Study for a suspension bridge with a main span of 3700 m.

Transcription

1 Study for a suspension bridge with a main span of 3700 m. Kees van IJselmuijden, Alex Swart, Sander Meijers, Joris Smits, Liesbeth Tromp, Peter Hagenaars Royal HaskoningDHV, Amsterdam, the Netherlands Jaco Reusink IGWR, Rotterdam, the Netherlands Contact: kees.van.ijselmuijden@rhdhv.com Abstract For the E39 in Norway, there is currently a concept for a bridge crossing of 3700m with 2 floating piers; the intermediate piers are incorporated because a single span is deemed to be unfeasible. This project inspired the authors to perform a study for this crossing of the fjord with 1 single span of 3700m. Recent developments in material show that lighter structures are possible for bridges. Fiber Reinforced Polymer is one of these high potential materials. In this paper we study if it s possible (beneficial) to design such a structure using Fiber Reinforced Polymer both in the cables and the deck structure. The main advantage of this material is its high strength, the reduction of structural dead weight and the significant reduction of maintenance compared to traditional bridge materials. The main difficulties that had to be overcome were the aerodynamics of the deck, the resistance against horizontal wind loading and the strength verifications of the suspension cables. An architect s opinion and impressions are included to give an idea of the structure under consideration. Keywords: Long span suspension bridges, cable-stayed bridges, Fiber Reinforced Polymer, maintenance reduction, aerodynamics. Figure 1. Architectural impression of the design 1

2 1 Introduction The market for extreme long-span bridges still growing and because the limits of conventional materials are being reached it is necessary to focus for new options. Fiber reinforced polymer (FRP) is a material that provides such an option. It has a significantly higher ultimate tensile strength and a much lower unit weight compared to steel. These are necessary requirements in order to construct a bridge with a main span of 3700 m or more. To realise a bridge with this span the use of FRP for both the suspension cables as well as the deck structure is considered. Aramid cables are considered that have a maximum working stress of σ t =2500 N/mm² and a density of a mere ρ=1450 kg/m³. These characteristics result in the necessary tremendous weight reduction. Earlier studies [1,2,3,4] have concluded that a 3700m span with traditional materials would not be feasible; because the self-weight of the cable would be too heavy. The light weight of the structure could give too much aerodynamic instability. To overcome these difficulties we considered light materials and designed a deck with a very high stiffness to overcome the lower Young modulus. Another reason to use FRP is that it has good maintenance properties. More maintenance is required over the full lifetime for corrosion protection of a steel bridge. FRP doesn t need the same amount of maintenance; the protection is there for UV and aesthetics only, the FRP will not corrode. 2 Assumptions This is a first technical feasibility study, in which we want to concentrate on the following criteria: 1. weight of the structure 2. vertical deflection 3. horizontal deflection 4. stresses in the FRP deck and Aramid cables 5. difference between vertical and torsional frequencies We made the following assumptions: - for the stability of the deck 5% extra weight of the deck is taken into account; - for lateral stability a twin-deck is applied; - for the characteristic wind force 1.5 kn/m 2 is assumed; - Asphalt 100mm on 8 m width road deck - Traffic load 37.5 kn/m per deck - Maximum vertical and horizontal deflection allowed is L/200. [5] - FRP materials is used for the bridge deck and the cables. (Later it can be seen which materials makes more sense to use). - Cables with Aramid fibres (but Carbon fibres are also possible) are used. - The concrete pylon is excluded from this study. The challenge is to develop a structure, which balances the properties of the structure and is able to resist the traffic and wind loads robustly. 3 Analysis The Dip-span ratio for a suspension bridge must be between 5 and 10, the calculation of the bridge is based on the picture below to have round numbers:! =!"## = 8,22!!"# Figure 2. Span 3700 m, Pylon 450 m above deck. 3.1 Road deck The deck only supports 2 driving lanes, so normally one single deck would satisfy. However, if we look at stability, a twin deck is preferable. We selected a distance of 30m center to center, in the longitudinal direction for the vertical cables. In the transverse direction the distance between the cables is 48m. 2

