EACWE 5 Florence, Italy 19 th 23 rd July Keywords: flutter, extradosed bridge. ABSTRACT

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1 EACWE 5 Florence, Italy 19 th 23 rd July 29 Flying Sphere image Museo Ideale L. Da Vinci Flutter analysis of an extradosed bridge in Hungary M. Hunyadi Budapest University of Technology and Economics, Department of Structural Engineering hunyadi@vbt.bme.hu H-1111 Budapest, Bertalan L. u. 2., Hungary Keywords: flutter, extradosed bridge. ABSTRACT The work presents a wind tunnel investigation and analysis to determine the flutter behavior of a new extradosed bridge with spans of m to be built in Hungary. Wind tunnel investigation gave static aerodynamic coefficients and flutter derivates of the model with a scale of 1:1. The analysis was realized on a sectional model, only a two degree of freedom model of the mid-span section of the bridge was analyzed in a temporary cantilevered constructional phase. The obtained critical wind speed according to flutter were in the range of 5-6 m/s. The flutter coefficients determined for a mean angle of attack from above the horizontal were burden with errors particularly in the range of lower reduced velocities, thus other reasoning was employed to obtain an answer to the stability question of the deck at that angle. Finally the stability of the structure against aeroelastic instability was confirmed. 1. INTRODUCTION A new bridge will be constructed on the motorway M43 in the south of Hungary. The bridge will Contact person: M. Hunyadi, Budapest University of Technology and Economics, Department of Structural Engineering, H-1111 Budapest, Bertalan L. u. 2., Hungary., telephone , FAX hunyadi@vbt.bme.hu

2 cross the river Tisza at Szeged. An extradosed superstructure was designed with spans of m, the total length of the structure is 372,6 m. The almost 3 m wide, three cellular composite deck consists of upper and lower prestressed concrete slabs with steel webs of trapezoidal cross section. The depth of the deck is 4,8 m. The transversal rigidity of the deck is assured by steel trusses at every 5, m. The prestressed deck is supported by a system of 64 stay cables anchored in the two 22 m high pylons. Figure 1: Bridge cross section (Courtesy of Pont-TERV). Since today no such structural form with these dimensions has been used in Hungary several special studies were investigated, among others aerodynamic instability analysis. Even though a preliminary study proved that the structure holds against aerodynamic instability problems with adequate safety level, detailed test series were investigated in the detail design phase. The analysis concerned only the aerodynamic stability of the deck, the stability analysis of the cables and other structural members was made by the designer of the bridge. The primary goal of the analysis was to determine the safety of the structure against flutter in temporary construction phases, when due to the cantilever construction method used the deck is in its most vulnerable position. The construction of the bridge has started in spring 29 with the drill of the piles. The deck will be constructed with the balanced cantilever construction method, where the superstructure is consecutively elongated in both directions from the piers. In the constructional phases only the steel-concrete composite structure will be made, the installation of the bridge s equipments (railing, pavement) will go on when the two branches of the deck will be connected. 2. WIND TUNNEL INVESTIGATION A wind tunnel investigation for flutter instability analysis was done at the Department of Fluid Mechanics (28) for the first time in Hungary. The aim was to determine both aerostatic and aeroelastic coefficients for the deck. A sectional model was used instead of a full structural test, not only because the latter would have been too expensive and would have demanded too much time, but even because of the size constraints of the available wind tunnel s diameter. The experimental study was made in the Theodore von Karman Wind Tunnel Laboratory in such a way that it could result the aerostatic coefficients and even the aeroelastic ones according to Scanlan (1996). The 295,4 mm wide and 5 mm long model of the deck was made of aluminium and balsa at a scale of 1:1 and was supported and forced by a mechanical robot arm. The same model was used for the investigation of aeroelastic forces at both temporary and final constructional stage with the application of end plates on only one end or on both end of the model ( semi-finite and infinite models, resp.). The geometry of the model agreed with the design plans: two directional crossfall, inclined trapezoidal webs, no railings.

