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The accuracy of main cable construction in suspension bridges is directly influenced by the sag of the strands during the erection process. Thus, effective methods for controlling strand sag are crucial. However, the current control standards and methods are primarily based on practical engineering experience, lacking quantitative analysis and a sufficient basis. This paper aims to address this gap by summarizing four commonly used strand sag control methods and proposing a quantitative analysis model that considers the influence of random factors. The model quantifies the impact of these methods on the main cable shape and strand tension after cable tightening. To illustrate the practical application, a suspension bridge is utilized as a case study. The results of the study illustrate a linear relationship between the main cable sag and inter-strand distance, with each control method exhibiting a varying linear change rate. Moreover, the discrepancy in strand distance contributes to uneven strand tension after cable tightening. Random errors contribute to the dispersion of the main cable sag and strand tension, which are further exacerbated by cumulative errors between layers of general strands. Based on the study's results, this paper provides valuable references for the erection and control of the main cable in suspension bridges. [ABSTRACT FROM AUTHOR]

The main bridge of Wanlong Bridge under construction is the first spatial self anchored suspension bridge with elliptical steel tower in the world. The saddle of this bridge adopts an self-adaptive space cable saddle combined with casting and welding, which has the following technical difficulties: the force of space cable saddle is complex. The longitudinal stiffness of the elliptical tower is large, and the slip resistance of the main cable saddle is prominent. The bottom of the saddle is a flexible support, the cable saddle and the main tower are co-deformed, and the tower-saddle connection structure is complicated in force transmission. In order to master the key technology of the main cable saddle and the tower-saddle connection structure of the self-anchored suspension bridge with elliptical tower and space cable, this paper carries out a systematic study by using numerical analysis method. The research conclusions are as follows: (1) When the bridge is subjected to (dead load+car+crowd+tap water+temperature+wind), the minimum friction coefficient µ that satisfies the requirements is 0.215, and the 12 mm vertical friction plates are required. (2) The maximum Von Mises stress and maximum vertical deformation of the main cable saddle under the condition of maximum cable force are 186.2 MPa and 1.572 mm, which meet the requirements of strength and stiffness. (3) In the structure connecting the main cable saddle and the steel tower, the force of the main cable saddle is transferred to the web of the steel tower in the form of vertical shear force through the supporting baffle. The shear force of the supporting baffle at the end is significantly greater than that of the middle baffle, and the non-uniformity coefficient of shear transfer is 1.29. (4) The support plate of the main cable saddle has a certain angle at the edge of the saddle area. The maximum longitudinal angle under the condition of empty cable is 0.366‰ rad, which should be taken into consideration in the saddle pushing construction. [ABSTRACT FROM AUTHOR]

A suspension bridge that uses suspension cables as the major bearing structure has the most robust spanning capacities. There are two types of anchorage: gravity-type anchorage and tunnel-type anchorage (TTAs). The TTAs structure exhibits complex mechanical and deformation characteristics under tens of thousands of tons of load transferred from bridge cables. A large-scale field model test method is proposed to reveal the mechanical rock mass properties of the TTAs under different loading conditions, and its theoretical and related technologies are studied based on more than twenty years of applications. Four parts are included in the study. Firstly, the technical development of the TTAs model test is summarized with practical engineering applications. On this basis, the theoretical basis of the field model test of the TTAs is studied from two aspects: the scale representativeness and the similarity theory of the model test. The technical points of the recommended TTAs field test are proposed in the third section. Finally, to evaluate the potential bearing properties of the TTAs in a planned super-large railway suspension bridge, a case study with a large-scale TTAs model test in the field is introduced. The test results show that TTA technology can supply sufficient bearing capacity to the high-tonnage railway suspension bridge with a total cable load of 860MN under complex and fractured rock mass condition. The composite TTAs structure bearing a load of tens of thousands of tons transferred from main cables in the design of highway or railway suspension bridges represents significant technical progress in rock mechanics. Highlights: Based on more than twenty years of applicaitons, a large-scale field model test method is proposed to reveal the mechanical rock properties of the tunnel-type anchorage(TTAs) under different loading conditions, and its theoretical and related technologies are studied. In order to evaluate the potential bearing properties of the TTAs in a planned super-large railway suspension bridge with a toal cable load of 860MN, a case study with a large-scale TTAs model test in the field is introduced. [ABSTRACT FROM AUTHOR]

