Suspension Bridge Research Articles

Aeroelastic analysis of non-conventional and slender suspension bridges

The aim of this study was to investigate the dynamic effects of wind actions on bridge cross sections, with a goal to propose design charts for non-conventional and slender bridge decks. An eigenvalue analysis was conducted first and the results were validated experimentally. Subsequently, aeroelastic analysis of the bridge deck section was performed. This analysis encompassed the analytical method adhering to the Eurocode and computational fluid dynamics simulations. Both methodologies indicated that the bridge was susceptible to vortex-induced vibrations. To mitigate these vibrations, wind noses provide better stability than the currently used guide vanes. The effect of changing deck width was also studied. Wider and more streamlined sections displayed better aeroelastic performance. The study also revealed that the Eurocode overestimates the derivatives of aerodynamic moment coefficient by 53% to 93%. Consequently, optimized charts are proposed to enhance the accuracy of torsional divergence and flutter speed calculations, facilitating the safe and efficient design of such bridges.

Influence of Main Cable Displacement-Controlled Device of Long-span Suspension Bridge on Seismic Performance of Structure

Influence of Main Cable Displacement-Controlled Device of Long-span Suspension Bridge on Seismic Performance of Structure

Rich Dynamics for a Model Arising in the Study of Suspension Bridges

Rich Dynamics for a Model Arising in the Study of Suspension Bridges

Wheatstone Bridge MEMS Hydrogen Sensor with ppb-Level Detection Limit Based on the Palladium-Gold Alloy.

On some occasions, such as new energy clinics, monitoring the trace hydrogen at the ppb level is necessary. The traditional resistive hydrogen sensors based on the Pd alloys are very difficult to realize such an extremely low detection limit. To achieve a detection limit at the ppb level and also ensure good stability, a MEMS hydrogen sensor was designed in a suspended Wheatstone bridge structure, with all four resistive arms defined on a sputtered Pd-Au alloy thin film. For the Wheatstone bridge sensor, absolute response (Ra) and relative response (Rs) are defined to describe the sensitivity of the sensor, and the effect of annealing temperature on baseline drift is investigated using the baseline zero drift parameter (DBZD). By testing the sensors across a hydrogen concentration range of 20 ppb to 3 v/v%, the optimal annealing temperature (250 °C) and operating temperature (60 °C) were identified. Under these conditions, the sensor exhibited a detection limit as low as 20 ppb with a power consumption of only 4.6 mW. At the same time, the response and recovery times of the sensor were 6 and 19 s, respectively, toward 3 v/v% hydrogen. After testing over a 100-day period, Ra fluctuated only 0.0026%, indicating that the hydrogen sensor had good long-term stability for low-concentration detection. More results also showed that the sensor has good repeatability, selectivity, and humidity resistance. With the wide measurement range (20 ppb to 3 v/v%), the sensor has the potential to meet hydrogen detection requirements in multiple scenarios.

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

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

Analytical assessment of suspension bridge's 3D curved cable configuration and cable clamp pre-installation angle considering the main cable torsional and flexural stiffnesses

For a suspension bridge with a spatial cable system, the 3D curved main cable undergoes large lateral and torsional deformations during construction, which increases the difficulty of construction control. If using the traditional ideal flexible cable assumption, the torsional deformation cannot be analyzed. Therefore, incorporating the main cable's torsional and flexural stiffnesses in shape-finding analysis remains highly challenging. This study develops an analytical method for determining the target configuration of the main cable by applying the multi-segment catenary method and the Cosserat rod model. The closed-form solution of the geometrically exact force-displacement-strain relationships is derived, comprehensively considering the tension, shear, bending, and torsion of the main cable, as well as the initial curvatures and axial strains in the reference configuration. Then a two-layer shape-finding framework is established, with the first layer being recursive calculations of the cable shape and the second layer being numerical calculations of the nonlinear governing equations using the Levenberg-Marquardt method. Furthermore, a novel method for calculating the pre-deflection angle of the cable clamp in the free cable state is presented for the first time. A classic cantilever model and a suspension bridge with the spatial main cable are studied to investigate the accuracy of the proposed algorithms. Numerical results indicate that when the spatial main cable is twisted, the bottom edge of the cable cross-section moves outward along the transverse direction of the bridge. The torsion of the main cable includes both elastic deformation and rigid body displacement caused by the bidirectional bending effect. At the mid-span, the torsional angle of the main cable cross-section is 10.088°, and the pre-deflection angle of the cable clamp at the mid-span should be set to 10.851°. Moreover, the target configuration is highly sensitive to the flexural and torsional stiffnesses of the main cable while the effect of shear deformations on cable configurations can be ignored.

