Cable stayed bridges with a 3D truss composite deck

Transcription

1 Cable stayed bridges with a 3D truss composite deck Pedro Ricardo Chainho Sequeira Department of Civil Engineering, Architecture and Georesources, Instituto Superior Técnico, Technical University of Lisbon, Portugal July 2012 Summary The paper presents the design of a cable stayed bridge with a composite 3D truss deck with a V shaped cross-section. The transparency of the bridge as well as overall aesthetic quality are taken as the main goals of the final design solution. Choices made during the conceptual design are explained and some of the alternative solutions are compared with the adopted design solution. The most common construction methods are discussed. 1 Introduction Modern cable-stayed bridges have been built for half a century and they are still the latest trend in bridge design. In the last decade of the XX century the maximum span has increased from the 456 meters of Annancis bridge to almost double that length with the construction of the Tatara bridge and its 890 meters main span. After that it took almost 10 years to get a new record and break the 1 kilometer main span with the Sutong bridge [1]. Cable stayed bridges are now the main choice for spans ranging from 300 to 900 meters. While some engineers were pushing the structural limits of this new type of bridges and attaining those long spans records, others were more focused on the different design possibilities allowed by this suspensions system. New tower shapes and cable arrangements have been used, mostly on smaller spans where it is easier to introduce new concepts, and aesthetically solutions have been attained. That is one of the reasons that has led cable stayed bridges to be built, even today, in smaller span ranges, where they have to compete against more conventional deck solutions. An overall trend in bridge construction is the increased use of composite decks; these allow a faster and more effective construction phase than a concrete deck while being overall cheaper than a fully steel solution. Truss decks have been used for a long time in suspended and girder bridges, its main advantages being the overall stiffness and transparency. An early example of a composite 3D truss deck is the Lully Viaduct in Switzerland which is now almost 20 years old (Figure 1a). More recently a 3D truss with a W cross section was used in a cable stayed bridge in Portugal, the Rainha Santa Isabel Bridge (Figura 1b). The W shaped cross section allows the deck width to be around 30 meters, and has enough space for the bottom slab, made of concrete, to be used as a pedestrian walkway [1]. This last example represents a different type of innovation in cable stayed bridges, since most new designs in the shorter span range introduce changes in the tower shape and the suspensions arrangement, while the deck types have mostly been limited to girder, box-girder or slab decks.

2 Figure 1-3D Truss decks: Lully Viaduct (a) and Rainha Santa Isabel Bridge (b) [1; 2] 2 Conceptual Design The main span was set at a modest 128 meters, with a typical 2 masts arrangement and suspended back spans with about half that length. The axial suspension of the deck is the obvious choice for this type of cross section, and that allows for a cleaner and more transparent look when the bridge is viewed from a skew angle since there is no apparent cable crossing. As for the cable arrangement a harp system was adopted, since it is often considered the most aesthetically pleasing, and it has a good synergy with the truss deck. This is particularly true if the diagonals have the same slope as the cables, like in the The Øresund Bridge [3]. The same scheme was adopted, leading to a small number of diagonals, which also increases the deck transparency. Each segment, composed of 2 diagonals on each truss plane spans 8 meters, the same distance adopted for the spacing of the cables at the deck level, which is a typical value for a composite deck with axial suspension. The option of doubling the number of diagonals is analyzed later on, the main advantage of that option being the smaller distance at which the top chord is supported. Figure 2 Side view of the final bridge solution. The deck should support 2 lanes of traffic in each direction, and 2 meter sidewalks were adopted on each side, which has led to a deck width of 21 meters. That is enough to provide 3 meters in the middle of the deck for the single mast and the safety barriers to protect the stay-cables. Spacing between the top chords was set at 11 meters, approximately half of the width of the deck, to balance the negative transverse bending moments in the slab. The 11 meter span means that the slab

