Cable-stayed Suspension Bridge Research Articles

A Novel Analytical Model for Structural Analysis of Long-Span Hybrid Cable-Stayed Suspension Bridges

The hybrid cable-stayed suspension bridge is used to combine the advantages of cable-stayed and suspension bridges and hence has a broad prospect for application. The conventional simplified analytical models of the hybrid bridge are usually developed based on a schematic with the cable-stayed and suspension systems working separately without any overlapping zone, which cannot represent the modern hybrid bridge system. In this study, a novel analytical model is proposed based on the modified suspension–elastic foundation beam theory to estimate the mechanical performance and deflection of the hybrid bridge system with the consideration of the overlapped section between the suspension and stayed cables. The governing equations of the hybrid bridge system are developed based on the elastic foundation beam theory and the deflection theory, which are derived separately in the hybrid section, the pure suspension section and the cable-stayed section. The general solution of each section is presented. The Transfer Matrix Method is then employed to solve the unknowns from one end to the other, which are in turn used to solve the internal forces of the hybrid bridge system caused by the concentrated load. In addition, in view of no variation in the unstressed length of the main cable, the compatibility equation of the main cable is established with consideration of the longitudinal displacement of the main tower, which is used to derive the formulas for the internal force and deflection of the hybrid system. The model can be easily complied in any programming platform, such as Matlab, with simple input parameters, which can eliminate the complex finite element modeling process. Hence, it can be easily used in the preliminary design stage to determine the optimal size and layout of the bridge. Then, a case study is presented for the verification of the proposed model under a vertical load, which is simplified from the Xihoumen Bridge, a combined highway and railway bridge with a main span of 1488 m. Good agreement is obtained between the proposed model and the finite element method. Meanwhile, it is found that there exists a negative deflection zone for the main beam at a distance from the concentrated vertical load, which is mainly caused by the deflection of the main cables, leading to the cambering of the beam.

Parameter Study and Optimization of Static Performance for a Hybrid Cable-Stayed Suspension Bridge

The hybrid cable-stayed and suspension (HCSS) bridge is known for its stability and cost-effectiveness, with significant application potential. This study examined the static performance of an HCSS bridge with a 1440 m main span. A finite element model (FEM) was developed to assess key parameters, such as the span-to-rise ratio, cable-to-hanger ratio, pylon stiffness, steel–concrete interface, and cable stiffness. Through FEM analysis and parameter optimization using the zero-order and first-order optimization methods in an ANSYS module, key design variables were optimized. The results show that an inappropriate span-to-rise ratio negatively impacts mid-span girder forces, while increasing the cable-stayed area enhances the overall stiffness. Main cable stiffness plays a crucial role in load-bearing and deformation control. Significant force differences were observed between stay and hanger cables, with axial force in the main girder increasing from the side span to the pylon under dead load. Bending moments in the transition region varied widely under combined loads. Optimizing parameters, such as the span-to-rise and cable-to-hanger ratios, significantly improved the mechanical performance of HCSS bridges, offering valuable insights for future designs.

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

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

Effects of key parameters of hybrid cable-stayed suspension bridge on the fatigue resistance of side hangers in bonding zones

Hybrid cable-stayed suspension bridges (HCSBs) have excellent mechanical and spanning capacities. However, their hangers in the bonding zones experience high cyclic stresses, and their fatigue failure jeopardize HCSB safety. This study adopted a HCSB finite element model and applied the influence line method to assess the effects of the following six factors on the stress amplitudes of side hangers: ratio of hanger force to vertical force in the stay cable in the bonding zone, relative stiffness of the main beam in the bonding zone, number of hangers in the bonding zone, arrangement pattern of stay cables and hangers, suspension-to-span ratio, and number of auxiliary piers. The exemplary HCSB had asymmetric span arrangement and a main span of 1400 m. Nodal loads were imposed on the main beam in the entire bridge to obtain the influence lines of each hanger and identify the most unfavorable hanger. The values of the above six parameters of the model varied to obtain the new influence lines of each hanger and identify the most unfavorable hanger in the new reasonably completed state. The stress amplitudes of the hangers thus obtained ware compared with those in the original model, reflecting the effects of these six factors on the stress amplitudes in the most unfavorable hanger. Based on the above, the cyclic stress amplitudes of the side hangers were reduced by installing additional stay cables with optimization of their arrangement pattern and relative cross-sectional areas. The results are considered instrumental in improving the fatigue resistance of HCSBs hangers under realistic bridge engineering scenarios.

