Static analysis of box‑girder bridge under the influence of Indian railway vehicle loading using ANSYS finite element model

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Page 2 of 16 Shaikh and Nallasivam Advances in Bridge Engineering (2022) 3:25 challenges for engineers in terms of research and design. A thorough investigation into the analysis of thin-walled box-girder bridges has been published in the following literatures. Begum Z (Begum, 2010) investigated the behaviour of steel box-girder bridges using the publicly available FEM software ANSYS. The author examined the performance of straight and curved box-girders and compared the findings of the analytical model using the software DESCUS-II. A comparison of the findings produced using DES-CUS-II and the ANSYS finite element model revealed that the two sets of results were in good agreement. Zhu et al. (Zhu false, 2016) successfully analysed the vibrations of thin-walled rectangular beams using the finite element method. Using Hamilton's principle, the dynamic governing equations were derived, and then the finite element implementation was approximated. Finally, numerical cases were presented to demonstrate this theory's viability. Gupta and Kumar (Gupta & Kumar, 2018) used the widely available FEM software CSiBridge to calculate the flexural behaviour of curved box-girder bridges. The purpose of this study was to determine how simple single-cell and skewcurved concrete box-girder bridges respond to bending. The author studied the influence on the behaviour of the bridge due to the change in skewness angle. A 3D finite element model was made using CSiBridge software and analysed. It was seen that the skewness of the bridge improved its effectiveness in various response results. Hamza et al. (Hamza false, 2019) evaluated the ultimate load capacity of a horizontally curvedbox steel beam using a non-linear finite element technique. The results showed that the satisfactory breadth-to-depth ratio was around 0.3 and 0.4 when the angle of curvature was ranging from 0 & 90 degrees and between 0.4 and 0.5 when the angle of curvature was between 90 o and 180 0 . Also, the analysis indicated that the reduction in bearing load capacity with increasing beam curvature is the same no matter what the b/d ratio is. Preeti et al. (Agarwal false, 2022) used CSiBridge software to simulate and analyse a single-cell and double-cell rectangle-shaped box-girder bridge under the influence of varied IRC loadings. Stress and deflection limits were examined for various span-depth ratios. The author performed static and free vibration studies and compared the results to verify the applicability of the modelling procedure. Lizhong et al. (Jiang false, 2022) used ANSYS software to investigate the dynamic influence of a train on the seismic action of a track system and a bridge. In this research, a combined finite element model of a bridge with a high-speed railway vehicle was developed by taking into account a simply-supported beam element bridge with the China Railway Track System (CRTS) II plate and a high-speed train. The model's accuracy was technically and experimentally confirmed. Taking into account the unpredictability of the vibration, the impact of the train body on the earthquake-exposed bridge model was examined. In addition, the amount of consequence of a moving train body on the seismic effect of bridge structures by varying the heights of piers was investigated. The results demonstrated that the train's dynamic impact considerably decreased the seismic effects of supports and piers and that the effect itself reduced as the height of the pier increased. Jiang Hui et al. (Hui false, 2021) performed dynamic and vibrational analysis on the CRTS II ballastless track system. An improved coupling dynamic model of a bridge having a ballastless track system (CRTS III) and a high-speed train was developed using ABAQUS. The research object was a high-speed railway simply-supported box-girder bridge with multiple spans over an active strike-slip fault. The validity of the established model was fully examined. After simulating the lateral ground movements in a defective fissure zone, short-term dynamic evaluations of the high-speed train-track-bridge coupling system under 3D earthquake excitations were conducted. Guolong Li et al. (Li false, 2022) suggested a dynamic analysis method for vertically coupled vehicle-track-substructure under forced excitation and used the method to study how local fastener failure affects the dynamic effect of the vehicle and track. The failure of a fastener was simulated using methods that cancel the forced vibration transmission, which means that the interaction between the substructure and rail at that point was not taken into account. It was found that the local fastener failure had a small effect on how the substructure and car-body shook, but it had a big effect on how the wheel and rail shook. Chirag Garg (Chirag Garg & Kumar, 2014) studied the effects on deflection and stress contour by changing the basic shape, like varying the length, width, and thickness of the bridge, using SAP2000 software. It was seen that the modified one with longer overhanging beams and thicker joints is the more sturdy structure of the different cases for this box shape. This gave more rigidity at the fixed parts and reduced the stresses on the whole beam, making it more stable as it reduced the amount of bending force at the fixed end. Muthanna Abbu et al. (Abbu false, 2013) performed 3D Finite Element analysis of the combined box-girder bridge to predict the actual bridge response using ANSYS software. A field test is used to compare the predictions of several FE models to the results of the test. Experiments show the importance of complete shear connections, which are necessary in combined boxgirders and are one of the most crucial considerations to think about. Both vertical displacements and normal stresses predicted numerically at key sections are quite similar to the results of tests. MTR Jayasinghe (Ranasinghe & Jayasinghe, 2016) provided a simple design technique that confines the design iterations as much as possible to reduce the number of computations needed. The rules for figuring out the cross-sectional sizes have also been talked about. A full example of how to design a three-span continuous bridge has been given. Nancy Hammad et al. (Hammad false, 2020) presented an effective and genuine computational tool to analyse and arrive at the optimum design of a pre-stressed box-girder bridge with a high-speed railway vehicle. The design and analysis of the simply supported box-girder bridge are accomplished using CsiBridge and a finite element software, SAP 2000, as per Eurocode and the Egyptian Code of Practice. Anita M. Jagid et al. (Jangid & Bhaskar, 2018) examined static and dynamic behaviour while demonstrating the linear dynamic response of trapezoidal and rectangular boxgirder bridge decks. Using FEM-based software, response spectrum analysis has been carried out. The results showed that the bending moment, shear forces, deflection, and time period of a trapezoidal box-girder increase as the length of the span goes up, while the spectral acceleration and fundamental frequency go down. The study showed that the trapezoidal box-girder bridge superstructures were more secure than rectangularshaped girder bridge superstructures. Virajan Verma et al. (Verma & Nallasivam, 2021) made a model of the thin-walled steel curved box-girder bridge and looked at its different response variables when it was loaded by the Indian Railway using 1D beam elements and MATLAB code. The analytical results, which were calculated using MATLAB code based on finite elements, were shown in the form of different stress results caused by different combinations of Indian Railway loads. The effect of changes in radius and span length on the different response parameters has also been looked into. R. Manjula et al. (Manjula & Amrutha, 2021) used the Indian Road Congress (IRC) requirements for trapezoidal and rectangular sections to analyse three different types of box-girders with SAP2000. Researchers have looked at how box-girders with the same depth but different widths behave. Using SAP2000, a parametric study is done for different reactions like axial force, bending moments, and shear force. From the above mentioned literatures, it was seen that the static analysis of the model was required for different combinations of Indian railway loadings. Moreover, in most of the studies, the models were solved numerically using 1D beam elements. A study of different combinations of loads was needed in order to find the worst case possible.
Vehicle loads are one of the most significant external excitations of bridges and are critical in a variety of load combinations. Therefore, comprehensive research is required for the evaluation of a bridge that is susceptible to damage and is in danger of collapsing. The present study is limited to the non-closed form of the FEM static analysis of the model. However, this research will aid designers in obtaining relevant information for the further analysis of free vibration and the dynamic analysis of the model. To overcome the limitations mentioned above, the following areas of the concept will be studied:

Geometry
The finite element model of the bridge having 5 spans of 32 m each continuous box girder is shown in Fig. 1. The model contains abutments and piers as substructure, whereas the superstructure includes the bridge deck, sidewalk, kerb, and railway sub-track system. Figure 2 shows the box girder component of a straight deck with 0° skewness and a vertical axis of symmetry. The deck is 12.6 m wide and 3.08 m deep, with double railway track systems serving as the train's carriageway. The track systems are spaced 3.8 m   center to center. The sidewalk is 1.5 m wide on either side. The kerb has a base width of 0.4 m and a height of 0.85 m. Figure 3(a-d) shows the detailed elevation and cross-section of the abutment and pier. The height of all the piers is the same. The pier is 15-24 m long, has rounded ends, and is made of solid elements. Table 1 reports the sectional properties of the bridge deck (Jiang false, 2022), whose cross-section is depicted in Fig. 4.
The track system is made up of the lateral block, rail, fasteners, precast base track, cement asphalt mortar (CAM) layer, and concrete foundation slab. The sliding layer of the sub-track as shown in Fig. 5, has a width of 2.95 m and a thickness of 0.006 m. On the top of the sliding layer, there is a concrete supporting layer of 2.95 m × 0.19 m in size. The concrete layer and base track are joined together using a CAM layer of 2.55 m x .03 m in size. The dimension of the base track is 2.55 m × 2 m. The cross-section detail of the track system has been depicted in Fig. 6. Additionally, the spring element has been utilised to design rail fasteners for the connection of rail and base track as shown in Fig. 7. Table 1 presents information on the rigidity of the spring elements.

