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Field measurements of the wind-induced response of a cable stayed bridge: Validation of previsional studies
Journal of Wind Engineering and Industrial Aerodynamics 74—76 (1998) 883—890
Field measurements of the wind-induced response of a cable stayed bridge: Validation of previsional studies D. Delaunay*, G. Grillaud Centre Scientifique et Technique du BaL timent (C.S.T.B.), Service Ae& rodynamique et Environnement Climatique, 11 rue Henri Picherit, BP 82341, 44323 Nantes Cedex 3, France
Abstract Field measurements of the wind turbulence and the wind-induced response of the Iroise cable-stayed bridge, near Brest in the far west of France, have been carried out. This bridge is located in the wake of an older three-arched bridge which had to be streamlined following results of computational and wind-tunnel studies in order to suppress wake interaction effects on the cable stayed bridge. The objective of these field measurements was to check the validity of the wake turbulence characteristics used in the design (according to the wind-tunnel studies), and of the previsions of the dynamic response obtained by a combined approach: theoretical computations and experiments on a taut-strip model. The measurements have allowed to validate the previsional studies. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Bridge; Wind turbulence; Wake interaction; Dynamic response; Vibration modes; Structural damping; Aerodynamic damping; Field measurements; In situ validation
1. Introduction With strong prevailing winds, the 400 m span cable-stayed bridge “Pont de l’Iroise” in Brest (France) is subjected to the wake turbulence generated by an older bridge “Pont Albert Louppe”, a three-arched bridge located upstream. In 1990, during the design stages of the cable-stayed bridge, wind-tunnel studies were performed in order to estimate the characteristics and the effects of this wake turbulence and to propose improvements by streamlining the older bridge deck. The dynamic response of the bridge was measured on a taut-strip model and computations were made using a quasi steady classical spectral approach [1]. As a result of these studies, the old bridge was equipped with “appendices” which were expected to eliminate vortexshedding phenomena (Fig. 1) from the wake of the arch bridge. These appendices were * Corresponding author. 0167-6105/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 0 8 0 - 4
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Fig. 1. The upstream bridge, equipped with streamlining appendices, in the background the cable stayed bridge in construction phase (24 m long on the upwind face of the top of each arch).
located on the upwind face of the top of each arch where the solidity of the arch is maximum (Fig. 1). The objective of the field measurements was to validate these approaches, both for the estimation of the wake turbulence exciting the new bridge, and for the resulting vertical and torsional deck displacements of the first vibration modes. Full-scale turbulence measurements are compared to corresponding wind-tunnel data in order to validate the model scale wind simulation. The measured deck displacements are then compared to the wind-tunnel results and to the theoretical computations.
2. Experimental setup Three tilted Gill 3D propeller anemometers (2.1 m distance constant), implemented on the main span of the cable-stayed bridge, measured turbulence at the deck level (31.5 m high), 3 m upstream of the deck at three characteristic points. When the wind is perpendicular to the Albert Louppe bridge, the point A is located downstream a pier, the point C is downstream an arch top (maximum wake effect), and the point B at an equal distance from A and C (Fig. 2). A similar 3D anemometer located at the top of the north tower (116 m high) gave a reference point for the comparisons with wind-tunnel measurements. Three accelerometers were set inside a deck section (Fig. 2), 25 m from the mid-span point (1/16 span length) in order to measure the dynamic response of the bridge for the first mode of horizontal flexion, the first three modes of vertical flexion, and the first torsional mode. These modes, involving the lowest frequencies, represent the main
D. Delaunay, G. Grillaud/J. Wind Eng. Ind. Aerodyn. 074—76 (1998) 883–890
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Fig. 2. Locations of the anemometers and the accelerometers on the Iroise Bridge.
dynamic behaviour of the structure. The signals were low-pass filtered at a frequency of 5 Hz. All these signals were sampled at a frequency of 10 Hz in blocks of 4096 points (about 7 min duration). The sequences were stored for wind directions between 220—280°, if the wind speed at the reference point was greater than 15 m/s. About 14 h of data were collected between 24 October 1995 and 22 May 1996. They correspond to a range of mean wind speed from 15 to 23 m/s. Only the most stationary sequences were considered for the analysis.
