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Article

Mechanical Performance Analysis and Parametric Study of the Transition Section of a Hybrid Cable-Stayed Suspension Bridge

by
Lijun Jia
1,
Jiawei Xu
1,
Kedian Luo
1,
Weihui Li
2,*,
Yangqing Liu
3 and
Huiteng Pei
1,2
1
Department of Bridge Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
2
Jiangxi Communication Design and Research Institute Co., Ltd., Nanchang 330052, China
3
Jiangxi Provincial Communications Investment Group Co., Ltd., Project Construction Management Company, Nanchang 330052, China
*
Author to whom correspondence should be addressed.
Buildings 2024, 14(6), 1805; https://doi.org/10.3390/buildings14061805
Submission received: 17 May 2024 / Revised: 8 June 2024 / Accepted: 11 June 2024 / Published: 14 June 2024
(This article belongs to the Section Building Structures)
Browse Figures
Versions Notes

Abstract

:
Hybrid cable-stayed suspension (HCSS) bridges enjoy broad application prospects due to their excellent stability and economic benefits. The mechanical response of the transition section between the two subsystems of this novel bridge type is a common concern in the design and use stages. This paper took the design scheme of an HCSS bridge with a main span of 1440 m as the research object. A global finite element model (FEM) of the example bridge and local finite element models of the transition section were established, and the mechanical performance of the subsystem and components of the transition section was investigated. Moreover, parametric studies were conducted to investigate the influences of varies structural parameters on the mechanical performance of the transition sections of HCSS bridges. The results show that the mechanical behavior suddenly changes significantly at the transition between the cable-stayed section and the suspension section. Performance mutations in the transition section of a HCSS bridge can be improved by changing structural parameters, such as the transition section length, the number of cross cables, the area of the outermost cables, and the distance between the outermost cables and adjacent cables. The present findings may provide a reference for the better understandings and design of HCSS bridges.