3 The cables are connected in the transverse direction with a steel cross girder. In the longitudinal direction the deck is connected to this steel cross-girder this also supports the FRP deck. 3.2 Main road deck: The main road deck carries the traffic and is supported by crossbeams every 1.5 m. The height of the continuous road deck is designed for a maximum deck deflection over L/200 = 1500/200 = 7.5mm. An FRP deck with a height of 150mm is needed. The deck principle is based on the vacuum infusion technique, like the existing InfraCore manufactory system of FiberCore. Figure 3. road deck principle A simplified calculation based on a single span (instead of a continuous beam) shows that the displacement is acceptable. For a deck with a width of 3 m (one lane) of traffic, according to the Eurocode the truck load is 600 kn and the UDL is 10 kn/m 2. The deck has the following characteristics: h [mm] Table 1. Top deck properties b [mm] EI y [kn*m 2 ] GA [kn] The conversion factor η c according [6] for aging and dry/wet climate is This results in a deflection by UDL of 0.2mm and by truckload 2.5mm, total 2.7mm. The maximum stresses with flanges of 20mm thickness are around 26 MPa. 3.3 Deck segment of 30 m The design is based on a center-to-center distance of 30m between the cables. Every 1.5 m an FRP-crossbeam is located beneath the road deck. This crossbeam is manufactured as a sandwich panel with 2 outer plates of 10mm thick. By using a sandwich the structure is more resistant against buckling so the material is applied most effectively. In the longitudinal direction a longitudinal FRPbeam is designed (also sandwich panels) for now assumed every 2m over the full height. There is an opening within the sandwich construction, so allparts of the deck can be inspected from the inside. Each single deck can accommodate 2 traffic lanes. However more width is required for lateral stability reasons. In this paragraph the local effect of a deck with a single span of 30m instead of a continuous beam is verified. A bridgedeck width of 8 m (two lanes) of traffic according the Eurocode is assumed. The truck load is 600 kn kn = 1000 kn and the UDL is 3x10+3x2.5 = 37.5 kn/m 2. The deck has the following properties: Table 2. Deck structure 30 m long 8 m width h [mm] b [mm] EI y [MN*m 2 ] GA [MN] The conversion factor η c according [6] is This results in a deflection by UDL of 29.8mm and by truck load 42.7mm, total 71.5mm < 30000mm/200 = 150mm. The maximum stresses with flanges of 20mm thick are around 26 MPa. 3.4 Global deck for 3700 m span For the total span a deck wider than 8 m and a twin deck are needed. The wider deck is needed for the stability and for the wind forces. 3

4 Figure 4. Bridge deck principle At this stage in the study the structure is not optimized; the aim of the study is only to prove that for a long span a deck with FRP material is possible. The structure (without the pylons) is modeled in Sofistik and with the form finding model; the deck moments and deflection for dead loads are optimized. In the Sofistik model the wider deck is modeled as a beam. 3.5 Steel cross beam Figure 5. Sofistik model For the connections of the twin decks and hangers, a steel cross-beam is used. The width of the cross girder is 2m and the height of the girder is 3.5m at the outside where the hang cable is connected. The FRP deck can be placed with the road deck on top of the steel crossbeam and the bottom of the deck on a steel cantilever on the steel crossbeam. Figure 6. Deck principle This means that the deck is always supported. The connection between the deck and the steel crossbeam is made with adhesive and steel bolts. 3.6 Suspension cables As an alternative to steel cables, CFRP cables are possible for long span bridges, but these have some disadvantages. It is not easy to anchor the Carbon Fiber Cables and they are also not easy to transport. An Aramid fiber cable based on the FibreMax principle was used for the cables. The main issue for these cables is the lower stiffness (E = MPa). For long spans the deflection is therefore more than a Carbon fiber with the same diameter. But the main advantage is that it can be anchored based on a fixed length. The cable is made in the exact length required. The cable will be dimensioned on stiffness rather than strength; stresses in the cables are low. Aramid Polymer G = 129 GPa Tu = 2760 MPa Ts = 2500 MPa 4

