A CABLE-STAYED FOOTBRIDGE IN BORMIO (ITALY)

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1 A CABLE-STAYED FOOTBRIDGE IN BORMIO (ITALY) Matteo MORATTI Project Manager Studio Calvi Srl Pavia, Italy Dario COMPAGNONI Civil Engineer Studio Compagnoni Bormio, Italy Gian Michele Calvi Professor Università di Pavia Pavia, Italy Summary The bridge has a single span of about 66 m passing over an important road and the Frodolfo river. The reinforced concrete deck is curved in plan and in elevation, and has a thickness varying between 280 mm and 450 mm and is sustained by single steel pylon, hinged at the base. The main structure has been built in four days, without any temporary support, using fiveidentical prefabricated deck sections, each of which is 12 m long, and a monolithic steel pylon 35 m tall to which the deck sections are anchored by means of four cables each. The total construction cost has been of approximately 500,000. The bridge is technologically highly innovative, very light and beautifully inserted in the environment and very cost effective. It has provided a great benefit to the community (it is used by thousands of people every day, particularly during the high tourism season), in terms of reduction of walking distances, increase of safety and convenience. Dynamics tests were performed in situ during the different construction stages. The pseudo-static and dynamic experimental response of the structure is compared with the results of finite elements analyses. The relevant design and construction aspects are presented and discussed in the paper. Keywords: cable-stayed footbridge; environmental impact; method of construction; high-performance self compacting concrete; viscous damping; pseudo-static and dynamic tests. 1. Introduction The bridge is designed to connect two parts of the medieval village of Bormio, in the Italian Alps, separated by a main road and the Frodolfo river. On the west side it is located at the main centre of the town (with a population that may vary from three to twenty thousand, depending on the time of the year), on the east side, also dating back to the medieval age, several sky lifts reach altitudes of about 3,000 meters and create a very attractive ski resort, where world class races are often organized. The east side is only a couple of meters higher in elevation, but before opening the bridge from the west side it was necessary to descend several meters, to cross the road and the river (on a now demolished small bridge) and to walk up again on the east side. The construction of the bridge allowed significant reduction in difficulties and time required to walk between the two parts of the town, with beneficial effects for all sorts of business and leisure activities, but also inducing many people to walk instead of using a car, therefore improving life quality and reducing pollution and energy consumption. During the design phase the environmental impact was also evaluated by a topographic software usually adopted in design of radio-communication systems. The introduction of the footbridge in a three-dimensional model of the territory around the village permitted to valuate the visibility of the top part of the pylon from an hypothetical point of view placed at two meter height from the ground level (see fig. 2). 1

2 Fig. 1 Complete view of the bridge from south Pylon Fig. 2 Visibility map of the tip of the pylon (green indicates visibility, red indicates no-visibility) 2. Design philosophy and geometry The design choices were essentially guided by the environmental constraints: no intermediate support was really possible and, only on the west side topography and building locations permitted a relatively easy construction of foundations; on the same side, an underground parking under construction provided some free anchoring mass; the beauty of the valley and the presence of an ancient stone bridge required a light structure, with minimum interference with the surroundings; the construction time on site needed to be reduced to a minimum, to mitigate as much as possible traffic interruption on the main road. The cable-stayed technology satisfied the design requirements permitting easier and quicker construction stages (the pylon and the five pre-cast segments of the deck were assembled on site in four days). The location of foundation and vertical structures did not increase the hydro-geological hazard. The environmental impact was minimized by the slenderness of the single bay 66 m long and about 300 mm thick. The cost was highly competitive with other solutions. The deck is not symmetrical with respect to the steel pylon, placed at about 8 m distance from the east abutment. The steel pylon is rotated both vertically (about 7 degrees) and horizontally, in order to optimize the force distribution in the deck and to eliminate the bending moments from the pylon, thus results to be perfectly compressed, coherently with the base hinged connection. The pylon is hinged at the base and its position is essentially governed by the actual loading, 2

3 with a variable inclination. Seven tendons (42 mm maximum diameter) restrain the pylon to the ground in the longitudinal direction, while in the transversal direction 4 additional cables -approximately orthogonal to the other seven- ensure stability. Fig. 3 Main geometry of the footbridge frontal view from south Fig. 4 Deformed shape under live loads of the f. e. m. model under the live load (from left to right: south-east view; east view; plan view) The deck is formed by five pre cast high performance concrete elements supported on 10 couples of thinner cables (22 28 mm diameter) mutually spaced at 6 m distance. Each segment has the same length (12 m) and the same radius of curvature both in plan (300 m) and in elevation (1200 m). The concrete cross section is 3 m wide and the profile is completed by lateral aluminium noses (0.3 m length) integrated with the corrugated floor to prevent local vortex-effects caused by wind action. The bridge deck is about 5 metres above the street and about 10 metres above the river-bottom. Fig. 5 Structural details (From left to right: hinged truss at the east-abutment; hinge at the base of the pylon; steel pylon during the cold-forming phase (note the steel wings) The in plane curved shape of the deck is contributing to equilibrate the horizontal load by arching action, whilst vertically the deck is free to rotate around an horizontal axis on the west side and is connected to the east abutment with a double-hinged 6 m long truss that allows vertical and longitudinal free movements and rotations of the deck (fig. 5). 3