1. Introduction

Cable-supported bridges are widely used in bridge engineering because of their structural, economical and aesthetic properties, especially for medium and large spans, as shown in Figure 1. These characteristics result from the rational arrangement of the structural components of the bridge, essentially comprising the cable system, girder, and pylons. The cable elements can be configured in cable-stayed and suspension arrangements [1]. Due to the mature development of the design theory and construction technology, cable-stayed bridges and suspension bridges with main spans exceeding 1000 m have become commonplace [2]. Recently, with economic development and transportation needs, many large-scale bridge constructions have been put on the agenda. For example, there are many straits that separate the two continents: the Strait of Gibraltar (13 km in width), the Tsugaru Strait (23.3 km in width), and the Bosporus Strait (30 km in width). Cable-stayed and suspension bridges represent significant milestones in bridge engineering to date, yet they fall short in traversing such exceedingly vast distances. As the span expands, the imperative to ensure the safety, applicability, service life, and manageability of bridges escalates, presenting challenges that are increasingly difficult to mitigate [3,4,5].
As the span of cable-stayed bridges increases, the following limiting factors are encountered: (1) The sag of the stay cable will reduce its efficiency [6]. (2) The substantial axial force in the main beam itself will cause a significant P-Δ effect [7]. (3) The bridge may become unstable during construction with the cantilever construction method [8]. (4) The issue of instability affects the main beam and compression-loaded towers [9].
The following are the factors considered to limit the increase in span of suspension bridges [10]: (1) Increase in span leads to poor overall wind resistance stability [11]. (2) The use of giant anchors in construction under unfavorable conditions (deep water and soft soil foundations) results in poor economic benefits [12].
As for a hybrid cable-stayed suspension (HCSS) bridge, this represents a novel composite structure consisting of a cable-stayed bridge and a suspension bridge. Therefore, HCSS bridges typically present better performances than conventional ones, and effectively improve structural stability, rigidity and spanning capacity, as well as reducing the pylon height and the anchorage volume [13,14,15,16,17]. Although the origin of HCSS bridges can be traced back to the 19th century, due to technical limitations, for a long time, HCSS bridges have only appeared as a design solution in many world-class bridge projects [1,18,19,20,21,22]. With the needs related to economic development and transportation, as well as the advancement of scientific research and construction technology, several HCSS bridges have already been built or are currently under construction in long-span engineering practices. For example, the earliest long-span HCSS bridge to be built is the third Bosphorus Bridge, with a span of 1408 m [23]. Moreover, the Tongling Rail-cum-Road Changjiang River Bridge (with a main span of 988 m, in China), the Libu Yangtse River Bridge (with a main span of 1120 m, in China) and the Xihoumen Bridge (with a main span of 1488 m, in China) are being constructed. HCSS bridges are no longer alternatives, and have gradually played an important role in engineering practices.
The design and analysis of HCSS bridges have a rich history, with early contributions providing the foundation for modern engineering practices [10,20,24,25,26,27,28]. These analytical expressions offer a robust framework for understanding the mechanical behavior of bridges. However, there are some problems that require urgent solution during the rapid development of HCSS bridges. As a composite structure composed of two different systems, the mechanical properties of the transition between the cable-stayed segment and the suspension segment of the HCSS bridge have become the primary concern. The discontinuous stiffness of the transition is the key factor affecting the mechanical properties of the main beam at the transition. As the cable-stayed system transitions to the suspension system, the stress state of the main beam changes, and the difference in stiffness of the structural system leads to the discontinuous deformation of the girder. Wang et al. [29] pointed out that the stiffness of the transition area changes greatly, and substantial internal forces and deformations will be generated under the action of live loads. Xiao et al. [27] used the wind–vehicle–bridge coupling vibration analysis method to study the bridge stiffness problem of a long-span cable-stayed–suspension collaborative system. The results show that there was a significant difference in the vertical stiffness between the suspension section and the cable-stayed section.
Besides this, although HCSS bridges can enhance the overall rigidity, the structure remains a cable structure, with inherent flexibility. Due to the large deformation of the structural system and the high stress of the cables, the outermost suspension cables of the HCSS bridge have large stress amplitudes under the action of alternating live loads, leading to a tendency of fatigue failure [20,30]. It is recommended to increase the number of suspension cables in the transition section in order to solve or improve the fatigue problem. Existing research is limited to improvement measures for excessive stress amplitudes in the outermost suspension cables, without revealing the stress mechanism of the suspension cables in the transition section. Furthermore, the number of publications to date concerning HCSS bridges accounts for only a small part of those on all cable bridges.
Based on the preceding statements, there is a stiffness discontinuity problem in the transition section of an HCSS bridge, which results in large internal forces and deformations under the action of live loads, especially train loads. Therefore, the research builds upon these classical studies, employing advanced numerical models to explore the mechanical responses of the transition sections in HCSS bridges. In this paper, the design scheme of an HCSS bridge, which is a two-tower, three-span bridge with a main span of 1440 m, is taken as an example to understand the mechanical performance of the girder and cables in the transition section under dead and live loads, using the finite element analysis (FEA) method. A global finite element model (FEM) of the example bridge and local finite element models of the transition section were established, and the mechanical performance of the subsystem and the components of the transition section was investigated. The effects of structural parameters, including the transition section length, the structural stiffness of the girder, the number of cross cables, the area of the outermost cables, and the distance between the outermost cables and adjacent cables on the mechanical performance of the transition components were studied. The analytical results obtained aim to provide a comprehensive understanding of the structural performance, and to contribute to the ongoing evolution of bridge design methodologies.

2. Example Bridge

Basic Information

This paper selects the design scheme of an HCSS bridge with a main span of 1440 m as the research object. The span arrangements of the HCSS bridge are (375 + 1440 + 375) m. There are three auxiliary piers supporting each side span. The elevation view of this bridge is shown in Figure 2. There is a two-lane railway in the center of the bridge, with four highway lanes on either side of the railway lane. A steel box girder with a height of 6 m and a width of 58.5 m is used in the main span, while prestressed concrete box girders with the same cross-sectional shape as the steel box are used in the side span. A cross-sectional view of the girder is shown in Figure 3. The pylons are concrete structures with a height of over 320 m. Each tower consists of two inclined legs and a cross beam at deck level, forming an A-frame. The key parameters of the entire bridge are listed in Table 1.
The cable system consists of main cables, stay cables and hangers, of which all are made of parallel high-strength steel wires. There are two main cables, with a spacing of 14 m and a diameter of 723 mm. The stay cables are arranged in a double-surface arrangement, with 22 pairs in the mid-span and side spans, respectively, on each side. The space between the stay cables of the side span along the girder is 16 m, while the space along the pylon is 2–3 m. The length of the transition area is 240 m, which was determined following a rigorous comparative analysis with a multitude of extant bridges, aiming at attenuating the propensity for fatigue damage. There are 32 pairs of hangers (10 pairs in the transition area); the space between the hangers along the girder is also 24 m. The cross-sectional areas of stay cables and hangers are shown in Figure 4.

