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The deformation of the main girder is an important manifestation of the overall stiffness of suspension bridges, which is essential for assessing bridge performance. Nevertheless, it is difficult to achieve satisfied prediction without fully considering the overall operational loads. To this end, this paper proposes a method to predict the deflection considering multiple operational loads using the monitoring data of a high‐speed rail‐cum‐road suspension bridge. Initially, an improved Gaussian process regression (GPR) model utilizing Bayesian optimization was employed to predict the deformation of the main girder under the condition of nontrain loads. Furthermore, the distinct contributions of temperature, wind, and vehicle load were analyzed. Subsequently, based on the strain and deflection induced by train loads, the sum of sinusoids method was proposed to construct fitting and shape function (FSF) for predicting the main girder deformation under the influence of train loads. Ultimately, the deformation considering overall loads was obtained by adding the deformation under the nontrain and train loads, and the predicted deformation result was verified using the measured data. When compared to other state‐of‐the‐art machine learning algorithms, namely, artificial neural network (ANN), support vector machine (SVM), and decision tree (DT), the improved GPR demonstrates the highest accuracy in predicting the deformation of the main girder under nontrain loads with R2 of 0.9478. In addition, the proposed sum of sinusoids FSF method accurately predicted the deformation of the main girder caused by train loads, with R2 of 0.934. The deformation of the main girder under the influence of overall loads can lay a foundation for the early warning and evaluation of the suspension bridges. [ABSTRACT FROM AUTHOR]

The deflection control of the main girder in suspension bridges, as flexible structures, is critically important during their operation. To predict the vertical deflection of existing suspension bridge girders under the combined effects of stochastic traffic loads and environmental temperature, this paper proposes an integrated deflection interval prediction method based on a Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), a probability density estimation layer, and bridge monitoring data. A time-series training dataset consisting of environmental temperature, vehicle load, and deflection monitoring data was built based on bridge health monitoring data. The CNN-LSTM combined layer is used to capture both local features and long-term dependencies in the time series. A Gaussian distribution (GD) is adopted as the probability density function, and its parameters are estimated using the maximum likelihood method, which outputs the optimal deflection prediction and probability intervals. Furthermore, this paper proposes a method for identifying abnormal deflections of the main girder in existing suspension bridges and establishes warning thresholds. This study indicates that, for short time scales, the CNN-LSTM-GD model achieves a 47.22% improvement in Root Mean Squared Error (RMSE) and a 12.37% increase in the coefficient of determination ( R 2 ) compared to the LSTM model. When compared to the CNN-LSTM model, it shows an improvement of 28.30% in RMSE and 6.55% in R 2 . For long time scales, the CNN-LSTM-GD model shows a 54.40% improvement in RMSE and a 10.22% increase in R 2 compared to the LSTM model. Compared to the CNN-LSTM model, it improves RMSE by 38.43% and R 2 by 5.31%. This model is instrumental in more accurately identifying abnormal deflections and determining deflection thresholds, making it applicable to bridge deflection early-warning systems. [ABSTRACT FROM AUTHOR]

The design of suspension bridges predominantly emphasizes wind and earthquake loads, frequently overlooking the consideration of extreme events in the design stage, thus posing a threat to bridge safety. The purpose of this research is to spread awareness among engineers for identifying weak zones in a bridge and to provide a new insight into how much damaging the blast loading could be for the long-span suspension bridges if not designed properly under the blast loads. The current dynamic analysis procedures for bridges under blast loads are complex and computationally expensive, making them unsuitable, especially for long-span bridges. To address this, a simplified dynamic analysis approach is proposed to assess the structural response and extreme limit state of suspension bridges exposed to blast loads. The method involves a bilayer solution: blast loading is modeled as nodal loads, and the structural aspect is represented by a three-dimensional (3D) fishbone skeleton finite-element (FE) model. Time-history simulations of blast loads are conducted for various bridge locations and explosive sizes. The parametric dynamic analysis reveals that the tower top node is the most vulnerable location in the suspension bridge under blast loads, which potentially exceeds the stress limits of nearby main cable elements and triggers the zipper-type progressive failure of the entire suspension bridge. Similarly, blasting at the deck nodes nearby tower on the main span side as well as on the side span side significantly amplifies axial stresses in nearby suspenders and the main cable, i.e., demand-to-capacity ratios of C18 and C19 surpass unity under BS4-6W and BS4-8W, respectively confirming that the failure state has reached for C18 and C19 under medium- to large-sized explosives. Therefore, it is recommended that the maximum demand-to-capacity ratio for all bridge components under medium- to large-sized explosives shall be kept below 0.8 to ensure the safety of the entire structure under extreme limit state. Practical Applications: This paper provides a methodology to investigate the structural redundancy of suspension bridges under extreme limit state by providing a bilayer solution: the blast aspect, which is simulated as nodal loads on the bridge road surface and the structural aspect, is simulated as a 3D fishbone skeleton FE model. The implicit dynamic analysis approach is adopted parametrically by considering variable explosive weights and locations. For each blast scenario, the time-history of nodal loads is applied to various locations of the bridge considering small- to large-sized blasts. From a practical viewpoint, this study is relevant to develop comprehensive understanding of the dynamic behavior exhibited by long-span bridges when subjected to extreme loading scenarios. In essence, the aim is to explore the benefits and applicability of this research to the design of long-span bridges under blast loading conditions. The simplified approach presented in this paper, along with the corresponding bridge response results, allows a bridge design engineer to analyze a suspension bridge effortlessly. This method eliminates the need for intricate computations required to assess blast pressure over a solid bridge model, enabling a straightforward visualization of the anticipated behavior under blast loading. The research serves a crucial role in checking and verifying the extreme limit state, in addition to assessing the serviceability and ultimate limit states according to AASHTO's requirements. For existing suspension bridges, the study proves beneficial in formulating a comprehensive blast-resistant plan through retrofitting and strengthening identified weak zones. Consequently, this research holds practical significance, serving as a foundation for further exploration and investigation into the effects of blast loading on various types of long-span bridges. [ABSTRACT FROM AUTHOR]