3. Wind characteristics 3.1. Mean wind velocity In the wind-tunnel studies [2], the reference mean wind velocity is V100 corresponding to a full-scale height of 100 m. Here V100 is deduced from the field measurements on the pylon at 116 m height, assuming a logarithmic law with a roughness length z of 0.5 cm between 116 and 100 m. 0 Depending on the points and the wind directions (range 234—250°), the ratio of the mean wind speeds measured at points A, B, and C to the reference mean wind speed V100, varies from 0.42 to 0.63. For the bridge design, the value of 0.74 was considered, following results of the wind-tunnel study [2]. So mask effects appear to be stronger than on the model, but field measurements are only made in the deck region closer to the upstream bridge. The configurations compared here are also slightly different because the removal of the solid handrails was initially proposed for the whole of the arch bridge (wind-tunnel configuration) but, afterwards, it was only carried out on the central part (60 m) of each arch on the “Albert Louppe” bridge.
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3.2. Turbulence intensities Turbulence intensities were computed for the three components of the wind velocity vector at the three deck locations and at the pylon top level. The high values of turbulence intensities at the deck level (Table 1), unusual for a sea wind, are characteristic of the wake of the Albert Louppe bridge. We can also note that vertical fluctuations are of the same order of magnitude, and sometimes greater than the longitudinal ones. By considering that the measurements at points A, B, C, for oblique winds, correspond to values at shifted points for perpendicular winds, we can evaluate the variations of the standard deviations of the fluctuations along the deck and compare field measurements with the wind-tunnel results. Fig. 3 shows that the agreement is Table 1 Measured turbulence intensities Wind direction
238—240 241—243 247—250
116 m reference
A point
B point
C point
(I ) u
(I ) v
(I ) w
(I ) u
(I ) v
(I ) w
(I ) u
(I ) v
(I ) w
(I ) u
(I ) v
(I ) w
0.06 0.06 0.06
0.06 0.05 0.06
0.04 0.04 0.05
0.15 0.16 0.16
0.15 0.13 0.13
0.15 0.15 0.15
0.20 0.21 0.23
0.21 0.21 0.21
0.23 0.23 0.26
0.20 0.18 0.14
0.17 0.14 0.11
0.22 0.18 0.14
Fig. 3. Normalized standard deviations of longitudinal and vertical wind fluctuations for a wind perpendicular to the Albert Louppe Bridge.
D. Delaunay, G. Grillaud/J. Wind Eng. Ind. Aerodyn. 074—76 (1998) 883–890
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good (in this figure, the standard deviations are normalized by the reference velocity V100). 3.3. Power spectral densities The computations of the power spectral densities (p.s.d.) of the wind fluctuations show that the longitudinal turbulent length scales are very short (about 9 m for the longitudinal component and 5 m for the vertical and the lateral ones). These lengths, of the same order than the upstream deck depth, are characteristics of a wake. The p.s.d. are compared to the values considered for the bridge design, deduced from the wind-tunnel measurements (Fig. 4). The comparison is made in the reduced frequency range concerned by the bridge dynamic behaviour (0.2—1.5 Hz), where the reduced frequency n* is defined as in Ref. [2], n*"fz/(0.7 V100), where f is the frequency and z the height above the river level (31.5 m). The p.s.d. are normalized as
Fig. 4. Normalized p.s.d. of wind fluctuation. Wind direction: 239° C location — wind-tunnel results; * field measurements.
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they were in the wind-tunnel studies: the longitudinal fluctuations p.s.d. are normalized by the variance of the fluctuations, while the vertical fluctuations p.s.d. are normalized by (0.14V100)2 which, in the wind-tunnel study, represents a mean variance of the vertical fluctuations. For the longitudinal component, the measured values are generally slightly lower than the wind-tunnel results. For the vertical component, and for the location immediately downstream the mid-span arch, wind-tunnel results sometimes underpredict the values of the p.s.d. (Fig. 4). However the important point is to note that the vortex shedding phenomenon which was generated by the non-profiled old bridge, has been eliminated by the geometrical improvements as anticipated from the windtunnel studies.