3. Finite Element Modeling

3.1. Global Model

The spatial geometric nonlinear finite element model (FEM) in Figure 5 was built in the software ANSYS 2020 R2, in which the cable system was simulated by the 3D truss element LINK10, which was set to be subjected to tensile force only; the girder and the pylons were simulated by the 3D beam element BEAM4, in which the girder was in the form of a single beam, which was connected to stay cables and hangers through the stiffening arm. The key parameters of the structural members used in this model are shown in Table 2. The live loads in the global FEM were selected according to Chinese standards [31,32]. The vehicle load was taken as highway-class-I, and the train load was taken as high-speed railway ZK, as shown in Figure 6. Each load was applied in the longitudinal direction on the corresponding lane. Table 3 illustrates the boundary conditions of the finite element model, where X represents the transverse direction, Y represents the vertical direction and Z represents the longitudinal direction. The number 1 in the table means that the direction is constrained, while the number 0 means that the direction is not constrained.

3.2. Local FEM of the Transition Area

The mechanical properties of the transition area of the HCSS bridge are sophisticated. Therefore, it is necessary to build a local FEM to investigate the stress distribution in the girder. Local finite element models of the girder segments near the outermost hanger and the outermost stay cable positions were established, respectively. According to the Saint-Venant principle [33], to ensure that the local analysis results are valid, the imposed boundary conditions should be far away from the key study area, and the scope of the local model should be large enough. In addition, due to the impact on computational efficiency caused by an excessive model scale, the interception range during the analysis process cannot be too large. Consequently, the central part of the finite element model (FEM) was simulated by element SHELL63 with a span of 48 m, a size considered optimal to capture the critical area between the outermost cables and their neighbors. This precise depiction ensured that the cable spacing (uniformly 24 m along the girder) was accurately represented in the model. In addition, the end of the model was simulated by the 3D beam element BEAM4, each with a length of 12 m, to provide a suitable framework for applying force-based boundary conditions at the end of the model. The shell-beam models of the transition built by software ANSYS 2020 R2 are shown in Figure 7. The LINK10 truss element was used for both hangers and stay cables, and the cable end at the girder shared a node with the anchorage point at the girder.
Element SHELL63 and 3D beam element BEAM4 were connected at the interface by rigid constraints. The ends of stayed cables and hangers not connected to the girder were constrained in all degrees of freedom. Additionally, to accurately simulate the stress state of the selected girder segments in the entire bridge structure, the girder end forces and the axial forces of the stay cables and hangers obtained from the global FEM under dead load were applied to local FEMs. The axis forces of the hangers and stay cables were implemented by imposing initial strain on the truss elements. The train and vehicle load were equivalent to uniform load and the pressures acting on the corresponding lanes, respectively.

3.3. Model Validation

To verify the validity of local FEMs, dead load effects were compared between the global FEM and local FEMs, as shown in Table 4. The maximum vertical displacement errors of the girder center of the outermost hanger model and the outermost stay cable model were 3.83 mm and 2.77 mm, respectively, which are relatively small errors. Moreover, the results regarding the axial force of cables with local FEMs agree well with the results obtained with the global FEM, for which the maximum difference is less than 2%. Local FEMs are thus deemed reasonable.

4. Mechanical Properties of the Transition Section

As mentioned before, it is crucial to understand the mechanical properties of the transition section under different loads. Besides this, the top and bottom plates, serving as the principal structural components of the steel box girder, effectively delineate its stress-bearing characteristics. Therefore, this section is dedicated to a detailed investigation of the stress distribution and vertical displacement patterns of the top and bottom plates under different load conditions.

4.1. Local Stress Distribution of the Transition Section Girder

4.1.1. Stress under Dead Load

Figure 8 shows the stress component distribution along the transverse direction of the top and bottom plate sections, where the outermost hanger and outermost stay cable are located under dead loads. The selected cross-section of the plates was within the vehicle loading area. The results show that the stress distribution patterns of the girder at the outermost hanger and the outermost stay cable in the top and bottom plates under dead load are similar. There is stress concentration at the connection between the cables and the girder. The longitudinal normal stresses (SZ) of the top plate in the principal diaphragms are mainly tensile stresses, while those of the bottom plate are mainly compressive stresses, which present a less uniform distribution.

4.1.2. Stress under Dead and Live Loads

Figure 9 shows the stress component’s distribution along the transverse direction of the top and bottom plate sections, where the outermost hanger and outermost stay cable are located under dead and live loads. Likewise, it can be reasonably inferred that the stress distribution in each segment’s girder in the transition area has the same pattern. Compared to Figure 8, the live load has a significant effect on the girder stress between the two hangers in the transverse direction. The transverse stress (Sx) and longitudinal stress (Sz) of the top plate vary drastically in this region. The bottom plates of the selected cross-section are mainly tensile stresses under the actions of dead and live loads.

