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The interface force condition on the cross section of parallel steel wire strands is an important basis for studying the longitudinal friction and slip behavior of wires. In this study, force-chain superposition was proposed to solve the transmission and distribution of transverse forces between parallel wires. The calculation rules for the basic parameters in the solution were determined, and a wire-drawing experiment was designed to verify their applicability. A two-dimensional discrete model corresponding to the cable cross section was established. According to the source and characteristics of the transverse load, the force system is decomposed into two directions to form two force chain analysis paths so that the model assumptions can be applied properly. A recursive algorithm was proposed to solve the two force chains, and symmetry conditions were applied at the coupling position to make the system self-consistent. The normal forces acting on the interface points were obtained by superimposing the results onto the two force chains and were verified against finite element analysis (FEA) results. A long-span cable-stayed bridge was considered as an example to investigate the interface force condition of its cables, based on which the approximate development length of the broken wires and the interface extrusion force of the multilayered beam model were established. The results indicate that the slight twisting of the parallel wire strands under the action of a large cable force provides 85% of the total interface forces, and the normal force is significantly concentrated in the central area of the cross section. The approximate development length of the central wire is only 25.9% of that of the outermost wire, and the minimum slip friction force between the layers accounts for only 21.2% of the maximum value for the multilayered beam model, confirming that the interface force condition has a significant impact on the longitudinal friction and slip behavior of cable wires. [ABSTRACT FROM AUTHOR]

In view of the insufficiency of bidirectional seismic control of long-span cable-stayed bridges as well as the limitations of existing schemes, a multi-direction damping system (MDDS) was proposed and investigated in this manuscript, which can provide seismic resistance bidirectionally. The new damping system owned a unique middle connecting structure, which overcomes the disadvantages that axial instability caused of excessive long rod and the demand of large installing space of traditional dampers. Both the performance stability and constitutive relationship of MDDS were verified by engineering tests, and the equivalent design method was then proposed and proved to be applicable. A detailed finite element numerical model of a super-long (main span over 800 m) column-type pylon cable-stayed bridge which equipped with MDDS in practice was established, the fragility curves of critical components were obtained by non-linear time history analysis, which exhibited the high efficiency of MDDS seismic performance in both transversal and longitudinal directions. Through extracting the median fragility value of 35 sections of the pylon under four damping cases, i.e. setting dampers transversely (TDS), longitudinally (LDS), bidirectionally (BDS), and MDDS, it can be concluded that MDDS performed far better on seismic resistance than LDS and TDS, and made the similar contribution with BDS. On account of half number of damper setting and the reduction in installing space demand, MDDS becomes the optimal choice in practical application for its economic efficiency and superiority. Furthermore, the optimal horizontal installing angle of MDDS was derived through six angle cases which was based on the system-level fragility curves comparison. [ABSTRACT FROM AUTHOR]

Long-span cable-stayed bridges are subjected to the risk of collision from passing ships. Conducting experimental study on the collision of bridges and vessels is difficult due to high cost and limited space. In this paper, the behavior of a 1 018-m long-span cable-stayed bridge subjected to ship collisions is numerically studied. Finite element models of the entire bridge and ships are established. Four different dead weight tonnages (DWT), namely, 2 700, 12 000, 30 000, and 75 000 t, with impact velocities of 1 m/s to 6 m/s are investigated. The complete collision process under different loading scenarios is simulated, from which the collision force, bridge responses and local damage are obtained. The calculated collision force is significantly affected by the impact velocity and DWT, and exhibits a linear relationship with the impact velocity. Comparison with design codes shows that different codes vary significantly in estimating the collision force and Eurocode provides most accurate results. The effect of the material model on the collision force is also studied. This numerical study provides a reference for the ship collision design of long-span cable-stayed bridges. [ABSTRACT FROM AUTHOR]

• The temperature distribution of a cable-stayed bridge is obtained by integrating heat-transfer analysis and monitoring data. • The heat-transfer analysis and structural analysis share a unified FE model, resulting in an efficient and accurate analysis. • The numerical results have a good agreement with the field monitoring data. Varying temperature is a major load of long-span cable-stayed bridges. The temperature effect on the structural behavior may mask the influences of other loads. Conventional studies on the thermal behavior of bridges are limited to regression analyses based on measurement or numerical studies of 2D or local 3D models. This study investigated the global 3D temperature behaviors of a three-tower cable-stayed bridge through the integration of field monitoring and unified numerical simulation. A 3D refined model of the bridge with thermal elements was built, and the thermal boundary conditions were determined from environmental field monitoring data for the global 3D heat-transfer analysis. The calculated temperatures agreed well with the field monitoring counterparts. The temperatures were then input into the same global finite element model with mechanical elements for structural analysis. The temperature-induced structural responses, including the structural displacements and forces, agreed well with the measurement counterparts. The temperature-induced structural response variation pattern and sensitivity were summarized and quantified. This unified numerical simulation enables an efficient and accurate analysis of the global 3D thermal behavior of bridges, as compared with the conventional 2D or local 3D simulation. [ABSTRACT FROM AUTHOR]