4. Dynamic response of the cable-stayed bridge The spectral densities of the deck accelerations were computed for samples of 4096 points and, for given wind conditions, at least 8 spectra were averaged to give a sampling error of less than 35% on a spectral point estimate. Table 2 gives the peak frequencies for the considered modes as well as those obtained by computations [1]. The peak frequencies are slightly higher than those computed but these computed frequencies correspond to an early design of the bridge. Since 1990 until completion in 1994, the design of the bridge was subsequently improved, in particular additional viscoelastic dampers were added between two lateral piles and the lateral spans of the bridge. The efficiency of these dampers in terms of additional damping and additional stiffness is not well known and has never been characterised. However they can explain the difference between the initial computed frequencies and the measured frequencies. The modal amplitude standard deviations of the displacements were deduced from the acceleration measurements assuming that the real mode shapes are similar to the computed mode shapes. A comparison between field measurements, taut-strip model measurements [3], and computations, is given in Fig. 5a for the first vertical mode. There is a good agreement with only slightly lower values for the field measurements. If we take into
Table 2 Vibration modes frequencies Vibration frequencies
Field measurements
Computations 1990
Vertical bending 1 Vertical bending 2 Vertical bending 3 Torsion 1 Horizontal 1 Horizontal 2
0.31 0.45 0.65 0.84 0.285 0.34
0.29 0.40 0.56 0.74 — —
D. Delaunay, G. Grillaud/J. Wind Eng. Ind. Aerodyn. 074—76 (1998) 883–890
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Fig. 5. Comparison between wind-tunnel results, computations and full-scale measurements.
account the mode shift frequencies between field measurements (0.31 Hz) and the taut-strip model and the computations (0.29 Hz), and noting that the aerodynamic damping prevails over the structural damping for this mode (high reduced velocity), we can transpose the site measurement amplitudes as the square root of the global damping. Then the accordance with measurements on the taut-strip model is very good (transposed field measurements, Fig. 5a). This confirms also that in this particular turbulence field, with very small length scales, the aerodynamic admittance of the deck of the cable-stayed bridge does not introduce a reduction effect. We can also confirm the important slope of the response curve versus wind speed in this velocity range introduced by the “narrow band” spectral density of vertical component of the wind. For the 2nd and the 3rd mode of vertical bending, the field measured values are far less than the wind-tunnel and the computed results (Fig. 5b and 5c). The transposition made for the first mode cannot be carried out for the other modes because the structural damping is preponderant in these cases. This damping has not been characterized as the recorded displacement signals are not long enough to provide
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a reliable estimate. However, the real structural damping is probably far greater than the initial model values, due to the effect of the additional dampers. This can explain the differences. Uncertainties on the modal shapes can also contribute to these differences, as measurement locations were not far from the vibration nodes for these modes. Concerning the first torsion mode, the site measurements are also in agreement with the wind-tunnel values (Fig. 5d).
5. Conclusion Field measurements were carried out on a cable-stayed bridge located in the wake of an arch bridge. These experiments confirm the results of previsional studies conducted at design stage using a taut strip model in the CSTB boundary layer wind-tunnel and a spectral approach theoretical computation. Both the turbulent wind characteristics in the wake of the arch bridge and the response of the cablestayed bridge submitted to this particular excitation are in agreement with the results of these earlier studies. The main discrepancies concern the response of the 2nd and 3rd vertical flexural modes which are lower than the expected ones as a result of the improvements of the bridge between earlier design stages and the final project. Additional full-scale measurements are planned to identify the structural dampings of the considered modes of the bridge.
References [1] G. Grillaud, A. Chauvin, J. Bie´try, Comportement dynamique d’un pont a` haubans dans une turbulence de sillage, J. Wind Eng. Ind. Aerodyn. 41—44 (1992) 1181—1189. [2] C. Barre´, G. Grillaud, Caracte´risation dela turbulence en aval du pont Albert Louppe ame´nage´: e´tude en soufflerie atmosphe´rique sur mode`le au 1/250 e`me, CSTB Report EN-AS 90.2C. [3] G. Grillaud, J. Bie´try, P. Jan, Effets du vent sur le pont a` haubans de l’Elorn: Etude en soufflerie atmosphe´rique sur mode`le ae´roe´lastique, CSTB report EN-AS 90.1C.