4.2. Vertical Displacement

Figure 10 shows the vertical deflection of the top and bottom plates under different loading conditions. The vertical displacement of the plate is distributed uniformly along the transverse direction under dead load, and gradually increases along the transverse direction from the center to the edge near the outermost hanger and stay cable areas, while in the area where the dead and live loads act, the vertical displacement of the plate reaches its minimum value. Besides this, the vertical displacement value under dead load is close to 0, indicating that the local models are reasonable.
The vertical displacements of the top plate in the outermost hanger section under two load conditions are 0.19 mm and 17 mm, respectively, and those of the bottom plate are 0.20 mm and 10 mm, respectively. As for the outermost stay cable section, the vertical displacements of the top plate under two load conditions are 0.10 mm and 18 mm, respectively, and those of the bottom plate are 0.10 mm and 12 mm, respectively. It can be seen that there is distinct relative deflection between the two plates.

5. Parametric Study

5.1. Influence of Structural Parameters on Mechanical Performance of the Transition Section Girder

The mechanical performance of the girder at the transition section of the HCSS bridge is mainly affected by the structural stiffness, which is controlled by the two substructure systems and the stiffness of the girder at the connectional section. According to Liang et al. [28], ensuring a smooth transition in the stiffness of the girder is a critical prerequisite for the rational design of the transition section in large-span hybrid bridges, facilitating structural coherence and enhancing overall performance efficiency. Therefore, the stiffness of the girder and the length of the transition section were selected as variables to explore the impacts of different stiffness settings on the mechanical properties of the main beam at the transition section.

5.1.1. Effect of the Girder Stiffness

Since changing the stiffness of the girder in the cable-stayed section affects the side span section stress, only the stiffnesses of the transition section and the suspension section girders were changed. The change in stiffness is achieved by adjusting the elastic modulus of the girder’s material to reduce the impacts of other parameters. The test settings are shown in Table 5. Group 1 has the design scheme of the control group, and the stiffness values of the girders in different sections remain consistent.
Figure 11 shows the rotation (ROTY) and displacement (UY) of the girder under different girder stiffness settings. As the stiffness of the girder in the transition section and suspension section increases, the amplitudes of rotation and displacement under the action of live load gradually decrease. When the stiffness of the transition section girder and the suspension section girder is twice the stiffness of the cable-stayed section girder, the rotation and displacement amplitude are minimal. Compared with the girder with a stiffness of 1:1:1 (group 1), the rotation amplitude decreases more than 20%, and the displacement amplitude decreases by about 10%.

5.1.2. Effect of the Length of the Transition Section

The length of the transition section is defined as the distance between the outermost stay cable at the mid-span and the outermost hanger. The length of the transition section was here varied by the number of cross cables, as shown in Figure 12.
Figure 13 and Figure 14 show bending moment and rotation envelope diagrams of the girder with numbers cross cables of 0, 4, 10 and 12, respectively. As the length of the transition section increases, the sudden changes in bending moment and rotation at the interface between the cable-stayed section and the transition section are improved. When no cross cables are used, the sudden changes in bending moment and rotation at the transition of the cable-stayed section and the suspension section are obvious. When the number of cross cables increases to 10 pairs, there is basically no sudden change in the bending moment and rotation.
The changes in bending moment and rotation amplitude at the interface of the girder in the transition section under different numbers of cross cables are shown in Table 6. As the number of cross cables increases, the bending moment and rotation amplitude at the interface between the cable-stayed section and the transition section (interface 1) decrease significantly, with the bending moment amplitude decreasing by 34.3% and the rotation amplitude decreasing by 29.3%. However, the bending moment and rotation amplitude change slowly at the interface between the transition section and the suspension section (interface 2). Considering the stress and deformation of the transition section, the change in the length of the intersection section has a greater impact on interface 1 than on interface 2.
In summary, the stiffness of the girder has little effect on improving the rotation and vertical displacement of the girder under live load, while the length of the transition section has a significant impact on the stress and deformation of the transition section girder. This shows that the decisive factor in the stress state of the transition section girder is not the stiffness of the local girder, but the stiffness of the structural system composed of cables, pylons and girders. By adjusting the overall structural parameters, such as the number of cross cables, a smooth transition from the cable-stayed system to the suspension system can be achieved, and the stress state of the girder in the transition section can be well improved.

