Flying Sphere image Museo Ideale L. Da Vinci Mitigation of the Wind Buffeting on a Suspended Bridge by. Smart Devices

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1 EACWE 5 Florence, Italy 19 th 23 rd July 2009 Flying Sphere image Museo Ideale L. Da Vinci Mitigation of the Wind Buffeting on a Suspended Bridge by Smart Devices M. Domaneschi, L. Martinelli Department of Structural Engineering, Politecnico di Milano domaneschi@stru.polimi.it, luca.martinelli@polimi.it P.zza L. da Vinci, 32, Milano, Italy Keywords: simulations, smart control, wind buffeting, spatial correlation, suspended bridge. ABSTRACT A suspended bridge model, developed at the numerical level in the Ansys finite element code, is used to simulate the structural response under wind excitation. Advanced structural control solutions are modeled also, with due attention to their feasibility and reliability. Two strategies have been implemented herein for the bridge protection. The control devices are defined as smart systems combining together different features and they are organized in different geometric schemes. The control strategies have been compared to each other and with the uncontrolled configuration. Their efficacy is shown and the factors contributing to their positive performance are highlighted. 1. INTRODUCTION The world today is faced with a growing need of control of the great, and still increasing, number of large structures as suspended bridges. The modern design of complex structures must be in line with Contact person: Marco Domaneschi, Department of Structural Engineering, Politecnico di Milano domaneschi@stru.polimi.it P.zza L. da Vinci, 32, Milano, Italy, FAX

2 the definition and evaluation of performance, while safety must be assessed under different conditions. Structural control solutions can give an important contribution so as to satisfy the high standards of performance, feasibility and safety. Dynamic loading from interaction with the wind is regarded as the most aggressive external excitation for long-span flexible structures in terms of displacements and internal actions. The numerical simulations here presented consider wind loading on the towers, the cables and the deck of a suspended bridge. The wind load, here simulated as a spatially correlated process, acts in the horizontal direction, transversal to the deck. The structural response is compared with a previous investigation, Domaneschi (2006), which adopted a coarser bridge model and a completely correlated wind loading condition. In this work the attention is focused on a passive control solution, this enhances both the reliability and robustness of the control, reduces the on-line computational efforts and simplifies or eliminates the need of data transmission. When compared to active solutions, in fact, the passive one does not require power supply, control feedback connections and computing power to produce the control forces; in addition, a diffuse sensor network for the structure monitoring is not required. This implies, Casciati et al. (2004), Domaneschi (2005), a huge simplification in all the control implementation with an important contribution toward the application and feasibility of the system. The wind loading descends from generated 3D turbulent wind fields non-homogeneous in space to consider the atmospheric boundary layer, Martinelli et al. (2001), Martinelli et al.(2005). 2. GEOMETRY The suspended bridge is the Shimotsui- Seto Bridge in Japan, spanning from the side of Mt. Washu to the Hitsuishijima Island. This is a single span stiffened truss suspension bridge. The main dimensions can be summarized as follows: length, 1446m (940m the main span); towers height, 149m; vertical distance of the main girder from the towers foundation, 31m; main girder section: 30m for width and 13m for thickness. The main cables, the suspenders and the main girder are in steel, the towers have been built in concrete. Figure 1 shows the main dimensions of the bridge. a) b) c) Figure 1: Bridge geometry (Courtesy of Dr. M. Nishitani HBSE-JP): (a) longitudinal profile, (b) deck section, (c) tower.