A Simplified Approach for Dynamic Analysis of Suspension Bridges under Extreme Limit State

A Simplified Approach for Dynamic Analysis of Suspension Bridges under Extreme Limit State

Effect of Vehicle Load on the Fatigue Cracks of the Center-stay for a Steel Girder Deck in a Suspension Bridge

Steel deck systems are widely used in cable-stayed and suspension bridges because of their various advantages. However, the direct effect of vehicle loads often leads to fatigue cracks in steel decks, particularly at the intersections of the longitudinal and transverse ribs, which have been the focus of most studies. In the target bridge of this study, unlike the location where fatigue cracking generally occurs, cracks were detected in the vertical stiffener inside the stiffening girder just below the center-stay and that adjacent to the center-stay. A precise analysis was performed to determine the cause of fatigue cracking, and the analysis model was verified by comparing it with the results of an existing load test. This study examined the effects of heavy vehicle loads by adjusting the vehicle weight and changing the position of the vehicle. This study confirms that as the vehicle load increases, fatigue cracing may occur in the internal vertical stiffener of the center-stay stiffening girder, leading to subseuent cracs in the external center-stay.

Micro-structure-property relationship of heavily drawn steel wires for large span suspension bridge cables

The outstanding combination of high strength and ductility of bridge cable steel wire is attributed to the cold drawing process with intermediate equivalent strain. However, the micro-structure-property relationship of heavily drawn steel wires for large span suspension bridge cables is not well understood. In this study, defects-controlled deformation in nano-scale interfaces between ferrite and cementite phases with heavily cold drawing process was investigated using high-resolution transmission electron microscopy and molecular dynamics simulation. The excessive thinning of the cementite lamellar thickness observed from the morphology suggested the evolution of the Fe3C/Fe interface in the cold-drawn wires, namely, the partial cementite deformation during the drawing process. Drawing strain played a major role in the occurrence of partial cementite nano-crystallisation. This was because the change in cementite morphology was the primary cause of cementite free energy increase, which ultimately led to cementite phase instability. The decrease of yield strength during the drawing process of the bridge cable steel wire was caused by the inverse Hall-Petch effect resulted from the nodule rotation. When the nodule morphology became flat, the inverse Hall-Petch effect was suppressed. At this time, the strengthening mechanism caused by cementite nano-crystallisation ensured the improvement of tensile strength of steel wire when the dislocation density was close to saturation.

Deformation and internal force of multitower suspension bridges: Numerical modeling and analytical analysis

An analytical model for predicting the deformation and internal forces of multitower suspension bridges is proposed in this paper. Equilibrium differential equations and deformation coordination equations are established based on deflection theory and coupling analysis of bridge components, in which the vertical stiffness contribution of girders and the longitudinal stiffness of all towers are considered. The equations for the deformation and internal forces of the bridge components, including towers, hangers, cables, and girders, are derived taking into account the live loads to which the multitower suspension bridge is subjected. The equations capture the mechanical characteristics of the bridge components, and the results can be obtained explicitly with the proposed model, notably improving the calculation efficiency. The applicability and efficiency of the proposed model are verified by two finite element model examples featuring two and three towers. A parametric analysis is performed to investigate the impact of major bridge parameters using the proposed model. The analysis results indicate that the longitudinal stiffness ratio of the mid-tower to the main cable plays an important role in the key design indices, including girder deflection and safety factor of anti-slipping of the saddle. A suitable stiffness range for the mid-tower is obtained by the proposed model.