Boundary conditions, Element Type & Meshing
The concrete slab is bonded to the bridge deck. A CAM layer is used to join the concrete slab and precast base track. The transverse movement of the precast concrete slab is restricted by the lateral stopper. The precast concrete slab and the base slab are separated between adjacent girders at the girder end.
As a result, the continuous rail fastener system is the only thing keeping the neighbouring girders in place. The deck of the bridge is supported on the abutment andpier using a fixed bearing modelled as a spring element, whose stiffness has been mentioned in Table 1. Also, the rail fastener system is modelled as a non-linear spring element with a discrete spacing of 0.6 m. The longitudinal stiffness of the spring is also mentioned in Table 2. At every point, two fasteners were attached to the left and right sides of the bottom face of the rail to provide stability and restrict the transverse movement of the rails. The length of the spring element is taken as the thickness equal to that of a rail pad, which is generally 0.085 m. Tables 3 and 4 show the relationships between the different parts of the model and the size of their mesh. The selection of a reasonable size for various components based on mesh convergence is required for reliable outcomes. The optimum finer mesh was adopted in this analysis. Also, using a finer mesh will increase the computational cost of the analysis.

Material properties
All the materials are assumed to be isotropic and homogenous. Box girder bridges are designed using concrete having a higher grade and strength. A minimum grade of M40 is required for the deck. Table 5 and Table 6 show the material properties of the various bridge and railway sub-track system components, respectively.

Load combination
Different load combinations as per the Indian railway standards, as defined in [17], have been taken into consideration for the purposes of static analysis. Symmetrical and asymmetrical loadings have been used and investigated for each combination. In each example of symmetrical loading, both tracks were loaded near the center of the bridge with certain load combinations. However, in cases of unsymmetrical loading, only one track system is loaded. Figure 8 illustrates the alignment for load combinations 1 to 5.

Numerical problem
In this paper, a numerical problem involves multi-span concrete box girders spanning 32 m each and a width of 12.5 m subjected to Indian Railway loading for broad gauge. The different properties of materials are presented in Tables 4 and 5, and different load combinations are depicted in Fig. 8. Figure 4 shows the cross-section of the deck. Both symmetrical and unsymmetrical loading have been analysed for each individual case. In the event of symmetric loading, both of the track systems were loaded in the center; however, in the situation of unsymmetric loading, only one of the two tracks was loaded. The assemblies of loads in both conditions have been shown in Figs. 9 and 10 respectively. Within the scope of this investigation, each and every possible combination of loads found on Indian railways was investigated, and the findings are presented in Table 7. The vertical deflection of the box girder bridge is significantly lower than that of every other type of bridge. The plot of total deformation and deformation corresponding to different axes against various load combinations has been shown in Fig. 11. The results reveal that load case 1 provides the largest total deformation, which is equal to 3.8745E-03 m. The equivalent (Von-Mises) stress, principal stress, and maximum shear stress for load combination 1 are shown in Fig. 12(a-c). Figure 13 shows the graph of stresses against different load combinations. Figure 14(a-d) represents the total deformation and deformation along different axes..

Conclusion
This paper presents an essential concept of FEM modelling and the study of the static response of a box girder bridge that supports two railway sub-track systems loaded with different combinations of Indian Railway loadings. The analysis was performed on a 5-span bridge using a non-closed form solution based on ANSYS software, and various responses of deformations and stresses were determined. However, the FEM modelling procedure could be used to study any box-girder bridge with more spans. It is observed that the unsymmetrical loading under combination 2 caused the bridge to experience the greatest amount of total deformation, which was measured to be 10.703 E-03 m at the center span of the bridge. The deflection of the bridge under both symmetric and unsymmetric railway loads was within the permissible range. This is because, according to the author (Křístek false, 2006), a box girder bridge with a span of 100 m to 140 m can normally bend not more than 12 E-02 m or 2 E-01 m. The maximum equivalent (Von-Mises) stress in the model is found to be 28.349 MPa, which is due to the symmetric loading of load case 5. In addition to that, the maximum principal stress and maximum shear stress are found to be 20.678 MPa and 16.26 MPa, respectively. Thus, from this study, designers may find that the FEM method could be used to analyse straight box girder bridges under any type of railway loading.

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