4 The adopted solution permitted a scheme of hinged stayed monolithic beam reducing the redundancy of the whole system and, consequently, the sensitivity to thermal loads, shrinkage, creep and steel relaxation. The double-hinged truss is connected to two viscous devices to provide additional vertical damping and to increase the user s comfort. 3. Technology The shallow foundation of the steel pylon is a RC plate, with a rectangular base, 8 m by 9 m in plan and 1.2 m thick. It was placed under the parking floor at a depth of about 8 metres with respect to the level of the street. A RC-column with a square section with 2 m sides, raises from the foundation to the base of the pylon. The pylon is simply supported on a pot device settled on a concrete plinth 3 m tall with an octagonal plan shape. Eight hi-strength post-tensioned re-bars (bonded type) were placed to confine the element due to the high local compressive and tensile stress (fig. 6). Fig. 6 Structural details (From left to right: post-tensioned concrete plinth at pylon base; anchorage niches in the retaining wall; cable tensioning at the east-wall ) The five deck segments were casted in factory with high strength (compressive strength class C40/50) self compacting concrete using special curved iron formwork (fig. 7). Fig. 7 Deck segment (From left to right: steel cages in the steel form before pouring; detail of the steel anchorage of the cable) The section of each segment was characterized by four continuous beams with lower and upper RC slabs 50 mm thick. In the transversal directions 3 equally spaced beams were also provided. The plan and the profile were the same for each segment, the thickness was variable between 280 mm at the east abutment and 450 mm at the west side due to the increasing axial force. The main section of the deck resulted double symmetric (fig. 8). The ends of the segment were endowed with a couple of self-centring steel devices, to be used during the construction phase to provide temporary continuity. 4

5 Fig. 8 Main section of the deck (hatched zone indicates RC, dimensions in mm) The rotated pylon was a monolithic 35 m steel pipe (812 mm external diameter) with a second external, cold-formed co axial pipe (19 m long, mm variable diameter) welded to the internal one by six radial steel wings. The pot device (fig. 6 and fig. 8) has a compressive capacity of 10,000 kn at the ultimate limit state. A maximum rotation of 0,012 rad under the live load action is expected. Each tendon is made by high strength wires which were hot dip galvanized. The ropes were pre-stretched in factory with a force of 1/3 of the nominal breaking load before assembling. The sockets of the cables are anchored by gravity in two orthogonal RC walls (1 m thickness) of the underground parking (fig. 6). Fig. 9 Bearing devices (from left to right: horizontal hinged bearings at the west abutment; preparation of post-tensioned connections for the bearings; pylon pot bearing) At the west abutment the deck was restrained by three mono-lateral (compression only) bearings: one in the vertical direction and two connected to the extremities of the longitudinal beams to provide bending moment capacity in the horizontal plane. To withstand the tensile forces acting during the construction phase and under the wind load the horizontal bearings were post-stressed by hi-strength re-bars restrained to the west abutment (fig. 9). 4. Method of constructions As already discussed, only the pylon foundation, the abutments and the anchor walls for the fixed cables were constructed on site, while the contemporary construction of an underground parking lot reduced the needs of excavation and simplified the job (fig. 9). During construction, a temporary connection between the deck sections was provided by steel self centring couplers, later on included in concrete injections that made the deck fully continuous (fig. 11). The pylon was transported overnight in a single piece and mounted with the help of two cranes; within the next three days it was possible to position and cable-suspend the five deck sections (fig. 10), prefabricated elsewhere. The pylon was positioned using topographic measurements and it was longitudinally and transversally restrained to the ground by one cable in each direction. A crane had to keep it in place until the second deck segment had been assembled, thus providing equilibrium together with the weight of the rotated pylon. The remaining deck segments and cables were assembled in sequence, anchoring in turn two longitudinal cables and one transversal cable for each segment. The regulation of the deck profile was obtained post tensioning the four cable of each segments without significant effects on the pylon inclination, because of the essentially isostatic situation resulting from temporary self-centring couplers between the deck elements (fig.11). 5