Field measurements of the wind-induced response of a cable stayed bridge: Validation of previsional studies D. Delaunay*, G. Grillaud Centre Scientifique et Technique du BaL timent (C.S.T.B.), Service Ae& rodynamique et Environnement Climatique, 11 rue Henri Picherit, BP 82341, 44323 Nantes Cedex 3, France
Abstract Field measurements of the wind turbulence and the wind-induced response of the Iroise cable-stayed bridge, near Brest in the far west of France, have been carried out. This bridge is located in the wake of an older three-arched bridge which had to be streamlined following results of computational and wind-tunnel studies in order to suppress wake interaction effects on the cable stayed bridge. The objective of these field measurements was to check the validity of the wake turbulence characteristics used in the design (according to the wind-tunnel studies), and of the previsions of the dynamic response obtained by a combined approach: theoretical computations and experiments on a taut-strip model. The measurements have allowed to validate the previsional studies. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Bridge; Wind turbulence; Wake interaction; Dynamic response; Vibration modes; Structural damping; Aerodynamic damping; Field measurements; In situ validation
1. Introduction With strong prevailing winds, the 400 m span cable-stayed bridge “Pont de l’Iroise” in Brest (France) is subjected to the wake turbulence generated by an older bridge “Pont Albert Louppe”, a three-arched bridge located upstream. In 1990, during the design stages of the cable-stayed bridge, wind-tunnel studies were performed in order to estimate the characteristics and the effects of this wake turbulence and to propose improvements by streamlining the older bridge deck. The dynamic response of the bridge was measured on a taut-strip model and computations were made using a quasi steady classical spectral approach [1]. As a result of these studies, the old bridge was equipped with “appendices” which were expected to eliminate vortexshedding phenomena (Fig. 1) from the wake of the arch bridge. These appendices were * Corresponding author. 0167-6105/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 0 8 0 - 4
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Fig. 1. The upstream bridge, equipped with streamlining appendices, in the background the cable stayed bridge in construction phase (24 m long on the upwind face of the top of each arch).
located on the upwind face of the top of each arch where the solidity of the arch is maximum (Fig. 1). The objective of the field measurements was to validate these approaches, both for the estimation of the wake turbulence exciting the new bridge, and for the resulting vertical and torsional deck displacements of the first vibration modes. Full-scale turbulence measurements are compared to corresponding wind-tunnel data in order to validate the model scale wind simulation. The measured deck displacements are then compared to the wind-tunnel results and to the theoretical computations.
2. Experimental setup Three tilted Gill 3D propeller anemometers (2.1 m distance constant), implemented on the main span of the cable-stayed bridge, measured turbulence at the deck level (31.5 m high), 3 m upstream of the deck at three characteristic points. When the wind is perpendicular to the Albert Louppe bridge, the point A is located downstream a pier, the point C is downstream an arch top (maximum wake effect), and the point B at an equal distance from A and C (Fig. 2). A similar 3D anemometer located at the top of the north tower (116 m high) gave a reference point for the comparisons with wind-tunnel measurements. Three accelerometers were set inside a deck section (Fig. 2), 25 m from the mid-span point (1/16 span length) in order to measure the dynamic response of the bridge for the first mode of horizontal flexion, the first three modes of vertical flexion, and the first torsional mode. These modes, involving the lowest frequencies, represent the main
D. Delaunay, G. Grillaud/J. Wind Eng. Ind. Aerodyn. 074—76 (1998) 883–890
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Fig. 2. Locations of the anemometers and the accelerometers on the Iroise Bridge.
dynamic behaviour of the structure. The signals were low-pass filtered at a frequency of 5 Hz. All these signals were sampled at a frequency of 10 Hz in blocks of 4096 points (about 7 min duration). The sequences were stored for wind directions between 220—280°, if the wind speed at the reference point was greater than 15 m/s. About 14 h of data were collected between 24 October 1995 and 22 May 1996. They correspond to a range of mean wind speed from 15 to 23 m/s. Only the most stationary sequences were considered for the analysis.