3 Figure 2: Wind tunnel arrangement. A robot arm forced the vertically positioned model. 2.1 Static aerodynamic coefficients The static coefficients have been determined at different angles of attack (from -1 to +1 ). Six dynamometers incorporated in the robot arm measured the resulting drag, lift forces and torsional moment. Figure 3: Drag, lift and moment coefficient in function of angle of rotation of the deck at different wind speeds (1, 15 and 2 m/s). Negative angles means wind from above, positive values means wind from below the deck. The diagrams of the static aerodynamic coefficients show that their first derivatives are positive in the range of an angle attack of -1 to +1. This means that the deck does not have problematic or pathologic behavior, thus its behavior form will be as it can be assumed for box girder sections and shows a stable behavior in terms of single degree of freedom flutter instability. At an oblique wind from above the horizontal with angle of attack of -6, which is parallel to the slope of the cantilever of the cross section, local discrepancies are seen in the diagrams.

4 2.2 Flutter derivatives A * derivatives α = A * 1 A * 2 A * 3 A * H * derivatives α =-6 H * 1 H * 2 H * 3-6 H * A * derivatives α = 4 H * derivatives α = A * 1 A * 2 A * A * H * 1 H * 2 H * 3-6 H * A * derivatives α =+6 4 H * derivatives α = A * 1 A * 2 A * A * 4-2 H * H * 2 H * 3-6 H * Figure 4: Flutter derivates plotted versus reduced velocity in the range -3.

5 In the sense of the deck, vertical and torsional forced motion tests were required for the determination of the corresponding flutter derivatives. The robot arm was able to make movement with a frequency up to 2,5 Hz, the used highest wind speed was 2 m/s. The used turbulent intensity was,5%. To prevent the distortions of the measures due to gravity the model was placed vertically. The used wind velocities resulted in reduced velocities in the range of 5,5 to 75. Although results in the range of reduced wind speed above 2 were out of interest, they were retained to judge the character of the derivates resulted. The data provided by the dynamometers were corrected by the forces due to forced motion with no wind. Although no precise data were at disposition in lower reduced velocity range the results obtained by the detailed analysis did not require the investigation of new test series. Flutter derivatives were determined at mean angles of attack of -6, and + 6. The forced harmonic lateral motions have had amplitudes of ±3 mm, the rotational motions amplitudes were ±1 for a mean angle of attack of and ±4 for mean angles of attack of both -6 and +6. The data provided by the wind tunnel tests were verified through relations between the measured data themselves, and with results of previous measures. We can observe on fig. 4 that the derivatives A * 2 and A * 4 for angle of attack of +6 have opposite signs compared to ones that could be supposed and compared to the ones at other angles of attack. Polynomials that annulated at zero reduced wind speed were fitted to the experimental data. 3. AEROELASTIC INSTABILITY ANALYSIS The stability analysis was composed of two main steps. First, the critical wind speed has had to be determined, at which flutter instability occurs. In the second step, we had to determine the highest possible value of wind speed in the analyzed direction. The ratio of these two values represented the safety of the deck against flutter. 3.1 Dynamic behavior of the bridge Dynamic analysis of the bridge at temporary stages resulted in eigenfrequencies of,55 Hz,,78 Hz and 2,33 Hz for bending modes, and 2,47 Hz and 2,8 Hz for torsional modes. Only the first eight modes were examined. Although all six combinations of these frequencies were analyzed, only two of them could have been critical: where both bending and torsional frequencies were close to each other. n=,55 Hz n=,78 Hz n=2,47 Hz n=2,33 Hz n=2,8 Hz Figure 5: Bending and torsional mode shapes and their frequency from the first eight modes taken into account (Courtesy of Pont-TERV).

