Transverse Mechanical Behavior of Hangers in a Rigid Tied Arch Bridge under Train Loads. I: Static and Dynamic Response

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1 Transverse Mechanical Behavior of Hangers in a Rigid Tied Arch Bridge under Train Loads. I: Static and Dynamic Response * Ding Youliang 1, Zhao Hanwei 1, Li Aiqun 1,2 and An Yonghui 3 1 Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing , China; 2 Beijing University of Civil Engineering and Architecture, Beijing , China 3 Department of Civil Engineering, Dalian University of Technology, Dalian , China Abstract The rigid hanger is one of the main load-bearing components in a rigid tied arch bridge which is common used in high-speed railway lines, and the mechanism for influences of train loads on the hangers is required to be clarified. Based on the Dashengguan Yangtze River Bridge, this paper investigates the transverse static and dynamic response of rigid hangers in the rigid tied arch bridge under train loads from three foci. Firstly, the accurate finite element model of the rigid tied arch bridge is established within ANSYS environment. Secondly, a simplified load model and its load cases that can reflect the mechanical characteristics of high-speed rail Electric Multiple Units is established. Thirdly, the transverse static and dynamic response of hangers in 2 field load cases are presented. The conclusions show that the transverse dynamic displacement at long rigid hangers are required to be paid more attention. This work gives a suggestion which lays a foundation for the better design, maintenance and long-term monitoring of hangers in a long-span rigid tied arch bridge. Key words: High-speed trains; Rigid hangers; Tied arch bridge; Transverse dynamic and static response Introduction Large-scale bridges play a vital role in the modern economy (Feng and Feng 2015). The high-speed railway of China has grown rapidly in the past 10 years. As a typical project of tied arch bridges, the Dashengguan Yangtze River Bridge was constructed on the Beijing-Shanghai high-speed railway line of China due to its large stiffness, less usage of steel and the good capability in span compared to other types of bridge (for *Correspondence to: Ding Youliang, School of Civil Engineering Southeast University, Sipailou 2, Xuanwu District, Nanjing, Jiangsu Province, China. *Professor * civilchina@hotmail.com

2 example the cable-stayed bridge and the suspension bridge) with the same span. Therefore, its long-term performance is required to be investigated. Hangers are one of the main load-bearing components in a long-span bridge (Deng et al. 2015), and the mechanism of influence of high-speed train loads on the hangers vibration must be clarified; some promising works which focus on hangers have also been conducted in recent years. De Freitas et al. (2004), Turmo and Luco (2010) studied the dynamic responses of suspension bridge hangers based on FE analysis. Ju and Lin (2003) presented the mechanical behavior of hangers of a tied arch bridge affected by the vertical and longitudinal vibration of the girder. Li and Zhang (2009) studied the dynamic mechanical behavior of short hangers due to the vertical and longitudinal vibration of the bridge deck, and investigated the hangers stress distribution. Lepidi and Gattulli (2014) studied the dynamic characteristics of the tied arch bridge and the suspension bridge. Shao et al. (2015) studied the impact effect analysis for hangers of the tied arch bridge by vehicle-bridge interaction model. Moreover, some researchers analyzed dynamic properties and behaviors of hangers based on the field tests (Malm and Andersson 2006; Andersson and Karoumi 2012). Li et al. (2012) explored the dynamic behaviors and damage evaluation of arch bridge hangers using the SHM system which serves for the design and maintenance of the tied arch bridge. Kim et al. (2012), Faridani and Barghian (2012) explored the dynamic performances of suspension bridge hangers using FE model analysis. An et al. (2015) proposed a rapid test method for damage diagnosis of suspension bridge hangers. However, on the one hand, it can be seen that studies about the arch bridge hangers mechanical behavior under train loads are still very lacking; on the other hand, compared with studies about the vertical and longitudinal dynamic mechanical behavior of hangers, little has been found in the literature about the transverse mechanical behavior of hangers. In the present work, the transverse vibration of hangers is studied based on the nonlinear dynamic analysis from the view of the system of rigid hangers and the main girder in the FE model. The space distribution of transverse dynamic displacements of hangers in 2 load cases are presented. A Brief Description and Finite Element Model The mechanical behavior of high-speed railway bridges is a continuous and longterm process. The hangers mechanical behavior caused by main girder s vibration is generally required to be studied due to their significance for structural safety of the tied arch bridge. Dashengguan Yangtze River Bridge (Figure 1), the first 6-track railway arch bridge in the world, the high-speed railway bridge with the highest loading capacity in the world, and the longest high-speed railway arch bridge with a continuous arch of the design speed of 300km/h in the world, is selected as the research object to study the dynamic mechanical behavior of hangers vibration of the tied arch bridge. As shown in Fig. 2, it consists of six tracks that include two lines on the downstream side for the Beijing-Shanghai High Speed Railway, two lines on the upstream side for the Shanghai-Wuhan-Chengdu Railway. The side view of Dashengguan Yangtze River Bridge and the hanger numbers are

