Wind tunnel study on the Pescara footbridge

Transcription

1 EACWE 5 Florence, Italy 9 th 3 rd July 9 Wind tunnel study on the Pescara footbridge Flying Sphere image Museo Ideale L. Da Vinci A Zasso, M. Belloli, S. Muggiasca Dipartimento di Meccanica, Politecnico di Milano alberto.zasso@polimi.it Via La Masa, 56 Milano, Italy Dipartimento di Meccanica, Politecnico di Milano marco.belloli@polimi.it Via La Masa, 56 Milano, Italy Dipartimento di Meccanica, Politecnico di Milano sara.muggiasca@polimi.it Via La Masa, 56 Milano, Italy Keywords: footbridge, wind tunnel, wake effects, flutter derivatives. ABSTRACT This paper deals with the aerodynamic project of the new Pescara footbridge. This is a flexible and slender structure less critical than a normal bridge in terms of structural issues, it is lighter and subjected to relatively small accidental loads. The most important thing to be considered while designing it is the dynamic response to time dependent forces, as the excitation exerted by the pedestrians and by the wind (Kreuzinger H. ()). This second aspect needs a deep analysis to determine the dynamic stability and the excitation due to the turbulent wind. Experimental analysis to determine the static and dynamic wind actions are needed because of the very particular design of the bridge itself. In fact, it is a stayed bridge with two different curved decks, one for the bicycles and one for the pedestrians, see Figure where a render of the structure is presented. Figure : Render of Pescara Footbridge The two decks are not symmetrical respect to the bridge axis, they have similar shape but they are characterized by different dimensions, in particular the bicycle deck have a larger chord than the pedestrian one (B=3. m for pedestrian section and B=4. m for the bicycle section). The relative position of the two girders changes along the bridge, with the maximum distance at mid-span. Scaled Contact person: S. Muggiasca, Dipartimento di Meccanica, Politecnico di Milano sara.muggiasca@polimi.it Via La Masa, 56 Milano, Italy, , sara.muggiasca@polimi.it

2 models of the two girders have been realized and an appropriate experimental set-up has been adopted to measure the static aerodynamic coefficient and the flutter derivatives, keeping into account the non symmetry of the bridges and also the wake effects. Each deck has been distinctly studied considering the two possible exposures: wind blowing from the sea and wind blowing from the country (Figure ). EXPERIMENTAL SET-UP While designing the experimental set-up two different main issues must be considered: the need to test with the wind incoming from opposite directions, because of the not symmetric shape of the deck and the need to analyse the wake effects. It has been decided to realise two frames: a dynamometric ( for the dynamometers design see Cigada ()) one and a dummy one. Both the frames can carry both the models and each one can be installed on opposite direction in order to measure the forces exerted by the sea wind and by the land wind. Thanks to the large dimension of the test section, it was also possible to place the two models in the wind tunnel simultaneously, evaluating the wake effects when the decks are at the maximum distance (Figure 3 (b)). An appropriate constrain system let us install the upwind deck at the right height. PEDESTRIAN BICYCLE WIND FROM SEA WIND FROM COUNTRY Figure : Pedestrian and bicycle deck sections: geometry of the models and wind direction (a) (b) Figure 3: Sectional model in the wind tunnel: (a) test on a single deck (b) Wake effect tests. The measurement set-up was finally completed by three accelerometers to define the dynamic model behavior and a pitot tube to measure the dynamic pressure acting on the deck. Three computer-controlled hydraulic actuators (figure 3 (a)) let us impose to the model the desired motion, i.e. torsional or flexural in a wide range of frequencies. The procedure used to perform these tests is well described in Diana et al. (4) applied to the Messina bridge sectional model. Forced motion tests have been performed to measure the static wind coefficients and the flutter derivatives.

3 Figure 4 shows the reference system adopted during the tests. WIND Figure 4: Adopted reference system STATIC AERODYNAMIC COEFFICIENTS AND FLUTTER DERIVATIVES To define the static wind actions on both the girders of the footbridge, the static aerodynamic coefficients have been measured as a function of the angle of attack. The targets of this investigation are to define the wind loads on the full bridge, to define the wake effects on the downwind deck and to understand, using the quasi-static approach, the aerodynamic stability of the structure. Figure 5, Figure 6 and Figure 7 show respectively drag, lift and moment coefficients for the pedestrian deck for the wind coming from the land side, the same quantities are reported also when the model is in the wake of the other girder. The windshield effect due to the upwind deck is clearly visible on the drag coefficient: there is a reduction of the coefficient, that is calculated using the free stream velocity. The downwind deck is invested by a lower mean wind speed resulting in a lower drag force..9 deck in the wake single deck.8.7 C D θ Figure 5: Drag Coefficient measured on the pedestrian deck, wind blowing from the land side, with and without wake effects. Figures 6 and 7 report, respectively lift and moment coefficients: it is clear that the presence of the upwind deck induces a deflection of the incoming wind. This is visible in the differences among the curves with and without the upwind deck.