Dynamic response of a sea-crossing cable-stayed suspension bridge under simultaneous wind and wave loadings induced by a landfall typhoon

Sea-crossing bridges with long spans are sensitive to wind and wave environments. The estimation of the dynamic response under simultaneous wind and wave loadings is hence important for the safety of bridges, especially during the landfall of typhoons when extreme wind and wave actions usually occur. In this paper, a framework combining the simulation of typhoon wind and wave fields, calculation of aerodynamic and hydrodynamic loadings, and structural analysis was adopted to assess the dynamic response of a sea-crossing bridge. A cable-stayed suspension bridge located in the typhoon-affected area was taken as an example. The inhomogeneity of wave loading, the time-varying dynamic response of bridges during the landfall process, and the effect of critical wave load calculation on extreme response were presented and discussed. Results demonstrated that wave loadings at different pies show strong inhomogeneity during the landfall process. The typhoon-induced simultaneous wind and wave loadings could affect not only the amplitude of the power spectrum density but also the number of dominant modes of the response. In addition, the error brought by excluding the wave inhomogeneity and the time lag of wind and wave in estimating the extreme response was acceptable when the maximum wind loadings were adopted.

Analytical assessment of the full-bridge response to the vertical live load: An algorithm for hybrid cable-stayed suspension bridges

Hybrid cable-stayed suspension bridges combine the advantages of cable-stayed and suspension bridges, mitigating their deficiencies. Due to its super spanning ability, this novel form of bridge enjoys a bright application prospect as a large-span structure. This study introduces an analytical algorithm to estimate the full-bridge response of a hybrid cable-stayed suspension bridge with a vertical uniformly distributed load applied to the main beam. This method is based on the assumption that all parameters, such as the geometric configuration, internal force distribution, and material properties, of the whole bridge under a dead load are known; then, it analyzes the full-bridge response under a live load. First, the minimum and independent basic unknown parameters of the full-bridge response are determined. Next, the governing equations are derived and solved based on the conservation of unstressed length of each section of cable, closure of span lengths and elevation difference in different spans, and conditions for stress balance of the main beam. Thus, the values of basic unknown parameters are obtained. Finally, they are substituted into the governing equations to estimate the full-bridge response, including each bridge component’s internal forces and deflections. The proposed analytical method involves no iterative procedures when dealing with nonlinear problems but only focuses on the bridge’s state with and without loading. The results are obtained directly by solving the equations, which have the advantages of high efficiency, simplicity, and clear physical meaning. Finally, the feasibility and effectiveness of the proposed method are verified by a finite-element-based calculation of an exemplary asymmetric cable-stayed suspension cooperation system bridge with a main span of 1400 m.

High-mode vortex-induced vibration and its mitigation of no-hanger main cable of the side span in a cable-stayed suspension bridge

In recent years, harmful vortex-induced vibrations of high-order modes of super long stay cables have been observed on several cable-stayed bridges with the main span near 1000 m. The possibility of high-mode vortex-induced vibrations of the no-hanger main cable of the side span of a cable-stayed suspension bridge was carefully investigated based on wind tunnel tests by using a three-dimensional elastic test model. First, the cable’s three-dimensional elastic test model was designed and manufactured. Second, a series of wind tunnel tests were carried out to measure the no-hanger main cable’s wind-induced responses. The results show that large-amplitude oscillation of the test model was observed under the wind angles of 0°, ±50° and +60°, and the highest mode observed in the test is 16th order. The Strouhal number for α = 0° is about 0.195, while the values for α= ±50° are about 0.12. Third, the effects of structural damping and helical wire on the high-mode vortex-induced vibration of this main cable were studied in detail. The results show that the high-order vortex-induced vibration of the cable can be successfully mitigated by increasing the damping ratios up to 0.25% or by the helical wire with a pitch of 12D.