Translation abstract Wind‐induced vibrations on the hangers of the ÖBB‐RheinbrückeThe ÖBB‐Rheinbrücke near Lustenau is a new type of steel‐concrete composite arch structure with a span of 102 m. The main supporting structure is a Langer's beam with twelve round steel hangers on each side of the bridge, each 100 mm in diameter, with a maximum hanger length of 18.9 m. In arch bridges of this type with steel hangers, wind‐induced hanger vibrations can cause high‐frequency, high‐amplitude stress fluctuations in the hangers and their connections. This can be problematic from a fatigue point of view. After completion of the bridge, extensive monitoring was carried out as planned with the aim of obtaining information about the hanger vibrations that occur and the resulting damage to the material in order to determine whether vibration‐reducing measures need to be taken. In the course of monitoring and evaluation, it was found that wind‐induced hanger vibrations can cause fatigue‐relevant stress ranges to occur. This article presents the effects of two different physical phenomena, such as vortex‐excited transverse vibrations and rain‐wind‐induced vibrations, on the service life of the structure, as well as vibration‐reducing measures that help to mitigate these effects. [ABSTRACT FROM AUTHOR]

Generalized structural and aerodynamic torsional stiffness of a suspension bridge with a main span length of 3000m are discussed first qualitatively in terms of analytical models. Two torsional divergence (TD) modes, symmetric and asymmetric, are compared in terms of the evolution of generalized torsional stiffness properties. It demonstrates that symmetric TD occurs prior to the asymmetric TD in a vast range of main span lengths. Numerical simulations of TD are then performed by the static finite element (FE) method. The results turn out a much lower critical wind speed of TD presented by the analytical model, due to stiffness degradation caused by main cable deformations. Finally, the effects of two types of countermeasures are examined. The replacement of the original deck section by a central slotted one can boost the critical wind speed of TD by 30%. Widening the main cable spacing enhances almost linearly the system’s critical wind speed. A combined countermeasure of a slotted bridge deck and widened main cable spacing stabilizes substantially the system’s aerodynamic static stability, resulting in a 45% increase in the critical wind speed of TD. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Applied Mechanics is the property of Chinese Journal of Applied Mechanics 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.)

This study aims to address the complexities in the calculation of the tangent stiffness matrix and the issues of divergence in iterative calculations in the shape-finding process of existing suspension bridge main cables. The research investigates the factors influencing the computational errors of existing cable element theories and the convergence or divergence of the main cable shape-finding calculations. First, a nonlinear equation for calculating the height of the cable element is constructed. Subsequently, a formula for cable height calculation is established according to the differential equations of the deformed cable element. Finally, considering the mass conservation principle before and after the cable deformation, a nonlinear system of equations for the configuration of the cable element is derived. Given the symmetric nature of the mid-span structure and loading in most suspension bridges, it is inferred that the point of the lowest slope of the main cable in the completed bridge state serves as the symmetry center of the structure. Consequently, a symmetric main cable shape-finding method is developed. A comparative analysis between the proposed method and existing iterative methods was conducted in terms of calculation accuracy and convergence behavior. The results indicate that the difference in horizontal cable force at the IP point between the two methods is 1.9 kN, and the difference in unstressed length is 2.5 mm. The calculation efficiency of the symmetric main cable shape-finding method is more than twice that of traditional iterative algorithms, with the number of iterations required for convergence generally being lower than that of traditional methods. For initial values that cause divergence in traditional iterative methods, the symmetric main cable shape-finding method achieved convergence within 10 iterations. The derived cable element theory and the symmetric main cable shape-finding calculation method can lay a theoretical foundation for the refined and efficient calculation of the main cable shape-finding process. [ABSTRACT FROM AUTHOR]

