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Suspenders play a crucial role in transmitting loads from the bridge deck to the main cable in a suspension bridge. They are susceptible to fatigue due to repeated dynamic loads, particularly traffic loads. Traffic Load Models (TLMs), typically created using Monte–Carlo simulation and Weigh-In-Motion (WIM) data, are employed to evaluate this fatigue. However, these models often overlook practical vehicle trajectories and spatio-temporal distribution, which compromises the precision of fatigue assessments. In this study, we introduce a novel 2D Intelligent Driver Model (2D-IDM) that incorporates actual vehicle trajectories, with a particular focus on transverse vehicle movement. This enhancement aims to improve the fidelity of existing TLMs. To provide a clear, qualitative, and quantitative understanding of the effects of fatigue evaluation with or without actual trajectory characteristics, we have structured this paper as a comparative study. We compare our proposed model, denoted as TLM S-3, with two observation-based models (O-1 and O-2) and two simulation-based models (S-1 and S-2). We conducted an experimental case study on a long-span suspension bridge, where the actual traffic load trajectory was obtained using a WIM-Vision integrated system. To calculate fatigue damage considering both longitudinal and transverse directions, we established a multi-scale Finite Element Model (FEM) using solid element types to simulate the bridge girder. This model can generate the stress influence surface of the bridge and has been verified in both static and dynamic aspects. Our detailed comparative analysis demonstrates the consistency of the proposed 2D-IDM with the actual measured traffic load trajectories. This indicates that our approach can enhance the fidelity and precision of fatigue evaluations for bridge suspenders. [ABSTRACT FROM AUTHOR]

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]

Vortex-induced force (VIF) identification and modelling of a long-span bridge are often conducted in terms of aeroelastic sectional model tests in wind tunnels. However, there are uncertainties inherent in wind tunnel model tests so that vortex-induced vibration (VIV) still occurs in real long-span bridges designed according to wind tunnel test results. This paper presents a framework for VIF identification of a long-span bridge based on field-measured wind and acceleration data. The framework is composed of the four steps: (1) decompose field-measured acceleration response time histories using variational mode decomposition (VMD) method; (2) obtain velocity and displacement response time histories using frequency domain integration (FDI) method; (3) establish and update the finite element model and identify the generalized VIF time histories of the bridge; and (4) identify the parameters in the polynomial VIF models and decide the most suitable VIF model. The proposed framework is finally applied to a real suspension bridge with a recent VIV event. The results show that the proposed framework can accurately identify the generalized VIF acting on the bridge from the field-measured acceleration and wind data, and the derived most suitable VIF model can produce almost the same vortex-induced response (VIR) as the measured ones. [ABSTRACT FROM AUTHOR]

Aging, corrosive environments, and inadequate maintenance may result in performance deterioration of civil infrastructures, and finite element model updating is a commonly employed structural health monitoring procedure in civil engineering to reflect the current situation and to ensure the safety and serviceability of structures. Using the finite element model updating process to obtain the relationship between the structural responses and updating parameters, this paper proposes a method of using the wavelet neural network (WNN) as the surrogate model combined with the wind-driven optimization (WDO) algorithm to update the structural finite element model. The method was applied to finite element model updating of a continuous beam structure of three equal spans to verify its feasibility, the results show that the WNN can reflect the nonlinear relationship between structural responses and the parameters and has an outstanding simulation performance; the WDO has an excellent ability for optimization and can effectively improve the efficiency of model updating. Finally, the method was applied to update a real bridge model, and the results show that the finite element model update based on WDO and WNN is applicable to the updating of a multi-parameter bridge model, which has practical significance in engineering and high efficiency in finite element model updating. The differences between the updated values and measured values are all within the range of 5%, while the maximum difference was reduced from −10.9% to −3.6%. The proposed finite element model updating method is applicable and practical for multi-parameter bridge model updating and has the advantages of high updating efficiency, reliability, and practical significance. [ABSTRACT FROM AUTHOR]

In the wind tunnel test, the full-bridge aeroelastic model needs to simulate both the shape and dynamic characteristics of the real bridge, and modal parameters are key dynamic parameters. Therefore, it is essential to identify the modal parameters of the model accurately. To get accurate modal parameters of the long-span bridge model in the wind tunnel test, the applications of the Hilbert-Huang transform for modal parameter identification were analyzed in this paper. Then a band-pass filter is designed to filter the original signal so that the intrinsic mode function obtained by empirical mode decomposition can satisfy the single-component signal requirement and eliminate the mode mixing effect effectively. Meanwhile, the endpoint data extension method based on SVM (Support Vector Machine) was presented to restrain the end effects of empirical mode decomposition. Finally, taking the Oujiang Bridge as the engineering background, the improved algorithm was applied to modal parameter identification of the bridge under ambient excitation. The modal parameters such as modal frequency and damping ratio were obtained. The reliability of the improved method was verified by comparing the identified modal parameters with the results of the finite element method, and it turns out that the improved method can reduce the frequency identification error of vertical bend, lateral bend, and torsion to 1.01%, 4.07%, and 1.68%. The results indicated that the improved method based on the Hilbert-Huang transform can accurately identify the main modal parameters of the structure and can be better applied to identify the modal parameters of long-span bridge structures. [ABSTRACT FROM AUTHOR]