5.2. Influence of Structural Parameters on Mechanical Performance of Stayed Cables and Hangers in the Transition Section

In the transition section of an HCSS bridge, while the load-bearing status of the girder is of paramount concern, the stay cables and hangers, as principal force-bearing components, also warrant significant attention. Extensive prior research [20,34,35] has demonstrated that the arrangement and mechanical properties of the cables are crucial to the transition section. Consequently, three key parameters (the number of cross cables, the cross-sectional area of the outermost cables and the distance between the outermost hanger and the adjacent hanger) become the focal points of investigation in this section.

5.2.1. Effect of Number of Cross Cables

Figure 15 shows the relationship between the internal force amplitudes of the outermost hanger and the outermost stay cable under two loads and the number of cross cables. As the number of cross cables increases, the internal force amplitude of the outermost hanger decreases significantly, while the internal force amplitude of the outermost stay cable increases, and the increase rate changes from fast to slow. This is because, as the number of cross cables increases, the stiffness of the structural system in the transition section increases, causing the load proportion of the stay cables to further increase. It can be seen that setting up cross cables can significantly reduce the internal force amplitude under the live load of the outermost hanger, and improve the cable force distribution in the transition section. As the number of cross cables increases, the structural transition becomes smoother.

5.2.2. Effect of the Cross-Sectional Area of the Outermost Cables

Figure 16 shows the relationship between the internal force amplitude and stress amplitude of the outermost cables and their own cross-sectional area. When the relative cross-sectional area ratio increases from 0.5 to 2, the relative ratio of the internal force amplitude of the outermost hanger increases from 0.54 to 1.27, with an increase of 73%, while the relative ratio of the stress amplitude decreases from 2.16 to 0.32, with a decrease of 184%. On the contrary, the increase in the internal force amplitude of the outermost stay cable (with an increase of near 200%) is much greater than the decrease in the stress amplitude (with a decrease of 94%). The results show that although increasing the cross-sectional area of the outermost hanger increases the internal force amplitude under the action of live load, it has a greater effect on reducing the stress amplitude, which can greatly alleviate the possible fatigue damage problem of the outermost hanger. Since increasing the area of the outermost stay cable results in excessive internal force amplitude under the live load, it is recommended not to increase the area to solve the fatigue problem.
Moreover, as the relative ratio of the outermost cable cross-sectional area increases, the mechanical response change rate slows down, which shows that when the outermost cable cross-sectional area increases to a certain extent, the effect on improving the outermost hanger fatigue performance becomes smaller, and the outermost stay cable may even cause excessive internal force amplitude.
Additionally, the relationship between the stress amplitudes of two adjacent cables and the cross-sectional area of the outermost cable was also studied, as shown in Figure 17. As the cross-sectional area of the outermost cable increases, the stress amplitudes of the two adjacent hangers also decrease. The first adjacent hanger decreases by 86%, while the second hanger decreases by only 19%. As for the outermost stay cable, the stress amplitude of the adjacent stay cables also continues to decrease, with the first adjacent stay cable decreasing by 44% and the second decreasing by 35%. It can be seen that increasing the cross-sectional area of the outermost cables also has a significant impact on improving the stress amplitude of adjacent cables, but as the distance increases, the impact on cables farther away becomes smaller and smaller.

5.2.3. Effect of the Distance between the Outermost Hanger and the Adjacent Hanger

In order to study the effect of adding auxiliary hangers on the fatigue resistance of the outermost hanger, that is, reducing the stress amplitude by changing the distance between the outermost hanger and the adjacent hanger, different internal force amplitudes of the hangers at three distances were studied. The results of the comparison with the original model (24 m) are shown in Figure 18.
As the distance between the outermost hanger and the adjacent hanger increases from 1 m to 50 m, the relative ratio of the internal force amplitude of the outermost hanger increases from 0.63 to 1.14, with an increase of 51%, while the relative ratio of the internal force amplitude of the first adjacent hanger decreases from 1.74 to 0.83, with a decrease of up to 91%. The results show that increasing the distance to the auxiliary hanger by a certain amount plays an important role in reducing the internal force amplitude of the outermost hanger. During the change in the distance between the outermost hanger and the adjacent hanger, it can be considered that the distance between an auxiliary cable and the outermost hanger changes. When the distance is 1 m, it can be understood that the auxiliary rope does not play a role, but only doubles the cross-sectional area of the outermost hanger. Therefore, the internal force amplitude result is similar to that shown in Figure 17a. As the distance increases, it gradually evolves into two hangers, and the auxiliary rope comes into play.
Moreover, the addition of an auxiliary hanger introduces a complex interplay of factors that affect the dynamic behavior of the transition section. Specifically, the auxiliary hanger alters the natural frequencies and mode shapes, leading to a more favorable dynamic response under varying load conditions [24,25]. The optimal distance is identified as the one that maximizes the reduction in internal force amplitude while maintaining an acceptable level of structural performance and constructability.