Ship collision is rare, yet it leads to serious consequences once it occurs, in particular for long-span bridges. This study investigates dynamic responses of a long-span, rail-cum-road cable-stayed bridge under ship collision through finite element analysis. Three ship tonnages were investigated, which are 3000, 5000, and 8000 t, respectively. The displacement, velocity, and acceleration of the bridge under ship collision are analyzed. The collision process is simulated in two explicit steps to improve the computational efficiency. First, the collision force is determined through a collision simulation of the ship to a rigid body that simulates the massive bridge pier. The collision force is then applied to the bridge to analyze the dynamic responses of the bridge. The simulation results of the collision force are compared with four different design codes. Analysis results from different codes show significant discrepancies, demonstrating lack of reliability of the formula recommended by the codes. The results indicate that the maximum displacement and acceleration occur at the top of the bridge pylon. The bridge's responses under ship collision decrease as the collision angle increases from 0° to 20°. [ABSTRACT FROM AUTHOR]

Cable breakage (loss) events can be disastrous to cable-stayed bridges because of potential risks of progressive collapse following the initial failure of stay cables. To avoid turning a cable-breakage hazard into a disaster, it is important to rationally assess the risk through accurately predicting the nonlinear dynamic behavior of the bridge subjected to various types of cable-loss events. With a recently developed advanced finite element (FE)-based nonlinear dynamic simulation platform, a comprehensive numerical investigation of cable-loss incidents on a long-span cable-stayed bridge is conducted by focusing on post-breakage performance. Parametric studies are carried out to evaluate the impacts from various important parameters related to cable-breakage process and service loads from stochastic traffic and wind. Several parameters associated with cable-breakage processes, such as the breakage duration, time-transient curve and initial state, are found to influence the dynamic performance of the bridge notably. The results also indicate that service traffic and wind loads as well as complex coupling effects with the bridge are important to the bridge response following cable-loss events. In the final part of the study, response envelope analysis is made and a comparative investigation is also conducted between the results from the advanced FE-based nonlinear dynamic approach and those from the equivalent static approach as suggested by the Post-Tensioning Institute (PTI). [ABSTRACT FROM AUTHOR]

• Design, fabrication, and erection of a large-scale outdoor full-bridge aeroelastic model at a geometric scale of 1:50 were described in detail. • The aeroelastic model was validated by the modal tests including free vibration test and ambient vibration test. • The buffeting responses of the girder, tower and cable force of the aeroelastic model in normal natural wind were investigated. To overcome the limitations of existing experimental methods (including wind tunnel tests and field measurement experiments) for the study of bridge wind engineering, the research group at the Dalian University of Technology recently proposed to study the wind-resistance behaviours of long-span bridges through large-scale outdoor full-bridge aeroelastic models in natural wind. Several full-bridge aeroelastic models have been constructed, including a 1:50 model of a long-span cable-stayed bridge, which had a total length of 41.76 m and a height of 6.0 m. This paper systematically introduces the design, fabrication, and dynamic testing of the aeroelastic model. Taking the safety, adjustability, durability, and cost of the aeroelastic model into account, new approaches for the design of the main girder envelope, core beam of the bridge tower, and connections of the aeroelastic model are proposed. Free vibration tests and ambient vibration tests were utilised to measure the modal parameters of the aeroelastic model. The identified modal parameters were consistent with those calculated by finite element analysis, suggesting that the design and fabrication of the model were valid. The representative wind field data and measured buffeting responses of the aeroelastic model were presented. [ABSTRACT FROM AUTHOR]

• Cable-supported bridges exhibit nonlinear structural vertical-torsional coupling. • Practical approach for assessing nonlinear mode coupling in structures. • Span length influences nonlinear structural vertical-torsional coupling. • Suspension bridges are more nonlinear than cable-stayed bridges. Using simplified mathematical representations of suspension bridges, mathematicians have demonstrated that a vertical dynamic forcing can cause large torsional vibrations due to geometric nonlinearities of the bridge that appear to be a structural dynamic instability. Compared to the extensive research that has been conducted on the dynamic behavior of cable-supported bridges, the approach used by the mathematicians appears too simplistic. This is due to the fact that the dynamic force considered by the mathematicians is approximate compared to actual dynamic loadings on bridges, especially those originating from wind. However, they raise a point that is not considered in the wind design of cable-supported bridges, i.e., a possible nonlinear structural coupling between the modes of vibration that could be detrimental to the bridge performance. Therefore, this paper presents a preliminary investigation of nonlinear vertical-torsional coupling in long-span bridges using a simplified practical approach. The proposed method relies on the finite element method and nonlinear pushover analyses. Using this approach, the nonlinear structural coupling is assessed for the numerical models of five suspension bridges and two cable-stayed bridges. The method allows determining the nonlinear stiffness parameters of equivalent systems having between one and three degrees of freedom (lateral, vertical and torsional). Since the proposed technique relies on the modes of vibration and can account for the interaction between the vertical and torsional effects, it can be used to judge which ones of the bridges considered are likely to be the most susceptible to nonlinear mode coupling under wind loads. The analysis results for the seven bridges shows that the suspension bridge system has a greater nonlinear vertical-torsional coupling in comparison to the cable-stayed system. Additionally, it is demonstrated that the span length has an influence on the vertical-torsional coupling. The results also show that the nonlinear coupling is slightly affected by lateral effects. [ABSTRACT FROM AUTHOR]