3 3. NUMERICAL MODEL In comparison to a previous work (Domaneschi, 2007) this study introduces new refinements in the numerical model of the structure and the wind loading. Focusing the attention on the structural set up the improvements consist in: a detailed deck discretization by frame elements; spatially correlated wind loading as the dynamic excitation; applied on the deck, towers and cables. Two types of elements have been used in the numerical model (Figure 2): beams for the towers and the deck; tension-only trusses for the cable and the suspenders. The element characteristics have been fixed by the real dimensions of the structural members. The linear elastic material characteristics can be summarized as follows: Steel of the deck beams: elastic modulus KN/m 2, Poisson 0.3, mass density 78KN/g Steel of the main cables: elastic modulus KN/m 2, Poisson 0.3, mass density 78KN/g Steel of the suspenders: elastic modulus KN/m 2, Poisson 0.3, mass density 70KN/g Detail Figure 2: bridge finite element model. 4. BOUNDARY CONDITIONS AND MATERIALS The whole model is fixed to the ground (by assigning zero displacements in three directions) at the bottom of the towers, at the edges of the main cables and at the deck's ends. In the uncontrolled model, the deck is rigidly linked to the towers and the extremities at the bents. The loads considered are the gravity load and the external wind load applied on the towers, the deck and the cables, in the horizontal direction transversal to the deck axis. In this new development of the problem only the drag contribution is accounted for and in the simplest form. The main improvement consist in the simulation of the excitation by a spatial correlated approach, Solari et al. (2001), Hao et al. (1989). 4.1 Wind velocity generation. Wind forces on structures are usually schematized by the sum of their mean static part and a nil mean

4 fluctuation, generally treated as a stationary process in space and time. The wind field is represented by the vectorial temporal law of velocity at point M: v( M, t) = vm ( M ) + v ( M, t) (1) where t is the time, v m is the mean wind velocity vector and v is the vectorial zero mean turbulent fluctuation of v around v m. Considering x, y, z, a Cartesian reference system with origin in the mid span of the deck, z is the vertical axes, x is the axes coincident with longitudinal axes of the deck, y is the transversal axis. So the vectorial zero mean turbulent fluctuation v can be expressed as v ( M, t) = iu ( M, t) + jl ( M, t) + kw ( M, t) (2) where i, j, k are the unit vectors in the directions x, y and z, respectively; u, l, w are the longitudinal (x), lateral (y), vertical (z) turbulence components. For the aim of this structural control study, the turbulence components u and w are fixed to zero. The wind velocity is spatially correlated. This last condition represents an improvement of the previous investigation presented in Domaneschi (2007). In light of the previous observations, the structural model is subjected to a turbulent wind field, having mean velocity transversal to the longitudinal bridge axis; turbulence is modeled by generating artificial velocity time-histories, according to a specific 3-D turbulence model by Solari et al. (2001). The model is based on the definition of direct spectral densities and coherency functions; the latter can relate different components at the same points ( point coherencies) or equal components in different points ( space coherencies). This last option is applied in this study. Decay of space coherencies with distance is of exponential type. The model is completely defined when average velocity, the terrain factor, the roughness length and the minimum height are given. Here by the Eurocode 1 classification as sea or coastal area (terrain category 0). The wind velocity records are generated, according to the procedure by Hao et al. (1989), in series of n st points starting from the time history at the starting station. The wind velocities are seen as stochastic processes with zero mean, for the turbulent component, and known spectral density S 0 (ω) for all the stations. In light of the previous assumptions the cross spectral densities S ij (ω) between the stations can be written as functions of the coherency functions γ ij (ω) and S 0 (ω). The following matrix can be written ( ) ( ) ( ) γ 11 ω γ 12 i ω... γ i ω 1nst ( i ) ( )... ( i ) γ 21 ω γ 22 ω γ 2n ω st S ij (ω) = S 0 (ω) (3) γ n 1( i ω ) γ n 2( i ω )... γ n n ( ω ) st st st st The circular frequencies are assumed varying in the interval ω N ω ω N ( ), where ωn = 2π / 2 t is the Nyquist frequency. The velocity time histories at the v i stations are processed by the finite series: i N i m n n i m n + m=1 n=1 v i (M,t) = A ( ω ) cos[ ω t + β ( ω ) φ ] i=1..n st (4) Where φ mn are the phase angles described as random variables with uniform probability density between 0 and 2π, which are statistically independent from φ rs for m r and n s. The amplitude A im and the phase angle β im are selected so as to satisfy equation (3). mn