3 shown in Figure 1; it is a double continuous steel truss girder and a continuous steel truss arch bridge with a main span arrangement of 108m+192m+336m+336m+192m+108m. The main arch has the height of 84m, span ratio of 1/4, the arch foot height of 12m and the arch dome height of 53m. The special steel ball bearings are used in this bridge. All hangers of the Dashengguan Yangtze River Bridge are rigid hangers. The bridge has a total of three rows of hangers (Fig. 2(a)). The cross sections of the closest hangers to the arch foot are H-shaped sections, and the rest are box sections. The hangers sections are shown in Fig. 2(b) Beijing Shanghai Span 1 Span 2 Fig.1 The Dashengguan Yangtze River Bridge (unit: m) Downstream Upstream Arch rib Hanger B-S High speed railway S-W-C Railway Box girder (a) Fig.2 Sectional view: (a) the left side view of the bridge; (b) the cross sections of the hangers (unit: mm) (b) Fig.3 FE model of the Dashengguan Yangtze River Bridge

4 Fig. 3 shows the three-dimensional FE model of the Dashengguan Yangtze River Bridge which is established within ANSYS software. The arch ribs, hangers, stiffeners of the box girders are established with BEAM188 element; the crossbeams of box girders and floor slab are established with SHELL181 element. A total of nodes and elements are found in the whole bridge model, in which of them are beam elements and the other of them are shell elements. Boundary conditions of the FE model are set as follows: the boundary conditions of the mid bridge piers are restrained with all translational DOFs (longitudinal X, transverse Y, and vertical Z), the boundary conditions at the arch foot and the side spans on both sides are restrained in the Z direction (vertical) and Y direction (transverse). The hangers and girders are restrained with 6 DOFs. Acceleration of gravity is 9.8 m/s 2. Damping ratio of hangers and all steel trusses is set to ε=0.02, while damping ratio steel box girders is set to ε=0.03. Load Model and Load Cases This section discusses the mechanical behavior of hanger and main girder of Dashengguan Yangtze River Bridge under high-speed train loads. The load model used for the FE model analysis consists a series of moving loads. The vehicle parameters of the load model are determined from the prototype (CRH3) of trains on the Beijing- Shanghai high-speed railway line. The vehicle prototype is an Electric Multiple Units (EMU) including 8 carriages. The weight of an empty EMU is 380t and an EMU has the seating capacity of 601 people. Assume the average weight of per person is 80kg (Ministry of Railways of People's Republic of China 2001), each carriage s weight is G = 53510kg, the vertical excitation force generated by a wheel is F = (G/8) 9.8N/kg = N according to the CRH3 type EMU in the work (Sun et al. 2014). Due to the large length of a single carriage (24m), the load model of the carriage is divided into 8 point loads, and the loads of an EMU with 8 carriages are grouped as 8 8 F. The train load is shown in Fig. 4. In Fig. 5, the two lines on the bottom right are the Beijing-Shanghai high-speed railway tracks; the two lines on the upper left are the Shanghai-Wuhan-Chengdu railway tracks; the trains drive on the left in China. The load cases 1~2 are shown in Fig. 5 and Table 1. The speed 237.6km/h is the average speed of the one-year s data from the SHM system of Dashengguan Yangtze River Bridge. Moving Train Load: 8 8 F Fig. 4 Moving train load

5 Transverse displacement(m) Side Hangers (Row 1) Middle Hangers (Row 2) Side Hangers (Row 3) Load cases1 Load cases 2 Fig. 5 Load cases on the arch bridge Table 1. Load cases on the Dashengguan Yangtze River Bridge Load case number Railway line Driving direction Load case 1 Beijing-Shanghai from Beijing to Shanghai Load case 2 Beijing-Shanghai from Shanghai to Beijing Train speed 237.6km/ h 237.6km/ h Transverse Static and Dynamic response of the Hangers In structural nonlinear vibration theory, the transverse vibration of hangers in a rigid tied arch bridge is generated due to the main girder s vibration induced by the eccentric train loads. The interaction of hangers and main girder in the rigid tied arch bridge results in the complex dynamic responses. Figs. 8~13 show the dynamic and static transverse displacements (absolute values) of hangers at spans 1 and 2. x Dynamic Static 4 2 Hangers of Row3-Span2 Hangers of Row2-Span2 Hangers of Row1-Span2 Hangers of Row3-Span1 Hangers of Row2-Span1 Hangers of Row1-Span Hanger Number Fig. 8. Maximum transverse displacement response of hangers within load case 1 (unit: m)