The stiffness of suspension bridges, which are flexible systems composed of main cables and stiffening beams, is frequently increased by adding one or more pairs of central buckles in the midspan. This study examined a suspension bridge with flexible central buckles, proposing a set of analytical calculation methods for the shape-finding of the main cable under dead load and the structural deformation and internal forces under any uniform live loads. The proposed method is based on the known bridge design parameters. First, the suspender and central buckle tension of each hanging point of the stiffening beam was determined by the multipoint rigid support continuous beam method. After assigning these tensions to the suspenders and the central buckles, the multisegment catenary theory was used to derive the equation for each main cable segment in turn. The constraint equation was established through the closure condition of the height difference within the span. The equation was then transformed into an objective function to be programmatically solved, determining the completed bridge state. To determine the live load response of the bridge, the deformation and position relationships of the main cable, main beam, and bridge towers were analyzed in sequence, with known live load parameters. Five types of constraint equations were established through the conservation of the unstrained length of each main cable segment, the coordination of the force and deformation of each suspender, the coordination of the force and deformation of each central buckle, the closure of span length and height difference in each span, and the force balance of the main beam. Then, they were converted into an objective function to be programmatically solved, leading to the live load response of the structure. Finally, a case study of a suspension bridge with a main span of 1,050 m was used to verify the feasibility and effectiveness of the proposed method. The structural deformation and internal forces provided by the analytical solution for the live load action had good accuracy, which is in good agreement with the finite-element method results. Long-span suspension bridges, compared with traditional small- and medium-span bridges, have greater flexibility, and they are more prone to large deflection and deformation under live loads such as vehicles. To improve the structural stiffness of suspension bridges, engineers often set central buckles connecting the cable and stiffening beam in the middle of the span. The current method of calculating the live load response of suspension bridges depends on finite-element modeling. However, when purchasing and using finite-element software, it is often expensive. At the same time, the finite-element method (FEM) modeling process is relatively complex and exhibits low efficiency. In addition, Link10 element in the current commercial finite-element software ANSYS (version 16.0) cannot consider its geometric nonlinearity, which will produce deviation to the results. Therefore, this paper proposes a set of accurate live load analytical algorithms for suspension bridges with central buckles, which are solved by the same number of basic unknowns and constraint equations. It is helpful to reduce the dependence of practitioners on finite-element software and can also be used as the verification and supplement of finite-element results. [ABSTRACT FROM AUTHOR]

Suspenders of long-span suspension bridges are thin structural components that are easily accessible to the public and in proximity to fast moving traffic. Their vulnerability and exposure to hazards make them especially prone to the risk of malicious or accidental damage. Albeit, the effect of suspender loss on the behavior and performance of long-span suspension bridges has not yet been thoroughly investigated. In this paper, therefore, using computational simulation, member removal analysis is undertaken to shed light on how a typical long-span suspension bridge responds to sudden loss of a single suspender. Two factors, the location of the lost suspender and live load cases, are addressed in the study. Simulation results show that only structural members in the immediate vicinity of the lost suspender are significantly affected by sudden suspender loss, while the rest of the bridge is hardly affected. The study suggests that single suspender loss scenarios in long-span suspension bridges like the prototype bridge investigated in this work do not trigger appreciable nonlinearity in the system or even cause the main cables to overcome friction at the saddles. As such, single suspender loss scenarios in bridges like the prototype system can generally be assessed using common analysis and design software. [ABSTRACT FROM AUTHOR]

A reasonable lateral stiffness of the bridge mid-tower should ensure that the deflection-to-span ratio and sliding resistance coefficient satisfy the design requirements. However, if this stiffness is determined by the deterministic parametric analysis, the above two verification indices may exceed the threshold due to the randomness of the high-dimensional structure and load parameters. To satisfy the structural safety requirements of a three-tower suspension bridge during its design life, this study proposes a method to quickly and accurately evaluate the reliability indices of the deflection-to-span ratio and sliding resistance coefficient of the three-tower suspension bridge. Based on advanced first-order second-moment, the proposed method transforms the reliability problem into an optimization problem with constraint functions, uses the single-cable theory to establish the limit state function, and combines the manta ray foraging optimization algorithm and penalty function to derive the reliability index. The effectiveness of the proposed method is verified by performing Latin hypercube sampling for an examplary three-tower suspension bridge. These results prove that the new technique avoids tedious finite element simulation and surrogate model fitting, ensuring the accuracy of the reliability index while improving the calculation efficiency. The study further identifies critical structural parameters by parametric analysis. Based on the inverse reliability, the dimensionless stiffness range for the mid-tower with the randomness of the parameters is derived, and the preliminary design method of the lateral stiffness of the mid-tower based on the reliability is established. [ABSTRACT FROM AUTHOR]

The Huanghe River bridge on Fenghuang Road in Jinan is a three-tower four-span spatial cable self-anchored suspension bridge with the largest span and width in the world today. Two system transformation schemes, namely side suspenders tensioned before the center suspenders, Scheme 1, and side and center suspenders tensioned simultaneously, Scheme 2, are determined according to the engineering characteristics, tendon span of cables and simulation analysis of the bridge. Through systematic comparison and analysis of the key parameters such as the length of the hanger connecting rod, the anchorage force of the hanger and the difference of the vertical and horizontal deflection angles in the process of system transformation of the two schemes, Scheme I is finally determined as the recommended scheme owing to its small anchorage force of the side span hanger, short length of the connecting rod, small number of hanger tension processes and jacks, and outstanding exxonomical efficiency. After the system transformation by side fint and center second is taken, the measures values and theoretical values of the suspension cable force, main cable shape and stiffening girder alignment of the bridge are consistent and meet the requirements of the specification, [ABSTRACT FROM AUTHOR]