6. Conclusions

This study presents numerical investigations into the mechanical performance of the girders and cables in the transition section under dead and live loads based on the design scheme of a hybrid cable-stayed suspension (HCSS) bridge with a main span of 1440 m. A global finite element model (FEM) of the example bridge and local finite element models of the transition section were established to investigate the mechanical performance of the subsystem and the components of the transition section. Moreover, the effects of structural parameters, including the transition section length, the structural stiffness of the girder, the number of cross cables, the area of the outermost cables, and the distance between the outermost cables and adjacent cables, on the mechanical performance of the transition components were studied. The results are considered instrumental in providing a reference for better understanding HCSS bridges under realistic bridge engineering scenarios.
Based on this study, the following conclusions can be drawn:
  • At the transition between the cable-stayed section and the suspension section, there is a sudden and significant change in the mechanical properties. By adjusting the overall structural parameters, such as the number of cross cables, a smooth transition from the cable-stayed system to the suspension system can be achieved, and the stress state of the girder in the transition section can be effectively improved. In contrast, local parameters such as the stiffness of the girder have little effect;
  • The stress distribution in each segment girder in the transition area has the same pattern. The live load has a significant effect on the girder stress between the two hangers in the transverse direction. There is stress concentration at the connection between the cables and the girder. There is distinct relative deflection between two plates.
  • As the number of cross cables increases, the internal force amplitude of the outermost hanger decreases significantly, while the internal force amplitude of the outermost stay cable increases. Cross cables can significantly reduce the internal force amplitude under live load of the outermost hanger, and improve the cable force distribution in the transition section.
  • Increasing the cross-sectional area of the outermost hanger has a more significant effect on reducing the stress amplitude, which can greatly alleviate the fatigue damage problem that may occur on the outermost hanger. However, since increasing the area of the outermost stay cable will lead to excessive internal force amplitude, it is recommended not to increase the stay cable area so as to solve the fatigue problem. Moreover, increasing the cross-sectional area of the outermost cables also has a significant impact on increasing the stress amplitude of adjacent cables, but as the distance increases, the effect on further cables becomes smaller and smaller;
  • Adding an auxiliary hanger at a certain distance plays an important role in reducing the internal force amplitude of the outermost hanger. This can also be achieved by changing the distance between the hangers;
  • The research presented herein emphasizes the importance of addressing structural continuity and the strategic arrangement of cables within the transition section during the initial design stages of HCSS bridges, which is anticipated to result in enhanced performance characteristics for such bridges in the future.

Author Contributions

Conceptualization, L.J. and W.L.; form analysis, L.J. and J.X.; data curation, K.L., Y.L. and H.P.; formal analysis, L.J. and J.X.; funding acquisition, W.L.; investigation, J.X. and K.L.; methodology, L.J., J.X. and W.L.; project administration, W.L.; software, J.X. and K.L.; validation, L.J., J.X. and W.L.; visualization, J.X., K.L., Y.L. and H.P.; writing—original draft, L.J.; writing—review and editing, J.X., Y.L. and H.P. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded by the Jiangxi Provincial Department of Science and Technology, grant number 2024ZG002 and Jiangxi Provincial Department of Science and Technology, grant number 2023H0008.

Data Availability Statement

Some or all of the data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request (the design scheme of the HCSS bridge and FE data).

Acknowledgments

The authors are greatly indebted to the anonymous reviewers for their valuable comments and suggestions, which helped in improving the overall quality of this manuscript greatly.