6 Transverse displacement(m) x Dynamic Static Hangers of Row3-Span2 Hangers of Row2-Span2 Hangers of Row1-Span2 Hangers of Row3-Span1 Hangers of Row2-Span1 Hangers of Row1-Span Hanger Number Fig. 9. Maximum transverse displacement response of hangers within load case 2 (unit: m) From Figs. 8~9 it can be found that: (1) The maximum values of dynamic and static transverse displacement of hangers in a row present at the long hangers with box section in the middle position of a span (hanger 11 of spans 1 and 2). (2) Due to the influence of eccentric load, the transverse displacements of hangers under load cases 1 are greater than the transverse displacements of hangers under load cases 2. (3) Along the train traveling direction, the transverse dynamic displacements of hangers at span 2 are greater than those at span 1, which indicates that the vibration of hangers at span 2 is greater than that at span 1. Conclusions An accurate FE model of a rigid tied arch bridge called Dashengguan Yangtze River Bridge is established. A simplified load model corresponding to the mechanical characteristics of high-speed railway EMU is established. The transverse dynamic displacements of hangers in 2 load cases are presented by nonlinear dynamic analysis. Some conclusions can be summarized as follows: Due to the differences in geometry, sectional form, spatial position of the hanger and the train speed, the transverse dynamic and static mechanical behaviors of each hanger subsystem are different under the high-speed moving eccentric train load: along the trains traveling direction, the dynamic transverse displacements of hangers at the second span are greater than those at the first span, which indicates that the vibration of hangers at the second span is greater than that at the first span. The maximum of transverse dynamic displacements appears at the long hangers at the middle position of a span. Hangers in the row farthest from the loading track have the greatest transverse dynamic displacement A suggestion is given as follows. In the design, the maintenance and the long-term monitoring of a long-span rigid tied arch bridge, the transverse dynamic responses, stability and fatigue performance of hangers are required to be paid more attention, especially those long hangers close to the middle position of a span.

7 Acknowledgement The authors gratefully acknowledge the National Basic Research Program of China (973 Program) (2015CB060000), the National Science and Technology Support Program of China (2014BAG07B01), the National Natural Science Foundation ( & ), the Program of Six Major Talent Summit Foundation ( ), the Fundamental Research Funds for the Central Universities and Priority Academic Program Development of Jiangsu Higher Education Institutions (No. ). The author gratefully acknowledges the support of the China Railway Major Bridge (Nanjing) Bridge and Tunnel Inspect & Retrofit Co., Ltd. References An, Y. H., Spencer, B. F., Ou J. P. (2015). A Test Method for Damage Diagnosis of Suspension Bridge Suspender Cables. Computer-Aided Civil and Infrastructure Engineering, 30(10): Andersson, A., and Karoumi, R. (2012). Attenuating resonant behavior of a tied arch railway bridge using increased hanger damping. 6th International Conference on Bridge Maintenance, Safety and Management (IABMAS): Stresa, ITALY. Bridge Maintenance, Safety, Management, Resilience and Sustainability, JUL 08-12, 2012, De Freitas, M. S. T., Viana, R. L., and Grebogi C. (2004). Basins of Attraction of Periodic Oscillations in Suspension Bridges. Nonlinear Dynamics, 37(3), Deng, L., Wang, W., and Yu, Y. (2015). "State-of-the-Art Review on the Causes and Mechanisms of Bridge Collapse." J. Perform. Constr. Facil., /(ASCE)CF , Faridani, H. M., Barghian, M. (2012). Improvement of dynamic performances of suspension footbridges by modifying the hanger systems. Eng Struct., 34, Feng, D. and Feng, M. (2015). "Model Updating of Railway Bridge Using In Situ Dynamic Displacement Measurement under Trainloads." J. Bridge Eng., /(ASCE)BE , Ju, S. H., and Lin, H. T. (2003). Numerical investigation of a steel arch bridge and interaction with high-speed trains. Eng Struct., 25(2), Kim, H. K., Kim, N. S., Jang, J. H., and Kim Y. H. (2012). Analysis Model Verification of a Suspension Bridge Exploiting Configuration Survey and Field-Measured Data. J. Bridge Eng., /(ASCE)BE , Lepidi, M., and Gattulli, V. (2014). A parametric multi-body section model for modal interactions of cable-supported bridges. J. Sound Vib., 333(19), Li, D. S., Zhi, Z., and Ou J. P. (2012). Dynamic behavior monitoring and damage evaluation for arch bridge suspender using GFRP optical fiber Bragg grating sensors. Optics & Laser Technology, 44(4), Li, Y. B., and Zhang, Q. W. (2009). Vibration Effect on Gloss sectional Stress Distribution of Short Suspenders in Arch Bridges. Journal of Tongji University(Natural Science), 37(2), , 233 (in Chinese).

8 Malm, R., and Andersson, A. (2006). Field testing and simulation of dynamic properties of a tied arch railway bridge. Eng Struct., 28(1), Ministry of Railways of People's Republic of China (2001). Temporary Specification for 200km/h speed level above railway vehicle design and test the strength of identification. Academy of Railway Sciences, Beijing (in Chinese). Shao, Y., Sun, Z. G., Chen, Y. F., and Li, H. L. (2015). Impact effect analysis for hangers of half-through arch bridge by vehicle-bridge coupling. Structural Monitoring and Maintenance, 2(1), Sun Z. X., Zhang Y. Y., Guo D. L., Yang, G. W., and Liu, Y. B. (2014). Research on running stability of CRH3 high speed trains passing by each other. Engineering Applications of Computational Fluid Mechanics, 8(1), Turmo, J., and Luco, J. E. (2010). Effect of Hanger Flexibility on Dynamic Response of Suspension Bridges. J. Eng. Mech., /(ASCE)EM ,

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