A reliable numerical procedure is proposed for the geometric nonlinear dynamic analysis of suspension bridges subjected to earthquake excitations. The geometric nonlinearities of cable members are captured by the catenary element derived from exact analytical expressions of elastic catenary, while the geometric nonlinearities of tower and girder members are predicted by nonlinear beam element which can undergo large deflections and rotations. An incremental-iterative solution based on Newmark-β direct integration and Newton–Raphson iteration is adopted for solving the nonlinear equation of motion. The results are compared with those generated by ANSYS to show the accuracy and efficiency of the proposed procedure. [ABSTRACT FROM AUTHOR]

Given the 516 Arouca pedestrian suspension bridge's design and characteristics, the owner, a municipality, required a set of tests in order to evaluate its aerodynamic characteristics and dynamic response, aiming at both structural safety and user comfort. Wind tunnel tests were performed over a sectional scaled model to obtain the static aerodynamic coefficients and dynamic response. The tests were carried out on different bridge configurations—a deck with people and a deck with an arch for secondary cables (connecting each suspension point to the catenary on the opposite side of the deck)—for the static coefficients. For the dynamic response, only the deck alone was tested. A major challenge had to be overcome, as the main displacement mode belonged to a swing movement, to assemble a wind tunnel setting, requiring a suspension system allowing wind displacements. A persistent trend of small amplitude displacements was identified, influencing user comfort and contributing to the installation of the secondary cables, but no aerodynamic instabilities were identified. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Railway Science & Engineering is the property of Journal of Railway Science & Engineering Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Triple-cable design of suspension bridges with an ultrawide main girder can improve their mechanical properties, making it lucrative for numerous engineering scenarios. However, its realization requires assigning an appropriate share of the dead load of the main girder supported by three main cables to avoid the middle main cable overload by the main girder's dead load since the latter would impair the mechanical behavior of the upper transverse beams in the towers and deteriorate the whole bridge's torsional stiffness. Therefore, this study proposes an analytical approach for dead load allocation to the suspension bridge with three main cables, which adjusts the share of the main girder's dead load supported by three main cables via changing the unstrained lengths of the hangers. The main advantage of the proposed approach is that it can consider both uniform and nonuniform allocations. The spatial model for the suspension bridge with three cable planes is first converted into a plane model. The relationship between unstrained lengths of the three hangers in the same cross section is determined via the deformation compatibility conditions and one of the following options: (1) equality of stiffness of the two side hangers in the case of a symmetrical plane model; or (2) energy conservation conditions in case of an asymmetrical one. The proposed method was applied to an example of a triple-cable suspension bridge with a main span of 2,100 m and a width of 75 m, and its analytical solutions were compared against finite-element method calculation results. An increase in the share of the main girder's dead load supported by the two side main cables increased the torsional stiffness of the whole bridge and reduced the vertical load exerted by the middle main cable on the top transverse beam of each tower. Meanwhile, variation of the share of the main girder's dead load supported by the side and middle main cables only slightly influenced the whole bridge's vertical and lateral stiffness values. The aforementioned adjustment by the proposed method could be accomplished without increasing the steel consumption of the bridge cables. The results could provide references for the design, static, and dynamic response analysis of similar triple-cable ultrawide suspension bridges. Installation of an ultrawide deck in a conventional two-cable suspension bridge requires resolving the following two major problems: (1) the main girder has a significant spatial effect, which considerably adds to the difficulty of design and analysis; and (2) at the midpoint of the main girder section, the deflection may be excessively large. The height of the main girder has to be increased to improve the stiffness, leading to high steel consumption and high construction cost. These problems may be solved by adding a cable plane (one more main cable and the corresponding hangers). Based on the findings and the major contributions of this paper, we can achieve random dead load allocation ratios by just adjusting the unstrained lengths of hangers. The application of triple-cable systems may be a great potential approach to increase the overall torsional stiffness. Meanwhile, changing the share of the dead load supported by the side and middle main cables has a slight effect on the total cable-steel consumption. It shows that the method presented in this paper will not increase the construction cost. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Architecture & Civil Engineering is the property of Chang'an Daxue Zazhishe and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study investigates the transverse structural performance of an ultrahigh performance concrete (UHPC) lightweight composite deck (LWCD) in a large cantilever cable-stayed bridge with an ultra-wide single cable plane, which is different from previous double-cable-plane cable-stayed and suspension bridges. To this end, large-scale cantilever model testing and linear and nonlinear finite element (FE) modeling are performed. The results show that during the test all cracks were progressively propagated from the fixed end to the cantilever end, and they showed a dense distribution on the UHPC surface at the end of the test. The presence of U-ribs alters the local stiffness and stress distribution, thereby promoting UHPC crack initiation on the top of the left web of the U-rib. In the elastic stage, strain differences between the top and bottom UHPC surface are <30 με, showing an approximate axial tension characteristic. In the crack development stage, the strain differences increase with the load, showing a bending-tensile stress characteristic, especially at the top of the U-rib. The bending-tensile stress characteristic becomes more significant from the fixed end to the cantilever end with decreasing girder height. The maximum transverse stress of 10.51 MPa obtained from FE modeling with load combinations is smaller than the nominal cracking stress of UHPC layers (i.e., 10.7 MPa), confirming the linear response and safety of engineering practice. • The transverse structural behavior of large cantilever steel-UHPC composite bridge decks is examined by model test and FEM. • A linear relationship is observed between load and maximum crack width (<0.2 mm) as UHPC cracks densify under transverse loads. • The presence of U-ribs alters the local stiffness, thus promoting UHPC crack initiation on U-rib's left web (fixed end side). [ABSTRACT FROM AUTHOR]