4 deck in the wake single deck C L θ Figure 6: Lift Coefficient measured on the pedestrian deck, wind blowing from the land side, with and without wake effects.. -. deck in the wake single deck C M θ Figure 7: Moment Coefficient measured on the pedestrian deck, wind blowing from the land side, with and without wake effects. On the other hand, considering the not shielded results, there are some criticalities: the lift coefficient first derivative presents negative values for angle of attack around deg. Negative values of this quantity, with the adopted reference system, indicate that a dynamic instability is possible according to the quasi-static approach. It was observed for both the wind directions (from the sea and from the land). Also the moment coefficient is characterized by negative first derivative and also this term could indicate the occurrence of a dynamic instability. The first derivatives of moment and lift coefficients, according to the quasi-static theory, are the direct terms of damping due to the force field. Obviously these indications are referred only to the fluid-dynamic terms while the stability threshold must be calculated keeping into account also the structural response.

5 In particular, to completely investigate the aerodynamic behavior of the deck it is necessary to measure the flutter derivatives on a wide range of reduced velocities. Equation reports the definition of the flutter derivatives according to the reference system reported in figure 4 (Zasso (996), Scanlan (996)). * iω z * π z * iω Bθ * Fz = qbl h + h4 h * + h3 θ V V ω B V * iω z * π z * iωbθ * Fθ = qb L a + a4 a * + a3 θ V V ω B V () Figure 8 shows as an example the flutter derivatives h* e a* as a function of V* for different mean angle of attack. (pedestrian deck, wind blowing from the sea). 8-3 deg deg 3 deg.5-3 deg deg 3 deg 6 h* 4 a* V* V* Figure 8: Flutter derivatives as a function of reduced velocity V* measured on pedestrian deck, wind blowing from the sea, for different mean angle of attack : (a) h* (b) a*. The flutter derivatives confirm the critical behavior of the pedestrian deck, in particular, the h* parameter assumes negative values for reduced velocities higher than 7. FREE MOTION RESULTS Free motion tests have been carried out to confirm the results obtained from forced motion tests: the aim is to verify the occurrence of the instability keeping into account the structural response, in particular the bridge geometry and the static loads define the modal deflected shapes and the kinematic relations among deck displacement and rotation. The pedestrian deck seems to be the more susceptible to wind actions, when the wind is coming from the sea. Figure 9 shows the experimental set-up installed in the wind tunnel test section, in order to reproduce the correct kinematic relationship among deck displacement and rotation. To evaluate the energy introduction due to the wind, i.e. the possible occurrence of an instability, decay and build-up tests have been carried out. Equation reports how the aerodynamic energy introduction is evaluated, ξ TOT is the damping to critical ratio measured during a free motion test, ξ S is the structural damping measured by means of a decay in still air and ξ AER is the damping due to the aerodynamic force field. A negative value of ξ AER means that the wind is introducing energy into the system. ( z) = ( z) + ( z) ξ ξ ξ TOT S AER ()

6 Figure 9: Experimental set-up to perform free motion test on the pedestrian deck, with wind blowing from the sea side Decay and build-up tests performed on suspended model confirm the results obtained from forced motion tests, in particular it is possible to note that for wind velocity higher than 9 m/s the bridge became instable. Figure and Figure report, respectively, the structural damping and the total damping for free motion test at different wind speed. 8 x ξ s z [mm] Figure : Structural non dimensional damping as a function of the oscillation amplitude

7 ξ TOT -.5 decay V=7.7 m/s decay V=8.7 m/s -. build-up V=9. m/s build-up V=9.7 m/s z [mm] Figure : Total damping (structural and aerodynamic) measured during free motion tests as a function of the oscillation amplitude, at different wind speed. Figure clearly shows that for wind velocity higher than 9 m/s the bridge became instable, in particular at low vibration amplitudes. To improve the performance of the deck, the design of the barrier has been modified in order to increase the aerodynamic damping. Figure a and b show the barrier of the bridge with and without the winglet, whose purpose is to increase the critical wind speed. Figure : Original barrier (a) and modified barrier (b) Basically the idea is to add to the deck a winglet whose lift force first derivative is positive; Figure 3 reports the trend of the total damping of the structure, structural and aerodynamic, with and without winglet, as function of the incoming wind velocity. There is an improving in the performance of the deck, in particular the critical wind speed increases form 8 m/s up to m/s, substantially and increase of 5% of the wind velocity that produces instability of the bridge.