Continuous structural health monitoring of long-span bridges, such as suspension bridges, is essential for ensuring stability, and various efforts have been undertaken towards this goal. The hanger cables of suspension bridges play a crucial role in transmitting the main loads within the cable support structure. Therefore, monitoring the tension of hanger cables is vital for maintaining structural stability. Traditionally, the vibration method has been utilized for operational suspension bridges to indirectly estimate the tension of suspension bridge hanger cables. This method involves measuring the natural frequencies for vibration modes from the cables and their geometric conditions. In this study, digital camcorders and tripods were employed to measure the hanger cable response conveniently and efficiently. The response measured by digital camcorders is displacement based, posing challenges in measuring the natural frequencies for high-order modes required by the vibration method. Typically, systems for measuring structural response incorporate white noise components across all frequency domains, complicating the identification of cable frequency component characteristics when the response frequency measured by a digital camcorder is lower than the white noise frequency. Furthermore, measurements taken with a digital camcorder may suffer from low resolution due to long distances and optical limitations, hindering the measurement of high-frequency response components. To address these challenges, this study introduced a back analysis method to estimate tension using the natural frequencies of low-order modes. The method defines the difference between measured natural frequencies and those predicted by finite-element analysis as the error function. Optimization was then conducted using the univariate search method to minimize this error function. The findings suggest that the tension estimated by applying only the first natural frequency of hanger cables through the back analysis method closely aligns with estimates obtained using the vibration method. This research highlights the potential of using standard digital camcorders as an accurate and cost-effective means for estimating hanger cable tension. [ABSTRACT FROM AUTHOR]

Extensive vehicle fires threatening suspension bridges in the last decade have aroused an emerging demand to estimate the fire safety of hanger systems. One of the paramount tasks for evaluating the fire resistance of hangers is to calculate their temperatures. However, as plans always lag behind events, no competent temperature calculation methods are available now for engineers, whether vehicle fire models, thermal boundaries on hanger surfaces, or cross-sectional heat transfer formulations. This paper addresses these three issues and then proposes an integrated framework for assessing the thermal response of hanger systems subjected to vehicle fires. Vehicular fires were classified into five grades, adapted to cars, buses, light goods trucks, medium goods trucks, and tanker trucks, respectively. This hierarchy was validated using 16 full-scale vehicle fire tests in opening or tunnel conditions. An empirical formulation of thermal radiation developed for pool fires was adopted to envelope the heat flux applied by passenger vehicle fires on the hanger surface and was validated using five tests. Radiation from truck fires was constructed using a cuboid solid radiative flame. The spatial heat fluxes surrounding Grade-5 vehicle fires typified by tanker fires were computed using the computational fluid dynamics method validated by two large-scale outdoor trench fires. With these quantitative thermal boundaries on hanger exteriors, the transient temperature across the hanger section was derived using the lumped capacitance method, validated by finite-element models in various scenarios. As a multigrade temperature estimation methodology proposed for hangers subjected to vehicle fires, this method is easy to implement. It can serve in future structural fire design of critical suspension bridges with high exposure risks to vehicle fires. [ABSTRACT FROM AUTHOR]

During suspension bridge erection, tensions in its anchor span strands undergo continuous changes until the completed bridge state is attained. Calculating the precise tension values in the anchor span strands is critical to ensure the structural safety of the entire bridge under construction. To this end, an analytical method is proposed to determine the actual tensions in anchor span strands at the strand erection and tensioning stage, during which a temporary constraint on the splay saddle is removed as appropriate, and the resulting coupling relationship between strand tensioning and splay saddle rotation is considered. Then, based on the condition for moment equilibrium acting on the splay saddle, we determine the timing for letting the splay saddle stand on its own and the deflection angle of the splay saddle between the position with temporary constraint and that in the free-cable state. Further, the actual tensions in the anchor span strands are estimated during bridge erection. The proposed method ensures that the values of strand tensions and splay saddle position with all strands tensioned coincide with those required for the free-cable state. The innovation of this study is that it permits one to avoid the strand tension adjustment after tensioning the strands according to the values calculated by the proposed method. The performed calculations prove that strand tensions on the left and right sides are symmetrical before the temporary constraint of the splay saddle is removed and asymmetrical after this event. However, for the same layer of strands, the tensions on the two sides still tend to be symmetrical. The proposed analytical method is user-friendly and reliable, which was verified by a case study. [ABSTRACT FROM AUTHOR]