Aeroelastic instability and buffeting are two wind-induced phenomena for long-span bridges. In the traditional method, aeroelastic instability and buffeting are analyzed separately. If geometric and aerodynamic nonlinearity are required, aeroelastic instability is normally calculated based on finite-element methods, and buffeting is carried out based on linearization of structural and aerodynamic nonlinearity. Then, the standard frequency-domain methods are utilized on the eigenvalue decomposition. However, for ultralong-span bridges, aerostatic deformation, aeroelasticity, and buffeting are strongly coupled. During buffeting, the bridge deck pitching will change both structural stiffness and aerodynamic loads; therefore, the nonlinearity should be included in the long-span bridge buffeting analysis. This paper establishes a reduced-order modeling procedure to simulate the wind-induced buffeting vibration for long-span bridges including the nonlinear aeroelasticity and buffeting force. First, the mode-based vibration formulas are derived to consider both structural and aerodynamic nonlinearity through polynomial expansion. Next, the numerically simulated turbulence is imported into the vibration governing equation, and the structural response can be calculated using the time-domain integration method. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) has attracted significant attention over the past two decades due to its ability to provide real-time insight into the condition of structures. Despite the development of several SHM systems for long-span bridges, which play a crucial role in the assessment of these structures, studies focusing on short- or middle-span bridges remain scarce. This research paper presents an efficient and practical bridge monitoring and warning system established on a middle-span bridge, a key crossroad bridge located in Shenzhen. The monitoring system consists of sensors and measuring points that collect a substantial amount of data, enabling the close monitoring of various operational indicators to facilitate the early detection of threshold exceedances. Based on this system, the subtle condition of the bridge can be evaluated, and the operational condition of the bridge can be studied through the comparative analysis of the collected data. Over four months of monitoring, data including the strain and creep of the main beam, the strain and settlement of piers and the crack width of the bridge body are observed. Furthermore, the real-time operational status of the bridge is analyzed and evaluated through the combination of the collected data and the structural finite element model. [ABSTRACT FROM AUTHOR]

Structural displacement monitoring is one of the major tasks of structural health monitoring and it is a significant challenge for research and engineering practices relating to large-scale civil structures. While computer vision-based structural monitoring has gained traction, current practices largely focus on laboratory experiments, small-scale structures, or close-range applications. This paper demonstrates its applications on three landmark long-span suspension bridges in Turkey: the First Bosphorus Bridge, the Second Bosphorus Bridge, and the Osman Gazi Bridge, among the longest landmark bridges in the world, with main spans of 1074 m, 1090 m, and 1550 m, respectively. The presented studies achieved non-contact displacement monitoring from a distance of 600 m, 755 m, and 1350 m for the respective bridges. The presented concepts, analysis, and results provide an overview of long-span bridge monitoring using computer vision-based monitoring. The results are assessed with conventional monitoring approaches and finite element analysis based on observed traffic conditions. Both displacements and dynamic frequencies align well with these conventional techniques and finite element analyses. This study also highlights the challenges of computer vision-based structural monitoring of long-span bridges and presents considerations such as the encountered adverse environmental factors, target and algorithm selection, and potential directions of future studies. [ABSTRACT FROM AUTHOR]

The nonlinear characteristics of bridge aerodynamics preclude a closed‐form solution of limit‐cycle oscillation (LCO) amplitude and frequency in the post‐flutter stage. To address this issue, a long short‐term memory (LSTM) network is utilized as the reduced‐order modeling of nonlinear aeroelastic forces on the bridge deck section, and it is repeatedly employed to generate force inputs at spanwise nodes of a three‐dimensional (3D) finite element model (FEM) of the long‐span bridge (using spatial beam elements). All LSTM networks are dynamically coupled through FEM, and the 3D nonlinear flutter response is accordingly obtained. To improve the simulation accuracy and reduce the required training data of the standard LSTM network, both general knowledge (motivated by the gating mechanism and mathematical models for information processing) and domain knowledge (resulting from the basic understanding of bridge aerodynamics) are leveraged to, respectively, customize the LSTM cell and network architecture. In addition, a fast‐training algorithm effectively combining the linear convergence of stochastic gradient descent and superlinear convergence of modified Broyden–Fletcher–Goldfarb–Shanno is developed to improve the training efficiency of the obtained knowledge‐enhanced LSTM network. To further advance the computational efficiency of the coupled LSTM‐FEM nonlinear flutter analysis, the convolution‐based numerical integration is adopted in the finite element modeling of long‐span bridge dynamics. A case study of a long‐span suspension bridge under strong winds demonstrates the proposed 3D nonlinear flutter analysis presents high simulation efficiency and accuracy and can be utilized to effectively obtain the nonlinear LCO characteristics in a wide range of post‐flutter wind speeds. [ABSTRACT FROM AUTHOR]

Structural health monitoring (SHM) systems have been widely applied in long-span bridges and a large amount of SHM data is continually collected. The harsh environment of sensors installed at structures causes multiple types of anomalies such as outlier, minor, missing, trend, drift, and break in the SHM data, which seriously hinders the further analysis of SHM data. In order to achieve anomaly detection from a large amount of SHM data, this paper proposes a long-short term memory (LSTM) network-based anomaly detection method. Firstly, the proposed method reduces the workload for preparing training sets. Secondly, the purpose of real-time anomaly detection can be met. Thirdly, the problem of high alarm rate can be avoided by utilizing double thresholds. To validate the effectiveness of the proposed method, a case study of finite element model simulation is firstly introduced, which illustrates the detailed implementation process. Finally, acceleration data from the SHM system of a long-span suspension bridge located in Jiangyin, China is employed. The results show that the proposed method can detect anomaly with high accuracy and identify abnormal accidents such as a ship collision quickly. [ABSTRACT FROM AUTHOR]

As flexible structures, suspension bridges usually undergo significant deformation under live load when carrying rail traffic, jeopardizing the safety of passing trains. In engineering practice, suspension bridges with short extended spans have been applied to reduce the beam-end rotation angle under live load. However, the extended span layout is still determined empirically, and optimizing the span layout of such bridges to reduce maximum deformation under live load requires further investigation. This study proposes an analytical method for solving the maximum deformation responses of suspension bridges with extended spans under live load based on deflection theory and the extreme value analysis method. The proposed method can accurately solve the deformation responses of suspension bridges with extended spans caused by live load. It also allows one to analyze the most unfavorable live load distribution and the maximum deformation under live load, avoiding the redundant search process of the finite element method. Furthermore, the proposed method is applied to analyze the influence of the extended span layout on the maximum deformation responses under live load. The results show that adequately increasing the length of the first extended span and decreasing the length of the second extended span is beneficial to reduce the maximum beam-end rotation angle and the maximum curvature of the main beam. • The method can effectively solve the deformation responses in extended-spans suspension bridges under specific live load. • The method can determine the most unfavorable live load distribution and the maximum deformation responses under live load. • An in-depth analysis is conducted on how the extended span layout influences maximum deformation responses under live loads. • The method merges the deflection theory with extreme value analysis method, laying the groundwork for structural design. [ABSTRACT FROM AUTHOR]