5 4.2 Drag forces on the structural members. When the bridge structure is immersed in a wind field it is subjected to several disturbances which can be summarized as follow the stationary component, due to the mean flux component; the turbulent component, due to the wind fluctuations around the mean value; the self-excited component, due to the movements of the structure itself; the vortex shedding behaviour, with possible synchronization of the structural vibration. Experimental investigations allow to assume the different behaviours can occur in different frequency ranges. So they can be analyzed separately, neglecting their interaction. In addition, neglecting the forces due to the synchronization, the attention is focused on the buffeting excitation. In other words, on the mean and fluctuating component of the wind forces in the along-wind direction (ESDU Report n 81027, n 71012; CNR-DT 207/2008). In light of the previous assumptions the drag force results: 1 2 FD ( M, t) = ρcd( α)[ v( M, t)] A( M ) (5) 2 Where ρ is the air density, α is the attack angle, A(M) is the surface area exposed to the wind action and C D the drag coefficient, evaluated by wind tunnel tests. This initial study is focused on the simple load condition which consists in the wind flux normal to the longitudinal dimension of the bridge. This condition simplifies the generation of the velocity time histories while being among those giving rise to the large exciting forces on the structural members. For the aim of this control study, only the drag spatial-correlated wind forces are considered. The drag force coefficient C D in the mean wind direction is evaluated for each bridge section, according to ESDU Report n 81027, as the product of the base drag coefficient C D0 and opportune coefficients which account for the following secondary effects: a. flux orientation with respect the longitudinal dimension of the bridge; b. drag force reduction on a leeward element due to the screening effect of another windward element. C D0 is the drag coefficient which characterizes an isolated element. Or, in other words, an element without any screening effect and immersed in a perfectly orthogonal flux. Evaluation of the drag coefficient C D is performed for the deck from the available wind tunnel test curve, which relates the attack angle with the drag coefficient (Figure 3). For the bridge towers, the suspenders and the main cables, from literature documents (ESDU Report n 81027, n 71012; CNR-DT 207/2008) guiding in evaluating the drag coefficient for different geometries as those here considered. The resulting coefficient has been assigned to the corresponding groups of bridge elements. In particular the following considerations are assumed: the wind forces are applied along the main cables, the deck and the towers; the forces are concentrated in the nodes with a tributary area which considers the contribution of different elements (for example half length of the main cable between two suspenders and half of the suspender, half length of the deck between two suspenders and half of the suspender); each surface is considered with its own drag coefficient and the screening coefficient. Figure 4 depicts a typical module of elements subjected to the wind action while Table I summarizes the numerical values for the drag coefficients applied to the bridge elements. Figure 5 reports the variation of the drag force coefficient (product between the drag coefficient C D and the tributary area) along the bridge axis: in particular Figure 5a is focused on the module composed of the main cable and suspenders, Figure 5b on the module composed of the suspender and deck. It is worth noting the strong reduction at the extremities of the bridge where the suspenders are not present and the gradual increments from the middle to the towers position due to the different length of the suspenders.

6 5 4,5 4 3,5 3 CD C D 2,5 2 1,5 1 CD(0)=1,94 C D (0)=1.94 0, Figure 3: Deck drag coefficient vs. attack angle (courtesy of Dr. M. Nishitani HBSE JP). α[ ] α[ ] Nodes where the wind forces are concentrated Module main cable suspender Module deck suspender Wind Figure 4: bridge modules for the wind nodal force computation. Table I: Drag coefficients for the bridge elements C D Screening effect Deck Wind tunnel test (Figure 3) - Suspender Main cable 0.7 Accounted Tower 1.84 Accounted 5. STATIC AND MODAL ANALYSES The uncontrolled configuration is initially implemented in a linear static analysis with the mass density of structural materials. The resulting displacements field is used to correct the nodes position in the overall bridge model: the initial nodes vertical coordinate is moved up by the vertical displacement resulting from the analysis. With this procedure the configuration of the bridge coincides with the design problem and includes also the initial stress state induced by the mass density, Domaneschi, (2007).