This study investigated the nonlinear dynamic behavior of suspension bridge subjected to multi-frequency boundary excitations. Firstly, the nonlinear dynamic model of the suspension bridge subjected to multi-frequency boundary excitations is established. The in-plane vibration equations are derived based on Hamilton's principle, taking into account the effects of geometric nonlinearity of the girder-deck and main cable as well as the stiffness of hangers. Secondly, the Galerkin method is used to solve for the frequencies and corresponding mode shape functions. Thirdly, the corresponding modulation equations are obtained based on the multiple scales method, and the 3:1 internal resonance between two symmetrical modes is analyzed. Combined with numerical analysis, the nonlinear dynamic behavior between modes of the suspension bridge is demonstrated through the frequency–response, force–response, and time history curves. The results indicate that the drift phenomenon appears when perturbing the amplitude and frequency of the different excitations, and the system exhibits intricate dynamic responses. [ABSTRACT FROM AUTHOR]

In this article, we study a mathematical model for a one-dimensional suspension bridge problem with nonlinear damping. The model takes into consideration the vibration of the bridge deck in the vertical plane and main cable from which the bridge deck is suspended by the suspenders. We use the multiplier method to establish explicit and generalized decay results, without imposing restrictive growth assumption near the origin on the damping terms. Our results substantially improve, extend, and generalize some earlier related results in the literature.

Copyright of Journal of Southeast University / Dongnan Daxue Xuebao is the property of Journal of Southeast University 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.)

Suspension bridges are the most common type of bridge used to cross the ocean. The cable clamps in suspension bridges clamp the main cables by bolt preload, but the elastic interaction of the bolts reduces the preload, which is detrimental to the force in suspension bridges. However, research on the factors influencing the elastic interaction of cable clamp bolts in suspension bridges is currently limited. This paper aims to explore the law of influence of external factors on the elastic interaction of bolts through a combined approach of theoretical analysis, full-scale experiment, and finite element simulation. The results indicate that the average preload loss was reduced by about 27% when the elastic modulus was increased by about 110%. The average preload loss was reduced by about 45% when the bolt center distance was increased by 75%. The number of bolts has a small effect on the elastic interaction, which can be ignored. When the preload of bolt installation was increased by 133%, the average preload loss was reduced by approximately 125%, which was almost a linear relationship. Tightening the bolt from the center bolt creates greater elastic interaction. The conclusions can provide suggestions for reducing the elastic interaction of bolts in the design and construction of suspension bridge cable clamps. [ABSTRACT FROM AUTHOR]

In a suspension bridge, slippage may occur at the saddle–cable interface during an earthquake. A refined finite element model of the saddle–cable interface is proposed which considers the compressive force and friction force at the curved contact surface. To investigate the saddle–cable slippage during an earthquake, the finite element model of a suspension bridge was built, and nonlinear time history analysis was conducted. Furthermore, the effects of the friction coefficient at the saddle–cable interface, the pounding between the suspension bridge and the approach bridges, the fluid viscous damper, and the rigid central buckle were evaluated by parametric analysis. The result shows that the saddle–cable slippage affects the overall seismic response of the suspension bridge slightly. The saddle–cable slippage is affected significantly by the friction coefficient of the saddle–cable interface, fluid viscous damper, and the rigid central buckle. [ABSTRACT FROM AUTHOR]