6 Fig. 10 Sequence of assembling the deck segments Fig. 11 Temporary self centring couplers (clockwise: plan view; section B; detail of the steel pin; section A-A with the RC transversal beam cast on site to make the deck continuous) The bridge was completed with additional concrete connections, corrugated aluminium floor and steel parapets. An electric heating system was included below the floor to prevent icing. The light was provided by floor washer led devices. 5. Finite element analyses 5.1 Structure modelling Two models were developed; in the first one the deck was simulated by a single equivalent beam section according to Wilson and Gravelle procedure [1]. In the second one (shell model) the deck is more accurately modelled by a number of beam elements, representing each single concrete beam inside the deck, connected to upper and lower plate-elements. 6

7 The first model required 82 frame elements, the second one 377 frame and 552 shell elements. In both cases an iterative procedure was implemented to consider equilibrium in the displaced position. Each cable was modelled by one single element. The local dynamic behaviour of each cable was later evaluated by simplified models according to Eurocode 1 Appendix C rules[2] to avoid galloping. The same approach is adopted for fluttering problem. Modal and non linear time history analyses with moving load along the deck were carried out in order to verify the effects of vertical and horizontal accelerations on the users (Eurocode 2 part 2 [3]). Fig. 12 Finite element models: equivalent beam (left) and shell model (right) 5.2 Equivalent Beam Section model vs. Shell Model A comparison between the two different modelling choices (equivalent beam and shell model) was obtained considering periods of vibration and participating masses for corresponding vibration modes, as shown in Fig. 13. It can be observed that in order to obtain a total of participating mass of about 90 % in all the three directions x, y and z, 31 modes are needed in the beam model while 173 modes have to be considered in the shell model. The y and z directions reach a participating mass of 90 % at the 60th mode, it is the x direction to require a larger number of modes. Fig. 13 Modal period and participating mass: beam model (left) and shell model (right) The first twenty modes of vibration of each model are shown in fig. 13 and in Table 1: it can be observed that the frequencies are very well comparable. The modes where larger differences are noted (e.g.: modes 10, 11, 18, 20) are those characterized by a more significant participation of the x direction in the modal shape, coherently with the already observed major discrepancies. Fig. 14 Comparison between the modal frequencies obtained from the beam and the shell models (left); theoretical1st modal shape for shell model (right) 7

8 Table 1The first 20 modes obtained from the shell and beam models SHELL MODEL BEAM MODEL N T Ν X direction Y direction Z direction N T Ν X direction Y direction Z direction [sec] [Hz] [%] [%] [%] [sec] [Hz] [%] [%] [%] 1 1,103 0,906 0,351 0,219 51, ,037 0,964 0,268 0,511 46, ,591 1,692 0,037 35,405 4, ,609 1,641 0,689 14,162 8, ,578 1,731 0,236 31,079 3, ,578 1,729 0,248 52,803 0, ,450 2,221 0,046 0,089 5, ,454 2,201 0,204 0,250 4, ,340 2,946 0,026 0,267 2, ,367 2,725 0,000 4,257 0, ,325 3,080 0,026 5,765 4, ,341 2,936 0,107 6,065 13, ,252 3,974 0,014 0,229 1, ,272 3,683 0,057 0,190 3, ,236 4,239 0,076 0,059 1, ,243 4,124 12,410 0,035 2, ,189 5,297 0,894 1,307 0, ,203 4,931 0,332 0,104 0, ,172 5,830 5,165 0,004 2, ,186 5,378 0,309 1,097 0, ,170 5,899 1,891 0,006 0, ,152 6,582 0,002 0,674 0, ,149 6,732 0,022 0,092 0, ,147 6,806 0,000 0,001 0, ,127 7,868 0,024 0,000 1, ,111 8,975 0,235 0,000 0, ,124 8,083 0,026 0,279 0, ,110 9,130 0,034 0,186 0, ,099 10,056 0,061 3,143 0, ,099 10,072 0,055 1,969 0, ,098 10,183 0,032 0,079 0, ,097 10,290 0,169 8,213 0, ,093 10,714 0,464 6,694 0, ,088 11,334 0,014 0,200 1, ,087 11,527 12,204 0,060 0, ,077 12,996 37,240 0,015 0, ,080 12,464 0,005 0,000 2, ,076 13,079 1,770 0,000 0, ,076 13,084 39,504 0,018 0, ,071 14,112 29,168 0,041 0, Tests in situ 6.1 Pseudo-Static behaviour The hinged truss and the 5th segment of the deck were loaded by water tanks (for a total length of 12 m) to obtain an equivalent gravity load of 7,5 kn for each meter of the deck. Experimental displacements of deck and of tip of pylon are compared with the theoretical predictions provided by f. e. m. model in fig. 16. Fig. 15 Pseudo static test (From left to right: loading phases, longitudinal displacement at the east abutment) 8