Experimental investigation on the performance of Cable-Girder anchorage structure of hybrid Cable-Stayed suspension bridges

As the key component of the stay cable connecting the girder and tower in the hybrid cable-stayed suspension system, the cable anchorage structure needs to bear the powerful cable force transmission function. Compared with normal anchorages, the structural features of a new type of anchor box structure cable-girder anchorage (CGA) that has strong bearing capacity and more uniform stress distribution for a long-span hybrid cable-stayed suspension bridge with steel box girder was investigated by a 1:2 scale specimen test and a series of finite-element analysis. Through finite element analysis (FEA) and test results, the stress distribution and cable load transfer pathway of anchor box structure are obtained. The test results show that the CGA design is reasonable and reliable. The four welds connected to the anchor box support plates and the steel box girder webs bear 87% of the cable force load transfer, and the remaining 13% of the cable load is delivered from the anchor box bearing plate to webs. A large stress concentration in the six welds, but the maximum von Mises stress (VMS) of welds is 130–151 MPa. According to the parametric studies,the installation angle of the anchor box considerably affects the stress characteristics. Also, the thickness and length of the anchor box plate are changed, the transmission and distribution proportion of the cable force between the main welds of the anchor box increase alternately.

Analytical algorithm for the full-bridge response of hybrid cable-stayed suspension bridges under a horizontal transverse live load

Hybrid cable-stayed suspension bridges (HCSSB) enjoy broad application prospects due to their excellent stability and economic benefits. The full-bridge response of this novel bridge type under a live load is a shared concern during the design and use stages. This paper proposes an analytical algorithm for solving the full-bridge response under the horizontal transverse live load. First, the entire bridge is subdivided into several components, and the mechanical model and response calculation theories are built for each component. However, some critical parameters for solving these models are still unknown, and these unknown parameters are treated as basic unknown quantities. The system of governing equations is built, considering the conservation of the unstrained lengths of cables, closure of span lengths, and elevation difference across the spans. Finally, the system of governing equations is solved to obtain the full-bridge response. The results include the deformation and internal force of the main cables, main beam, towers, stay cables, and hangers. Finally, the feasibility and effectiveness of the analytical method are verified in an HCSSB with a main span of 1400 m by comparing the full-bridge response results against those from the finite element model.

The first steps towards the restoration and seismic strengthening of the historic cable-stayed suspension bridge of Deir ez-Zor in Syria

Introduction. The historic cable-stayed suspension bridge of the city of Deir ez-Zor in Syria, which is an architectural monument, is described. The history of its creation at the beginning of the twentieth century and its destruction during the hostilities in 2013 is given. The importance of this bridge for the city and for the country as a whole is indicated, which was the reason for its choice as an object of research.Aim. The study is intended to contribute to the restoration and (or) subsequent seismic strengthening of the cable-stayed suspension bridge of Deir ez-Zor.Materials and methods. A detailed description and characteristics of the above-mentioned bridge, built according to the system of the French design engineer Albert Gisclard, according to the project of the design engineer Gaston Leinekugel Le Cocq and the construction company “Arnodin”, are given. Suspension and cable-stayed bridges are compared and distinctive features of Gisclard bridges are listed. Radial cablestayed trusses are described and the scheme of load distribution in suspension and cable-stayed bridges is illustrated. Examples of the calculation of the stay cables and their cross-sectional area are briefly given, which can be used in the restoration of the bridge and its cable stays. The method of protecting the bridge from wind and seismic influences is considered.Results. Lines of influence for radial cable trusses of the Gisclard system are illustrated, showing tension and compression zones in the cable stays. Stiffening cables are recommended for adding to the design of multi-span cable-stayed and suspension bridges, as they increase their rigidity. To protect the cable-stayed suspension bridge of the city of Deir ez-Zor from wind and seismic vibration, a method of damping or reducing wind and seismic vibration using magnetorheological liquid dampers with tuned mass is proposed.Conclusions. Conclusions are drawn about the feasibility of seismic strengthening of the Deir ez-Zor bridge together or after restoration with the help of the above-mentioned dampers, which allow protecting the bridge, while maintaining its authenticity and original exterior appearance.

