Dynamics of structures STAYED BRIDGE HS train

Paper resume: STAYED BRIDGE High Speed train dynamics effect track

1. DYNAMICS OF STRUCTURES PAPER RESUME: “DYNAMIC RESPONSES OF A CABLE-STAYED BRIDGE UNDER A HIGH-SPEED TRAIN WITH RANDOM TRACK IRREGULARITIES AND A VERTICAL SEISMIC LOAD” AUTHORS: DI MU, SUN-GIL GWON, DONG-HO CHOI HANYANG UNIVERSITY

2. INTRODUCTION The authors assess THE DYNAMIC RESPONSE OF a CABLE STAYED BRIDGE USING A TRAIN-BRIDGE SYSTEM UNDER HIGH-SPEED TRAIN LOADS, TRACK IRREGULARITIES AND EARTHQUAKE EXCITATIONS. TO DO SO, THEY USE A PARABOLIC CABLE ELEMENT, THEN They COUPLED the EQUATION OF MOTION OF THE TRAIN AND the CABLE-STAYED BRIDGE SYSTEM, then DERIVED AND SOLVED USING THE TIME INTEGRATION METHOD. RESULTS OF THE ANALYSIS ARE SHOWN AND RECOMMENDATIONS ARE GIVEN.

3. INTRODUCTION The effects of track quality and seismic load are investigated through dynamic responses of the train-bridge system. Loads several classes of tracks to assess The effects of track quality. Various levels of seismic intensities to assess The effects of seismic loads. Response Bridge behavior is represented by vertical displacement of the deck and tensions in cables. Train behavior is represented by the maximum acceleration of vehicle.

4. Train-bridge interaction system cables Stay cables are modeled using a three-dimensional parabolic cable element instead of catenary due to simplicity and good approach. 3d parabolic element model Element Stiffness matrix Cable equilibrium equation

5. Train-bridge interaction system BRIDGE The deck and the tower are modeled as frame elements and the piers and abutments as hinges or rollers. The cables are modeled as 3d parabolic element Cable stayed bridge traveled by high-speed train

6. Train-bridge interaction system FRAME ELEMENT Each frame element has 12 Dof , Which are used to build the stiffness matrix considering nonlinear behavior. EQUATION OF MOTION FOR THE BRIDGE

7. Train-bridge interaction system Model of the train the train used in the model is etr (Italy) that use connectors. The train has 10 dof . EQUATION OF MOTION of the train

8. Train-bridge interaction system Track irregularities Random irregularities based on measured results of real tracks. Quality of the track use the federal railroad administration from class 1 to 6. irregularities Power spectral density Vibration amplitude

9. Train-bridge interaction system Equation of motion of the train-bridge system (1) The vertical displacement z of a wheelset is represented bY bridge nodal displacements and track irregularities.

10. Train-bridge interaction system Equation of motion of the train-bridge system (2) the nonlinear eom due to mass, damping and stiffness varying with respect to the position on the train. It is solved using integration methods in matlab .

11. Case study cable stayed bridge, Roller supported, 88 CABLES, two intermediate towers Etry500y train

12. Case study Effects of railway track quality The Impact factor of track irregularities in the deck vertical displacement with respect to track quality and train speeds is shown. When the track quality worsens the impact factor for all speeds increase significantly.

13. Case study Effects of railway track quality The Impact factor of track irregularities in the cable tensions with respect to track quality and train speeds is shown. When the track quality worsens the impact factor for all speeds increase significantly.

14. Case study Effects of railway track quality Maximum vertical acceleration of all vehicle bodies with respect to track quality and train speeds is shown. When the track quality worsens from 6 to 2 class the maximum vertical acceleration triples. Class 2 and 4 tracks don’t comply with the maximum passenger comfort acceleration of 1.0 M/S2.

15. Case study Effects of SEISMIC LOAD The Impact factor of SEISMIC LOAD UNDER THE VERTICAL ACCELERATION OF EL CENTRO EARTHQUAKE. the deck vertical displacement with respect to SEISMIC INTENSITY LEVELS and train speeds is shown. THE SEISMIC LOAD INCREASES THE RESPONSE ON THE LEFT PART OF THE MAIN SPAN BUT DECREASES ON THE RIGHT PART. IMPACT DECREASES WITH SPEED.

16. Case study Effects of SEISMIC LOAD The Impact factor of SEISMIC LOAD USING THE VERTICAL ACCELERATION OF EL CENTRO EARTHQUAKE. the CABLE TENSIONS With respect to SEISMIC INTENSITY LEVELS and train speeds is shown. THE SEISMIC LOAD IN SOME CASES REDUCE THE IMPACT FACTOR OF THE CABLE TENSIONS. IMPACT DECREASES WITH SPEED.

17. Case study Effects of SEISMIC LOAD The Impact factor of SEISMIC LOAD USING THE VERTICAL ACCELERATION OF EL CENTRO EARTHQUAKE. Maximum vertical acceleration of all vehicle bodies with respect to SEISMIC INTENSITY LEVELS and train speeds is shown. LARGER SEISMIC LOADS INCREASE THE VERTICAL ACCELERATION BUT SUGNIFICANTLY LESS THAN POOR TRACK QUALITY.

18. conclusions the DYNAMIC RESPONSES OF A SIMPLIFIED CABLE-STAYED BRIDGE UNDER HIGH-SPEED TRAIN IS ANALYZED USING A TRAIN-BRIDGE SYSTEM. THE SYSTEM IS MODELED USING THE FINITE ELEMENT METHOD AND THE EQUATIONS OF MOTION. TRACK IRREGULARITIES SINIFICANTLY INCREASE THE DYNAMIC RESPONSES OF THE TRAIN-BRIDGE SYSTEM. WHEN THE TRACK QUALITY WORSENS THE DYNAMIC VERTICAL DISPLACEMENT OF THE MAIN SPAN INCREASE SEVERAL TIMES COMPARED TO THE STATIC DEFORMATION. MAXIMUM VERTICAL ACCELERATIONS ARE GREATLY ENLARGED WITH WORSE TRACK QUALITY, 2 AND 4 TRACKS CANNOT PROVIDE RUNNING COMFORT. STRONGER SEISMIC LOADS AFFECTS THE RESPONSES OF THE BRIDGE AND TRAIN. WHEN THE TRAIN SPEED INCREASES THE EFFECT OF SEISMIC LOADS DECREASES. FASTER TRAINS CAUSE MAXIMUM VERTICAL ACCELERATIONS, THEN IN EARTHQUAKE THE TRAIN SHOULD IMMEDIATELY DECELERATE.

19. Thank YOU