3 has to be prestressed in the transverse direction. In this case flat ducts with 4 cables each will be used to minimize de eccentricity loss, and a spacing of about 70cm was adopted to guarantee a uniform compression of the slab. Top and bottom chord and diagonal were used with the following properties: Circular hollow tubes (S 460 JOH) Outside diameter (mm) Thickness (mm) Area (mm2) Top chord Bottom chord Diagonals Table 1 Tubular truss members dimensions. The height of the deck was chosen to balance the reduced force on more vertical diagonals, at the expense of making them longer, and therefore more prone to buckling. A distance of 3 meters, measured vertically between the centers of the top and bottom chord was adopted. This means that the deck slenderness is much lower than on typical cable stayed bridges where the height of the deck is set to provide stiffness as well as to resist the longitudinal bending moments, while in this case the main constrain is the diagonals efficiency for carrying vertical loads. Figure 3 Cross section of the deck. The cables have 43 strands, and are anchored in a steel plate near the bottom chord. The plate can be welded either directly on the bottom chord or in the diagonals near the joint, thus being hidden behind the diagonals in a side view. This last option has the advantage of reducing the diagonals equivalent span, thus reducing buckling instability. The last 2 cables on each side of the bridge are be anchored at the abutments, which allows a better control of the deck deformations under live load actions. It also guarantees that the deck will be pushing down at the abutments even when the traffic loads are only acting in the main span. Since the deck is axially suspended, the mast typologies are limited to a single mast or one with an inverted Y shape. The later has additional restrains for the harp cable arrangement since it requires cables anchored at lower heights. With that in mind the single mast was adopted, besides that it is also the simplest solution which goes in line with the proposed design goal. The height of the last cable anchorage is set at 33.6 meters above the deck, approximately ¼ of the main span, which is near the top of the range used for cable stayed bridges, since that s where the harp arrangement is more effective. The external dimensions of the mast are set at 3*2 meters (longitudinal*transversal) to control its slenderness as well as to guarantee enough internal space to allow cable stressing operations to be done from inside the mast. That option is particularly important in this case since the passive anchorages can then be set bellow the deck, where the stressing operations are impossible. A pre-fabricated steel anchor box is used to maximize the internal space of the mast and it acts compositely with the concrete section thanks to shear connectors. There is a need to have an

4 opening in the slab for the mast to go trough, since it is connected to the pier just above the bottom chord. Because of its size the opening requires a complex detailing of the slab in that area, unlike the smaller openings that allow the cables to go trough the slab. The pier supports the deck at the top chords, meaning rotation due to torsion is eliminated which is very important since the stay system does not control the torsion of the deck along the span. It must also have an opening so the bottom chord can be made continuous over the support section. The pier geometry is also restrained by the diagonals, which in this case lead to a pier width of just 1 meter under the bearing. A stiffened steel plate is used to connect the top chord to the bearing, allowing a more uniform force transfer between the 2 elements. It also elevates the top chord, which increases the space between the diagonals needed for the pier. Figure 4 Pier dimensions and the pier - top chord connection. 3 Construction Method Cable stayed bridges have lighter decks than girder bridges with the same span, which is an advantage when it comes to the erection of the deck, and it is one of this topology advantages in the shorter spans. This is even more true when the deck is composite, since there is the possibility of setting the light steel structure in place before adding the concrete. That is one of the reasons for the increased use of this type of decks in the last years in the medium and smaller spans. In this aspect the 3D truss deck has the advantage of having a very light and stiff steel structure that also forms a closed section, which gives it a good torsional behavior. In the long span range the construction method typically used is the balanced cantilever since it allows the area under the spans to be free during construction, and the big number of segments make this method more cost effective. In the smaller spans the incremental launch of the deck and the use of temporary supports are a possible option, and those possibilities contribute to this typology competitiveness on shorter spans. Launching of the deck is a construction method with great synergy with composite decks, since it is possible to launch the steel structure, using lighter equipment and possible temporary piers and just add the concrete after this phase is completed. In this deck the bottom chord has a span of 10 meters between diagonals in the pier section which means that when the deck is supported at midspan there will be a big bending moment in the bottom chord. This problem counteracts the otherwise particularly well adapted light and stiff deck, and diminishes the launching span that can be attained, leading to a need to have 2 temporary supports in the main span. If the segments were only 4 meters long the launching span could be increased using the same bottom chord section, and then the launching could be completed with only one temporary support in the main span.