Accurate vehicle-induced deflection prediction is critical to bridge structural management and maintenance. However, most existing studies use finite element models and weigh-in-motion (WIM) system to predict the deflection of bridges, the cost of building finite element models is expensive. An accurate and low-cost vehicle-induced deflection prediction framework is developed in this study. In this framework, the calculation method of the spatio-temporal distribution matrix of the vehicle loads is proposed. A fusion attention mechanism bidirectional long short-term memory (ATT-BiLSTM) model is used to predict vehicle-induced deflection. Taking a suspension bridge in China as an example, the accuracy of short- and long-term vehicle-induced deflection prediction is tested, and different deep learning models are used for comparison. The results show that the proposed framework can predict short-term vehicle-induced deflection with a mean absolute error (MAE) of less than 2 mm, which can also accurately predict the extrema of vehicle-induced deflection within a certain time window. The proposed framework is independent of finite element models and lowers the cost of bridge deflection prediction. • An accurate and low-cost vehicle-induced deflection prediction framework is developed in this study. • The calculation method of the spatio-temporal distribution matrix of the vehicle loads is proposed. By using a fusion attention mechanism bidirectional long short-term memory (ATT-BiLSTM) model, the vehicle-induced deflection of the bridge is predicted. • Taking a suspension bridge in China as an example, the accuracy of short- and long-term vehicle-induced deflection prediction is investigated. [ABSTRACT FROM AUTHOR]

To explore a cost-efficient bridge structure system and expand the options for long-span bridges in mountainous regions, we propose an innovative cable-stayed deck arch (CSDA) bridge with significant potential benefits. This paper discusses the conceptualization, structural design considerations, and implementable construction methods of this bridge-type. We trial designed two CSDA bridges with span arrangements of 268 + 350 + 268 m and 280 + 3 × 380 + 280 m to demonstrate the versatility of our proposal in different topographic situations and its ability to accommodate both single and multiple main spans. The finite element analysis confirms the mechanical properties and structural feasibility of the conceptual designs. A comprehensive comparison with other types of bridges under identical conditions reveals that this new hybrid bridge is not only lightweight in structure, excellent in performance, and elegant in form, but also cost savings and with minor environmental impact. The preliminary study indicates that the CSDA bridges are suitable for the construction demand of high-rise pier and long-span bridges in mountainous terrain, and also an economical option for the main span between 350 to 400 m. • An innovative cable-stayed deck arch bridge is proposed, taking into account the design considerations and construction methods. • The bridge type accommodates different hilly terrain conditions and can be arranged with either single or multiple main spans. • The cable-arch load ratio is derived analytically and has proved the rationality of the structure system. • The proposed bridge exhibits excellent structural performance and other advantages. [ABSTRACT FROM AUTHOR]

• A comprehensive analysis is conducted to reveal the mechanism of widespread failure of light poles on an elevated bridge. • Large eddy simulation is performed to model the wind filed and aerodynamic pressures on the light poles. • Nonlinear Finite Element modeling is conducted to analyze the structure responses of the light poles. • The bridge superstructure can significantly enhance the local wind field, leading to increased wind loads (mean & fluctuating) on light poles. • Under enhanced wind loads, significant plastic strains/stresses develop at the bottom of the light poles. Light poles are critical secondary structural components that support the functionality and safety of transportation systems. However, they are tall slender structures vulnerable to wind load. This research attempts to analyze the mechanism of the widespread failure (69 poles failed) of light poles on an elevated highway bridge exposed to Category 4 Hurricane Laura (2020). First, large eddy simulation is performed to simulate the wind field and the aerodynamic pressure on light poles considering and without considering the presence of the bridge superstructure, respectively. Simulation result shows that the presence of the bridge superstructure strengthens the local wind field and the aerodynamic pressures. A nonlinear finite element model is created to simulate the structural responses. Research results indicate that, when considering the presence of the bridge superstructure, stresses at the pole bottom exceed the yielding strength and significant inelastic strains are developed, which is the main cause of the widespread pole failure. The present study can be used to evaluate the current design standard for luminaire pole structures on elevated bridges. [ABSTRACT FROM AUTHOR]

The present article proposes a novel framework for analyzing the dynamic responses of suspended monorail vehicles running over curved bridges under crosswinds. In this model, the curved bridge model is established with the finite element method and vehicles are simulated as a multibody system. Subsequently, a wind model is proposed with the wind tunnel test, spectral representation method, and yaw wind-decomposition method, taking into account the effects of the angle between the wind and vehicle changes when vehicles pass through the curved bridge. Finally, a suspended monorail curved bridge is analyzed to demonstrate the effect of the wind model on the vibration of the system. The results show that wind direction has a great effect on the lateral dynamic response of curved bridges, the lateral force of guiding tire, and the vertical force of running tire. The influence of crosswind on the dynamic response of the vehicle decreases with the increase of running time of vehicle on curved bridges. [ABSTRACT FROM AUTHOR]