Reasonable completed state evaluation for hybrid cable-stayed suspension bridges: An analytical algorithm

Hybrid cable-stayed suspension bridges have broad application prospects due to their superior spanning ability, excellent overall stiffness, and economical efficiency, which outperform other long-span bridges. An analytical approach is proposed to determine the reasonable completed bridge state of hybrid cable-stayed suspension bridges in the paper. The specific steps are as follows: Firstly, the vertical supports offered by some stay cables and hangers in the main span to the main beam are estimated by assuming a continuous beam on multi-point rigid supports. For regions where both stay cables and hangers are used, the ratio of hanger force to the vertical force in the stay cable is assigned manually. Next, according to the assumption that the horizontal component force exerted by the main cables on both sides of the bridge tower and each pair of stay cables on the bridge tower are equal, the configuration and the internal force of the main cables and the stay cables are determined using the multi-segment catenary theory. The vertical forces exerted by the main and stay cables on the towers are summed up to estimate the axial force and strain acting at each position of the tower. In the side spans, the difference between the vertical support reaction in the continuous beam on multi-point rigid supports and the vertical force in the stay cable is used to calculate the weight of ballast of the main beam. The weight of ballast is apportioned as a uniformly distributed load acting on no more than three segments. The horizontal forces exerted by the stay cables on the main beam are summed up to estimate the axial force and strain acting at each position of the main beam. Finally, the analytical data of the full bridge are obtained as inputs of the finite element model. These data include the node coordinates and internal forces of the main cables, stay cables, towers, and the main beam. The calculation results obtained by the analytical method can be used for the preliminary design of hybrid cable-stayed suspension bridges. The proposed analytical algorithm can quickly solve the reasonable completed bridge state without complex adjustment of cable forces. It has the benefits of simplicity, high accuracy, and a clearly defined physical meaning. Finally, we verify the reasonability and effectiveness of the proposed analytical method in an asymmetric hybrid cable-stayed suspension bridge with a main span of 1400 m.

Analytical Model for Early Design Stage of Cable-Stayed Suspension Bridges Based on Hellinger-Reissner Variational Method.

The cable-stayed suspension bridge is one type of bridge that has been increasingly applied to bridge engineering, especially in cross-sea projects. However, the complex combined system of this type of bridge makes it quite difficult for researchers to make a quick decision of the parameter values during the design stage. The Hellinger–Reissner method is applied here to analyze the deformation and force of the structural members in the bridge. The advantage of this method is that the solving of deformation and force is independent of each other, which would enhance the accuracy of the final results. Different load conditions are also considered in the analysis. The results from the present method are compared with test results and finite element analysis, and show good agreements. It implies that the Hellinger–Reissner is a comparatively more efficient method to help designers choose the key parameters for cable-stayed suspension bridges.

Analysis of a long span cable-stayed suspension hybrid bridge considering variable intermediate side span supports

The bridges supported by high strength steel cables are the substitute to attain very lengthy bridge. Usually, cable supported bridge systems known as cable-stayed bridge and suspension bridge are used to achieve longer span bridge. In the cable-stayed bridge system better stiffness is achieved due to inclined stayed cables. In suspension bridge systems longer central span is achieved by provision of stiffened deck. The novelty in structural form, material technology and analysis methods offer further long span cable supported structural system. By combining the cable-stayed bridge and suspension bridge in a bridge, an innovative form of hybrid cable-stayed suspension bridge may offer enhanced behaviour. Mathematical model for innovative form of hybrid cable-stayed suspension bridge is addressed. The geometrical parameters play important role in structural behaviour of the cable-stayed suspension hybrid bridge. Nonlinear static analysis and modal analysis are carried out using SAP2000 software. The effects of intermediate side span support on the static and dynamic behaviour of cable-stayed suspension hybrid bridge are presented in the form of time period of bridge in lateral, longitudinal, vertical directions and pylon bending.