Finding the main cable shape is an essential step in the design and construction of suspension bridges. In this paper, shape-finding and force-assessment of suspension bridges based on loop adjustment are proposed and realized via the finite-element method. Here, loop adjustment refers to the process where the appropriate adjustment coefficient is chosen based on the results of the last modeling and deviations from the design goals to approach the target main cable shape gradually and to satisfy the design requirements. This method adopts a full-bridge model, which provides the comprehensive account of interactions between different components of the suspension bridge, including towers and stiffening girders, as well as the effect of tower compression and splay saddle rotation. Based on the full-bridge model in the completed bridge state, the inverted removal method is used for the calculation of key construction parameters in the free cable state, such as prebias of tower saddles, predeflected angle of splay saddles, and installation position of cable clamps. The proposed method's feasibility and effectiveness are verified by its application to two particular suspension bridges, namely, the Great Belt Bridge (Denmark) with a main span of 1,624 m and the Jindong Bridge over the Jinsha River (China), with a main span of 730 m. Results of shape-finding and force-assessment both have good accuracy, which are generally consistent with those obtained by other methods. [ABSTRACT FROM AUTHOR]

Cable structures hold a special place for the cost of suspension bridges. Considerable development of the structural cable material leads to design and construction of long‐span suspension bridges. Thus, designing cable structures that are cost‐effective and reliable is significant for these mega structures. The overall layout of a main cable is consistent with constant number of elements per span since the design of the first suspension bridge. However, the reduction of main cable area in regard to design loads could play an important role in saving cost of long span suspension bridges. This paper presents the strand reduction approach for the cable structure design of suspension bridges. The proposed approach has been implemented by releasing the required number of parallel wire strands in main cable of the suspension bridge at specific locations in accordance with axial loads on main and hanger cables where released strands are transformed into a hanger cable with special types of clamps. The strand reduction approach is named as "saddle‐clamp system" and has been compared with the current design of 1915 Canakkale Bridge. The results indicate that the strand reduction method provides 7.6% to 34.1% material quantity deduction for the cable structures of the suspension bridge. [ABSTRACT FROM AUTHOR]

Multiwire cable structures equipped with clamps are widely used in civil engineering, such as suspension bridges, and their bending stiffness is always neglected in design. However, in practice, bending can be important locally when the sudden changes of cable curvature occur due to hanger forces loaded group by group during construction. Moreover, the main cable, composed of high-strength steel wires, has a secondary sectional bending stiffness that changes and with its tension state, being small (flexible) at the first stages and increasing gradually until reaching a notable rigidity (stiff). This, along with the effect of clamps leads to a Flexible-Stiff Coupling Multi-stiffnesses (FSCM) properties with geometrical and mechanical nonlinearities. Ignoring this might introduce uncontrollable shape errors during installation. To fill the gap of a shape analysis considering the FSCM, an analytical method as Chord Substitution Method (CSM) is proposed. The chord line geometry of the structure is taken as an independent object, and then the system equilibrium can be represented with a set of chain pole equations based on an established physic model of cable segment. The extension of each chord rod is modeled with a composite-chord-spring considering both axial and bending geometric stiffnesses. The cable curvature effect at clamps can be modeled by correcting external forces to satisfy a bending compatibility condition. The effectiveness of the CSM is validated by a previous model test found in the literature, and a real example is used for comparative studies. This method might be promising for a refined construction design and monitoring control of such structures. • An analytical method for the shape analysis of multiwire cable structures considering FSCM is derived. • FSCM can be fused into a chord line equilibrium based on an assumed physic model. • The bending effects are realized through a segmentation strategy and a spring system. • The CSM outperforms the general approaches in prediction precision. • The error laws introduced by FSCM is quantified in a real example. [ABSTRACT FROM AUTHOR]

Summary: Damage of bridge cables is mainly manifested as the decrease in cable forces. These forces are affected by the boundary conditions, cable length, cable stiffness, and cable appendages, making it hard to identify the cable forces. Based on the substructure isolation method, this study proposes an approach for cable force identification to judge cable damage by adding virtual supports to each cable so that the cables share the same length and boundary conditions. The cable forces can then be identified according to the relationship between the natural frequency and cable forces. The basic concept is that the boundary sensors are transformed into virtual supports by a linear combination of the convolution of measured responses to achieve the zero boundary response. A finite element model of a suspension bridge was used to validate the proposed method in a simulation. When the virtual supports were added to the cables, the relationship between the cable forces and the natural frequency was almost linear, and the cable damage could be successfully identified with 5% noise. Finally, the effectiveness of the proposed method was verified experimentally, and the natural frequency of the isolated cable substructure was confirmed to be a highly sensitive damage indicator. [ABSTRACT FROM AUTHOR]