This work aims to develop a reasonable pre-camber design method for long-span cable-stayed bridges by investigating the high-speed train-bridge interaction under complex environmental loads, including ambient temperature, concrete creep, and concrete shrinkage (CCCS). First, an integrated dynamic model of the train-track-cable stayed bridge system (TTCSBS) is established using multibody dynamics and finite element theory and validated through field test. Then, the temperature change features at several key positions on the long-span bridge are investigated using long-term monitoring data. Temperature-induced bridge deformation is calculated by applying the established bridge finite element model (FEM) and compared with test results. CCCS-induced bridge deformation is determined through numerical calculations that consider the bridge's structural and material properties. On this basis, the effects of bridge deformation caused by environmental loads on vehicle-bridge dynamic interaction are investigated in detail, and a new bridge pre-camber design method is proposed to counteract the effects of both environmental and train dynamic loads. Results indicate that the proposed model's simulations align well with field test data. The long-span bridge deformation induced by the environmental loads intensifies the dynamic responses of a running vehicle, particularly the wheel-rail vertical force and car-body vertical vibration. However, it has slight influence on train-induced bridge vibration. The proposed pre-camber design method for long-span bridges, which accounts for long-term environmental load action, effectively ensures good vehicle service performance. The research results could provide useful guidance for the design of long-span bridge systems. • An integrated dynamic model of the train-track-cable stayed bridge system is established and validated by the field test. • An effective methodology for reconstructing long-span bridge temperature is developed and validated by long-term monitoring data. • Effects of the ambient temperature load and CCCS load on the vehicle-long span bridge interaction are revealed. • A new pre-camber design method is proposed considering both dynamic train loads and long-term environmental effects. [ABSTRACT FROM AUTHOR]

Finite element model updating (FEMU) is a frequent method for minimizing the differences between actual and predicted bridge structural behavior. However, static model updating for long-span bridges usually requires load tests to obtain the response under known static loads, which is costly due to long traffic interruptions. To offset this disadvantage, a static FEMU method based on long-term monitoring data is proposed to update the model in real-time by taking stochastic traffic loads with certain statistical characteristics as known static loads. First, the theoretical relationship between stochastic traffic flow statistical characteristics, static response statistical characteristics, and structural stiffness parameters is established. An objective function based on the probability characteristics of the long-term vehicle-induced response is constructed. Then, the FEMU process based on monitoring data is introduced, including the acquisition of the finite element model vehicle-induced response, the extraction of the actual vehicle-induced response based on the monitoring data, the selection of model updating parameters, and the application of the global-local parameter updating optimization method. Finally, the effectiveness of the proposed method is verified by applying numerical examples and real bridge examples to a long-span suspension bridge. It can be concluded that the proposed method can achieve FEMU based on long-term monitoring data, avoiding the inconvenience and large cost caused by load tests. The accuracy and efficiency of the model updating can meet the engineering requirements well through comparison with the result of the traditional load test method. • This paper presents a static finite element model updating method based on the statistical characteristics of long-term monitoring data during normal operation, avoiding the inconvenience and large cost caused by the previous model updating method based on the load test. • The proposed method takes stochastic traffic load with known probability characteristics as known static load, and can realize model updating well by reducing the error of the actual response probability characteristics and finite element model prediction response probability characteristics. • The probabilistic characteristics of long-term vehicle-induced static response are related to structural stiffness parameters and probabilistic characteristics of stochastic traffic flow. When the probabilistic characteristics of stochastic traffic flow are the same, the static response probabilistic characteristics are related to only the structural stiffness parameters. [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]

In the wind tunnel test of a long-span bridge model, to ensure that the dynamic characteristics of the model can satisfy the test design requirements, it is particularly important to accurately identify the modal parameters of the model. First, the stochastic subspace identification algorithm was used to analyze the modal parameters of the model in the wind tunnel test; then, Grubbs criterion was introduced to effectively eliminate outliers in the damping ratio matrix. Stochastic subspace identification algorithm with Grubbs criterion improved the accuracy of the modal parameter identification and the ability to determine system matrix order and prevented the modal omissions caused by determining the stable condition of the damping ratio in the stability diagram. Finally, Oujiang Bridge was used as an example to verify the stochastic subspace identification algorithm with Grubbs criterion and compare with the results of the finite element method. The example shows that the improved method can be effectively applied to the modal parameter identification of bridges. [ABSTRACT FROM AUTHOR]

• Correlation of vibration data is found to be mode-related and traffic flow independent for linear time invariant bridges. • Vehicle load can be modeled as a uniformly modulated non-stationary process (UMNSP) under the invariant weight distribution. • RoMS is employed as correlation-based damage indicator under UMNSP assumption and proven effective in real-world application. Structural damage identification and condition assessment is the most direct goal in structural health monitoring (SHM). Vibration-based methods (VBM) using the global dynamic responses (displacement or acceleration), including modal-based methods and statistical methods, have been comprehensively investigated in the last few decades in the SHM community. These two types of methods face challenges in practice due to the indicators being sensitive to the environment and insensitive to local damage. It is curious whether new features of data in high-dimension space can be found and the new features can be used as damage indicators. This study proposes a method based on the correlation of the global dynamic responses in high dimensional space for damage identification. It is proved that the ratio of mean square (RoMS) between any two responses (two-dimensional space) is dependent on the modal parameters of the structure only and changes only with the damage of the structures. Therefore, it can be used as a damage indicator. The proposed method is validated through a finite element numerical analysis on a cable-stayed bridge and the monitored acceleration of a real-world suspension bridge, and is further compared with the modal analysis methods. The results show that the proposed method can accurately identify the damage and is sensitive to local damage compared to modal parameters. [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]