3. Wind characteristics 3.1. Mean wind velocity In the wind-tunnel studies [2], the reference mean wind velocity is V100 corresponding to a full-scale height of 100 m. Here V100 is deduced from the field measurements on the pylon at 116 m height, assuming a logarithmic law with a roughness length z of 0.5 cm between 116 and 100 m. 0 Depending on the points and the wind directions (range 234—250°), the ratio of the mean wind speeds measured at points A, B, and C to the reference mean wind speed V100, varies from 0.42 to 0.63. For the bridge design, the value of 0.74 was considered, following results of the wind-tunnel study [2]. So mask effects appear to be stronger than on the model, but field measurements are only made in the deck region closer to the upstream bridge. The configurations compared here are also slightly different because the removal of the solid handrails was initially proposed for the whole of the arch bridge (wind-tunnel configuration) but, afterwards, it was only carried out on the central part (60 m) of each arch on the “Albert Louppe” bridge.
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3.2. Turbulence intensities Turbulence intensities were computed for the three components of the wind velocity vector at the three deck locations and at the pylon top level. The high values of turbulence intensities at the deck level (Table 1), unusual for a sea wind, are characteristic of the wake of the Albert Louppe bridge. We can also note that vertical fluctuations are of the same order of magnitude, and sometimes greater than the longitudinal ones. By considering that the measurements at points A, B, C, for oblique winds, correspond to values at shifted points for perpendicular winds, we can evaluate the variations of the standard deviations of the fluctuations along the deck and compare field measurements with the wind-tunnel results. Fig. 3 shows that the agreement is Table 1 Measured turbulence intensities Wind direction
238—240 241—243 247—250
116 m reference
A point
B point
C point
(I ) u
(I ) v
(I ) w
(I ) u
(I ) v
(I ) w
(I ) u
(I ) v
(I ) w
(I ) u
(I ) v
(I ) w
0.06 0.06 0.06
0.06 0.05 0.06
0.04 0.04 0.05
0.15 0.16 0.16
0.15 0.13 0.13
0.15 0.15 0.15
0.20 0.21 0.23
0.21 0.21 0.21
0.23 0.23 0.26
0.20 0.18 0.14
0.17 0.14 0.11
0.22 0.18 0.14
Fig. 3. Normalized standard deviations of longitudinal and vertical wind fluctuations for a wind perpendicular to the Albert Louppe Bridge.
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good (in this figure, the standard deviations are normalized by the reference velocity V100). 3.3. Power spectral densities The computations of the power spectral densities (p.s.d.) of the wind fluctuations show that the longitudinal turbulent length scales are very short (about 9 m for the longitudinal component and 5 m for the vertical and the lateral ones). These lengths, of the same order than the upstream deck depth, are characteristics of a wake. The p.s.d. are compared to the values considered for the bridge design, deduced from the wind-tunnel measurements (Fig. 4). The comparison is made in the reduced frequency range concerned by the bridge dynamic behaviour (0.2—1.5 Hz), where the reduced frequency n* is defined as in Ref. [2], n*"fz/(0.7 V100), where f is the frequency and z the height above the river level (31.5 m). The p.s.d. are normalized as
Fig. 4. Normalized p.s.d. of wind fluctuation. Wind direction: 239° C location — wind-tunnel results; * field measurements.
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they were in the wind-tunnel studies: the longitudinal fluctuations p.s.d. are normalized by the variance of the fluctuations, while the vertical fluctuations p.s.d. are normalized by (0.14V100)2 which, in the wind-tunnel study, represents a mean variance of the vertical fluctuations. For the longitudinal component, the measured values are generally slightly lower than the wind-tunnel results. For the vertical component, and for the location immediately downstream the mid-span arch, wind-tunnel results sometimes underpredict the values of the p.s.d. (Fig. 4). However the important point is to note that the vortex shedding phenomenon which was generated by the non-profiled old bridge, has been eliminated by the geometrical improvements as anticipated from the windtunnel studies.