A cable-supported bridge is usually a key junction of a highway or a railway that demands a higher safety margin, especially when it is subjected to harsh environmental and complex loading conditions. In comparison to short-span girder bridges, long-span flexible structures have unique characteristics that increase the complexity of the structural mechanical behavior. Therefore, the system safety of cable-supported bridges is critical but difficult to evaluate. This study proposes a novel and intelligent approach for system reliability evaluation of cable-supported bridges under stochastic traffic load by utilizing deep belief networks (DBNs). The related mathematical models were derived taking into consideration the structural nonlinearities and high-order statically indeterminate characteristics. A computational framework is presented to illustrate the steps followed for system reliability evaluation using DBNs. In a case study, a prototype suspension bridge is selected to investigate the system reliability under stochastic traffic loading based on site-specific traffic monitoring data. The numerical results indicated that DBNs provide an accurate approximation for the mechanical behavior accounting for structural nonlinearities and different system behaviors, which can be treated as a meta-model to estimate the structural failure probability. The dominant failure modes of the suspension bridge are the fracture of suspenders followed by the bending failure of girders. The degradation of suspenders due to fatigue-corrosion damage has a significant effect on the system reliability of a suspension bridge. The numerical results provide a theoretical basis for the design on cable replacement strategies. [ABSTRACT FROM AUTHOR]

Suspension bridges are supported by main cables that continue beyond the pillars to deck-level supports and must be anchored at each end of the bridge. The dynamic characteristics of the main cables are key indicators used to assess the structural health status of a bridge. In situ real-time health monitoring is an effective way to assess the dynamic characteristics. This paper presents a case study using vibration-based wireless smart sensors deployed on the main cables of a large-scale three-pylon suspension bridge to obtain its dynamic features. The methods of anti-aliasing filtering, statistical analysis and main cable tension force estimation were proposed and embedded into wireless smart sensors to provide autonomous data processing. According to the analysis of the vibration data from the main cables, the results demonstrate that the main cables have been in a stable state over time, and wireless smart sensors are promising for autonomous main-cable monitoring of large-scale three-pylon suspension bridges. [ABSTRACT FROM AUTHOR]

Compared with suspension bridges with a single main cable in each cable plane, adding a cable with a different sag may increase the vertical stiffness, but also increase the demand of frictional resistance at the saddles. To ensure antislip safety, the frictional resistance must be greater than the unbalanced cable tension. This study presents an innovative saddle to accommodate two main cables and analyzes the frictional resistance through mechanical analyses that were validated by finite-element analysis. A nonlinear finite-element model of a double-cable three-tower suspension bridge is established to determine the maximum unbalanced cable tension. The effects of key design parameters on antislip safety are investigated. The results reveal that the proposed saddle structure increases the frictional resistance. Strategies to enhance antislip safety include increasing the flexural stiffness of the middle tower, the ratio of dead load distribution, and the sag of the top cable. Decreasing the sag of the bottom cable helps improve the antislip safety of the top cable but compromises the safety of the bottom cable. This study provides new insights into the design and evaluation of multispan suspension bridges. [ABSTRACT FROM AUTHOR]

In suspension bridges, cable anchorage system is the critical structure for cable tension transmission. For traditional rear anchor girder anchorage system and pre-stressed anchorage system, problems such as local compression and inconvenient construction are inevitable. This paper presents the development of a novel PBL anchorage system used in the 4th Nanjing Yangtze River Bridge. This PBL anchorage system adopted grouped perfobond rib shear connectors (known as PBL shear connectors) in the independent perforated steel plate. Two full-scale specimens were extracted from the practical design. The load–slip curves and the strain developments were obtained. The results revealed the reliable load-carrying capacity and very slight residual slip after the cyclic unloading from the design load. The load carried by each row of PBL shear connectors proved the distributed load-carrying capacity. Finite-element analyses were conducted in ANSYS, which agreed well with the test results. Further parametric analyses focusing on the spacing and rows of PBL shear connectors were conducted. Based on the analysis results, the design methods of the PBL anchorage system were suggested. [ABSTRACT FROM AUTHOR]

This paper proposes an enhanced mechanical model for analyzing the vertical deformation of suspension bridges under large structural deformation scenarios. The model can be superior to the traditional deflection theory by incorporating several factors frequently overlooked, including the horizontal displacement of the main cable, the elongation of the hanger, and the bending of the tower, and a two-step analysis strategy is proposed to integrate these factors into a comprehensive analysis approach. On this basis, a numerical solution based on the weighted residual method and a nonlinear adjustment algorithm is developed to solve the nonlinear model. The case study of a suspension bridge is presented to demonstrate the applicability and accuracy of the proposed method, and the results are compared with those obtained from the finite element method and the deflection theory, which confirm that the proposed method can produce more accurate results than the deflection theory, especially when the bridge deformation is large enough. The subsequent comparative analysis reveals that the horizontal deformation of the cable and the bending of the towers are the key points contributing to this improvement. • The established model newly considers the horizontal displacement of main cable, hanger elongation, and tower bending. • The proposed two-step analysis strategy results in an efficient and precise algorithm for solving the established model. • The proposed model and algorithm shall be useful in the preliminary design of suspension bridges. [ABSTRACT FROM AUTHOR]

