantries (due to the large reduction in the self weight) (Ruiz- over time owing to the small redistribution of internal forces due Teran and Aparicio, 2008b). In addition, these systems allow the to time-dependent effects (Figure 7(d)). construction of bridges over deep valleys or wide rivers without

74 Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio 80.00

4.10 5.13 5.13 5.13 5.13 5.13 5.13 5.13 5.13 5.13 5.13 5.13 5.13 5.13 5.13 4.10 (a)

8.00

13.20 13.20

(b)

–0.53 MN m –0.46 MN m –0.53 MN m (c) 0.20 MN m0.29 MN m0.29 MN m0.20 MN m

2.74 MN m (d) 2.33 MN m . 3.46 MN m3.46 MN m 2 33 MN m 1.84 MN m 1.84 MN m

–4.00 MN m –4.00 MN m –4.02 MN m –4.02 MN m –0.93 MN m–0.93 MN m –0.78 MN m (e)

4.37 MN m 6.52 MN m64.67 MN m4.67 MN m .52 MN m 6.61 MN m6.61 MN m

. . –1 64 MN m . . –1 64 MN m . –0 57 MN m –0 57 MN m . –1 59 MN m . –1 59 MN m (f) –0 33 MN m

4.46 MN m 4.46 MN m . . . 4.42 MN m 3 49 MN m349 MN m 4 42 MN m 3.42 MN m (g) 0.5 0.4 0.3

2 0.2 0.1 0 Upward acceleration –0.1 Downward acceleration –0.2 Absolute acceleration Acceleration: m/s –0.3 –0.4 –0.5

Figure 7. Diagrams of an 80 m span under-deck cable-stayed bridge with multiple struts: (a) elevation of the bridge; (b) cross-sections of the deck; (c) bending moment diagram in permanent state due to self weight (184?86 kN/m), superimposed dead load (43?10 kN/ m) and prestressing of stay cables; (d) bending moment diagram in permanent state due to self weight, superimposed dead load, prestressing of stay cables, concrete shrinkage, concrete creep and relaxation of the internal prestressing; (e) bending moment envelope due to a uniformed distributed traffic live load equal to 52?8 kN/m (4 kN/m2); (f) bending moment envelope due to a point traffic live load equal to 600 kN; (g) envelope of vertical accelerations due to the passage, from the left to the right abutment, of two vehicles of 400 kN at 60 km/h. All dimensions in m.

Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio 75 using falsework (Schlaich and Werwigk, 2001; Ziyaeifar et al. 5.3. Elimination of piers and viaducts with unbalanced 1998) as the under-deck cable staying system can be used as a span distribution temporary bearing system. The implementation of under-deck and combined cable-staying systems in viaducts allows the elimination of certain piers 4.7. Large capacity for withstanding the sudden breakage (Figure 1). By the implementation of under-deck and combined of stay cables cable-staying systems, the main characteristics of the deck (such These bridges are able to overcome scenarios that are far more as depth, concrete strength, amount of reinforcement, amount of severe than that demanded by the codes in relation to the active steel, etc.) can be maintained, despite the existence of a accidental breakage and sudden loss of stay cables (Ruiz-Teran particular span in the viaduct being double the length of the and Aparicio, 2009a). The analysis of this accidental situation other spans (Ruiz-Teran and Aparicio, 2008c). In these cases, the must be performed through a proper dynamic analysis and not span subdivision can be achieved in permanent state prior to through the simple traditional approach based on dynamic time-dependent effects, although the losses due to time- amplification factors, that is suggested by many codes and dependent effects are not negligible. However, the hogging guidelines (ACHE, 2007; CEN, 2006a; 2006b; PTI, 2007; SETRA, bending moments in the larger span due to traffic live load 2001), as this approach has been shown to be unsafe (Ruiz-Teran would double those in other spans, since the efficiencies of the and Aparicio, 2007c; 2009a). cable-staying systems are not large enough due to the fact that the slenderness of the deck is not sufficiently high. The design strategy must be to counteract the increase in the bending 4.8. Linear behaviour moments due to traffic live load with the reduction of the These bridge types can be safely analysed through linear bending moments in permanent state resulting from the span analyses (Ruiz-Teran, 2005). The consideration of the mechan- subdivision. ical non-linearity of the prestressed concrete sections for ULSs implies the reduction of the flexural stiffness of the deck and, 6. OTHER APPLICATIONS consequently, the reduction of the non-dimensional parameter x These under-deck and combined cable-staying systems have (see Equation 1), and, consequently, the increase of the also been successfully used for roof structures (Saitoh and efficiency of the cable-staying system. This redistribution of Okada, 1999; Weichen and Liu, 2009) and self-launching internal forces is favourable for the design of the deck and does gantries (Pacheco et al., 2007). not affect the design of the stay cables, since their design is governed by the ULS of fatigue rather than by the ULS of normal 7. CONCLUSIONS stresses. The small geometrical non-linearity of the bridge does This paper has presented a general and critical overview of the not affect the design of the deck, although it must be considered developments achieved so far in under-deck and combined for the design of the struts. cable-stayed bridges over the last 30 years. In addition, the main features and fields of application for these types of bridges have 5. APPLICATIONS been highlighted. In summary, these bridge types have been introduced and developed by outstanding structural engineers 5.1. Single-span bridges (such as Leonhardt, Schlaich, Virlogeux, Manterola, Robertson Both under-deck and combined cable-staying systems are very and Cremer), have been constructed mainly in Germany, Japan, appropriate for single-span bridges (Ruiz-Teran and Aparicio, France and Spain, have very efficient structural behaviour, 2008a) (Figure 1). Nevertheless, there are certain differences require a small amount of materials for the deck (in comparison between the two systems that significantly affect the design. with conventional bridges without stay cables), allow sustain- Combined cable-stayed bridges required about half the cross- able design, have great construction possibilities and possess sectional area for the cables compared with under-deck cable- strong aesthetic characteristics. staying systems, due to the higher effective eccentricity of the combined cable-staying systems – approximately equivalent to REFERENCES the sum of eccentricities in mid-span and support sections. ACHE (2007) Manual of Stay Cables. Asociacio´n Cientı´fico- However, the need for back stays leads to a similar amount of Te´cnica del Hormigo´n Estructural, Madrid, Spain (ACHE) (in active steel. 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78 Bridge Engineering 163 Issue BE2 Developments in under-deck and combined cable-stayed bridges Ruiz-Teran?Aparicio