The First Egongyan Bridge in Chongqing, China was opened to traffic on December 27, 2000. It carries six-lanes of city traffic and two pedestrian paths, one on each side. It is a 600 m span suspension bridge. It was planned that the two pedestrian paths might eventually be converted to transit tracks in the future. However, with the rapid increase in urban traffic, the deck was transformed into an 8-lane bridge instead. Therefore, a new bridge parallel and adjacent to the old bridge was built for the rail transit. For aesthetic reasons, the city decided that the new bridge should also be a suspension bridge, with the same span length and tower height as the first bridge. The First Egongyan Bridge was a true suspension bridge with main cables anchored to ground anchors. However, the new bridge bridge's proximity to the first bridge necessitated the construction of a self-anchored suspension bridge that did away with a second set of ground anchors. This 600 m span happened to be the world's longest span for a self-anchored suspension bridge. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department 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 deformation of long-span suspension bridges in multiple loads is an important indictor to reflect their operation state. However, the correlation between multiple loads and structural deformation is difficult to quantify. Therefore, this study proposes an explainable machine learning model for the load-deformation correlation in long-span suspension bridges using eXtreme Gradient Boosting (XGBoost) and SHapley Additive exPlanations (SHAP). Firstly, the structural health monitoring system for a suspension bridge was used to construct the dataset for the training and testing of XGBoost model. Herein, temperature, wind and vehicle loads were used as the input variables, while midspan deflections and expansion joint displacements were treated as outputs. Subsequently, the hyperparameters of XGBoost model were optimized using grid search and 5-fold cross-validation to ensure its prediction performance. Then, the prediction results were compared with other four machine learning methods (i.e., linear regression, artificial neural networks, gradient boosted decision trees and CatBoost). Finally, the correlation between different loads and displacement responses were explained by the SHAP method to identify the contribution of the loads on deformation. The results show that the XGBoost model has the highest prediction accuracy. Compared to vehicle and wind loads, temperature significantly affects the deformation of long-span suspension bridges during daily operation. The effects of temperature and wind on bridge deformation are independent, and there is no significant interaction between these two factors.

Copyright of Journal of Southeast University (English Edition) is the property of Journal of Southeast University 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.)

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.)

In this paper, we discuss the asymptotic behavior of a linear problem that describes the vibrations of a coupled suspension bridge. The single-span road-bed is modeled as an extensible thermoelastic damped beam, which is simply supported at the ends. The heat conduction is governed by Cattaneo's law. The main cable is modeled as a damped string and is connected to the road-bed by a distributed system of one-sided elastic springs. First, utilizing the theory of semigroups, we prove the existence and uniqueness of the solution. Second, by constructing an appropriate Lyapunov functional, we establish exponential stability using the energy method. Numerically, we introduce fully discrete approximations based on the finite-element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. Then, we show that the discrete energy decays, and a priori error estimates are established. Finally, some numerical simulations are presented to show the accuracy of the algorithm and the behavior of the solution. [ABSTRACT FROM AUTHOR]

AbstractThe pile-caisson composite structure (PCCS) is an innovative underground anchorage foundation used to support large-span suspension bridges. This paper presents the displacement and the load transfer mechanism of the PCCS. The bearing responses of each individual pile in the PCCS were analyzed employing the finite element method, which was verified by the model test results. The peak bending moments borne by pile P11 and pile P53 in the PCCS exhibit the most significant disparity, with a difference that can reach up to 133.97%. Moreover, a parametric study utilizing numerical simulations indicates that augmenting the pile diameter and length, while reducing the pile spacing, can mitigate the displacements of the PCCS. However, there is an upper limit (i.e. S = 3.5d) for the pile spacing beyond which marginal benefits could be obtained. The findings of this study can provide guidance for the design and construction of the PCCS. [ABSTRACT FROM AUTHOR]

High-speed railway suspension bridges (HSRSBs) have been constructed with the new advancements in technology. The deformation prediction for HSRSBs is essential to their safety and maintenance. The conventional prediction methods are developed for bridges without high-speed railway. Different factors, including temperature (TEMP), time delay compensation (TDC), train live load (TLL), are considered in these methods. However, the train side (TS) and train instantaneous position (TIP) have a significant impact on deformation for HSRSBs, and they are not used in the prediction. More importantly, the coupling issue among different factors is so significant that it cannot be neglected. In this study, we propose a deformation prediction model based on a backpropagation (BP) neural network. This model uses different factors as model input, including TEMP, TDC, TLL, TS, and TIP. The coupling issue is addressed by using the new model. The new model was evaluated using a dataset of 10-day field measurements. It achieves a mean absolute error (MAE) of 8.81 mm, a mean relative error (MRE) of 9.82%, and coefficient of determination (R2) of 0.94. The new model will provide high-precision prediction for deformation and will be used in the development of an early warning system. [ABSTRACT FROM AUTHOR]

Fatigue cracks were found at the diaphragm cutouts in the orthotropic steel deck (OSD) of a self-anchored suspension bridge while the in-service time of the bridge was less than 10 years. The causes of fatigue cracks of the diaphragm cutout are investigated in this study. The fatigue cracks initiated from the intersections of the arc curves and the straight lines, which form the geometrical discontinuity to the cutout edge. The in situ monitoring and finite element analysis under fatigue load model indicate that the cracking region in the cutout is in bidirectional compression. However, the thermal-structural analysis and tests show that the rib-to-diaphragm welding process produces high tension residual stress at the cracking points of the cutouts. The cutouts are under tension-compression cyclic loading because of the coupled stress, which is derived from the vehicle-induced stress and the welding residual stress. The results show that the strain energy method can present a reasonable fatigue life estimation for the diaphragm cutouts with full consideration of the residual stress. [ABSTRACT FROM AUTHOR]

