Brandangersundet Bridge A slender and light network arch

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1 Brandangersundet Bridge A slender and light network arch Rolf Magne Larssen Dr. ing./ Ph.D. Dr. ing A. Aas-Jakobsen AS Oslo, Norway rml@aaj.no Rolf Magne Larssen, born 1958, received his Ph.D. in structural engineering from NTNU, Trondheim, Norway. He is working for Dr. Ing. A. Aas-Jakobsen AS, Consulting Structural Engineers, in Oslo with bridge design. His main area of research is structural dynamics. Space for a portrait 32 x 48 mm Svein Erik Jakobsen M.Sc. Dr. ing A. Aas-Jakobsen AS Oslo, Norway sej@aaj.no Svein Erik Jakobsen, born 1960, received his master in structural engineering from NTH, Trondheim, Norway. He is head of bridge division in Dr. Ing. A. Aas-Jakobsen AS, Consulting Structural Engineers, in Oslo. Space for a portrait 32 x 48 mm Summary The design of a slender and light network arch bridge for Brandangersundet on the west coast of Norway is presented. An extremely slender arch structure spanning 220 m with only 7.2 m between the arches, each consisting of a Ø711 mm steel tube, has been designed, constructed and installed at this location. The article presents benefits of the network arch concept, some procedures, solutions and results for buckling design of such a slender structure, and the final design of the Brandangersundet Bridge. Also challenges in the construction of such a bridge are addressed. As a conclusion, the network arch concept makes slender and transparent bridge structures possible without compromising the safety. Keywords: Bridge; design; construction; network arch; buckling design. 1. Introduction This paper presents the challenging design of the network arch bridge crossing the Brandangersund in Gulen, Norway. This arch bridge consists of two steel arches connected by a wind bracing and a post-tensioned concrete road slab suspended in the arch by inclined hangers. The bridge is designed for low traffic conditions and has thus only one road lane in the main span. The structural configuration of the network arch distribute loading in an optimal manner giving the possibility of using a very slim cross-section for the arch. Thus the result may be an extreme slender arch bridge with an attractive transparent layout that does not hide the landscape behind. The design for low traffic condition makes further increase of the slenderness possible. Due to the extreme slenderness documentation of the buckling capacity is a major task in the design process. The location at Brandangersundet Fig. 1: Brandangersundet Bridge is well suited for the network arch concept with a medium wide and deep fjord surrounded by low terrain and a demand for a sailing channel. A load carrying structure above the roadway would thus be beneficial. However, a challenge is that the former bridge of this

2 type built in Norway had only a span length of 84 m and was built in The concept was at that time introduced by Per Tveit, [1] who also participated in the design and construction of the bridge. 2. The concept of a network arch 2.1 What is a network arch? Figure 2 gives a schematic description of arch bridges with arches above the roadway. As it can be seen different concepts of carrying the roadway exists. Among these different concepts the network arch has some benefits which are studied more in this section. The definition of a network arch given by Per Tveit is: Network arches are bowstring arch bridges with inclined hangers which have multiple intersections, [2]. Fig. 2: Arches simple arch, arch with vertical hangers, arch with inclined hangers and network arch 2.2 Benefits of the network In figure 3 the critical buckling shape of three different configurations of hangers for such an arch bridge is shown. The network changes the critical buckling shape of the in-plane buckling in a radical manner. For dead load the buckling factor for the three different configurations become 1.57, 1.65 and 6.40 respectively. The elastic buckling load is thus more than 4 times larger for the network arch than for the other hanger configurations. The critical buckling value for a bridge structure is obviously the global buckling mode. For the vertical and the inclined hangers the out of plane buckling for even a narrow bridge like the one investigated here is far above this in-plane value, provided a normal wind bracing. For the network arch the in-plane buckling factor trends to be equal to the out of plane factor. Thus the slenderness of the arch may be increased. Another great benefit achieved by the network is the optimal distribution of loading from the roadway to the arch. The axial force in the arch is approximately at the same level for the different concepts. In figure 4 bending moments both in arch and roadway are shown with actual size for the three different layouts investigated here. The bending moments in the Fig. 3: Buckling shape for different arches arch is more than 10 times larger

