Sectional model test study on vortex-excited resonance of vehicle-bridge system of Shanghai Bridge over Yangtse River

Abstract

It is necessary to study how vehicles influence the vortex-excited resonance of vehicle-bridge systems, because lock-in wind speed is low and vortex-excited resonance is sensitive to any change in the main girder sections. Based on the Shanghai Bridge over the Yangtse River, the vortex-excited resonance of a 1∶60 scale sectional model was tested in a TJ-1wind tunnel, with or without vehicles at the attack angle of 0°, +3 and -3°, respectively. The conversion relationships between the resonant amplitudes of the sectional model and that of the prototype bridge were also established by mode shape correction. The result indicates that: 1) for the bridge with vehicles, the vertical vortex-excited resonance is accompanied by torsion vibration with the same frequency, and vice versa, 2) the amplitude of vortex-excited resonance of the bridge with vehicles is much larger than that of the bridge without vehicles, and 3) the lock-in wind speed of the vortex-excited resonance becomes smaller due to the disturbance of vehicles. It is obvious that vehicles bring about changes in the aerodynamic shape of the main girder. Therefore, the influence of vehicles on vortex-excited resonance performance of vehicle-bridge systems, in terms of both amplitude and mode, should not be ignored.

Keywords

vehicle-bridge system / sectional mode / vortex-excited resonance / wind tunnel test / mode shape correction

Introduction

Vortex-excited resonance of closed box-girder bridge decks has attracted attention in recent years. For a long span bridge, the vortex-excited resonance of beam is produced due to the fact that when airflow rounds a bridge section, vortex develops on two sides of the section [1–3]. And this leads to alternately changing pressure, and the section develops crosswind. Frequency of the crosswind is “locked” and vortex-excited resonance happens at lock-in wind speed. As a lively example of a real bridge, during the final phases of deck erection and surfacing of suspended spans of the Storebalt Bridge, the vertical deck oscillations of low frequency were observed by workers and supervision staff.

Wind does not only lead to the discomfort of passengers but also causes damage and deterioration of the bridge. Aerodynamic performance of bridges is very sensitive to sectional shape and detailed structure of the section. Wind acts on vehicles as well as on bridges, and the vehicles on a bridge can change the airflow somehow. The wind tunnel test of vehicle-bridge system is mainly focused on the train-bridge system today. Li et al. [4], Huang et al. [5], Xia et al. [6], have undertaken a great deal of research work in the field of vehicle-bridge-wind system. However, they all used the quasi-static model to calculate the force of vehicle and wind which is considered to act on vehicles and bridges separately.

Vortex-excited resonance of beams usually happens at low wind speed and if the vortex-excited resonance happens frequently and sustains longer, they will cause fatigue damage to the bridge and discomfort of pedestrians and vehicle users. The vortex-excited resonance is the emphasis of wind resistance for bridges because the vortex shape has much to do with the shape of the bridge section. It is very important to study the vortex-excited resonance of vehicle-bridge system by means of wind tunnel test as the theory and numerical simulation methods of vortex-excited resonance have some limitations today. Based on the Shanghai Bridge over the Yangtse River, this paper presented a 1∶60 scale sectional model study in a TJ-1 wind tunnel and the main results on the vortex-excited resonance of vehicle-bridge system were given.

Engineering background

The Shanghai Bridge over the Yangtse River has an overall length of 1430 m with a 730 m main span and two side spans including two holes of 92 m and 258 m each (see Fig. 1). The tower reaches a height of 216.32 m. The twin box deck girder is 51.5 m wide and 4 m deep, composed of two steel boxes, 20.75 m wide.

Design of model

A 1∶60 geometrical scale for the sectional model of the Shanghai Bridge over the Yangtse River was selected for the requirement of similarity of the sectional model design (see Table 1). The dynamic sectional model scaling is determined by the velocity scaling and the frequency scaling. The main dimension of the sectional model refers to Fig. 2. The shape of the model should be similar to that of the beam, and the rigidity of the model should be as large as possible. The weight of the model should not exceed the design weight due to the scale of strain-gauge balance. The frame of the model was made of aluminum alloy and the surface was made of veneer lumber. The main structural stiffness of the model was provided by a spar, one in each box, consisting of an aluminum H-beam. The model has a simply-supported natural frequency in bending of 25 Hz.

Vehicle layout

When the vehicle is moving, the leading and following vehicles should keep a safe-distance on the same roadway. When the speed is 100 km/h, the distance between adjacent vehicles should not be less than 100 m. When the speed is 70 km/h, the distance should not be less than 70 m. In the test, the length of the sectional model is 1.7 m equal to 102 m of the actual length. So it is rational to place one vehicle on each roadway. Six kinds of typical vehicles were selected in the test. The dimension of the vehicles model refers to Table 2. The layout of the vehicles is shown in Fig. 3.

Equipment

The wind tunnel test for the vortex-excited resonance of 1:60 scale sectional main girder model was carried out in a TJ-1 wind tunnel in the State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University (see Fig. 4) based on the Shanghai Bridge over the Yangtse River. The test was conducted under six conditions of the bridge without vehicle and the bridge with vehicle for the attack angle of -3° , 0° and+3°. The equipments used in the test were as follows:

1) Boundary layer wind tunnel

All tests were performed in smooth flow in the TJ-1 boundary layer wind tunnel with the dimension of 1.8 m×1.8 m x 12 m. Its speed can be adjusted from 1 m/s to 30 m/s and it has a suitable contraction ratio to ensure low turbulence intensity and flow uniformity in the test section. The longitudinal turbulence intensity at the centre of the tunnel near the sectional model position was measured to be lower than 1%, which ensures that the wind speed was even at the height of the model. So the upstream speed profile needs not to be measured. In the test, Pitot tubes were used to measure the wind speed near the model, and it lay in front of the model and a little higher than the height of the model.