Study on the Application of Determinant-MTMD(TMDD) Vibration Reduction in Cable-Supported Pedestrian Suspension Bridge

In this study, multiple tuned mass dampers (MTMDs) were studied to understand their impact on the human-induced vibration response and comfort level of a pedestrian cable-supported suspension bridge. A spatial finite element model based on a specific engineering case was established. The dynamic characteristics of the bridge under human-induced loads were investigated, and its comfort level under human-induced vibrations was analyzed using the time-history method. Then, this study adjusted the design parameters of the dampers based on various optimal damper parameter expressions. Furthermore, the damping effectiveness of MTMD under different mass ratios (μ) was evaluated, and it was found that increasing the mass ratio significantly impacts damping performance. Finally, determinant-TMD (TMDD) was introduced, and a comparison between the damping effect, robustness, and performance of TMDD and MTMD was conducted. The results indicate that while increasing the mass ratio does not linearly affect maximum vibration acceleration, the damping effect increases initially and then stabilizes, with a damping rate converging at approximately 55%. However, with the TMDD approach, the maximum damping rate can reach approximately 70%, enhancing comfort levels from the “minimum CL3” achieved with MTMD to the “medium CL2” level. Additionally, while TMDD’s robustness is slightly inferior to MTMD at lower mass ratios, it demonstrates superior robustness at higher mass ratios.

A Novel Method of Bridge Deflection Prediction Using Probabilistic Deep Learning and Measured Data

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.

Deep learning-based automated identification on vortex-induced vibration of long suspenders for the suspension bridge

Large amplitude vortex-induced vibration (VIV) of long suspenders, caused by vortex-shedding and wake flow, will decrease the service life of high-strength wires and its anchorage systems, hence listed as an essential monitoring indicator of the structural health monitoring system in the suspension bridges. Traditionally, a static vibration amplitude limitation is usually predefined and used to identify VIV from continuously monitored acceleration data of bridge suspenders. Due to the complexity of the starting vibration of the suspenders, it may not be able to flexibly adapt to the suspenders VIV under different conditions. In addition, transient but significant vibration events may not be captured since it relies only on static vibration amplitude limits without considering the temporal information of vibration. To address the above-mentioned issues, a novel framework to autonomously identify the suspenders VIV is proposed using the multimodal fusion techniques with deep neural networks. The main contributions of the methodology are: i) by calculating the wind field and vibration characteristic, two vibration response parameters are identified as indexes for the identification of suspenders VIV based on the significant difference method of big data analysis; ii) Two different modal information of time history images and power spectral density (PSD) sequences are used as inputs to the convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) to extract the suspenders vibration response features from the time and frequency domain perspectives, respectively; and iii) The multimodal information is concentrated and enhanced by the multi-head attention (MHA) mechanism to achieve automated identification of the suspenders VIV. The proposed framework is validated with data collected from a full-scale long-span suspension bridge in comparison with the base model. The results show that the proposed framework can efficiently identify the full-cycle development process of the suspenders VIV. This study provides a convenient strategy for suspenders VIV identification, which can be used for bridge management and vibration mitigation device design.

Structural characterization of a suspension bridge by mapping the temperature effects on strain response based on neural network models

AbstractMapping the structural responses based on main loads to characterize signature of complex structures with high-dimensional features is a determinant factor for structural health monitoring (SHM). Current technological advances contribute to the optimization of data analysis, aiming to make the process less demanding in terms of time and computational demand. Machine learning (ML) models became popular due to their capacity to estimate structural behaviour based on the measurements gathered by the SHM systems. This work proposes a methodology supported by Neural Networks (NN) for the characterization and prediction of the structural behaviour based on thermal loads and structural responses. By comparing the observed values and predicted outcomes from the NN, it is possible to identify measuring errors, new trends or pattern variations that need further assessment. A sensitivity analysis is also proposed to confirm the model robustness and to characterize the influence of the temperature on the structural responses. The case study is the 25 de Abril’s bridge, located in Lisbon, Portugal.