Conflicts of Interest

Authors Weihui Li and Huiteng Pei were employed by the company Jiangxi Communication Design and Research Institute Co., Ltd. Author Yangqing Liu was employed by the company Jiangxi Provincial Communications Investment Group Co., Ltd., Project Construction Management Company. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Illustrative comparison of cable supported bridge designs: (a) Cable-stayed bridge. (b) Suspension bridge. (c) Hybrid cable-stayed suspension (HCSS) bridge.
Figure 1. Illustrative comparison of cable supported bridge designs: (a) Cable-stayed bridge. (b) Suspension bridge. (c) Hybrid cable-stayed suspension (HCSS) bridge.
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Figure 2. Elevation view of the HCSS bridge (unit: m).
Figure 2. Elevation view of the HCSS bridge (unit: m).
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Figure 3. Cross-sectional view of the box girder (unit: mm): (a) concrete box girder; (b) steel box girder (unit: mm).
Figure 3. Cross-sectional view of the box girder (unit: mm): (a) concrete box girder; (b) steel box girder (unit: mm).
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Figure 4. Cross-sectional areas of stay cables and hangers.
Figure 4. Cross-sectional areas of stay cables and hangers.
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Figure 5. The global finite element model (Green: displacement constraint; Yellow: rotation constraint).
Figure 5. The global finite element model (Green: displacement constraint; Yellow: rotation constraint).
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Figure 6. Live load schematic drawing for global finite element model.
Figure 6. Live load schematic drawing for global finite element model.
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Figure 7. Schematic diagram of the combined shell–beam model: (a) the outermost hanger section; (b) the outermost stay cable section.
Figure 7. Schematic diagram of the combined shell–beam model: (a) the outermost hanger section; (b) the outermost stay cable section.
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Figure 8. The distribution of stress components along the transversal direction under dead load: (a) the top plate of the outermost hanger section; (b) the bottom plate of the outermost hanger section; (c) the top plate of the outermost stay cable section; (d) the bottom plate of the outermost stay cable section.
Figure 8. The distribution of stress components along the transversal direction under dead load: (a) the top plate of the outermost hanger section; (b) the bottom plate of the outermost hanger section; (c) the top plate of the outermost stay cable section; (d) the bottom plate of the outermost stay cable section.
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Figure 9. The distribution of stress components along the transversal direction under dead and live loads: (a) the top plate of the outermost hanger section; (b) the bottom plate of the outermost hanger section; (c) the top plate of the outermost stay cable section; (d) the bottom plate of the outermost stay cable section.
Figure 9. The distribution of stress components along the transversal direction under dead and live loads: (a) the top plate of the outermost hanger section; (b) the bottom plate of the outermost hanger section; (c) the top plate of the outermost stay cable section; (d) the bottom plate of the outermost stay cable section.
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Figure 10. Vertical deflection contour of the plates under different loading conditions (unit: m): (a) the top plate of the outermost hanger section under dead load; (b) the bottom plate of the outermost hanger section under dead load; (c) the top plate of the outermost stay cable section under dead load; (d) the bottom plate of the outermost stay cable section under dead load; (e) the top plate of the outermost hanger section under dead and live loads; (f) the bottom plate of the outermost hanger section under dead and live loads; (g) the top plate of the outermost stay cable section under dead and live loads; (h) the bottom plate of the outermost stay cable section under dead and live loads.
Figure 10. Vertical deflection contour of the plates under different loading conditions (unit: m): (a) the top plate of the outermost hanger section under dead load; (b) the bottom plate of the outermost hanger section under dead load; (c) the top plate of the outermost stay cable section under dead load; (d) the bottom plate of the outermost stay cable section under dead load; (e) the top plate of the outermost hanger section under dead and live loads; (f) the bottom plate of the outermost hanger section under dead and live loads; (g) the top plate of the outermost stay cable section under dead and live loads; (h) the bottom plate of the outermost stay cable section under dead and live loads.
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Figure 11. Mechanical response of the girder under different girder stiffness settings: (a) ROTY; (b) UY.
Figure 11. Mechanical response of the girder under different girder stiffness settings: (a) ROTY; (b) UY.
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Figure 12. Schematic diagram of different cross cable arrangements: (a) 0 cross cables; (b) 4 cross cables; (c) 10 cross cables; (d) 12 cross cables.