5 requires no (or less) pre-tensioning when installing the cables; of course the cables can be tensioned. The length of the cables is controlled within the computerized production process and length tolerances can be kept to a minimum (up to < 1mm, depending on cable length). Figure 7, Aramid cables The cables are produced with endless winding technology. The technology is a totally automated process of continuous winding of parallel strands of fibres around two end terminations/fittings until the required cable strength or cable elongation has been reached. After the length has been programmed, the EWR (endless winding robot) computer calculates the amount of fibres and the amount of loops required for the specified cable. During the winding process the EWR maintains an equal tension in all fibres with an accuracy of 0.1%. This results in the highest break load, lowest strain and lowest possible diameter. It also ensures that cables are produced with constant quality. To avoid creep the length of the cables is adjusted during manufacturing by compensating for the creep. Among the design criteria the most critical are: Ultimate strength (breaking strength/mbl), which may also be dictated by applicable regulations or rules. Applied loads (min/max) during operation (and frequency of these loads) Maximum allowable elongation under load. Pin size Expected lifetime. All fibres in the cables are parallel wired, is accordance with steel parallel-wired cables. There is only elastic elongation of the fibre material. This Figure 8. Connection cable on Pylon As a result of the endless winding process the final strength (MBL) of the cable is achieved in the end termination; when pulled to break a FibreMax cable will always break in the end termination in a pre-designated area. For the design of the cable it is therefore also important to know the pin size. A pin size that is too small may result in early failure of the cable when pulled to break. The Cables will be pinned on the pylon and therefore the different cables (with a total diameter of 2 m) will spread out at the pylon (see figure 7 and 8). For a lay-out of the cable please refer to the picture below. Figure 9, Aramid cable principle 5

6 3.7 Pylons The pylon is assumed to be concrete. The pylons are placed in the water, but only in the shallow zone. 4 Results The following elements of the bridge have been checked based on the Sofistik analysis. 4.1 Deck structure Table 3. deck-structure Structure ULS N- force [kn] N-stress [MPa] Table 4. Cables Main cable D=2000mm Hang cable D=300 mm The maximum stress that is allowed in this phase is 2500MPa*0.9/(1.35*1.40)= 1190 MPa. The unity check of the main cable is UC= 452/1190 = 0.38 and is within limits. If the stresses are below a UC of 0.52 a lifetime of more than 100 years is possible [7] see also table VI/figure 10. Structure ULS N- force [N] N-stress [MPa] M [kn*m] σ [MPa] FRP-deck vertical FRP-deck horizontal δ [mm] The total maximum stress in the structure is around = MPa << 1.2%*18573MPa*0.81/ (1.15*1.5) = MPa (UC=33.62/129.2 = 0,26). Calculation of the allowed stress is based on the 1.2% strain of the used material at the outside of the structure multiplied with the conversion factor divided by the material factors m1 and m2, according the update CUR96 that is under construction now. The current CUR96 [6] will be replaced by a new CUR96 based on the principles of the Eurocode. The vertical deflection is limited to L/200= 3700m/200 = 18.5m. The displacement of 11.26m is within limits. The same holds for horizontal deflection 18.23m < 18.5m. The steel cross girder has not been designed in detail, but within the global dimensions it can be considered structurally feasible. 4.2 Cables Twaron 2200 (Aramid) are used in the main cable and the hangers. Figure 10. Lifetime Aramid cables based on continues breaking load under constant temperature. 4.3 Dynamic behavior Natural frequencies and corresponding mode shapes have been determined for the bridge structure on the basis of the SLS stress state. Frequencies Table 5. deck-structure LCnumber Frequency [Hertz] Torsion bending ε = torsion/bending 1.62 The first translational and torsional frequencies are and Hz respectively. In order to avoid flutter of the deck those frequencies should be well separated. According to the modified Selberg formula (see e.g. Banck & Almberg [4]) the 6