Introduction: During masticatory loading, dental bridges are subjected to various forces that might generate deflections in the bridge framework. For this reason, designing long-span bridges require great care about flexions that happen during the function. This can be compensated could be compensated by increasing occluso-gingival height, using rigid materials, and enhancing resistance to deflection by modifying the abutments' preparations. The current study hypothesied that the stress, deflection, strain, and deformation of the fixed partial dentures are guided by the three-dimensional configurations of the pontic areas, and all other parameters could be mutually changed with different influence on the overall outcome. Aim: The study aimed to evaluate the difference in the amount of stress, deflection, strain, and deformation on using different materials and configurations in the pontic and connector area of the dental bridge using the 3D Finite Element Analysis (FEA). Materials and Methods: An invitro virtual biomechanical analysis using 3D FEA method was conducted. 3D models were created from the Cone Beam Computed Tomography (CBCT) of a dentulous patient and two materials were selected for this study, Zirconia and enhanced graphene-based polymer. The study models were assembled into four groups as the following: Group I: 3-unit Zirconia fixed-fixed bridge; Group II: 3-unit Graphene fixed-fixed bridge; Group III: 4-unit Zirconia fixedfixed bridge; Group IV: 4-unit Graphene fixed-fixed bridge. Using FEA software a 600 N load was applied and the resultant normal stress, deflection, maximum equivalent strain and total deformation data were monitored, collected and interpreted. Results: The findings of the current study showed higher values of normal stress, deflection, equivalent elastic strain, and total deformation in Graphene-based bridges (group II and IV) than the Zirconia-based bridges (group I and III). It should also be mentioned that normal stress, deflection, equivalent elastic strain, and total deformation showed higher values in the threeunit bridge (group I and II) than their corresponding 4-unit bridge groups (group III and IV). Conclusion: This biomechanical analysis confirmed that the stress concentration and deflection of the fixed bridge are influenced by material characteristics. However, configuration of the pontic area could influence the studied mechanical parameters regardless the length of the dental bridge. [ABSTRACT FROM AUTHOR]

• An innovative precast concrete-encased concrete-filled steel tube column-to-column connection is proposed. • Five connection tests were conducted to investigate compression behaviour of the precast connection. • The proposed precast connection exhibited comparable compression resistance to continuous CECFST columns. • Comprehensive finite element modelling was performed to identify key variables that affect compression resistance of the connection. • A simplified analytical model was proposed to evaluate compression resistance of the precast connection. Concrete-encased concrete-filled steel tube (CECFST) is a new type of composite member featuring superior structural performance and high construction productivity. This form of structural members has been increasingly used as columns in high-rise buildings and as piers in long-span bridges. Recently, to promote the application of CECFST columns in countries short of labour, e.g., Singapore, North America and Europe, an advanced precast CECFST column-to-column connection with rapid construction and excellent tensile performance was developed by the authors. However, behaviour of the developed precast connection subjected to axial and eccentric compression has not been studied so far. In this paper, an experimental programme including five connection tests was conducted to investigate compression performance of the developed precast connection. The test results showed that compression resistance of the precast connection could achieve that of CECFST columns, indicating that it is feasible to connect CECFST columns by the newly proposed precast connection to enhance construction productivity. Furthermore, an extensive finite element (FE) modelling programme was carried out to generate more numerical data by conducting parametric studies. The experimental and numerical results showed that connection configuration plays a pivotal role in load-carrying capacity of the precast connection. Based on EN 1994-1-1, one simplified strength prediction model was proposed for the proposed precast CECFST column-to-column connection. Compared with experimental and numerical results, the predicted strength was conservative and consistent, indicating that the proposed approach can be used in the design of the precast connection. [ABSTRACT FROM AUTHOR]

• The numerical analysis method of tornado-induced vibration of the stay cable is developed. • The dynamic performance of the stay cable in the downburst and the tornado are compared. • The frequency characteristics of the cable vibration induced by small-scale extreme winds are investigated. The wind-induced vibration and its mitigation of ultra-long stay cables are critical to the safety of long-span bridges. Remarkable progress has been made in understanding and mitigating the vibration of stay cables in normal wind, while the cable response in small-scale extreme winds such as downbursts and tornadoes remains unclear. This study compares the dynamic performance of an ultra-long stay cable in a downburst and a tornado. Firstly, a downburst and its induced vibration of an ultra-long stay cable of a kilometer-level cable-stayed bridge are introduced based on the data recorded by the structural health monitoring system (SHMS). A tornado with the same intensity as the measured downburst is then simulated analytically at the bridge site. The tornado-induced vibration of the stay cable is obtained based on the finite element method. The dynamic performance of the cable under the downburst and the tornado, including the acceleration characteristics, displacement characteristics, and frequency characteristics, are investigated and compared. The result shows that large-amplitude cable vibration is found during the two extreme winds and the out-of-plane acceleration is larger than the in-plane acceleration. For the same wind intensity in this study, the acceleration of the cable caused by the downburst is much larger than that caused by the tornado. During the tornado, the in-plane displacement of the cable is much larger than the out-of-plane displacement, which is the opposite during the downburst. The frequency range of the cable vibration induced by the small-scale extreme winds is similar and it is about 2.5 ∼ 6 Hz, and the mode order is from the 10th to the 25th. [ABSTRACT FROM AUTHOR]

Highlights • Two scaled field tests in reticulated dome under blast loading were conducted. • The deformation modes of specimens were identified and discussed. • Strain rate sensitivity of material were considered in numerical evaluation. • The deformation history and energy absorption of the structure were also discussed. Abstract Long-span spatial structures are commonly used as landmarks in modern cities and may be potential targets of terrorist attacks; thus, it is important to study the dynamic behaviour of such structures under blast actions. In this study, experiments were conducted on two reduced-scale models which were designed and manufactured. The aims of the experiments were to (i) assess the accuracy of a numerical approach for simulating the structural dynamic responses based on the finite element software, "ANSYS/LS-DYNA", and (ii) survey the various failure modes of single-layer reticulated domes under an external blast loading. The numerical results showed a good agreement with the experiments when the empirical load model was used to study the elastic and inelastic deformation of a multi-curved shell. Additionally, the deformation, development of plasticity, and energy absorbing behaviour of each component were examined, and the following four major response patterns were identified: elastic vibration, slight damage, local failure, and global collapse. [ABSTRACT FROM AUTHOR]

