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# Analysis And Design Of Cable Stayed Bridge Pdf

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The influence of the stiffness of piers, pylons and deck in the behaviour of multi-span cable-stayed bridges under alternate live loads is analysed.

## Interaction between Track and Long-Span Cable-Stayed Bridge: Recommendations for Calculation

Geometric nonlinearity GN and initial internal forces IIFs are the basic characteristics of cable-stayed bridges, but now there is no effective method for analyzing the effect of them on bridge-track interaction of continuous welded rail CWR on cable-stayed bridge. A method for reconstructing the displacement-force curve of ballast longitudinal resistance was put forward according to the deformation of cable-stayed bridges under the completed bridge state.

With the multi-element modeling method and the updated Lagrangian formulation method, a rail-beam-cable-tower 3D calculation model considering the GN and IIFs of cable-stayed bridge was established. The results show that the method put forward to reconstruct ballast longitudinal resistance can prevent the impact of initial deformation of bridge and makes it possible to consider the effect of IIFs of cable-stayed bridge on bridge-track interaction.

The GN and IIFs play important roles in the calculation of rail longitudinal force due to vertical bending of bridge deck under train load and the variance of cable force due to negative temperature changes in bridge decks and rails with rail breaking, and the two factors can reduce rail longitudinal force and variance of cable force by The cable-stayed bridge can be simplified as a continuous beam bridge with different constraints at different locations, when rail longitudinal force due to positive temperature changes in bridge deck and train braking is calculated.

The construction of cable-stayed bridges has been booming since World War II, due to their reasonable force structure, ease construction, elegant shape, and strong span capability. The main spans of cable-stayed bridges have increased in length from the Cable-stayed bridges also are also more suitable for carrying rail traffic because of the high stability. Therefore, cable-stayed bridges have gained increasing acceptance from railway bridge engineers [ 4 ].

One current example is the Shanghai-Nantong Yangtze River Bridge designed for both road and rail traffic. When completed, it will be the longest cable-stayed bridge for both road and rail traffic in the world.

With the increasing of spans of cable-stayed bridges, the geometric nonlinearity GN effect will be more obvious. The GN effect mainly consists of the cable sag effect from the weight of the stay cables, the large displacement effect caused by the main beams, and the beam-column effect caused by the bending-compression of the main beams and bridge towers [ 5 ].

Around the world, researchers are conducting extensive researches on the train-bridge-track dynamic interaction to ensure the safety running of train [ 6 — 8 ] and bridge-track interaction to design continuous welded rail CWR on bridges [ 9 — 11 ]. However, the application of cable-stayed bridges in railway field occurred relatively recently, so few studies on bridge-track interaction of CWR on cable-stayed bridges have been presented, let alone research findings on the impact of GN and initial internal forces IIFs of cable-stayed bridges on bridge-track interaction.

The research group led by Wang et al. They also presented the superposition mode of loads on cable-stayed bridges when checking the stress in rail as well as the factors to be considered in checking the rail broken gap [ 16 — 18 ]. Zheng et al. Li et al. Cai et al. In these studies, the modulus of elasticity of the stay cables was modified according to the Ernst equation to consider the cable sag effect [ 22 ].

However, there are still two shortcomings in these models: 1 The stay cable force will continuously increase as the length of span increases, so it is still difficult to accurately simulate the cable sag effect even when the calculations are performed according to the modified modulus of elasticity. These shortcomings are obstacles not only in studying the bridge-track interaction of CWR on cable-stayed bridges, but also in correctly analyzing the impact of the bridge-track interaction on cable-stayed bridges.

Therefore, a rail-beam-cable-tower 3D model, with a new method for reconstructing the ballast longitudinal resistance curve and a suitable calculation method, is established to study the impacts of GN and IIFs on the bridge-track interaction of CWR on cable-stayed bridge. The rail of CWR on the cable-stayed bridge is locked after Phase II dead load including the weight of rail is exerted on the bridge, so Phase II dead load is involved in the analysis of completed state of the cable-stayed bridge [ 23 , 24 ], but this does not affect CWR on the bridge.

After locking the rail, the IIFs caused by the dead load will impact bridge-track interaction by changing the mechanical characteristics of the bridge under other loads. Based on the basic principle of bridge-track interaction, this paper presents a new method for reconstructing the ballast longitudinal resistance curve to make it possible.

The ballast longitudinal resistance in the above calculation models of CWR on bridges is mainly simulated with nonlinear springs [ 10 — 21 ]; the displacement-force D - F curves of the ballast longitudinal resistance are expressed by the solid lines shown in Figure 1. Suppose that the longitudinal displacement of a bridge node obtained from the completion calculation of a cable-stayed bridge is a ; in order to prevent the impact of the completion calculation on bridge-track interaction, the D - F curves of nonlinear springs connected with the bridge node are expressed by the dash lines shown in Figure 1 ; the mathematical model is expressed by where D is bridge-track relative displacement, F is the value of ballast longitudinal resistance, a represents the longitudinal displacement of the cable-stayed bridge nodes under completion calculation, and F max and u are the maximum force and yield displacement of ballast longitudinal resistance.