8 .3.5 winglet Corrimano Alette winglet..5. ξ TOT V [m/s] Figure 3: Total damping (structural and aerodynamic) measured during free motion tests as a function of wind velocity: a comparison of bridge deck with and without winglet. CRITICAL WIND VELOCITY To simulate the dynamic behavior of the real prototype a numerical model of the mechanical system as been developed, first of all it has been applied to the model tested in the wind tunnel, in order to validate the method and then the calculation has been done using the real prototype data. The model is with one degree of freedom, because the constrain system impose a kinematic relation among deck displacement and deck rotation. The equation of motion is reported in equation 3, where Q* is the force due to the aerodynamic actions. qɺɺ + ωξ Sqɺ + ω q = Q M * * Introducing the kinematic relation among displacement and rotation the aerodynamic forces, using the flutter derivatives, are as reported in equation 4. * * * * Fz = ρv BL h + h4 h * + h3 V V B V L L ω qɺ π q B qɺ q qɺ π q B qɺ q * * * * Fθ = ρv B L a + a4 a * + a3 V V B V L L ω Hence Q* become as reported in equation 5. * * * * * * * * * h h B a B a B h4 π h3 a3 B a4 π Q = ρv BL q q ɺ * * V VL VL VL BV L L ω L V ω assembling to the left side the aerodynamic terms the equation of motion becomes as reported in (3) (4) (5)

9 equation 6. * * * ρvbl * h B a B a B qɺɺ + ω ξ S + h * q ɺ + ωm L L L * * * * ρv BL h4 π h3 a3 B a4 π + ω q * * * = ω M BV ω L L L Vω in particular the damping to critical ratio of the system, considering structural and aerodynamic terms is as showed in equation 7 and it depends on the structural damping and on the flutter derivatives. ξ TOT * * * ρvbl * h B a B a B = ξs + * h ωM L L L (7) Figure 4 reports a comparison among the experimental findings obtained during wind tunnel free motion tests and the numerical results using different sets of flutter derivatives, as visible the model is affordable and it reproduce correctly the dynamic behavior of the physical model. (6).3.. Flutter: -3 deg Flutter: deg Flutter: +3 deg Free Moto motion Libero -. ξ TOT V [m/s] Figure 4: Total damping (structural and aerodynamic) as function of the wind velocity: a comparison among experimental and numerical results on the wind tunnel model. Once the model has been validated against the experimental results, it has been applied to the real prototype and figure 5 reports the total damping as function of the wind velocity for the real bridge. The critical wind velocity is about 5 m/s for the real prototype, consequently the decision is to increase the structural damping of the footbridge by adding additional damping devices, that are needed also to manage the pedestrian excitation.

10 ..5 Flutter: -3 deg Flutter: deg Flutter: +3 deg..5 ξ TOT V [m/s] Figure 5: Total damping (structural and aerodynamic) as function of the wind velocity, numerical results on the real prototype. CONCLUSIONS The paper deals with the analysis of aerodynamic characteristics of a new footbridge that will be built in Pescara. This kind of structure is very light and slender so the wind excitation is a main feature to be considered while dimensioning it. Forced motion and free motion tests have been carried out to define, respectively, the aerodynamic coefficients, the flutter derivatives and the free motion response. A numerical model to define the critical wind velocity has been developed, based on the experimental data, and it has been validated against the experimental findings. This model has been adopted to calculate the critical velocity of the real prototype and to determine the increase of the structural damping needed to grant the stability of the bridge at the design wind velocity. REFERENCES Kreuzinger H. (). Dynamic design strategies for pedestrian and wind actions, Footbridge Awards, Paris Cigada A., Falco M., Zasso A. (), Development of new systems to measure the aerodynamic forces on section models in wind tunnel testing, Journal of Wind Engineering and Industrial Aerodynamics 89, Diana G., Resta F., Zasso A. Belloli M., Rocchi D. (4). 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, 9, Zasso A. (996). Flutter derivatives: Advantages of a new representation convention, Journal of Wind Engineering and Industrial Aerodynamics, 6, Scanlan R.H., (996) Reexamination of sectional aerodynamic force functions for bridge, Journal of Wind Engineering and Industrial Aerodynamics, 89,