Long-span suspension bridges are subjected to wind-induced vibrations due to their large flexibility and low damping. Damped outriggers have been proposed recently to supplement damping and suppress multimode vibrations of main girders of long-span bridges, e.g., vortex-induced vibrations. However, when installed at multiple positions including tower-girder junction points and girder ends to further improve multimode damping effect, damping effects of the damped outriggers are interdependent. Additionally, the frequency curves of adjacent modes with respect to varying parameters of the damping devices could approach and intersect with each other, making it difficult to track mode orders and modal damping variations in design optimization. This study therefore proposes an optimization method to design damped outrigger parameters for maximizing multimode damping of the bridge. First, the bridge with damped outriggers is modeled generally using finite element method for dynamic analysis. Subsequently, two critical issues in the design, i.e., the mode tracking and multi-objective optimization, are respectively addressed by using the modal assurance criterion and the genetic algorithm. The proposed method is then applied to the Xihoumen Bridge with a main span of 1650 m. The results show that through the proposed optimization, 6 out of 7 modes vulnerable to vortex-induced vibrations can reach a damping ratio over 1.0%, which cannot be achieved by using damped outriggers of a uniform size. Furthermore, the required damper coefficients are decreased by 49.4%. The flexibility of the outriggers has been considered in the design. The developed method is promising in the design of other types bridge damping devices, e.g., multiple tuned mass dampers. • A method proposed for optimizing multiple damped outriggers for a suspension bridge. • Mode tracking in optimization addressed using the Modal Assurance Criterion. • Damper size reduced by 50% through optimization in the case study of a suspension bridge. • Balanced damping improvement for multiple modes achieved through the optimization. [ABSTRACT FROM AUTHOR]

This paper presents a diagnostic case study of a long-span bridge, which uncovered the root cause of unsymmetric vibration performance that appeared to point to deterioration. In this case study, two iterations of the structural identification (St-Id) process were applied to (1) develop a comprehensive finite-element (FE) model (inclusive of approach spans) representative of the general dynamic properties (frequencies and mode shapes), and (2) check that the response magnitudes were consistent with those expected from vehicular traffic. More specifically, this research confirmed the perceived vibration discrepancy with direct measurements, conducted a comprehensive (including approach spans) ambient vibration monitoring of the bridge, updated an FE model to match measured modal parameters, and performed a series of simulations to both validate the updated model and understand the root cause of the unsymmetric vibrations. Through this process, it was determined that the unsymmetric vibrations resulted from the approach span designs, which provided significantly different levels of lateral stiffness to the primary bridge. Additionally, upon repeating the test following the replacement of all expansion bearings with neoprene bearings, similar levels of vibration asymmetry were observed, which further supported the diagnosis that this behavior is an inherent characteristic of the bridge. In addition to introducing an iterative St-Id process that makes use of both modal parameters and magnitude information (derived from an ambient vibration test), this paper illustrates the importance of explicitly including the approach spans within the St-Id of long-span bridges. In this case, ignoring the influence of the approach spans would likely have resulted in the erroneous conclusion that some damage or deterioration within the main spans was causing the unsymmetric vibrations observed. [ABSTRACT FROM AUTHOR]

Long-span bridges have low vibration frequencies and small intrinsic damping, and hence are subjected to large-amplitude vibrations, e.g., vortex-induced vibrations (VIVs), which jeopardize the serviceability and safety of the bridge structures. This study proposes a novel concept to supplement damping to such bridges for multimode vibration mitigation, by damping rotations of the bridge girder during vertical and torsional vibrations instead of translational displacements that have been previously the focus of relevant studies. A salient advantage of the concept is that bridge girder rotations near its ends are relatively large during vibrations enabling adequate supplemental damping and also convenient implementation. The concept is realized by a damped outrigger, consisting of a stiff outrigger rigidly connected to the bridge girder and horizontal dampers connecting the end of the outrigger to a bridge tower or a pier. A tensioned beam with rotational constraints is first used to demonstrate damping effects of damped outriggers on suspension bridges. Considering practical parameter ranges, the maximal damping ratio provided by one damped outrigger to a specific mode is about 1.0%. Influences of the relative importance of axial tension and bending stiffness and outrigger stiffness are studied. Furthermore, finite element analyses of an existing suspension bridge with damped outriggers are conducted to verify the damping performance. Numerical results show that by installing one damped outrigger, 6 out of 7 modes that have been involved in VIV events of the bridge can achieve a damping ratio of approximately 1.0% or above. By installing damped outriggers at the two towers, more modes can achieve a relatively large damping ratio, suggesting excellent performance of damped outriggers in suppressing multimode vibrations of long-span bridges. • Damped outriggers proposed for vibration mitigation of long-span bridges for the first time. • Damping effect studied via a simplified model of a suspension bridge with damped outriggers. • Excellent performance in multimode vibration mitigation verified via finite element analyses. • Demonstration via a case study of an existing long-span suspension bridge. [ABSTRACT FROM AUTHOR]

• A novel steel-concrete joint is proposed for long-span high-speed railway arch bridges. • The joint combines the shear connectors, steel skeleton with outsourcing concrete and diaphragm. • A model test of the proposed SCJ specimen with a scale of 1/5 was conducted and investigated. • A nonlinear finite element model of the SCJ was established with high accuracy. • The experimental and numerical results indicated great mechanical properties of the SCJ. Steel-concrete joint is often used to connect steel and concrete structures in bridge engineering. In this paper, a novel steel-concrete joint, consisting of shear connectors, steel skeleton with outsourcing concrete and solid concrete diaphragm, is proposed for long-span high-speed railway arch bridges. The joint has the advantage of convenient construction and the concrete diaphragm at joint can ensure the smooth stress transmission of the arch. The mechanical behavior of the steel-concrete joint is investigated by conducting a down-scale model test with a scale of 1/5 under four loading cases. The stress distributions and crack patterns of the experimental specimen model are listed and analyzed. Then based on the experimental results, a nonlinear finite element model of the steel-concrete joint is established. Utilizing the local stress analysis of the model, the stress concentration near the concrete corner could be decreased by reducing the inclination size of corner. The results indicate that the proposed steel-concrete joint shows great mechanic properties, as well as reasonable force transfer behavior without damage during loading. The test and analysis of the joint are expected to develop the design of steel-concrete joints in arch bridges with complex structural composition. [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]