A key component of infrastructure seismic risk assessment is the execution of nonlinear time-history analyses with a suite of selected ground motions scaled to site-specific spectra. When interested in the evaluation of distributed systems residing near major active faults, such an approach is challenged by the scarcity of records adequately incorporating region and site-specific features known to impact the nonlinear response of distributed infrastructure substantially (pulses, spectral shape, spatial variability). This paper assesses the differences in the seismic demand posed to a suspension bridge as obtained from real ground motions selected based on state-of-the-art methods and arrays of site-specific simulated ground motions generated from physics-based wave-propagation models. The objective is to characterize the biases in structural response estimates introduced by the use of real ground motions in code-compliant approaches. A total of 15 realizations of an M7 Hayward fault earthquake and a detailed nonlinear simulation model representative of the West San Francisco–Oakland Bay Bridge are utilized as a case study. Damage limit states associated with structural drifts are defined for each bridge component as a function of the spread of plasticity. The results indicate that the median and variability of the demands posed by the simulated motions and real ground motions scaled to the same site-specific spectra are markedly different. Evidence from this study highlights the sensitivity of complex structures to multiple characteristics of the ground motions that might be biased by current scaling methods. Finally, fundamental characteristics of the scaled records leading to differences in the bridge response are discussed providing the basis to inform current ground motion selection and scaling procedures. [ABSTRACT FROM AUTHOR]

The pull-out method is a simple and effective method for detecting the preload of suspension bridge cable clamp bolts. However, research on the pull-out method is currently limited. The force principles governing the bolt during the pulling process are unclear, and the relationship between tension force and the desired preload remains uncertain. This paper aims to explore the force principles of bolts during the pull-out method detection process through a combined approach of theoretical analysis, full-scale test, and finite element simulation. The results indicate that the bolt preload increases during the pulling process. The preload detected by the pull-out method is not the initial preload of the bolt, but rather it exceeds the initial preload. The force relationships among various components are determined as follows: the preload subtracts the change value of the force exerted by the nut at the tension end, which equals the change value of tension force. Additionally, an analysis of the impact of the length of the bolt clamping section and the bolt area on the preload was conducted. Under the same bolt area, a shorter clamping section length corresponds to a greater increase in preload. With the same clamping section length, the increment of preload increases with the bolt area. These findings can serve as references for detecting and specifying the preload of the bolts. [ABSTRACT FROM AUTHOR]

Diaphragm walls have been widely applied in long-span suspension bridges due to superior mechanical performance and extensive adaptability to various geological conditions. However, limited studies focused on the structural behaviour of rigid joints for diaphragm walls. This paper hence presented the flexural performance of joints through experimental investigation and numerical analysis. Two types of joints were designed to compare the structural response in terms of failure modes and moment resistance. Parametric analysis was carried out to explore critical parameters that influenced the joint performance significantly. A related provision in a current design code was evaluated to check if it was compatible to predict the moment capacity of designed joints. Results suggested that concrete cracks dominated the moment resistance of joints, and numerical analysis was reliable to predict the damage development as well as the moment-deflection relationship. The joint with U-shaped rebar exhibited more excellent performance that the counterpart with C-T lock. The critical parameters that could affect the member behaviour consisted of reinforcement strength, reinforcement diameter and a distance between tensile reinforcement and beam edge. The current design code provided nonconservative estimations of moment capacity, and thus a reduction factor should be proposed to promote satisfactory application.

The deflection control of the main girder in suspension bridges, as flexible structures, is critically important during their operation. To predict the vertical deflection of existing suspension bridge girders under the combined effects of stochastic traffic loads and environmental temperature, this paper proposes an integrated deflection interval prediction method based on a Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), a probability density estimation layer, and bridge monitoring data. A time-series training dataset consisting of environmental temperature, vehicle load, and deflection monitoring data was built based on bridge health monitoring data. The CNN-LSTM combined layer is used to capture both local features and long-term dependencies in the time series. A Gaussian distribution (GD) is adopted as the probability density function, and its parameters are estimated using the maximum likelihood method, which outputs the optimal deflection prediction and probability intervals. Furthermore, this paper proposes a method for identifying abnormal deflections of the main girder in existing suspension bridges and establishes warning thresholds. This study indicates that, for short time scales, the CNN-LSTM-GD model achieves a 47.22% improvement in Root Mean Squared Error (RMSE) and a 12.37% increase in the coefficient of determination (R2) compared to the LSTM model. When compared to the CNN-LSTM model, it shows an improvement of 28.30% in RMSE and 6.55% in R2. For long time scales, the CNN-LSTM-GD model shows a 54.40% improvement in RMSE and a 10.22% increase in R2 compared to the LSTM model. Compared to the CNN-LSTM model, it improves RMSE by 38.43% and R2 by 5.31%. This model is instrumental in more accurately identifying abnormal deflections and determining deflection thresholds, making it applicable to bridge deflection early-warning systems.