4. Dynamic response of the cable-stayed bridge The spectral densities of the deck accelerations were computed for samples of 4096 points and, for given wind conditions, at least 8 spectra were averaged to give a sampling error of less than 35% on a spectral point estimate. Table 2 gives the peak frequencies for the considered modes as well as those obtained by computations [1]. The peak frequencies are slightly higher than those computed but these computed frequencies correspond to an early design of the bridge. Since 1990 until completion in 1994, the design of the bridge was subsequently improved, in particular additional viscoelastic dampers were added between two lateral piles and the lateral spans of the bridge. The efficiency of these dampers in terms of additional damping and additional stiffness is not well known and has never been characterised. However they can explain the difference between the initial computed frequencies and the measured frequencies. The modal amplitude standard deviations of the displacements were deduced from the acceleration measurements assuming that the real mode shapes are similar to the computed mode shapes. A comparison between field measurements, taut-strip model measurements [3], and computations, is given in Fig. 5a for the first vertical mode. There is a good agreement with only slightly lower values for the field measurements. If we take into
Table 2 Vibration modes frequencies Vibration frequencies
Field measurements
Computations 1990
Vertical bending 1 Vertical bending 2 Vertical bending 3 Torsion 1 Horizontal 1 Horizontal 2
0.31 0.45 0.65 0.84 0.285 0.34
0.29 0.40 0.56 0.74 — —
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Fig. 5. Comparison between wind-tunnel results, computations and full-scale measurements.
account the mode shift frequencies between field measurements (0.31 Hz) and the taut-strip model and the computations (0.29 Hz), and noting that the aerodynamic damping prevails over the structural damping for this mode (high reduced velocity), we can transpose the site measurement amplitudes as the square root of the global damping. Then the accordance with measurements on the taut-strip model is very good (transposed field measurements, Fig. 5a). This confirms also that in this particular turbulence field, with very small length scales, the aerodynamic admittance of the deck of the cable-stayed bridge does not introduce a reduction effect. We can also confirm the important slope of the response curve versus wind speed in this velocity range introduced by the “narrow band” spectral density of vertical component of the wind. For the 2nd and the 3rd mode of vertical bending, the field measured values are far less than the wind-tunnel and the computed results (Fig. 5b and 5c). The transposition made for the first mode cannot be carried out for the other modes because the structural damping is preponderant in these cases. This damping has not been characterized as the recorded displacement signals are not long enough to provide
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a reliable estimate. However, the real structural damping is probably far greater than the initial model values, due to the effect of the additional dampers. This can explain the differences. Uncertainties on the modal shapes can also contribute to these differences, as measurement locations were not far from the vibration nodes for these modes. Concerning the first torsion mode, the site measurements are also in agreement with the wind-tunnel values (Fig. 5d).
5. Conclusion Field measurements were carried out on a cable-stayed bridge located in the wake of an arch bridge. These experiments confirm the results of previsional studies conducted at design stage using a taut strip model in the CSTB boundary layer wind-tunnel and a spectral approach theoretical computation. Both the turbulent wind characteristics in the wake of the arch bridge and the response of the cablestayed bridge submitted to this particular excitation are in agreement with the results of these earlier studies. The main discrepancies concern the response of the 2nd and 3rd vertical flexural modes which are lower than the expected ones as a result of the improvements of the bridge between earlier design stages and the final project. Additional full-scale measurements are planned to identify the structural dampings of the considered modes of the bridge.
References [1] G. Grillaud, A. Chauvin, J. Bie´try, Comportement dynamique d’un pont a` haubans dans une turbulence de sillage, J. Wind Eng. Ind. Aerodyn. 41—44 (1992) 1181—1189. [2] C. Barre´, G. Grillaud, Caracte´risation dela turbulence en aval du pont Albert Louppe ame´nage´: e´tude en soufflerie atmosphe´rique sur mode`le au 1/250 e`me, CSTB Report EN-AS 90.2C. [3] G. Grillaud, J. Bie´try, P. Jan, Effets du vent sur le pont a` haubans de l’Elorn: Etude en soufflerie atmosphe´rique sur mode`le ae´roe´lastique, CSTB report EN-AS 90.1C.