• Investigate pounding performance of long-span girder bridges under earthquakes. • Seismic isolation bearings can reduce the probability of pounding by tuning responses of adjacent units. • Pounding is more likely to happen when considering near-fault motions and wave passage effect. For girder bridges located in regions with a high seismic hazard level, seismic isolation bearings are usually implemented to suppress the seismic inertial force transmitted from the superstructure to substructures, protecting the pier columns and foundations. However, whether potential pounding might happen for these seismic-isolated girder bridges between adjacent units are scarcely considered, especially for those with long spans where the wave passage effect is of great significance. This paper develops a finite element model for a typical hybrid truss-girder bridge, based on which the influence of seismic isolation bearings and wave passage effect on pounding is carefully investigated considering both near-fault and far-field motions. The results show that for this type of long-span girder bridges, pounding may happen even the adjacent bridge units are designed with similar vibration periods, especially when near-fault motions and wave passage effect are considered. Under non-uniform excitations with different apparent wave velocities, the employment of isolation bearings can reduce the relative displacement at expansion joints and thus improve the performance against pounding; however, the occurrence of pounding and damage of expansion joints cannot be fully avoided. Further, motions with lower apparent velocities generally correspond to more devastating responses, which should be particularly considered during engineering practice. [ABSTRACT FROM AUTHOR]

• Stress distributions, contact statuses and slip characteristics of strands and wires along arc contact paths in the saddle were explored. • Effects of pretension, applied load and coefficient of friction on contact and slip behaviors were investigated. • The friction and slip test rig between cable strands and saddle was established to explore slip characteristics, radial and tangential forces between strands and saddle. In order to ensure the anti-slip safety of main cable in the main saddle of long-span suspension bridge, contact and slip behaviors of main cable of the long-span suspension bridge were investigated in this study. Mechanical characteristics of main cable were explored according to statics theory. Finite element models were established to analyze effects of pretension, applied load and coefficient of friction on stress distributions, contact statuses and slip characteristics of strands/wires along arc contact paths in the saddle. A friction and slip test rig was developed to explore slip characteristics between strands and saddle in order to validate finite element models. The results show that there are micro slips at both ends and adhesion in the central region along the arc contact paths between strand/steel wire and saddle in all cases. The micro slips decrease with increasing pretension and coefficient of friction, and increase with increasing applied load. The strand and steel wire at the lower layer exhibit the easier gross slip and the larger difference between axial stresses at both ends as compared to those at the upper layer. The axial stress difference of strand increases with increasing pretension and coefficient of friction, respectively. The friction and slip tests show that the upper layer strand exhibits the larger maximum displacement amplitude corresponding to gross slip, and the tangential force increment of strand along the arc contact path decrease in the order: tight end, central location and loose end, which validates finite element models. [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]

Long-span metal culverts have been used for almost 50 years as an economical alternative to short-span bridges. Current design methods are based on two-dimensional finite element analysis using beam theory to represent the structure, or three-dimensional analysis employing orthotropic shell theory. However, neither analysis has been used to investigate the most critical position for trucks at the surface of long-span metal culverts. This paper shows results of three-dimensional finite element analysis, employing orthotropic shell theory and explicitly modeling the geometry of corrugated plates for a specific box culvert tested using a fully loaded dump truck. The analysis was then extended to study the effect of truck position on the response of long-span box and arch culverts. The finite element models, employing orthotropic shell theory and explicitly modeling the geometry of corrugated plates, successfully produced the behaviour of the culvert under truck loading for different truck positions. Culvert deformations were calculated within 7%-13% of the measured values at different locations. The bending moment at the crown was within 4%-17% of the values calculated using the measured strains. If three-dimensional finite element analysis is used to design these culverts, two design trucks should be considered (current design considers a single design truck). The highest moment or thrust is obtained when the truck tandem axles are located above the crown of the culvert. [ABSTRACT FROM AUTHOR]

Highlights: [•] Developed a multiple scale modeling scheme for orthotropic decks. [•] Verified the properties and responses of the equivalent orthotropic deck. [•] Provided a reasonable approach for long-span bridge performance modeling. [Copyright &y& Elsevier]

Structural identification (St-Id) of long-span bridges by ambient vibration testing provides a starting point for quantitatively characterizing the actual in-service mechanical characteristics and behaviors of these complex constructed systems. However, various uncertainties involved in the experimental and identification processes impact the reliability of St-Id, especially if vibration testing is the sole experiment. Such uncertainties represent perhaps the most fundamental barrier to more widespread applications of measurements in civil engineering practice. The goal of this paper is to leverage a vibration test of a long-span suspension bridge to illustrate a number of possible strategies for coping with the uncertainties confronted when identifying the dynamic characteristics of large-scale constructed systems. The design and implementation of a field test in the context of St-Id are first presented to illustrate how uncertainties can be mitigated by following a disciplined approach to designing the experiment. Next, data preprocessing strategies including data inspection, time window selection, band-pass filtering, averaging, and windowing are proposed to reduce data errors. Three separate postprocessing methods, including Peak Picking, PolyMAX, and Complex Mode Indicator Function, are executed independently to verify the reliability of the data processing results. Experimental results for both the towers and suspended spans are correlated with simulations from three-dimensional finite-element analysis of the long-span bridge for St-Id. [ABSTRACT FROM AUTHOR]

Abstract: Cable-arch bridge is a new type of hybrid bridge, and its development has great engineering significance. To understand the mechanical characteristics of cable-arch bridge, in the present work, a model cable-arch bridge was constructed, and its static behavior was investigated using the finite element method and experimental test. The analytical and experimental results were compared, and qualitatively good agreement has been exhibited. By considering the geometrical and/or material nonlinearity of the cable-arch bridge, the linear and nonlinear stability was studied further analytically. The results show that the cables and wind bracing have a significant influence on the mechanical behavior of the cable-arch bridge. Compared with arch bridges, the cable-arch bridge has a larger ultimate bearing capacity, a better in-plane and out-of-plane stability, and a superior capacity to resist various live loads. Such a cable-arch bridge should have a bright future in the development of long-span bridges. [Copyright &y& Elsevier]