For ballast track, the resistance to the longitudinal displacement of the rail is generally greater than the resistance of sleeper in ballast [ 25 ], so the resistance of sleeper in ballast plays a controlling role in the research of bridge-track interaction.

According to the code of China [ 26 ], F max and u are Figure 2 shows the arrangement of spans and bearings. When considering the longitudinal displacement of 3. If there is no displacement of bridge before locking the rail in the following calculation, it is called normal condition. The reconstructed ballast longitudinal resistance curve is used under displacement of bridge condition.

As the longitudinal displacement of the third span occurs before locking the rail, this displacement will not affect the rail longitudinal force according to the principle of bridge-track interaction. The rail longitudinal force should be the same under displacement of bridge condition and normal condition.

However, the bridge-track relative displacement should differ in the third span. The following shows the feasibility and accuracy analysis. According to the different loads, the calculation is divided into four conditions.

The first kind of load is positive temperature changes in bridge decks. The second kind of load is vertical bending of bridge deck under train load. The third kind of load is the breaking and acceleration of train.

The last is negative temperature changes in bridge decks and rails with rail breaking. For details, see Figure 3. Relative displacement difference is obtained by subtracting bridge-track relative displacement of normal condition from displacement of bridge condition. There exists no error in the data of 3. The rail longitudinal force under displacement of bridge condition perfectly matches that under normal condition as shown in Figure 4. The bridge-track relative displacement curves of the two conditions can also coincide with each other except the scope of the third span, but the difference is equal to the initial displacement of 3.

The numerical results agree with the previous theoretical analysis, so it can be said that the method for reconstructing ballast longitudinal resistance curve can prevent the effect of initial deformation of bridge on bridge-track interaction due to positive temperature changes in bridge decks.

The rail longitudinal force and bridge-track relative displacement are shown in Figure 5. According to the calculation results of Figure 5 , the rail longitudinal force and bridge-track relative displacement of the third span coincide with those induced by positive temperature changes in bridge decks, which also verifies that this new method can be used when vertical bending of bridge deck under train load is considered. ZK live load is still adopted, and the wheel-rail adhesion coefficient is 0.

Figures 6 a and 6 b , respectively, show the rail longitudinal force and bridge-track relative displacement. As shown in Figure 6 , the results are the same as those due to the positive temperature changes in bridge deck and vertical bending of bridge decks under train load, verifying that the method can be used for calculation when breaking and acceleration of train are considered.

According to the code [ 26 ], either of two rails on the bridge is considered broken. In Figure 7 , N , D , and RDD stand for normal condition, displacement of bridge condition, and relative displacement difference.

As shown in Figure 7 , the method can be used to prevent the initial displacement of the bridge from affecting bridge-track interaction for both the broken and unbroken rails, verifying the feasibility of the method when negative temperature changes in bridge decks and rails with rail breaking is considered.

According to the results of the calculations, the method for reconstructing ballast longitudinal resistance curve presented in this paper can be used to prevent the initial displacement of the bridge from affecting the bridge-track interaction under the four calculation conditions; therefore, it is suitable for completion calculations of cable-stayed bridges.

The same longitudinal displacement of the entire bridge is considered in the verification model, so when it is used to analyze the bridge-track interaction of CWR on a cable-stayed bridge, the actual longitudinal displacement of bridge nodes should be considered.

Different D - F curves can be established by changing parameter a of 1. The existing models for analyzing the bridge-track interaction of CWR on cable-stayed bridges are always 2D models, which greatly simplify the complicated space structure of cable-stayed bridges. Therefore, on the one hand, it is difficult for them to correctly reflect the actual mechanical behavior of cable-stayed bridges, especially when GN is considered.

On the other hand, it is also difficult to analyze the impact of IIFs of cable-stayed bridges on bridge-track interaction with a simplified model. Thus, a rail-beam-cable-tower 3D model is established to analyze bridge-track interaction of CWR on a cable-stayed bridge.

For details, see Figure 8. Different structures in the model are simulated with different types of elements according to their mechanical characteristics. The deck slabs are simulated with shell elements. In order to analyze the cable sag effect, a single stay cable is simulated with several bar elements connected end-to-end.

For a cable-stayed bridge, the cable force of some stay cables might decrease under load; however, it will not decrease to zero, so it is not necessary to consider the nonlinear characteristics.

The bridge tower is discretized and simulated with short equal-section beam elements via simplification. In order to simulate the connection between stay cables and towers, the sections of the bridge tower connected to the stay cables are simulated with rigid beam elements. The damping devices and ballast longitudinal resistance are simulated with special nonlinear springs.

The damping devices are only used when breaking and acceleration of train are considered, so their D - F curve should be updated according to 1.

Each calculation of the geometric positions of different nodes of the model is updated according to the Updated Lagrangian formulation UL method [ 27 ], based on which new stiffness matrices are formed to consider the beam-column effect and the large deformation effect within the model.