Form-finding method for the target configuration under dead load of a new type of spatial self-anchored hybrid cable-stayed suspension bridges

General form-finding problems of cable-supported bridges are established based on a design scenario in which rigidly fixed starting control points must be given as necessary design constraints prior to independent analysis of any of its cable subsystems. This article presents a form-finding method to address a new case, in which the starting control point serves as an intermediate, flexibly variable connection, to couple two related cable subsystems in a multi-nonlinear environment for the target configuration under dead load (TCUD) of a novel type of spatial self-anchored hybrid cable-stayed suspension (HCSS) bridge. A two-layer framework is proposed by integrating finite element analysis (FEA) and analytical formulas with optimization algorithms to form a self-regulated interactive analysis among subsystems in an iterative manner. The outer layer seeks to achieve self-equilibrium of the global system under the control information of the TCUD, while the inner layer optimizes the subsystems in terms of the initial tensions in the main cables, stay-cables, branches and hangers to obtain a rational mechanical state of the bridge. Then, the TCUD and the intermediate starting control points are determined. To achieve computational stability, a high-performance accelerated Steffens-Newton (ASN) differential algorithm is developed for the shape finding of the cable-hanger subsystem, whereas the non-dominated sorting genetic algorithm (NSGA-II) is adopted as a multiobjective optimizer for TCUD optimization of the other subsystems. The proposed framework is applied to a real-scale self-anchored HCSS bridge, and its validity and performance are demonstrated by comparison studies with a non-optimal scheme and in-field test data.

Structural Analysis and Redesign of a Cable-Stayed Suspension Bridge across Achankovil River in Kerala

Structural Analysis and Redesign of a Cable-Stayed Suspension Bridge across Achankovil River in Kerala

ACOUSTIC NOISE POLLUTION FROM MARINE INDUSTRIAL ACTIVITIES: EXPOSURE AND IMPACTS

The improvements in marine technological developments propagate urbanization in the ocean environment. The construction or operational activities of marine structures such as energy plants, oil platforms, pipe-lines, sea-tunnel passages, or cable-stayed suspension bridges, and vessel traffic are sources of underwater noise pollution. How underwater sounds such as piling, pole drilling, or machinery noises may affect the marine live is mostly ignored in marine construction, and there is lack of information regarding underwater sound effects on marine live in the oceans. Recently, a remarkable interest is developing concerning underwater sound effects, especially in aquaculture facilities, with experimentation of musical stimuli or various noises caused by pumps or filter systems on behavior and stress responses of fish in culture conditions. With the increase of urbanization and progressive development of marine industries, more and more pressure from human-generated (anthropogenic) underwater sound pollution may threaten marine mammals, fish species and invertebrates from underwater noises that in terms might be called as “Underwater Noise Pollution”. The future of marine life and that of human being, and the dramatic increase of underwater sound pollution is a new debate that needs to be controlled in a sustainable way with environment-sound approaches. Therefore the potential effects of various sound sources derived from marine industrial activities have been reviewed in this study.

The use of Classical Rolling Pendulum Bearings (CRPB) for vibration control of stay-cables

Cables are efficient structural elements that are used in cable-stayed bridges, suspension bridges and other cable structures. A significant problem which arose from the praxis is the cables’ rain-wind induced vibrations as these cables are subjected to environmental excitations. Rain-wind induced stay-cable vibrations may occur at different cable eigenfrequencies. Large amplitude Rain-Wind-Induced-Vibrations (RWIV) of stay cables are a challenging problem in the design of cable-stayed bridges. Several methods, including aerodynamic or structural means, have been investigated in order to control the vibrations of bridge’s stay-cables. The present research focuses on the effectiveness of a movable anchorage system with a Classical Rolling Pendulum Bearing (CRPB) device. An analytical model of cable-damper system is developed based on the taut string representation of the cable. The gathered integral-differential equations are solved through the use of the Lagrange transformation. . Finally, a case study with realistic geometrical parameters is also presented to establish the validity of the proposed system.