Abstract: A post-tensioned negative moment connection technique is proposed to strengthen old multiple span simply-supported T-section reinforced concrete (RC) girders. In this technique, old concrete is removed from girder ends and flanges, a diaphragm is placed between the two adjacent girder ends over the interior support and negative moment steel strands are installed in new cast-in-place concrete and post-tensioned to make continuity. A total of six two-span simply-supported T-section RC girders were cast and five of them strengthened using the provision of the proposed post-tensioned negative moment connections. Both laboratory tests and nonlinear finite element (FE) analysis were conducted to investigate the structural performance of the strengthened RC girders. The moment redistribution in the strengthened continuous RC girders was also measured and is discussed. It is shown that the proposed post-tensioned moment connection technique can reliably transfer the negative moment over the support and markedly increase member stiffness and the load-carrying capacity of existing multiple span simply-supported RC girders. The validity of the FE analysis was also demonstrated through comparisons with experimental results. [Copyright &y& Elsevier]

Abstract: This paper introduces new types of cable-stayed bridges with carbon fiber reinforced polymers (CFRP) stay cables and/or a CFRP bridge deck. For each of the two CFRP components, namely, CFRP stay cables and CFRP bridge deck, the key design parameters and design strategies were determined and the appropriate value of each key design parameter was suggested. Using the suggested parameter values, six types of cable-stayed bridges with a main span length of 1400 m were selected and modeled with the finite element method, through which the procedures of designing composite cable-stayed bridges with CFRP components were presented in details. From a mechanical-behavior viewpoint (static and dynamic) a comparative study of composite cable-stayed bridges with different CFRP components was performed through numerical simulations. The economical behavior of each type of cable-stayed bridges was also comparatively studied considering the varying material price. With the high strength-to-weight ratio and other advantages of CFRP materials, it was proven in this study that the use of CFRP stay cables and CFRP bridge decks in super long span cable-stayed bridges is feasible and these types of composite cable-stayed bridges could become an excellent alternative to steel cable-stayed bridges where super long spans are desired. [Copyright &y& Elsevier]

Stochastic seismic analysis of long-span bridges with Carbon fibre reinforced polymer (CFRP) cables are presented in this study through combination of the advantages of the perturbation based stochastic finite element method (SFEM) and Monte Carlo simulation (MCS) method. Jindo cable-stayed and Fatih Sultan Mehmet (Second Bosporus) suspension bridges are chosen as an example. Carbon fibre reinforced polymer cable (CFRP) and steel cables are used separately, in which the cable’s cross sectional area is determined by the principle equivalent axial stiffness. Geometric nonlinear effects are considered in the analysis. Uncertainties in the material are taken into account and Kocaeli earthquake in 1999 is chosen as a ground motion. The efficiency and accuracy of the proposed algorithm are validated by comparing with results of MCS method. It can be stated that using of CFRP cables in long-span bridges subjected to earthquake forces is feasible. [ABSTRACT FROM AUTHOR]

• A novel approach for alleviating the mid-tower effect of the multi-tower suspension bridges. • A simplified model for three-tower suspension bridge with central buckle. • The feasible dimensionless stiffness range for the mid-tower was obtained. Compared with traditional two-tower suspension bridges, three-tower suspension bridges have to face challenges caused by the mid-tower effect, which requires the stiffness of the mid-tower satisfying two contradictory parameters, the deflection-to-span and the saddle sliding resistance coefficient, simultaneously. Meanwhile, the central buckles are often utilized to reduce the live load deflection and the torsional vibration caused by wind in two-tower suspension bridges. This study proposes an analytical model for predicting the structural responses of three-tower suspension bridges with central buckle under vehicle loads and examines the effect of the central buckle on suppressing the mid-tower effect. The analytical model simplifies the bridge as a series of cables with horizontal spring constraints. The validation analysis based on the structural parameters of the Yingwuzhou Yangtze River Bridge using the nonlinear finite element method demonstrates that the error of the proposed model does not exceed 5%. The parametric investigations show that the central buckle can significantly improve the performance of three-tower suspension bridges by enhancing their stiffness and reducing the unbalanced tension of the main cable on both sides of the mid-tower. Three-tower suspension bridge with central buckle has a much wider feasible mid-tower stiffness range than that of the traditional three-tower suspension bridges, and the critical dead-to-live load ratio for the feasible dimensionless stiffness range has decreased from 6.7 to 4.4. [ABSTRACT FROM AUTHOR]

[Display omitted] • The derived formulas are very easy to use by engineers and other practitioners. • The proposed approach is applicable to ground- and self-anchored suspension bridges. • The sag effect of the side-span cable on the global thermal deformation is quantified. • The interaction of thermal deformations of main- and side-span cables is revealed. • The proposed formulas are verified by eight long-span suspension bridges worldwide. Deformation of a long-span suspension bridge is mainly caused by ambient temperature changes. The temperature-induced deformation of a bridge is usually calculated using complex three-dimensional finite element analysis, the mechanism of which is often unclear. In this study, we derive general, succinct analytical formulas of the thermal deformation of three-span suspension bridges. The deformation of different components is unified into a one-dimensional thermal expansion formula (δ L = L E θ · δ T) by introducing an equivalent length L E. The sag effect of side-span cables is characterized by the modification coefficients, which demonstrate that the neglect of the sag effect overestimates the thermal deformation. Furthermore, the thermal deformation of the main- and side-span cables and towers is found to interact with each other as a result of the cable tension changes with varying temperature. The analytical formulas are validated using eight long-span suspension bridges including the Akashi Kaikyo bridge, the longest main-span suspension bridge in the world. The closed-form solutions herein also apply to the self-anchored suspension bridges. [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]