In addition, according to the impact of the initial internal force on the stiffness matrices, the model can be used to study the impact of GN and IIFs on bridge-track interaction of CWR on cable-stayed bridges.

A twin-tower three-cable-plane cable-stayed bridge in China is taken as an example to explain the impact of GN and IIFs of cable-stayed bridges on bridge-track interaction of CWR.

The deck supports four-track railway. Two lines are mixed passenger and freight railways, while the other two are passenger dedicated lines. The towers are reinforced concrete structures, the part of which on the deck is inverse Y -shape, while the towers column beneath the deck is diamond-shaped.

The bridge is a separate tower-beam and consolidated tower-pier form. Bearings and damping devices are set between the towers and beam. See Figure 9 for the general layout of the bridge and a cross section of the main beam. In order to facilitate the comparison of different analytical states, rail expansion joints are temporarily ignored. The height, vertical moment of inertia, and transverse moment of inertia of the bridge profile are 2.

The fixed bearings for the simple-supported beams at each side are set apart from the cable-stayed bridge. The cable-stayed bridge and its approach spans are laid with ballast track using CHN60 rail. The area, vertical moment of inertia, and transverse moment of inertia of the rail profile are The height and top and bottom width of middle section of sleeper are The elastic Type-II fastener which matches the sleeper is used, and the longitudinal resistance of the fastener is demanded to exceed The impact of temperature changes of stay cables and bridge towers on bridge-track interaction is ignored for the purpose of this study.

The lower deck has four-track railway, in which the train load is subject to CR live load on two lines and ZK live loading on the other two. A completion calculation of the cable-stayed bridge is needed to determine the IIFs and the longitudinal displacement of bridge nodes. The displacement can be used to update the new ballast longitudinal resistance curves for evaluating the impact of IIFs of the bridge on CWR under different calculation conditions.

The results of the new and original ballast longitudinal resistance curves are shown in Figure The variation of cable force is the force corresponding to the dead load only. As shown in Figure 10 a , the rail longitudinal force corresponding to the new curve fluctuates near zero. The maximum value is 8.

## Design and Analysis of Cable Stayed Bridge

Abstract For longer span, cable stayed bridges are the first choice and to study its behavior under static and vehicle loading is important. Therefore, it becomes essential that the modelling of cable stayed bridge is more realistic and the analysis results are more satisfactory. There are different methods that can be used for structural model but in the present study two different types of structural model viz. Spine Model and Area Object Model are used for analysis of cable stayed bridge. Static analysis and moving vehicle analysis have been done in which IRC Class A vehicle load is applied and their load combination is considered for evaluating the results.

## Interaction between Track and Long-Span Cable-Stayed Bridge: Recommendations for Calculation

Bridge is an important part of infrastructure of land transportation, both roadway and railway. In a length of roadway or railway absolutely will pass rivers, valleys, or will pass seperated of roadway or railway intersection. To be able to pass those obstructions, bridges must be build. Bridge construction must be srongth enough to withstand heavy truck which pass over the bridge, must be strongth enough to withstand side wind blow, and must be strongh enough to withstand shake of earthquick. From the materials use, there are known woode bridge, steel bridge, concrete bridge and composite bridge, the bridge consist of steel and concrete.

The cable stayed bridge is an elegant, economical and efficient structure.

Geometric nonlinearity GN and initial internal forces IIFs are the basic characteristics of cable-stayed bridges, but now there is no effective method for analyzing the effect of them on bridge-track interaction of continuous welded rail CWR on cable-stayed bridge. A method for reconstructing the displacement-force curve of ballast longitudinal resistance was put forward according to the deformation of cable-stayed bridges under the completed bridge state. With the multi-element modeling method and the updated Lagrangian formulation method, a rail-beam-cable-tower 3D calculation model considering the GN and IIFs of cable-stayed bridge was established. The results show that the method put forward to reconstruct ballast longitudinal resistance can prevent the impact of initial deformation of bridge and makes it possible to consider the effect of IIFs of cable-stayed bridge on bridge-track interaction. The GN and IIFs play important roles in the calculation of rail longitudinal force due to vertical bending of bridge deck under train load and the variance of cable force due to negative temperature changes in bridge decks and rails with rail breaking, and the two factors can reduce rail longitudinal force and variance of cable force by

Anand Soni M. S University, Vadodara. C Simoes, J. Phani Kumar.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Casado Published Art. The social and economical importance of long-span bridges is extremely large; cablestayed bridges currently span distances ranging from to even more than m, representing key points along infrastructure networks and requiring an outstanding knowledge of their seismic response. Save to Library.

#### Mathematical Problems in Engineering

JavaScript is disabled for your browser. Some features of this site may not work without it. Master thesis. Utgivelsesdato Samlinger Institutt for marin teknikk []. This is a floating cable-stayed bridge with a total length of nearly 5 kilometers, where the floating part is supported by 19 pontoons. The main focus was put on studying the response caused by wind and waves, while ship collision was limited to analysing the global integrity of the bridge.

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