The opening of the Hålogaland Bridge December 2018 marked a milestone for modern suspension bridge design. It is an example of how technical knowhow is innovating the design of suspension bridges, in particular cable structure design. This paper will explain the overall design of the bridge with specific focus on the cable structure design including the main cables, anchorages, saddles and cable clamps. Furthermore, the construction of the bridge will be briefly mentioned focusing on the challenges of constructing such a major landmark structure in the extreme environment more than 300km north of the Arctic Circle. [ABSTRACT FROM AUTHOR]

In this paper, the linear dynamic analysis and active control of prestressed taut cable net structures are investigated by the wave scattering method. Wave motion equations of cables are firstly derived to obtain the wave dispersion characteristics, which are the combinations of the longitudinal tensile wave equations of bars and transverse wave equations of taut strings. The waveguide and scattering matrices of cables are then formed by the force balance and displacement boundary conditions. The derivation of the traveling wave model of cable net structures is accomplished by combining systematic scattering matrix with transmission matrix. Finally, the wave active control method is proposed based on the established traveling wave model. The comparison of results obtained by the wave scattering method with the finite element method shows an excellent agreement. But more importantly, it demonstrates that the computational efficiency of the wave scattering method is higher for dynamic analysis of large-scale cable net structures. The effectiveness of the proposed wave active control method is verified by a planar cable net structure. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The main disadvantage of suspension bridges is their increased deformability. One of the ways of suspension systems stabilization is giving certain bending stiffness to the suspension cables. This paper presents a revised theoretical and numerical analysis of the suspension bridge with rigid cable. Also, taking into account the bridge erection process the revised simplified method for the stress-strain analysis of suspension bridge with rigid cables is presented. Comparison of theoretical and numerical results is given. [Copyright &y& Elsevier]

With the development of the enhanced materials and techniques for analysis of bridge, long span cable-supported bridges are introduced. Cable-supported bridges comprise both suspension and cable-stayed high strength bridge systems. Both these forms of cable-supported bridge are flexible structures in behavior. These flexible systems are susceptible to the dynamic effects of wind and earthquake loads. With the increasing span of the bridge, the flexibility of the bridge is escalating. In this paper, an attempt is made to enhance the rigidity of long span bridge . For enhancing the rigidity of the bridge in lateral and vertical directions, a different configuration of the cable-stays of long span cable-stayed bridge is considered. To understand the response of the long span cable-stayed bridge, the modal time history analysis is carried out in SAP2000 software. The parameter considered to analyze the cable-stayed bridge is dissimilar to cable-stays configuration. The behavioral response of the bridge is presented in the form of a time period in lateral and vertical direction for structural members of the bridge. [ABSTRACT FROM AUTHOR]

The cables and hangers of old suspension bridges and the stays of cable-stayed bridges often suffer from steel corrosion. It is important to repair them by proper methods to prevent the further progression of corrosion. In this paper six repair methods were proposed and applied to cable specimens. Then, the specimens were exposed to severe corrosion environments and the effectiveness of the proposed repair methods was compared. Two different types of test cables were used in this study: parallel wire strands and spiral strands. The first test group used parallel wire strand cables consisting of 19 nongalvanized steel wires. This test was aimed at the main cables of the suspension bridges. Six repair methods were applied to these cable specimens: coating with zinc-rich paint, coating with epoxy resin paint, coating with zinc powder paste, filling with epoxy resin, filling with oil, and a dehumidification method. Then, the specimens were accelerated to corrode in a laboratory for 15 months. By investigating the mass loss owing to corrosion and appearance during this period, the effectiveness of the six repair methods was compared. For the surface wires, the dehumidification method was the most effective followed by the epoxy resin paint and filling, the zinc powder paste, and the zinc and epoxy resin paint on the surface. The oil filling was not very effective compared with other repair methods. The corrosion of the inside wires was much less than for the surface wires. The second group test used spiral strand cables consisting of seven galvanized steel wires. This test was aimed at the hangers of suspension bridges and the stays of cable-stayed bridges. The same repair methods and corrosion acceleration methods were used. By investigating the mass loss owing to corrosion and the appearance of both inside and surface wires during the 16-month period, most of the proposed repair methods were very effective compared with those of unrepaired strands. This study proves that even if cables are corroded proper repair work is effective in preventing further corrosion. [ABSTRACT FROM AUTHOR]