7 AC D [m 2 ] AC D [m 2 ] z [m] (a) (b) Figure 5: variation of the drag force coefficient along the bridge axis: (a) main cable and suspenders module, (b) suspender and deck module. Long-span bridge structures show usually low natural frequencies in their first modes of vibration. For this bridge model, a modal analysis is performed after the application of the static loads and the correction of the resulting deformed shape of the bridge. As a matter of fact the model for the extraction of the natural frequencies is set by fixing the mass density of the cables to zero. This procedure has been adopted so as to exclude the cables mode shapes which are numerous and could distort or over-charge the calculus. The mode shape extraction is performed by the Lanczos method. Table II reports a comparison between the calculated main natural frequencies and the real ones. The numerical model matches with a good resolution the target frequencies. Table II: Model and real bridge natural frequencies Mode Real frequency [Hz] Model frequency [Hz] Shape lateral symmetric vertical anti-symmetric vertical symmetric lateral anti-symmetric z [m] 6. TRANSIENT ANALYSIS The geometry of the bridge and the boundary conditions suggest to perform the transient analyses in large displacements establishing the equilibrium on the deformed shape. It means that the relation between displacements and strains in the structure is not linear and the solution is determined by numerical iterations with a tangent stiffness method, the Newton Raphson one. During the analyses, damping is modelled by means of a Rayleigh damping matrix enforcing a 1% damping ratio for the 1 st and 4 th mode. 6.1 Control solutions The attention is focused on the reliability and robustness of the control solutions, on the reduction of computational efforts and on the simplification of data transmission connections. When compared to active solution, the passive one does not require power supply, control feedback connections and processing power to produce the control forces, This implies a huge simplification in all the control implementation with an important contribution toward the application and feasibility of the system, Domaneschi (2005). Passive control strategies have been implemented herein for the protection of the suspended bridge and compared with the uncontrolled ones. They are robust in the sense that they require less operative

8 conditions for their functioning and the failure of a device does not influence the efficacy of the remaining ones, because none depends from any other. Figure 6: Control device: damper with a force threshold. * * * Additional transversal devices Figure 7: Top view of a bridge extremity: (a) first distribution of devices that has been analyzed; (b) second distribution of devices analyzed. The passive control solutions descend from those evaluated in Domaneschi (2007), the most effective control device is here implemented. Figures 6 depicts the device scheme, it is able to perform a rigid link until a force threshold controlled by coulomb friction; over the threshold the relative movement between the two nodes of the model is allowed according to a fixed damping factor. Two geometric distributions of the control devices are considered in this study. Both apply the control devices to the bridge between the deck and the peripheral supports. Figure 7a shows an outline of the first distribution where the control devices are placed at the extremities of the deck to manage the longitudinal movements and between the deck and the towers to manage the longitudinal and transversal movements, also by the support of a transversal beam. Figure 7b depicts the second configuration, similar to the first one but with additional devices in transversal direction applied between the deck and the bents. In both the configurations the deck is supported at the extremities in the vertical direction. 6.2 Mitigation of the wind effects Several simulations were performed on the bridge model with different control schemes in order to analyze its response under the wind signals. Only the most significant are presented herein. They are detailed in Table III and can be described as follows: the uncontrolled scheme consists in the deck rigidly linked to the towers and at the extremities to the bents. This is used as a reference for evaluating the effectiveness of the control system. The threshold and damping (TD) scheme applies the geometries of Figure 7a and 7b with the devices of Figure 6. The deck is rigidly linked in horizontal direction to the towers and the extremities at the bents until a force threshold. Over the threshold the movement of the deck is allowed according

9 to a fixed damping factor. Table III: Details on the control schemes used in the transient analyses CONTROL SCHEMES DEVICES DISTRIBUTION LONGITUDINAL DEVICES TRANSVERSAL DEVICES Uncontrolled - Rigid links Rigid links TDa Figure 7a Type Figure 6 threshold=100kn damper=1000knsec/m Type Figure 6 threshold=100kn damper=6000knsec/m TDb Figure 7b Type Figure 6 threshold=100kn damper=1000knsec/m Type Figure 6 threshold=100kn damper=6000knsec/m 6.3 Simulation results Results pertaining to the uncontrolled configuration and the control arrangements herein considered are reported in Table IV. It details the statistical parameters of the responses. It is worth noting a reduction in terms of internal actions and displacements. The mean values are substantially unchanged or slightly reduced; the standard deviation parameter is, however, generally smaller. This last is an important aspect in view of fatigue problems inherent to the structural members. Figure 8, 9 and 10 depict the structural responses of the TDb controlled configuration with the uncontrolled one. In particular they show the reduction of the standard deviation with also the maximum and mean values. The curves just discussed have to be considered representative also for the TDa configuration, as the comparison between Figure 8 and 11 can prove. Table IV: numerical results Control schemes Uncontrolled TDa TDb Deck displacement at mid span [m] Max Mean Min Sdv Tower base shear (leeward, in the horizontal plane, transversal to the bridge axis) [KN] Max Mean Min Sdv Tower base bending moment (leeward, in the vertical plane, transversal to the bridge axis) [KNm] Max Mean Min Sdv