5 Using a lifting equipment to place sections of the deck over temporary piers is a solution that allows supporting the deck only at the joints. In this case, since the steel structure is very light, it is the size of the segments that will determine the number of temporary piers required. These last 2 methods are particularly well adapted to bridges with shorter spans or when the area under the bridge may be obstructed by easy to erect temporary piers. After the steel structure is set in place the concrete may be casted in long sections and all the cables can be stressed in one operation to balance the permanent loads. Those two characteristics allow for a faster construction than in the balanced cantilever method, where the concrete is usually casted one segment at a time, and the cables are stressed one by one after the corresponding segment is set in place. Despite the downsides of the balanced cantilever method it was still chosen to analyze the structure since it can be adopted even when the space under the deck can t be obstructed. This is a typical restrain on urban areas, where these type of innovative and aesthetically appealing bridges have a greater chance of being built. It also allows for the deck and the mast to be built simultaneously, unlike the launching method that requires the deck to be set in place before the mast construction can start. A structural advantage over the other two methods is the smaller traction force in the center of the main span which is favorable to the slab verifications at the service limit states. The robustness of the steel truss in this case allows for the segments to be set 2 at a time, reducing the amount of welding needed in situ and only increasing the stresses in the structure by a small amount. It also allows each cable to be stressed in one operation during the cantilever stage (and not in 2 steps, before and after the concrete is casted, as in some composite decks) which makes the process faster and simpler. 4 Alternative solutions The comparison between the current solution and the alternatives is based solely on the traffic load analysis since it has a great influence on the limit state verifications. Traffic loads have the greatest impact on the bending moments in the base of the mast and in the deflections of the deck, because these can be controlled during the construction phase and set at low values under permanent loads. Besides that the fatigue verification of the cables is based only on them, and traffic loads stresses allow for an overall feel of how the structure behaves. 4.1 Segment length halved With the segment length reduced to 4 meters the main advantage is the lower bending moments that occur in the composite beam (top chord + deck slab), specially the one due to the concentrated traffic loads. Nonetheless, since the slab thickness is controlled by the transverse spans, this alternative does not lead to a lower deck weight. Instead it allows for a smaller section for the top chord and a lower quantity of longitudinal rebar. There is also a slight decrease on the axial force on the diagonals, since they are more vertical, but the gain here is marginal when compared to what would happen on a vertical truss. As it can be seen in the next table on the 3D truss there is a bigger increase in the total length of the diagonals (L diagonal /m) while the efficiency gain at carrying vertical loads, measured by the ratio between the vertical projection and the total length of the diagonal (L vertical /L) is lower than a similar variation on a vertical truss (2D).

6 Segment length (m) Spatial Truss (3D) Vertical Truss (2D) Σ L diagonal /m L vertical /L Σ L diagonal /m L vertical /L ou ou / Table 2 Efficiency of different segment lengths in 2D and 3D trusses. The moment at the base of the mast remains the same, and so does the compression on the bottom chord near the pier, but its length between nodes is only 4 meters, which reduces the susceptibility to buckling instability. On the other hand this last fact means that the space for the mast to go through the truss is reduced, and would require a new detailing of that area. The vertical deflection of the deck remains the same but the torsion behavior becomes worse and leads to a 25% increase in the rotation of the deck due to the eccentric traffic loading. This last result is somewhat counter-intuitive, but it can be explained comparing the increase in the number of diagonals to a spring which for a fixed length and section becomes more flexible as the number of spirals increases. On a perpendicular side view the original solution creates the illusion that the diagonals of the deck are aligned with the cables which gives the bridge a more harmonious feeling than on this alternative. This effect is lost when the view is skewed but it still remains much more transparent than on this alternative, as it can be seen in the picture on the right that represents a skewed view of the bridge at a 45 degree angle. 4.2 Reduced deck height Figure 5 Skewed side view of 4m and 8m segment lengths. As the deck height is lowered the axial force on the diagonals will increase, but their susceptibility to buckling instability will be reduced in a somewhat balanced manner for vertical spacing between the top and bottom chords close to the original 3 meters. In this variation the deck height is reduced in 60 cm which also means that all the diagonals will have the same length and slope. Figure 6 Comparison between the original and the alternative deck cross section.

7 Deck stiffness is lowered and the suspension system (cables and masts) takes a bigger role in carrying the vertical loads due to traffic that leads to a 10% increase in the bending moment at the base of the mast and a 13% increase on the tension variation on the cables due to the passage of the fatigue load model. The vertical deflection of the deck also increases by 10% when the traffic loads act only in the central span, and the rotation due to the eccentric loading is increased by 20% when compared with the original solution. In the pier zone the maximum compression in the bottom chord does not change, but the length between the nodes is reduced from 10 to 8 meters which means that the design resistance is increased. 4.3 Multiple spans Adopting multiple spans in cables stayed bridges is an option to cover big distances with fewer piers than a beam bridge while being cheaper and easier to build than a suspension bridge. Nonetheless this alternative has also been adopted in smaller spans, like in the Viaduct de La Arena in Spain that has 6 masts, and 5 central spans with only 105 meters each. In this alternative the same number of masts will be adopted, but the central and back spans will remain with the original lengths of 128 and 56 respectively. With this span arrangement the deck becomes more flexible despite the fact that the span length remains the same, this is particularly obvious when the traffic loads act alternately in the central spans. Figure 7 Live load scheme to obtain maximum deck deflection and mast bending moments. This leads to an increase in the vertical displacements of the deck, as well as an increase in the stresses of the suspension system. The maximum vertical displacement due to the distributed load increases by almost ¾ while the rotation due to the eccentric loading remains almost unaltered, since it is still blocked at the piers. The traffic loading more than doubles the moment at the base of the two central masts while the variation of tensions in the cables increases by only 10% when the fatigue vehicle crosses the bridge. Vertical Deflection (cm) UDL (distributed load) M mast (knm) TS (concentrated load) F cable (kn) 2 Masts 15, Masts 26, "6/2" 1,7 2,23 2,11 1,10 Table 3 Comparison between the typical two mast solution with a multiple mast alternative. 4.4 Single mast Unlike the previous alternative the option of using a single mast to support the main span is often used, specially in urban bridges: Very often, classical cable stayed solutions namely, symmetrical solutions with two pylons are not the most efficient ones to overcome difficult urban site conditions [4]. There is the possibility to have a symmetrical solution, but most often the backstays are earth anchored which means that the back span can be made smaller than the main span an increases the adaptability of the solution, this is the case in the Rainha Santa Isabel bridge. Like in the last example, usually the decks are axial suspended but the backstays are divided into two planes and anchored laterally which

