case study of参考版.docx

1、case study of参考版Case study of bridge with viscous dampers1 Protecting function of viscous dampers for expansion joints in long span bridgesViscous dampers are usually selected to be equipped at the bridge ends to restrict their displacements. Under this condition, viscous dampers and expansion joint

2、s are usually parallel in bridge structure. Whether the viscous dampers have the protecting function or not for expansion joint under the impact force caused by earthquake, wind and vehicle etc is focused in this case study.Xihoumen bridge is a sea-crossing suspension bridge (see Fig.1). The span le

3、ngth is 578m+1650m+485m. The main beams of the north side span and mid span are designed as continuous stiffening girder. Suspension structure with lateral wind-resistance bearings is designed between north side span and north bridge tower, and no lower beam is equipped in the north bridge tower. In

4、 the south bridge tower, lower beam is fixed and connected with huge force-reaction wall. So, the viscous dampers are installed between the stiffening girder end and the force reaction wall.Dynamic time-history analysis is done in El-Centro earthquake with probability 3% in 100 year return period. R

5、esults of protecting effect of viscous dampers for expansion joints in long span bridges are given in table 1&2 and shown in Fig.2&3. It can be found easily that the displacement and velocity responses of the Xihoumen super suspension bridge is reduced greatly with the installation of viscous damper

6、s between the stiffening girder end and the force reaction wall. And also the expansion joints of the suspension bridge can be protected reliably.Fig.1 The layout of Xihoumen suspension bridgeTable 1 Relative displacement amplitudes of Xihoumen suspension bridge with/without dampersResponsesMax. rel

7、ative displacement on northern bridge beam/mMax. relative displacement on southern bridge beam/mWithout damperWith damperWithout damperWith damperEarthquakeSite wave0.34540.13970.34130.1354El-Centro0.35350.19010.34980.1850Table 2 Relative velocity a mplitudes of Xihoumen suspension bridge with/witho

8、ut dampersResponsesMax. relative velocity on northern bridge beam/(m/s)Max. relative velocity on southern bridge beam/(m/s)Without damperWith damperWithout damperWith damperEarthquakeSite wave0.26350.13810.27390.1941El-Centro0.52650.45350.57520.4783Fig.2 Comparison of relative displacements of north

9、 beam endFig.3 Comparison of relative velocities of north beam end2 Case study on lateral response reduction of long-span railway cable-stayed bridge with viscous dampersThe long-span railway cable-stayed bridge is a semi-floating system with span length of 81m+135m+432m+135m+81m (see Fig.4). The ma

10、in bridge beam is a steel truss with width of 18m and height of 14m. The length of each truss section is 13.5m. High-strength steel wires are adopted and designed as materials of the 56 pairs of stable cables. The cable spacing distance is 2.5m-4.0m on the main bridge tower and 13.5m on the main bri

11、dge beam. The bridge surface is integral orthotropic steel plates. Dynamic responses are conducted by Midas software in three earthquakes with probability 2-3% in 50 year return period. The peak accelerations of the thee earthquakes are all the same of 0.21g. The specific installation places of the

12、viscous damper are shown in Fig.5. Computational results of dynamic transverse relative displacement responses between bridge pier and beam are shown in Fig.6 and the hysteresis curves of viscous dampers between damping force and displacement are shown in Fig.7. It can be found that the earthquake-r

13、eduction system is better than other systems by setting up viscous dampers between auxiliary pier, transition pier and bridge beam, for lateral seismic response of main tower, auxiliary pier and transition pier can be significantly reduced. Future more, seismic performance of pile foundations for au

14、xiliary and transition pier can be improved. Fig.4 The long-span railway cable-stayed bridge model (1# is transition bridge pier, 2# is auxiliary bridge pier, 3# is bridge main tower, 4# is bridge main tower, 5# is transition bridge pier, and 6# is bridge abutment)Fig.5 Installation places of viscou

15、s dampersFig. 6 Transverse relative displacement between 1#pier and bridge beamFig.7 Hysteresis curves of viscous damper at 2# bridge pier.3 Case study on seismic performance improvement for southern branch main bridge of a sea-crossing bridge with viscous dampersThe southern branch main bridge of t

16、he sea-crossing bridge in this case study is a semi-floating system with span length of 130m+290m+130m (see Fig.8). The cross-section of the main beam of the southern branch bridge is single-box concrete section with three holes. The height of the cross section is 3.5m and width is 32.2m. The height

17、 of the main bridge tower is 132.6m above the bridge pile. This bridge lies in the earthquake-prone areas and the peak acceleration is very big in this area. In this case study, the peak acceleration is 0.311g. In order to improve the dynamic responses of the bridge in design earthquake excitations,

18、 viscous dampers are selected and installed under the main bridge beam, namely between the main longitudinal bridge beam and the bridge pier (see Fig.9). Parameter analysis of viscous dampers, such as damping coefficients and damping index, is conducted so as to obtain the optimal damper parameters.