10 [m] [s] Controlled Uncontrolled Figure 8: Deck displacement at mid span for TDb configuration [KN] [s] Controlled Uncontrolled Figure 9: Base shear, transversal to the bridge axis, at the leeward tower, TDb configuration.

11 [KNm] [s] Controlled Uncontrolled Figure 10: Bending moment at the leeward tower base TDb configuration [m] [s] Controlled Uncontrolled Figure 11: Deck displacement at mid span for TDa configuration.

12 7. CONCLUSIONS This paper deals with the control systems of a cable suspended bridge. In each of the solutions offered herein, robustness and simplicity are given priority. Accordingly, passive systems are investigated. The control strategies have been compared with each other and with the uncontrolled structural configuration. Their efficacy in the reduction of the internal actions is reached. It is also worth underling the positive contribution of the structural devices in terms of damping in spite of the small relative displacements of the nodes where they are connected. New efforts are introduced in the numerical simulations with respect to a previous investigation on the same structure: the wind action is processed as spatial correlated and the drag forces are applied on all the structural element with the support of wind tunnel tests. The bridge deck is simulated reproducing the steel frame in detail. The modal analyses performed confirm the model identification. Future developments will consider the aspects on the aerodynamic forces, for the lift component in particular, which herein have not been implemented. 8. ACKNOWLEDGEMENTS The authors would like to express their gratitude to Prof. F. Perotti (Politecnico di Milano) and to Dr. M. Nishitani (Honshu-Shikoku Bridge Expressway Company Limited JP) for the indispensable support to this study. The MSc student M. Romano is also gratefully acknowledged for his support in the model development and the numerical simulations. 9. REFERENCES Domaneschi M. Passive Control Mitigation of the Wind Buffeting Effects on a Suspended Bridge. Proceedings of The Eleventh International Conference on Civil, Structural and Environmental Engineering Computing, Paper 13, St. Julians, Malta September ISBN Casciati F., Domaneschi M. Confinement of Vibration Applied to a Benchmark Problem. Proc. of Second European Workshop on Structural Health Monitoring, , Monaco D, July 7-9, Domaneschi M. Structural Control of Cable-stayed and Suspended Bridges. Ph.D. Thesis, University of Pavia, Italy, Martinelli L., Perotti F. Numerical analysis of the non-linear dynamic behaviour of suspended cables under turbulent wind excitation. International Journal of Structural Stability and Dynamics, vol. 1, pp , Martinelli L., Pomar A. Analysis of cableway non-linear oscillations induced by wind forces. In Proc. of the 6th Asian-Pacific Conference on Wind Engineering (APCWE-VI), C.K Choi, Y.D. Kim H.G. Kwak (Editors), Seoul (Korea), September, 12-14, 2005 (CD-ROM) Techno-Press, Daejeon, Korea. Solari G., Piccardo G. Probabilistic 3-D turbulence modelling for gust buffeting of structures. Prob. Eng. Mechanics, 16, 73-86, Hao H., Oliveira C. S., Penzien J. Multiple-Station Ground Motion Processing and Simulation Based on SMART-1 Array Data, Nucl. Eng. and Des., 111, , CEN European Committee for Standardization, Eurocode 1, EN , ESDU Report n 81027, LATTICE STRUCTURES. PART 1: Mean Fluid Forces on Single and Multiple Plane Frames Engineering Sciences Data Unit, London. ESDU Report n 71012, Fluid forces on non-streamlined bodies Background notes and description of the flow phenomena, Engineering Sciences Data Unit, London. WIND TUNNEL TEST OF NABOKU-BISAN-SETO BRIDGES WITH STIFFENING TRUSS, Shin Narui (in Japanese). CNR-DT 207/2008, Instructions for the wind effects and actions evaluations on buildings (in Italian).