6 3.2 Critical and maximum wind velocities The methodology to determine the critical wind speed according to the flutter instability was designed on bases of the theory described by dr. Imre Kovács. The complex analysis resulted in an oscillatory motion of the two degree of freedom system with a complex frequency at a given wind speed. When the imaginary part of the calculated frequency annulated the supposed structural damping ratio taken to,35, the critical value of wind speed was reached with the resulted motional state. Supposing many combinations of bending and torsional eigenfrequencies a lot of critical wind speeds resulted. The lowest of them gave the global critical wind speed, which has had to be higher than the highest wind speed than can occur at the bridge s site. In lack of wind map for Hungary the German wind map from the Eurocode was used in the determination of the 1 minute mean wind speed with 5 years return period for open water surface. The usage of wind speeds of the middle of Germany was confirmed by the good accordance of available measured wind speeds in the two regions. 1 minutes on which the wind speed was averaged is too long to provoke aeroelastic instability, lower averaging time lag and thus higher wind speed have been determined. As the instability of bridge decks can occur if the exciting constant wind speed is hold over a time period of minimum 2-3 oscillations of the deck the maximum wind speed of a duration of 5 seconds with p=,2 annual probability of exceedence was determined to be 35,5 m/s for horizontal wind. Lower values of maximum wind speeds belong to mean angle of attack different from. This effect was neglected in the verification to simplify the analysis. The critical wind speeds were calculated for all angles of attack which flutter derivatives were determined for. For mean angles of attack of and -6 (wind from above the deck) the determined critical wind speeds were 47,9 m/s and 56,1 m/s, respectively, denoting a stability of the structure against flutter with the 35,5 m/s determined maximal occurring wind speed for that region. For +6 angle of attack (wind from below the deck) critical conditions held at every examined wind speeds, the sum of structural and aerodynamic damping was negative for all wind speeds. The same phenomenon occurred for every considered bending-torsional frequency pairs at this angle of attack. We supposed that some errors burden the derivatives, as it can be concluded from fig. 4. The constraints of the test set-up did not allow obtaining derivative data for non-stationary conditions with reduced speeds lower than 5, values at which the resulted instability was determined. These have raised the questionability of the results given by the usage of the flutter derivatives for that angle of attack in the flutter analysis. Reanalyzing the model for different fictive parameters showed that the resulted solutions tended to the ones given by the other two angles of attack at high wind speeds. This showed us that unfortunately errors burden the wind tunnel test and/or the data processing particularly in the range of lower reduced velocities. Due to dead lines of the work there was no possibility to elaborate new wind tunnel tests. Our observations showed that small uncertainties in the values of flutter coefficients could result in huge distortions of critical value of wind speed. Based on the observations we can conclude that the wind tunnel investigation has to provide more precise flutter coefficients values, especially in the domain of lower reduced wind velocities, which could be achieved by maneuvering the model at higher frequencies. 4. CONCLUSIONS The work presents the wind tunnel investigation and analysis employed for the first time in Hungary to determine the flutter behavior of a bridge deck. As the deck of the extradosed bridge will be constructed by balanced cantilever method the analysis concentrated on the mid-span section in the intermediate erection phases. The cross section is a cellular box girder with cantilevers at both sides. The wind tunnel investigation gave static aerodynamic coefficients and flutter derivatives of the model with a scale of 1:1. The analysis was realized on a sectional model with two degrees of freedom. The experimental set-up constrained the reduced velocities to not to cover the highly non-stationary range, which plays important role in the instability study. The obtained critical wind

7 speed according to flutter were around 5 m/s. Comparison with the determined maximum wind speed of 35,5 m/s for the site confirmed the stability against flutter. High nonlinear effects and errors particularly in the range of lower reduced velocities burden the results for an angle of attack of a wind from below the deck. Other reasoning was used to confirm the stability at this angle. The results showed that the applied set-up was acceptable for the analysis of this bridge and that new test rig should be designed to achieve better experimental data for highly non-stationary conditions in future investigations. AKNOWLEDGMENTS The author would like to thank Prof. István Hegedűs and Imre Kovács for their helpful comments and suggestions during the work and that the author was involved into the project. REFERENCES BME Áramlástan Tanszék (28). Az M43 Tisza-híd szélcsatorna vizsgálata, Wind tunnel test of the M43 motorway bridge over Tisza river, report, in Hungarian. E. Simiu, R. H. Scanlan (1996). Wind Effects on Structures: Fundamentals and Applications to Design, John Wiley & Sons, New York. G. Diana et al. (24). Forced motion and free motion aeroelastic tests on a new concept dynamometric section model of the Messina suspension bridge, Journal of Wind Engineering and Industrial Aerodynamics 92 (24)