This study aims to address the complexities in the calculation of the tangent stiffness matrix and the issues of divergence in iterative calculations in the shape-finding process of existing suspension bridge main cables. The research investigates the factors influencing the computational errors of existing cable element theories and the convergence or divergence of the main cable shape-finding calculations. First, a nonlinear equation for calculating the height of the cable element is constructed. Subsequently, a formula for cable height calculation is established according to the differential equations of the deformed cable element. Finally, considering the mass conservation principle before and after the cable deformation, a nonlinear system of equations for the configuration of the cable element is derived. Given the symmetric nature of the mid-span structure and loading in most suspension bridges, it is inferred that the point of the lowest slope of the main cable in the completed bridge state serves as the symmetry center of the structure. Consequently, a symmetric main cable shape-finding method is developed. A comparative analysis between the proposed method and existing iterative methods was conducted in terms of calculation accuracy and convergence behavior. The results indicate that the difference in horizontal cable force at the IP point between the two methods is 1.9 kN, and the difference in unstressed length is 2.5 mm. The calculation efficiency of the symmetric main cable shape-finding method is more than twice that of traditional iterative algorithms, with the number of iterations required for convergence generally being lower than that of traditional methods. For initial values that cause divergence in traditional iterative methods, the symmetric main cable shape-finding method achieved convergence within 10 iterations. The derived cable element theory and the symmetric main cable shape-finding calculation method can lay a theoretical foundation for the refined and efficient calculation of the main cable shape-finding process.

For river crossing bridges, the vehicle-induced vibration can be transmitted to the bridge tower and foundation system. This vibration induced low frequency underwater noise radiation can cause great harm to aquatic organisms. A river crossing suspension bridge was selected to study the sound contribution and spatial distribution of the underwater noise. A bridge-sediment coupling finite element model was developed, and the vehicle-bridge-sediment interaction analysis was conducted to investigate the dynamic response of the coupling system. An acoustic finite element model was built to predict the underwater noise radiated from the tower and sediment, and the noise contribution of these two sound sources was compared. The research shows that the noise radiated from the bridge tower and the sediment is below 6.3 Hz, and the peak frequency is around 3.15 Hz. The noise radiated from bridge tower only has a larger contribution to the total noise level in its vicinity than the sediment, especially around the water surface. In other space, the noise generated through the sediment vibration plays a dominant role in the total noise. The radiated noise from the tower has lateral directivity, and the directivity of the sediment radiation is similar to the point sound source. [ABSTRACT FROM AUTHOR]

The present paper combined the natural environment excitation technology (NExT) with the eigen system realization algorithm (ERA) to identify the modal parameters of a suspension bridge. Firstly, the critical parameters in NExt–ERA, such as record length, window length, and ranks of the Hankel matrix, and their influence on identification accuracy have been discussed. Subsequently, based on the acceleration series obtained from the Xihoumen Bridge Health Monitoring System, 3015 sets of modal frequencies and modal damping ratios of the Xihoumen Bridge were identified under 7 sets of wind speeds by the NExt–ERA. Finally, the probability distribution and confidence interval of the structural modal damping ratios were analyzed. Besides, the dependence of identified frequencies damping ratios on wind speed was also discussed. The results show that at the same wind speed, the mean value, and variance of the torsional and lateral mode damping ratios are larger than those of the vertical mode, but this difference gradually decreases with the increment of wind speed. The modal damping ratios along three directions under different wind speeds all follow the generalized extreme value distribution, but wind speed affects the tailing properties of probability distribution of the vertical and torsional mode damping ratios. The estimated damping ratios could provide references for structural design and vibration control of similar long-span bridges. [ABSTRACT FROM AUTHOR]

The present work offers a comprehensive overview of methods related to condition assessment of bridges through Structural Health Monitoring (SHM) procedures, with a particular interest on aspects of seismic assessment. Established techniques pertaining to different levels of the SHM hierarchy, reflecting increasing detail and complexity, are first outlined. A significant portion of this review work is then devoted to the overview of computational intelligence schemes across various aspects of bridge condition assessment, including sensor placement and health tracking. The paper concludes with illustrative examples of two long-span suspension bridges, in which several instrumentation aspects and assessments of seismic response issues are discussed. [ABSTRACT FROM AUTHOR]