9 Vertical displacement [mm] exp. q = 2,5 kn/m -50 exp. q = 5 kn/m exp. q = 7.5 kn/m -75 Theoretical Length [m] Transversal [mm] Experimental -30 Theoretical Longitudinal [mm] Fig. 16 Comparison between theoretical and experimental results: deck vertical displacements (left) - origin of the longitudinal axes is at the connection of bridge deck and adjustment truss, on the east side; pylon tip displacements (right) 6.2 Dynamic behaviour Series of forced vibration tests were performed during different stages of construction to obtain experimental data on the dynamic response of the structure. Pseudo-harmonic excitations were applied at different fundamental points of the footbridge and the experimental modal shapes were computed. A series of eight accelerometers (capacitive type with high sensibility, Kistler ±2g 1000 mv/g), distributed along the structure as described in fig.16, were used to record the response with a 512 Hz sampling (acquisition card PCI MIO 16X National Instruments with 16bit resolution). In addition to modal shapes (fig. 17) and maximum displacements and velocities, damping values have been obtained. 1,2 Modal displacement 0,8 0, ,4-0,8 Mode I Mode II Mode III Mode IV Mode V Fig. 17 Distribution of accelerometers (left) and experimental modal shape (right) (Mode I: 1 Hz; Mode II: 1,75 Hz; Mode III: 2,75 Hz; Mode IV: 3,5 Hz; Mode V: 4,75 Hz) -1,2 7. Experimental data vs. shells model data A comparison between experimental and numerical data (shell model) is shown in fig. 18, where the five modes obtained from the experimental tests are depicted in correspondence of the appropriate numerical mode. The first five modes of the normalized shapes in the test match respectively the I, II, V, VI, VIII modes of the numerical results; this is confirmed by the correspondence of the frequencies, that are respectively: ν exp,i =1 Hz and ν theo,i =0,907 Hz; ν exp,ii =1,750 Hz and ν theo,ii =1,692 Hz; ν exp,iii =2,750 Hz and ν theo, V =2,941 Hz; ν exp,iv =3,500 Hz and ν theo,vi =3,077 Hz; ν exp,v =4,750 Hz and ν theo,viii =4,237 Hz. The correspondence between the modes is also due to the relationship between the theoretical and experimental modal shape; for this reason the modal shape is normalized in order to allow the comparison. The shapes are overlapped for the 1 st mode (see fig. 18). 9

10 Modal displacement Experimental mode I Theoretical mode I 1,2 0,8 0, Length [m] 0 Fig. 18 Comparison between theoretical and experimental modal results (left); Comparison between experimental and numerical 1sI modal shape (length origin at east hinge; νexp,i=1 Hz and νtheo,i=0,907 Hz) (right) 8. Conclusion The pedestrian bridge described in this paper presents several issues of innovation in design and construction technology. The structure is essentially structurally determinate, with a proper hinge at the base of the pylon, two aligned sets of anchoring cables, a vertical hinge connection at the west abutment and a truss connection on the east side. This has allowed a simple and quick construction and eliminates any stresses due to imposed deformations, related to live loads variation or to time dependent phenomena. As a consequence, the response of the structure is essentially governed by cable deformation, that however assures a proper user s comfort. The analysis results are well comparable with the experimental values, either in the case of simple models and in the case of more accurate ones, that provides greater accuracy in numerical predictions, but do not modify significantly the values of expected maximum displacement and vertical acceleration. The experimental results were obtained by dynamic tests, performed before and after providing some additional damping at the east abutment connection. The first test sequence indicated a total equivalent damping ratio slightly higher than 1%, reasonably comparable with the value of 1.5% adopted for design. A further significant reduction of acceleration and displacement was obtained through an additional 1% damping provided by non-structural elements (steel parapets and aluminium floor) and by the two small dampers added at the east abutment.. The bridge has been used for two years, with great satisfaction of users and local population, due to the bridge functionality, but as well to its beauty and to its significance has a well inserted environmental landmark. 9. Acknowledgments The Bormio Municipality commissioned the project and financed the construction of the footbridge. Studio Calvi Srl provided design and engineering services. All the administrative procedures were accomplished with the cooperation of the internal Technical Department of the Municipality. The Laboratory of Geomatica of the University of Pavia contributed to the environmental impact simulation. The footbridge was built by G.A.L. Srl, who contributed to the solution of a number of construction problems. The European Centre for Training and Research in Earthquake Engineering (EUCENTRE) of Pavia performed the dynamic tests in situ. 10. References [1] WILSON J. C., GRAVELLE W., Modelling of a cable stayed-bridge for dynamic analysis, Earthquake Engineering and Structural Dynamics, Vol. 20, 1991, pp [2] Eurocode 1, Actions on structures - Part 2-4: General actions - Wind actions, EN :2007 [3] Eurocode 2, Design of Reinforced Concrete Structures - Part 2 - Bridges, UNI-EN