8 provides an opportunity to give the cables an interesting shape as well as have a more slender mast since the backstays provide some lateral stability. In this alternative the back stays will be in the same plane as the main stays, since the harp arrangement requires cables to be anchored at lower heights which then create more obstructions if they were to be anchored laterally. This option has a particularly good synergy with this bridge for 3 reasons: The truss has a triangular opening of about 11 by 4 meters between the last two diagonals, which can be used to pass the back stays and connect them to the abutment; The high horizontal force originated by the harp arrangement will be balanced at the abutment with the force from the back stays; the back stays form a triangle which has a good synergy with the truss deck. In this alternative the 3 last bottom nodes on each side of the main span aren t supported by cables, compared to the original solution that supports all but the last node on each side. This allows for a mast almost 10 meters shorter while maintaining the same angle on the cables, and contributes to a more aesthetically pleasing solution. A variant that can be adopted is slightly tilting the mast away from the main span which besides the aesthetic reason also contributes to reduce the forces of the back stays. Figure 8 Side view of the single mast alternative. In this case the vertical deflection of the deck increases by about 40%, this is due to 3 main reasons: There is no deck continuity on the right abutment; the deck is supported in only 10 nodes, compared to the original 14; The mast is higher and the cables are on average longer and therefore the suspension system is more flexible. This is somewhat balanced because the back stays are earth anchored instead of anchored in the deck, and so provide more rigidity to the mast. Once again the rotation due to torsion does not change. The moment at the base of the mast is reduced, mainly for the distributed traffic load, because the mast is more restrained by the earth anchored back stays. As for the force variation on the cables, due to the fatigue vehicle passage, it increases by 12% because the 2 last cables on each side of the main span support a bigger deck length. Vertical Deflection (cm) ULS (distributed load) M mast (knm) TS (concentrated load) F cable (kn) 2 Masts 15, Mast 21, "1/2" 1,39 0,73 0,97 1,12 Table 4 Comparison between the typical 2 mast solution with a single mast alternative.

9 5 Conclusions This deck type has the traditional advantages of composite structures when it comes to the erection process and it allows for a very transparent solution to be created. The option to have a single mast supporting the main span was analyzed since it adds versatility which is important for the construction in urban spaces, where this bridge type with high aesthetic value would have the biggest chance of being constructed. One of the main problems of this deck type is that by definition the slab is only supported transversely at 2 points, which limits the slab geometry for a given deck width, and most of all, limits the width at which the system can remain efficient. For roadways with 6 or more lanes the slab spans would become too big, and for a 2 lanes roadway the need to have a central reservation of about 3 meters and the additional berms would mean the relationship between the roadway width and the total deck width would be small. Among composite decks this one has the disadvantage of making the incremental launching less effective, and in general making the geometry in the mast/deck/pier zone more complex. A serviceability related downside is the fact that the passive cables anchorages are set below the deck level, which makes them impossible to inspect without proper equipment. Due to these downsides it is not likely that this deck type will have a massive use in cable stayed bridges, but, because it is a novelty, it might still find its place and serve as a landmark somewhere. Figure 9 Multiple rendering views of the proposed two mast design solution.

10 6 References 1. Pedro, J. J. O. Pontes de Tirantes Concepção, Dimensionamento e Construção. Documentos de apoio à Disciplina de Pontes de Tirantes do D.F.A. em Engenharia de Estruturas, Junho de Dauner, H.-G.; Decorges, G.; Oribasi, A.; Wéry, D.; "The Lully Viaduct, a Composite Bridge with Steel Tube Truss". Dauner Ingénieurs Conseils. 3. Nissen, J.; Rotne, G.; Getting the Balance Right: The Øresund Bridge Design Concept IABSE Conference "Cable-Stayed Bridges - Past, Present and Future", Malmö, Sweden 2-4 June, Reis, A.; Pedro, J.; Pereira, A.; Sousa, D.; Cable-Stayed Bridges for Urban Spaces" IABSE Conference "Cable-Stayed Bridges - Past, Present and Future", Malmö, Sweden 2-4 June, 1999.