7 critical wind speed is dependent on the ratio of the translational and torsional frequency. With the present ratio of 1.6 and the geometry and inertia properties of the bridge it is found that the critical wind speed is 23m/s, which corresponds to 9 Beaufort and is marginally higher than the Golden Gate Bridge [8]. As at such high wind speeds turbulence tends to rule out flutter of the deck; the calculated critical wind speed is considered as a satisfactory value for this feasibility study. easier realization of aerodynamic and architectural shapes. An architect joined the team for this bridge and provided the architectural vision and design of the bridge. From an architectural view the true beauty of this bridge lies in the dimensions of it. The sheer size of the main span makes the deck appear like a spiders thread across the water. Figure 11. translation frequency, LC 2003 Figure 12. torsional frequency, LC 2008 Vortex excitation of the hangers has been examined by determining the Scruton number using a logarithmic decrement of The calculated Scruton number of 55 should guarantee insensitiveness to vortex excitation. 5 Architecture design In the E39 (1100 km) more suspension bridges are planned. A family of bridges, designed by an architect, makes the new E39 more recognizable and one of a kind in the world. For suspension bridges the architectural design has to follow the structural design. But FRP material used for the bridge deck is known for its formability and allows Figure 13. architectural impression On this scale cars and trucks become petty and details such as parapets and guardrails dissolve within the bigness of it all. On the overall scale the proportions of the outline of the Sognefjorden Bridge are more than slender, for what is a 500 meter pylon if the next pylon sits 3700 meters away on the other side of the fjord? The bridge is designed with curved decks, slightly tapering towards the middle span, and the void that divides both carriageways. The main aspect worthy of an architect s attention however is the design of the pylons. Various pylon configurations such as a single pylon in between the decks, two loose pylons on either side and even inclined pylons were soon abandoned for structural reasons. Figure 14. architectural impression 7

8 When designing a suspension bridge this big lateral wind induced forces are so high that a stiff portal of interconnected pylons is needed. This made us opt for an archetypical portal; straight pylons tapering slightly towards the havens interconnected at the top by a smoothly shaped transverse beam, a doorway in its bare essentials. The smoothened corners of the portal reflect the undulating landscape and bestow upon this artifact the appearance of a peace of drift wood found on the beach, bleached by salt and sun and discarded from its original sharp lines. 6 Conclusion In Chapter 2 it is outlined what is our focus in this feasibility study: 1. The resulting areal weight of deck is approximately 305 kg/m2 and is slightly lighter than other steel decks for suspension bridges. The weight of the main cable is reduced by around 75%. 2. The vertical deflection of m gives a ratio of 3700/11.23 = L/329 > L/200 [5]. 3. The horizontal deflection of m results in a ratio of 3700/18.23 = L/203 and is on target (L/200). 4. The stresses in the FRP deck and aramid cables have both unity checks below 0.40 and can be further optimized regarding the deflections. 5. The ratio between vertical and torsional frequencies is The critical wind speed is 23 m/s, which corresponds to 9 Beaufort. Overall the study shows that bridges with long spans can be designed with new structural materials such as FRP. The deck and the cables fulfil their functions and the stresses are lower than for steel structures, which is positive for the fatigue and allows further optimisation. The lightweight potential of FRP was less benefitted from, because the lower stiffness would require a larger cross section, which induces larger wind forces. The low maintenance for long span structures constructed with FRP materials is a major benefit. FRP material is already a proven material for bridge decks for spans up to 30 m; larger spans are possible but have not yet been built. The aramid cables have been used for heavy loaded structures. But both the decks and the cables have not yet been used for this scale of structures. This paper shows that realization of this kind of bridges with FRP is possible. More detailed calculations and tests are needed to further develop and optimise the design. 7 References [1] Chen W., Duan l. Bridge engineering handbook, second edition, Fundamentals, CRC press, Taylor and Francis Group; [2] Lewis W. J. Smith L. A Mathematical Model for Assessment of Material Requirements for Cable Supported Bridges: Implications for Conceptual Design. Warwick: University of Warwick; [3] Keller T., Use of FRP in Bridge Construction, Structural engineering documents 7, Zurich: IABSE-AIPC-IVBH; 2003 [4] F. Banck, O.R. Almberg, Application of CFRP cables in super long span cable supported bridges, a feasibility study, Master s thesis, Chalmers University of Technology, 2014 [5] Statenes vegvesen, Sognefjorden Feasibility Study of Floating Bridge, Main report; 2013 [6] CUR COMMISSION C124, Recommendation 96 Fibre-Reinforced Polymers in Civil Load- Bearing Structures, CUR Gouda, [7] Teijin, Static loading of Twaron and Technora, QBT , Arnhem, The Netherlands, 2010 [8] E. Simu, R.H. Scanlan Wind effects on structures, Fundementals and Applications to design, John Wiley & Sons, inc. New York, United States of America.,