3 Fig. 4: Bending moments from dead load for different arches for the vertical and inclined systems compared to the network. In the roadway the bending moments are more than 5 times lager. For concentrated loading (not shown) the differences between inclined and network systems are not significant. Obviously, vertical hangers show a rather high peak in bending moments due to a concentrated loading. For the investigated concepts the increase in bending moments in the arch is above 10 for the vertical hangers. Thus the network arch provides a concept where both in plane buckling of the arch in is effectively prevented and the vertical loading is effectively distributed into the arch as axial force with minimum bending moments. 3. Design of Brandangersundet Bridge 3.1 General The bridge shall cross a fjord with a width of minimum 220 m and provide ship opening of at least 18 m height. As the fjord is more than 60 m deep the bridge should span the whole width, and as the height of the surrounding terrain is about the required ship channel, a load carrying structure above the roadway would be beneficial. These criteria are met by the network arch concept. 3.2 Layout of the bridge The design process resulted in a layout as shown in figure 6, consisting of a main span of 220 m and two side spans of 30 and 35 m. The cross section of the main span is shown in figure 5. The design of the main span is made by two vertical steel arches with an arch rise of 33 m (15%). The distance between the arches becomes only 7.2 m due to the requirement of one traffic lane only for the bridge. The arches are made using a tubular cross section with external diameter of 711 mm and a thickness of 40 mm, increased to 60 mm at the ends. Structural steel grade used is S420N/NL. The arches are laterally connected by wind bracing made by Ø250 mm tubes of steel grade S355N. In the wind portal frame a tube of Ø611 mm is used. Fig. 5: Cross section of Brandangersundet Bridge A total of 44 hangers in each arch plane are used. The hanger arrangement was originally made according a scheme proposed by Brunn and Schanack [3] but due to the challenges of relaxing hangers some modifications of this scheme had to be developed. For the hangers locked coil strand cables with diameter 42 mm are used.

4 Fig. 6: Layout of Brandangersundet Bridge The roadway is made of posttensioned concrete of 200 to 400 mm thickness. The roadway is 5.0 m wide (one traffic lane) and have a total width of 7.6 m in the main span. The width is increased slightly at the ends of main span to have sufficient space for anchoring the arches onto the roadway. 3.3 The design process In general, several areas of concern were identified at the start of the detail design process. The main challenge was the effect the extreme slenderness would have on the structural response. Furthermore, the sensitivity of the bridge for wind loading as well as the construction method was identified as areas of major concern. The obvious challenge was the slenderness of the structure and the lack of experience with such structures. The former bridge of this type built in Norway had a span length of only 84 m and was built in Worldwide several bridges of this type have been built, from the Fehmarnsund in Germany which was built in 1963, [4], to the Providence River Bridge in USA, [5], which was built in The main span length of these bridges vary from below 100 m to above 300 m, but all bridges are designed for much heavier traffic loading than what is the case for the low traffic volume at this location. This challenge is addressed in the next section. Wind loading is in general a challenge for large bridges on the west coast of Norway. For locations as Brandangersundet additional difficulties may arise with a long channel leading the wind towards the bridge. For that reason the roadway was made continuous into the side span in order to stabilize the bridge for sideways vibrations. Due to this measure, wind loading does not give any concern for the bridge. The bridge response for wind is analysed both by traditional stochastic buffeting theory analyses and by time domain analyses, both based on special wind tunnel investigations for wind coefficients for the bridge deck. Construction and installation procedures are treated in section Buckling of the arch Documentation of the buckling capacity for this bridge has been given large focus in the design process. Structural stability for such complicated structures must be calculated based on a global analysis where both second order effects and global and local imperfections are taken directly into account. Thus both system buckling and local member buckling may be checked by the global analysis. This procedure was utilized in this project.

5 A critical issue in this respect is the determination of the shape and the size of the imperfections to be used in the analyses. At start of detail design, no clear guidelines for this were given in the Norwegian regulations. A set of rules was therefore determined based on the existing preliminary (i.e. preliminary in 2007 at start of design) recommendations in Eurocode Annex D; the shape should be based on elastic buckling modes of the structure and the size of the imperfection should be calculated based on eq. (1). Table 1: Size of imperfections for various buckling curves a b c d e min (mm) e max (mm) D e min e 0 = S D e max (1) where S is the arch length from start to maximum imperfection and e max,e min, D are values depending cross-section types/buckling curves, i.e. upon residual stresses, ref table 1. Calculations have been performed for two critical load regimes; loads mainly in the vertical direction (i.e. traffic loading) and loads mainly in the horizontal direction (i.e. wind loading). Elastic buckling modes for each of these two load regimes have been calculated and the structure has been checked for more than 30 modes in each regime. Typical buckling modes are shown in figure 7. Based on the determined buckling mode shape, the maximum imperfection is determined as described above and a structural model including the imperfection is generated. Based on this model, new load actions are calculated, and the utilization of the structure is calculated based on direct stress utilization. Maximum utilization of the steel arch without imperfections is 0.75 due to wind loading, and 0.65 due to traffic loading. Including imperfections these utilization ratios are 0.95 and Thus the buckling gives an increase in stresses of 30 to 45 %, not as much as one might fear for such a slender structure. Fig. 7: Two typical elastic buckling modes Furthermore non-linear buckling analyses were performed in order to document that the linear elastic analyses did not underestimate the buckling behaviour of the structure. A time domain analysis including both large deflections and non-linear behaviour of the hangers was performed. The behaviour of the steel material was also assumed non-linear, i.e. following a bi-linear material model. These analyses also intended to study the post-critical behaviour of the structure, i.e. the behaviour for a loading above the design load which the linear elastic design have proven the structure to carry. In the nonlinear analyses the live load was thus increased above the defined level, until collapse. A safety factor was thus introduced, a factor based on the value 1.0 for the normative load level for the bridge including load factors. In figure 8 the results are shown for the loading in