19、 The parameters studied in this case study are listed in Table 3. The influence of damper parameters, damping coefficients and damping index, to the energy dissipation ratios of the bridge are shown in Fig.10 & 11, respectively. According to the parameter analysis based on the figures of Fig.10 & 11

20、, the optimal damping parameters can then be easily obtained and given in Table 4. As a result, two vibration control plans are designed. The first one is that 4 viscous dampers are installed between the main bridge beam and the bridge pier of the main tower. And the second is that 4 viscous dampers

21、 are installed between the main bridge beam and the bridge pier of the main tower, and 4 dampers are installed between the main bridge beam and the transition bridge pier. However, the total damping coefficients of the two plans are the same for comparison purpose. Comparison of energy dissipation r

22、atio of the bridge with the two control plans are shown in Fig.12. The symbol meanings listed in the Fig. 12 are given in Table 5. Obviously, the analysis indicates that both relative displacement of key points and seismic response of key components could be obviously reduced with reasonably choosin

23、g the parameters and locations of dampers.Fg.8 The southern branch main bridge modelFg.9 Installation of the viscous damper under the main bridge beamTable 3 Parameters of the viscous dampersItemsParameter valuesDamping coefficient(kN/(m/s) )10002000300040006000800010000Damping index0.2/0.3/0.5/1.0(

24、a) Influence of C to displacement of beam end (b) Influence of C to displacement of top tower(c) Influence of C to moment of tower bottom (d) Influence of C to moment of top pileFig.10 Influence of damping coefficients C to the energy dissipation ratio of different parameter responses(a) Influence o

25、f to displacement of beam end (b) Influence of to displacement of top tower(c) Influence of to moment of tower bottom (d) Influence of to moment of top pileFig. 11 Influence of damping index to the energy dissipation ratio of different parameter responsesTable 4 The optimal damping parameters of the

26、 viscous damper used in the southern branch bridgeParametersValuesDamping coefficient C (kN/(m/s)0.3)6000Damping index 0.3Damping force F (kN)6000Max. Stroke D (mm)400Fig. 12 Comparison of energy dissipation ratio of the bridge with the two control plansTable 5 Symbol meanings listed in the Fig. 12.

27、SymbolsMeaningsDbMax. relative displacement between beam end and transition pierDtMax. relative displacement between top tower and bottom towerMtMax. moment in the bottom towerMtpMax. moment in the top of the tower pileMpMax. moment in the bottom of the transition pierMppMax. moment in the top of th

28、e transition-pier pile4 Case study on performance improvement of stay cable of Jianshao bridge using viscous dampersIn this case study, Jianshao cable-stayed bridge with 69,500m length and 6 main tower is introduced (see Fig.13). The span length is 70m+200m+5428m+200m +70m. The cables are made up of

29、 parallel high-strength steel wires with diameter size of 7mm. Totally, there are 576 stay cables and 432 of these stay cables are installed viscous so as to improve the vibration performance, see Fig.14. The parameters of the viscous dampers are given in Table 6.Site measurement values of the logar

30、ithmic decrement ratio of the No. Z5W-B10 cable with and without viscous dampers are given in Table 7. The free decay curves of the No. Z5W-B10 cable using also the site measurement method are shown in Fig.15. And the hysteresis curves of the viscous dampers are shown in Fig.16. The results show tha

31、t viscous dampers can be able to curb the vibration of stay cables, which can be the permanent vibration control measure for stay cables. And the results of the testing demonstrate that the viscous dampers show stable performance, all the performance index can meet the design requirements. The measu

32、red logarithmic decrement is above 6%, basically in compliance with the changing rule of the theoretical values, proving that the viscous dampers have sound vibration damping effect.Fig.13 Jianshao cable-stayed bridge (a) Before installation of viscous dampers (b) After installation of viscous dampersFig.14 Site installation of viscous dampersTable 6 Parameters