The Sorok Bridge is believed to represent the best solution for the construction of a cost-effective suspension bridge for several reasons. First, in the construction of the foundation, a decrease in the self-weight of the concrete open caissons due to their buoyancy allowed a reduction in the capacity of the floating crane when the caissons were fabricated on a floating dock and submerged into the sea. Second, the diamond shape of the pylons minimized the scale of the foundation and increased the transverse resistance against wind and earthquake loads. During their installation, the automatic climbing system was used for the complicated pylon geometry. Third, a trapezoidal steel box girder with a steel deck is more economical than other types in terms of the amount of steel needed; it could be erected using the large-block installation method because steel was used for the girder. Finally, the main cable was installed by the prefabricated parallel wire strand method without a hauling system, thus eliminating the cost of such a system and producing significant cost savings. [ABSTRACT FROM AUTHOR]

Abstract: The first part of the study deals with an iteration scheme for the nonlinear static analysis of suspension bridges by means of tangent stiffness matrices. The concept of tangent stiffness matrix is then introduced in the frequency equation govverning the free vibration of the system. At any equilibrium stage, the vibrations are assumed to take place tangent to the curve representing the force-deflection characteristics of the structure. The bridge is idealized as a three dimensional lumped mass system and subjected too three orthogonal components of earthquake ground motion producing horizontal, vertical and torsional oscillations. For purposes of illustration the results of analytical and experimental analyses for the Istanbul Bogazici Bridge have been presented. [Copyright &y& Elsevier]

Abstract: This paper presents a simplified analytical formulation, including closed-form algebraic expressions, for determining the critical flutter velocity of cable supported bridges. The formulae have been developed from the fundamental aeroelastic equations by introducing two assumptions: (1) Flutter derivatives may be approximated by expressions providing a frequency-independent description of self-excited forces. (2) The critical frequency is on the torsional branch of the solution and may be approximated by an uncoupled system of equations. The formulae have been tested for two typical cross sections, for a wide range of hypothetical structural configurations and the structural configurations of some well-known bridges. The numerical results produced by the formulae have been compared with results obtained by complex eigenvalue analysis, and it is concluded that the formulae give satisfactory results for all the cases considered. It is well known that multimodal effects may reduce the stability limits of an aeroelastic system. Hence, multimodal effects have been carefully studied to provide new insight into when a bimodal approach is sufficient, and when a more comprehensive multimodal approach is needed. [Copyright &y& Elsevier]

The effect of rigid ends is considered in the formulation of a general two-node cable element for the analysis of cable-supported structures. The stiffness matrix of the catenary cable element was derived as the inverse of the flexibility matrix, with allowances for self-weight and pretension effects. In modeling the cables of suspension bridge, distinction is made between single cables (e.g., stay cables and hangers) and multi segment cables (e.g., main cables). The unstressed length of each cable element in terms of the pretension force is determined by a trial-and-error procedure prior to structural analysis. Cable shape analysis was conducted to determine the configuration of main cables for cable-supported bridges under the dead loads. It was demonstrated that the effect of rigid ends cannot be ignored for taut cables, that is, cables with large pretensions. Further, the cable element derived can be reliably used in the analysis of cable-supported bridges, regardless of the sag magnitudes. [ABSTRACT FROM AUTHOR]

The quantum mechanical origin of the Klein-Gordon equation hides its capability to model many classical systems. We consider three examples of vibrating systems whose mathematical descriptions lead to the Klein-Gordon equation. These examples are adapted to applications such as the motion of suspended cables and Inca rope suspension bridges. We also discuss the correspondence between the classical and quantum settings of this equation as a way to provide an explanation of the concept of mass. [ABSTRACT FROM AUTHOR]

Cables are typically used in engineering applications as tensile members. Relevant examples are the main cables of suspension bridges, the stays of cable-stayed bridges, the load-bearing and stabilizing cables of tensile structures, the anchor cables of floating mooring structures, the guy-ropes for ship masts, towers, and wind turbines, the copper cables of electrical power lines. Since cables are characterized by non-linear behavior, analysis of cable structures often requires advanced techniques, like non-linear FEM, able to consider geometric non-linearity. Nevertheless, a traditional simplified approach consists in replacing the cable with an equivalent tie rod, characterized by a suitable non-linear constitutive law. Currently used equivalent constitutive laws have been derived by Dischinger, Ernst and Irvine. Since the equivalence is restricted to taut cables, characterized by small sag to chord ratios, these traditional formulae are not appropriate for uniformly loaded sagging cables: the main cables of suspension bridges are a particularly emblematic case. Despite some recent attempts to find more refined solutions, the problem is still open, since closed form solutions of general validity are not available. In the paper, general analytical formulae of the non-linear constitutive law of the equivalent tie rod are proposed, distinguishing two relevant cases, according as the length of the cable can vary or not. The expressions, derived by applying the general form of the theorem of virtual work, can be applied independently on the material, on the sag to chord ratio, on the load intensity and on the stress level, so allowing the replacement of the whole cable with a single equivalent tie rod. The expressions are critically discussed referring to a wide parametric study also in comparison with the existing formulae, stressing the influence of the most relevant parameters. [ABSTRACT FROM AUTHOR]