Figure 12. Schematic diagram of different cross cable arrangements: (a) 0 cross cables; (b) 4 cross cables; (c) 10 cross cables; (d) 12 cross cables.
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Figure 13. Bending moment envelope diagrams of a girder with different numbers of cross cables.
Figure 13. Bending moment envelope diagrams of a girder with different numbers of cross cables.
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Figure 14. Rotation envelope diagrams of a girder with different numbers of cross cables.
Figure 14. Rotation envelope diagrams of a girder with different numbers of cross cables.
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Figure 15. Influence of the number of cross cables on the mechanical performance of the outermost cables.
Figure 15. Influence of the number of cross cables on the mechanical performance of the outermost cables.
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Figure 16. Influence of the area of the outermost cables on mechanical performance: (a) the outermost hanger; (b) the outermost stay cable.
Figure 16. Influence of the area of the outermost cables on mechanical performance: (a) the outermost hanger; (b) the outermost stay cable.
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Figure 17. Influence of the area of the outermost cables on the mechanical performance of the two adjacent cables: (a) the outermost hanger; (b) the outermost stay cable.
Figure 17. Influence of the area of the outermost cables on the mechanical performance of the two adjacent cables: (a) the outermost hanger; (b) the outermost stay cable.
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Figure 18. Influence of the distance between the outermost hanger (unit: m) and the adjacent hanger on the mechanical performance of cables.
Figure 18. Influence of the distance between the outermost hanger (unit: m) and the adjacent hanger on the mechanical performance of cables.
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Table 1. Key parameters of the entire bridge.
Table 1. Key parameters of the entire bridge.
ParameterUnitValue
Span lengthLeft side spanm375
Main spanm1440
Right side spanm375
Steel box girderMaterial-Q345qD
Aream23.307
Concrete box girderMaterial-C60
Aream256.648
PylonMaterial-C60
Heightm335
Main cableMaterial-Steel
Tensile strengthMPa1860
Aream20.483
Stay cableMaterial-Steel
Tensile strengthMPa1860
HangerMaterial-Steel
Tensile strengthMPa1860
Table 2. Material and cross-sectional properties.
Table 2. Material and cross-sectional properties.
ComponentElastic Modulus
(GPa)		Poisson’s RatioCross-Sectional Properties
Izz
(m4)		Iyy
(m4)		Ixx
(m4)
Main cable1950.31---
Hanger1950.31---
Stay cable1950.31---
Steel girder2100.315.461728.05039.432
Concrete girder350.2194.60013,721.100570.042
Pylon350.21859.1801418.8802267.310
Table 3. Boundary condition of the global finite element model.
Table 3. Boundary condition of the global finite element model.
PositionDXDYDZROTXROTYROTZ
Anchor node of the main cable111111
Bottom of the pylon111111
Abutment110000
Auxiliary pier110000
Main cable and pylon111111
Girder and pylon110000
Table 4. Comparison of dead load effects between the two FEMs.
Table 4. Comparison of dead load effects between the two FEMs.
Dead Load EffectsGlobal FEMLocal FEMError
The outermost hanger sectionMaximum vertical displacement of the local model center (m)00.03830.0383
Axis force of cables (kN)H1312631591.05%
H2312631591.05%
SC154755421−0.99%
SC254755421−0.99%
SC3623963071.09%
SC4623963071.09%
SC511,23711,202−0.31%
SC611,23711,202−0.31%
The outermost stay cable sectionMaximum vertical displacement of the local model center (mm)00.02770.0277
Axis force of cables (kN)SC1′69826972−0.14%
SC2′69826972−0.14%
H1′53785324−1.00%
H2′53785324−1.00%
H3′289129170.90%
H4′289129170.90%
H5′28962752−1.52%
H6′28962652−1.52%
Table 5. Variable girder stiffness settings.
Table 5. Variable girder stiffness settings.
SectionRelative Stiffness Ratio
Group 1Group 2Group 3Group 4Group 5
The stayed section11111
The transition section111.51.52
The suspension section11.51.522
Table 6. Live load bending moment and angle amplitude at the joint interface under different numbers of cross cables.
Table 6. Live load bending moment and angle amplitude at the joint interface under different numbers of cross cables.
The Number of Cross CablesThe Tending Moment AmplitudeThe Rotation Amplitude
Interface 1Interface 2Interface 1Interface 2
4797.87581.631.3242.554
10629.19551.361.0192.469
12524.42548.940.9362.457
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MDPI and ACS Style

Jia, L.; Xu, J.; Luo, K.; Li, W.; Liu, Y.; Pei, H. Mechanical Performance Analysis and Parametric Study of the Transition Section of a Hybrid Cable-Stayed Suspension Bridge. Buildings 2024, 14, 1805. https://doi.org/10.3390/buildings14061805

AMA Style

Jia L, Xu J, Luo K, Li W, Liu Y, Pei H. Mechanical Performance Analysis and Parametric Study of the Transition Section of a Hybrid Cable-Stayed Suspension Bridge. Buildings. 2024; 14(6):1805. https://doi.org/10.3390/buildings14061805

Chicago/Turabian Style

Jia, Lijun, Jiawei Xu, Kedian Luo, Weihui Li, Yangqing Liu, and Huiteng Pei. 2024. "Mechanical Performance Analysis and Parametric Study of the Transition Section of a Hybrid Cable-Stayed Suspension Bridge" Buildings 14, no. 6: 1805. https://doi.org/10.3390/buildings14061805

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