Displacement-based Mode Pushover Analysis of Self-anchored Cable-stayed Suspension Bridge

As being a typical multi-freedom degree system structure, self-anchored cablestayed suspension bridge is significantly affected by higher modes in the earthquake response. Traditional force-based pushover analysis of reverse triangle or uniform distribution patterns will lead* to a certain error for the results of pushover analysis of self-anchored cable-stayed suspension bridge. An improved method of displacement-based mode pushover analysis is presented in this paper by combining the two stage horizontal displacement pattern with mode pushover. This improved method can take the contributions of higher modes into account. And the applicability of the method can be verified commendably by the selected examples. Traditional force-based pushover analysis considers the seismic load is equivalent to lateral load. And it judges whether the deformation ability of the structure and component can meet the need of design and use function by analysing nonlinear response of structures under the monotonic increasing horizontal lateral load applied to the structure with a certain distribution mode. The selection of the lateral load distribution mode can directly affect the analysis results of the pushover method on the seismic performance of whole structure in traditional force-based pushover analysis. Moreover, the problem of stiffness degradation after failure is not taken into account in this traditional wide application method. Seismic hazard, experiment and theoretical analysis indicate structural collapse is mainly due to the lack of deformation capacity and energy dissipation capacity during severer earthquake. In this case, the deformation capacity and the displacement response of structure will have an certain impact on the damage degree of structural members. Therefore, it is more reasonable to use displacement control on structural seismic response during severer earthquake[4]. Compared with the traditional force-based design, the displacement of structure can reflect the nonlinear reactive state more during severer earthquake, it also can control the behavior of structure better in earthquake. Consequently, the displacement-based seismic design method has been greatly developed[5-10]. There are three commonly used displacement-based seismic design method: ductility factor design, capacity spectrum and direct displacement-based design method. The basic thought of displacement-based mode pushover analysis is as follows: first, put monotonic increasing lateral displacement to bear on structure directly according to a certain horizontal displacement distribution mode, second, the final failure pattern of structure is obtained by pushover the structure to the target displacement, after that, whether the deformation ability of structure and component can meet the need of design and use function can be analyzed.

A numerical study on the structural integrity of self-anchored cable-stayed suspension bridges

A generalized numerical model for predicting the structural integrity of self-anchored cable-stayed suspension bridges considering both geometric and material nonlinearities is proposed. The bridge is modeled by means of a 3D finite element approach based on a refined displacement-type finite element approximation, in which geometrical nonlinearities are assumed in all components of the structure. Moreover, nonlinearities produced by inelastic material and second order effects in the displacements are considered for girder and pylon elements, which combine gradual yielding theory with CRC tangent modulus concept. In addition, for the elements of the suspension system, i.e. stays, hangers and main cable, a finite plasticity theory is adopted to fully evaluate both geometric and material nonlinearities. In this framework, the influence of geometric and material nonlinearities on the collapse bridge behavior is investigated, by means of a comparative study, which identifies the effects produced on the ultimate bridge behavior of several sources of bridge nonlinearities involved in the bridge components. Results are developed with the purpose to evaluate numerically the influence of the material and geometric characteristics of self-anchored cable-stayed suspension bridges with respect also to conventional bridge based on cablestayed or suspension schemes.

Economic performance of cable supported bridges

A new cable-supported bridge model consisting of suspension parts, self-anchored cable-stayed parts and earth-anchored cable-stayed parts is presented. The new bridge model can be used for suspension bridges, cable-stayed bridges, cable-stayed suspension bridges, and partially earth-anchored cable-stayed bridges by varying parameters. Based on the assumption that each structural member is in either an axial compressive or tensile state, and the stress in each member is equal to the allowable stress of the material, the material quantity for each component is calculated. By introducing the unit cost of each type of material, the estimation formula for the cost of the new bridge model is developed. Numerical examples show that the results from the estimation formula agree well with that from the real projects. The span limit of cable supported bridge depends on the span-to-height ratio and the density-to-strength ratio of cables. Finally, a parametric study is illustrated aiming at the relations between three key geometrical parameters and the cost of the bridge model. The optimization of the new bridge model indicates that the self-anchored cable-stayed part is always the dominant part with the consideration of either the lowest total cost or the lowest unit cost. It is advisable to combine all three mentioned structural parts in super long span cable supported bridges to achieve the most excellent economic performance.