6 Horr. displacement top of arch [m] no imperf. with imperf Safety factor SF Fig. 8:Non-linear buckling analysis for wind load horizontal direction, the wind loading case. This analysis showed that the bridge was able to carry 2.6 times the normative load. The analysis for loading in vertical direction (traffic load) showed even a higher safety factor. In these analyses the concrete was assumed to behave linear elastic as this structural part was designed to carry the normative load as normal for concrete structures. Thus would this structural part be the limiting part in real life. Even though the structure has an extreme slenderness, both types of analyses show that the arch behaves well and have a satisfactorily buckling safety. The analyses did not reveal any particular instability phenomena for such structures. The only obvious observation is that the arch itself without hangers is not stable. This is an important fact for the construction phase, but not for the completed structure. 4. Construction 4.1 General The final concern was the installation procedure that also had to be addressed in the design process, as the network arch could not be constructed at the bridge location. Two possible alternatives were identified: 1. To build the main span close to the bridge site and then slide it over the fjord 2. To build the main span at a location 5 km from the bridge site, and transport it to the bridge site on the water. Both options were open for the contractors. The latter was chosen by Skanska who was awarded the building contract. 4.2 Construction of the main span The construction of the bridge started in august The main span was built at the seaside on an industrial landfill at Sløvågen, approximately 5 km from the bridge site. Fig. 9: Construction of main span The concrete deck was cast first and then posttensioned. The installation of the arches on top of the concrete deck was performed 150 days after the posttensioning in order to minimize the concrete creep effect on the arch. The first construction challenge was to determine the actual casting length of the concrete deck. This in order to end up with deck of correct length to fit between the two side spans after posttensioning and 150 days concrete creep.

7 The arch was produced in Holland and was transported to the building site on a floating barge. The next challenge was to install the arch and the hangers. The slenderness of the arch made the structure unstable without the hangers. By temporary supports, temporary stays and mobile lifting equipment the arch was established and the hangers mounted. The contractor had chosen a challenging procedure of tensioning hangers pair by pair. This meant a numerous tensioning operations in order to produce a correct geometry of the arch structure. But after some heavy work during the summer of 2010, the main span was ready for transportation. 4.3 Transportation and installation of main span The transportation and installation of the main span was a spectacular operation performed in September Two floating shear leg type lifting vessels lifted the main span from the temporary building location in Sløvågen and transported the 1862 ton heavy bridge 5 km hanging freely in the hooks, see figure 10. Strict operational criteria were given for the transportation phase. Fortunately, the weather was optimal and operation was performed without any incidence. After 6 hours of transportation the main span was placed precisely on the prepared supports at Brandangersundet and the bridge was at last at its final destination. 5. Conclusion A slender and light network arch bridge has been made for Brandangersundet. An extremely slender arch structure spanning 220 m with only 7.2 m between the arches and a cross section of only Ø711 mm has been designed, constructed and installed. This concept makes slender and transparent bridge structures possible without compromising the safety. The Brandangersundet network arch represents an effective combination of steel and concrete as building material and the concept represents an optimal solution of traditional elements combined in a new manner. Despite the high slenderness for this bridge calculations have shown that both the buckling behaviour and buckling safety are satisfactory. Fig.10: Transportation of main span from Sløvågen to the bridge site

8 Fig.11: A slender and transparent network arch at Brandangersundet This has been an interesting project introducing many challenging tasks for the designer in order to produce optimal solutions for a rather new and demanding bridge concept. Due to an excellent cooperation between owner, designer and builder this project has become a success. 6. Acknowledgements The authors acknowledge the following: Per Tveit for a lifetime dedication for network arch bridges Skanska for a dedicated construction work Norwegian Public Roads administration as owner and technical verificator 7. References [1] TVEIT, P.., On arch bridges with inclined hanger Graduation thesis at The Norwegian Institute of Technology, Trondheim, 1955, p. 76. [2] TVEIT, P.., Design of Network Arches, Structural Engineering, 44(7), London; England, 1966, pp [3] BRUNN, B., and SCHANACK, F. Calculation of a double track railway network arch bridge applying the European standards Graduation thesis at TU-Dresden p. 320 [4] STEIN, P and WILD, H. Das Bogentragwerk der Femarnsundbrücke.. Der Stahlbau, 34(6) Berlin, B.R.D, 1965 pp [5] LANDIS, B. Spanning the river with some flair The Providence Journal, September 2006