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Abstract Non-stationary characteristic in nature wind has a great effect on buffeting performance of long-span bridges. The influence of key parameters in non-stationary wind velocity models on nonlinear buffeting responses of a super long-span suspension bridge was investigated in this paper. Firstly, four non-stationary wind velocity models are established by combing the time-varying average wind velocity with an exponential function and the fluctuating wind velocity with four modulation functions, respectively. These non-stationary wind velocity models have obvious non-stationary characteristics and then are validated by the classical power spectrum densities. Finally, three displacement responses of the bridge deck under four different independent variables of β in the exponential function and four modulation functions were compared, respectively. Results show that the turbulence intensities using two non-uniform modulation functions (NMF) are larger than those using uniform modulation functions (uMF). Moreover, the root mean square (RMS) values of three displacement responses increase with the decrease of β. Besides, the RMS values of three displacement under two NMFs are larger than those under two uMFs, and their RMS values under the second uMF are the smallest.

Suspension bridges are the most common type of bridge used to cross the ocean. The cable clamps in suspension bridges clamp the main cables by bolt preload, but the elastic interaction of the bolts reduces the preload, which is detrimental to the force in suspension bridges. However, research on the factors influencing the elastic interaction of cable clamp bolts in suspension bridges is currently limited. This paper aims to explore the law of influence of external factors on the elastic interaction of bolts through a combined approach of theoretical analysis, full-scale experiment, and finite element simulation. The results indicate that the average preload loss was reduced by about 27% when the elastic modulus was increased by about 110%. The average preload loss was reduced by about 45% when the bolt center distance was increased by 75%. The number of bolts has a small effect on the elastic interaction, which can be ignored. When the preload of bolt installation was increased by 133%, the average preload loss was reduced by approximately 125%, which was almost a linear relationship. Tightening the bolt from the center bolt creates greater elastic interaction. The conclusions can provide suggestions for reducing the elastic interaction of bolts in the design and construction of suspension bridge cable clamps.

In the complex mountain wind environment, especially in the strong wind, fluctuating wind speed is a non-stationary and non-Gaussian random process. With the increase of suspension bridges' span, they are more sensitive to wind-induced vibration response. In this paper, a non-stationary and non-Gaussian buffeting reliability analysis method for long-span bridges is presented. Firstly, the non-stationary wind speed is simulated by the modulation function based on the stationary wind speed model. Secondly, the load is obtained by simulated wind speed, the obtained loads are loaded on the finite element model by ANSYS and the whole bridge time-domain analysis is performed, the time history of displacement response is obtained. Thirdly, based on the first excursion failure criterion of random vibration, the samples of the non-stationary and non-Gaussian displacement time history are transformed into a standard Gaussian process through a modified Fleishman approximation method, and then the non-stationary Poisson distribution method is used for structural reliability analysis. Finally, a mountainous long-span suspension bridge is used as the engineering background, and the proposed reliability analysis method is applied to analyze the reliability of the bridge. The influence of different wind attack angles and modulation functions on the dynamic reliability of the bridge is further studied. The results indicate that the displacement response obtained by the transformation of non-stationary and non-Gaussian random process is less reliable than that obtained by traditional analysis method. Its dynamic reliability is maximum at 1 ∘ wind attack angle, the reliability of negative wind attack angle is lower than that of positive wind attack angle, and decreases with the increase of wind attack angle. The reliability obtained by using different modulation functions is lower than that of traditional method. If the traditional analysis method is still used for reliability analysis, it will produce unsafe consequences and reduce the engineering safety reserve. [ABSTRACT FROM AUTHOR]

Strong vibrations can cause considerable damage to structures and break materials apart. The main reason for the Tacoma Narrows Bridge collapse was the sudden transition from longitudinal to torsional oscillations caused by a resonance phenomenon. There exists evidence that several other bridges collapsed for the same reason. To overcome unwanted vibrations and prevent structures from resonating during earthquakes and winds, features and modifications such as dampers are used to stabilize these bridges. In this work, we study a nonlinear viscoelastic plate equation with variable exponents, which models the deformation of a suspension bridge. First, we establish explicit and general decay results of the system depending on the decay rate of the relaxation function and the nature of the variable‐exponents nonlinearity. Then, we perform several numerical tests to illustrate our theoretical decay results. Our results extend and generalize many earlier works in the literature. [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]