Copyright of Baltic Journal of Road & Bridge Engineering (Baltic Journal of Road & Bridge Engineering) is the property of Baltic Journal of Road & Bridge Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Self-anchored cable-stayed suspension bridge, as a new type of bridge, is rarely investigated. Based on spatial finite element model, dynamic characteristics of the Dalian Harbor's sea-route bridge belonging to long span self-anchored cable-stayed suspension bridge are obtained and some new dynamic traits such as preferential appearance of the vertical bending modes for girder are shown in comparison with those of earth-anchored cable-stayed suspension bridge. The vibration-restraining measure setting intersecting inclined cables is proposed because the main cables in the main span are subject to vibration and the most reasonable setting position, which is 0. 287 5 position of the main span, is given. The dynamic property is preliminarily analyzed with response spectrum method and the results show that the seismic responses of the kind of bridge are greater so that the anti-seismic design should be paid more attention to. [ABSTRACT FROM AUTHOR]

Wire fractures in the main cables of the Lysefjord Suspension Bridge display an approximate linear relationship with time. Uncertainties related to wire fractures in sub-layers, reduction of load-carrying capacity and lifetime, and future development of wire fractures have prompted extensive investigations of the main cables. Failure analyses of fractured Z-wire samples and fracture mechanics analysis concluded that cracks have initiated and propagated from surface imperfections. The potential for hydrogen atom generation and absorption that causes hydrogen-induced cracking is discussed. Hydrogen atoms result from the hot-dip galvanization process, or due to corrosion. Evaluation of remaining load-carrying capacity and the need for strengthening of the main cables are briefly discussed and methods for surveillance of wire fractures are presented. [ABSTRACT FROM AUTHOR]

Service life is an important yet somewhat nebulous consideration in the planning of suspension bridge rehabilitation projects. While it is often thought of in terms of time to physical failure of the asset, bridge service life is also defined by non-physical factors such as changing traffic loads and alternate levels of evaluation. This paper develops a conceptual model that defines service life as a function of physical and non-physical factors, thus offering a fresh perspective from which to base a more rational discussion on heavy trucks and their impact on bridge service life. An illustrative example demonstrates how this model may be applied in practice at the project level. Finally, federal truck weight reform is a pressing issue in the USA, and this paper concludes with a discussion on the implications this model has for network level studies concerning the impact of truck weight reform on bridge service life. [ABSTRACT FROM AUTHOR]

Copyright of Baltic Journal of Road & Bridge Engineering (Baltic Journal of Road & Bridge Engineering) is the property of Baltic Journal of Road & Bridge Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aim of this study concerns with the analysis of cable-stayed bridges at different erection stages during construction using the cantilever method. A finite element computation procedure is set up for the shape finding analysis of such structures during erection procedures. Two computational processes are established, one is a forward process analysis and the other is a backward process analysis. The former is performed by following the sequence of erection stages in bridge construction and the latter is carried out in the reverse direction of erection procedures. Both processes can be successfully applied for finding the initial shape of bridge structures during erection procedures. The structural behavior of the bridge structure at different erection stages has been examined in details, such as the pretension required in cable-stays and the corresponding structural configurations of the bridge, etc. The results of shape finding analysis at each erection stage not only provide the necessary data for the purpose of structural analysis and design, but also can be used for checking and controlling the erection procedure of the cable-stayed bridge during construction. The designed shape (pretension in cables and configuration) of the bridge can then be achieved and constructed. [Copyright &y& Elsevier]

Various factors contribute to the difficulty in designing the main suspension cable for the new San Francisco–Oakland Bay Bridge Self-Anchored Suspension Span (or East Bay Bridge Suspension Span). The key factors are bridge design life, cable geometry, cable anchorage layout, cable construction method, and cable corrosion protection system. This paper describes the unique main suspension cable geometry layout for the East Bay Bridge Suspension Span, reviews the available technologies for each of the aforementioned design considerations, and presents the final cable design recommendations. [ABSTRACT FROM AUTHOR]

The reliability assessment of suspension cables is today a major topic all around the world. Due to the large number of broken wires found—wide in suspension cables, rational and effective methods are therefore needed for assessing cable safety factors. Based on a simple mechanical and statistical model, this paper tempts to provide an approach for solving this problem. This model allows determining the cable residual strength as far as the behaviour of the constitutive components is correctly characterised. The model is based on Monte-Carlo simulations of individual unbroken wires while broken wires are randomly generated by a binomial distribution. The approach is applied to the Tancarville suspension cables by taking into account tensile test results, inspection data and weigh-in-motion records. The calculation of the residual strength is then compared to the dead and live load effects in order to provide a point-in-time safety factor of the suspension cable. [Copyright &y& Elsevier]

The article discusses physical factors affecting the functions of bridges. All structures seek balance through at least two gravitational factors, tension and compression. Material is in tension if it is being pulled and material is in compression if it is being pushed. In suspension bridges, the steel cables and hangers are always in tension, while the towers are in compression. Bridges must also sway in order to withstand the loads that transverse them. If a bridge does not sway, it will become brittle and eventually will collapse. A key component of stable and durable bridge design is the truss, a system of supporting pieces. To teach middle school students about bridge mechanics, a discussion should be made about a variety of bridge components.