2) Piezoelectric accelerometer sensor: CA-YD-103.

Four sensors were fixed on the arms symmetrically away from the centre of rotation of the model.

3) NI sampling panels and computer data acquisition system.

4) Six channels vibration amplifier YE5866.

5) Four channels dynamic signal analysis meter HP35670A. It was used to monitor the vibration frequency.

The later three equipments and computers were located in the control room.

Results and discussion

The vortex-excited resonance for the vertical and torsional motion of the models was observed for the bridge with and without vehicles.

Comparison of displacement at attack angle of 0°

Figures 5 and 6 show the curves of displacement-wind speed at the attack angle of 0°, and two vortex-excited resonance peaks are observed in each figure. It is found that the displacement of the bridge with vehicles varied larger than that of the bridge without vehicles. With wind tunnel speed increasing, the frequencies of vibration experienced three stages, vertical vibration frequency for the first stage, torsional vibration frequency for the second stage, and suspension system vibration frequency for the third stage.

As shown in Fig. 5, the bridge without vehicles does not have an obvious vortex-excited resonance; however, the bridge with vehicle has vertical vortex-excited resonance with the amplitude of 0.117 m when the lock-in wind speed range was from 2.4 m/s to 3.0 m/s. At the same time, the vertical vortex-excited resonance (see Fig. 5) was accompanied by torsional vibration (see Fig. 6) due to the uneven vehicle layout, uneven pressure and exquisite vortex-excited resonance. From Fig.6, the first peak value was the result of coincident torsional vibration (amplitude 0.011°). The frequency of vertical vortex- excited resonance (see Fig. 5) was 4.297 Hz (see Fig. 7).

As can be seen from Fig.6, the torsional vortex-excited resonance for bridges with vehicles happens with the amplitude of 0.08° when the lock-in wind speed was from 4.5 m/s to 5.3 m/s and at the same time accompanied with vertical vibration. As can be seen in Fig. 5, the second peak value was the coincident vertical vibration (amplitude 0.332 m). Its frequency was equal to the torsional frequency of 9.570 Hz (see Fig. 8).

Comparison of displacements at attack angle of+3°

Figures 9 and 10 show the curves of displacement-wind speed at the attack angle of+3°, and the displacement of the bridge with vehicles varies larger than that of bridge without vehicles, just like at 0° attack angle.

As can be seen from Fig. 9, the lock-in wind speed of vertical vortex-excited resonance moves from the range of 3.4 m/s–3.65 m/s for the bridge without vehicles to the range of 2.85 m/s–3.1 m/s for the bridge with vehicles, due to the disturbance of vehicles which made the lock-in wind speed smaller. As can be seen from Fig. 10, the two vertical vortex-excited resonances were accompanied by two coincident torsional vibrations with smaller amplitude.

Comparison of displacements at attack angle of -3°

As can be seen from Fig. 11, the bridge without vehicles has not obvious vortex-excited resonance at the attack angle of -3°, while the bridge with vehicle has obvious vortex-excited resonance with the amplitude of 0.122 m when the lock-in ranges are 1.35 m/s-1.5 m/s and 2.0 m/s-2.2 m/s. At the same time the sectional vertical vortex-excited resonance is accompanied by torsional vibration due to the uneven vehicle layout and uneven pressure (see Fig. 12). The frequency of the accompanied vibration is 4.321 Hz which is equal to the frequency of the vertical vortex-excited resonance.

From Fig. 12, the torsional vortex-excited resonance for the bridge with vehicle happens with the amplitude of 0.019° when the lock-in regions are from 4.52 m/s to 6.0 m/s and at the same time are accompanied with vertical vibration. As can be seen in Fig.11, the third peak value corresponds to the vertical vibration (amplitude 0.084 m). Its frequency is equal to the torsional frequency of 9.619 Hz.

Conclusions

The sectional model test on the vortex-excited resonance of the vehicle-bridge system of the Shanghai Bridge over the Yangtse River was studied in a TJ-1wind tunnel with the dimension of 1.8 m×1.8 m. A 1∶60 scale sectional model of the deck was built and mounted in a spring suspension system to investigate, in an aero-elastic context, a vehicle’s effect on the vortex-excited resonance of a bridge deck. After the analysis and comparison, the following conclusions can be drawn:

With the wind tunnel speed increasing, the displacement of the bridge with vehicles fluctuated larger than that of the bridge without vehicles and the frequencies of vibration experienced three stages, vertical vibration frequency for the first stage, torsional vibration frequency for the second stage, suspension system vibration frequency for the third stage. Due to the disturbance of vehicles, the lock-in wind speed of the vortex-excited resonance becomes smaller.

For the bridge with vehicles, the vertical vortex-excited resonance was accompanied by torsional vibration and their frequencies were equal. The coincident torsional/vertical vibration happens due to the uneven vehicle layout and uneven pressure with the exquisite vertical/torsional vortex-excited resonance.

The amplitude of vortex-excited resonance for the bridge with vehicles was larger than that of vortex-excited resonance for the bridge without vehicles. The vortex-excited resonance for the bridge without vehicles does not happen at the attack angle of 0°. The torsional vortex-excited resonance for the bridge with vehicles happens with the amplitude of 0.08° and the amplitude of coincident vertical vibration reaches 0.332 m.

References

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