Study on Multi-Crack Damage Evolution and Fatigue Life of Corroded Steel Wires Inside In-Service Bridge Suspenders

The parallel steel wires used in arch bridge suspenders experience random corrosion damage on their surfaces during service. Corrosion damage, including micro-cracks, pitting, and a combination of both, leads to significant stress concentration under axial loading, which affects the performance of the steel wires. The change in the stress field caused by surface damage alters the stress intensity factor at the crack tip, and the presence of adjacent crack tips significantly amplifies the stress intensity factor, thereby accelerating crack propagation. The development of small surface damages in the steel wires is difficult to control and observe through experiments. By utilizing finite element methods for simulation, it is possible to intuitively analyze the crack propagation process, the trend of stress changes at the crack tip, and the interaction between damages. Numerical simulation results based on Paris’ law indicate that corrosion pits have a certain impact on the stress intensity factor at the crack tip. The propagation process of coplanar double cracks is highly sensitive to the initial crack size and the distance between adjacent crack tips. When the crack spacing is less than the crack depth, the stress intensity factor at the adjacent crack tips exhibits significant amplification. Based on this phenomenon, the coplanar double-crack system can be simplified to a complete single crack for analysis. By comparing the fatigue life of the double-crack system with that of the equivalent single crack, the effectiveness of the simplification rule has been validated.

Ride comfort assessment of road vehicles on a long-span truss girder suspension bridge under crosswinds

The precise identification of the aerodynamic loads on vehicles is a fundamental concern in assessing the ride comfort of vehicles crossing long-span bridges in the presence of strong crosswinds. However, the consideration of aerodynamic interference between vehicles and truss girder bridges is limited in existing studies. Furthermore, in practical engineering, wind barriers are commonly installed to enhance the ride comfort of vehicles crossing long-span bridges, but previous studies have primarily focused on the impact of wind barriers on the aerodynamic coefficients and dynamic responses of vehicles. This paper focuses on the aerodynamic interaction between trucks and truss girder bridges, through wind tunnel testing. The aerodynamic coefficients of the vehicle with three different ventilation ratios and four different heights of wind barriers were obtained. The dynamic response of road vehicles on a truss girder suspension bridge with a main span of 965 m was numerically calculated using the coupled analysis of wind-vehicle-bridge system and measured aerodynamic coefficients considering aerodynamic interference. On this basis, the comfort of road vehicles was investigated with different section types of the girder and different wind barrier parameters, and it was evaluated accordance with the overall vibration total value (OVTV) recommended in the ISO 2631–1. It is found that the aerodynamic coefficients of road vehicles are sensitive to the type of wind barrier. Wind barriers can reduce the road vehicle’s aerodynamic loads at high wind yaw angles. Wind barriers can also improve the ride comfort of road vehicles on the long-span truss girder suspension bridge.

Test and Numerical Study on Blast Resistance of Main Girders Coated with Polyurea in Self-Anchored Suspension Bridges

Test and Numerical Study on Blast Resistance of Main Girders Coated with Polyurea in Self-Anchored Suspension Bridges

Analytical model analysis of suspension bridges with tower-girder-connected dampers

Recently the tower-girder-connected damper has been utilized to suppress multi-mode vertical vortex-induced vibration (VIV) of long-span suspension bridges. In this paper, an analytical solution is proposed for the damping ratio of vertical bending modes of a single-span suspension bridge, with a vertical or/and a rotational damper mounted near the end of the stiffening girder, which significantly simplifies the design procedure for tower-girder-connected dampers on suspension bridges. The damping effect and the accuracy of the analytical solution are validated for Humen Bridge. It is found that both the vertical and rotational damper with an appropriate parameter selected can supply significantly additional damping ratio to multiple bending modes of the suspension bridge. The rotational and vertical dampers work in a similar way and provide nearly the same maximum additional damping ratio for each mode. In particular, for the first two symmetric modes, regions of reduced motion near the ends of the stiffening girder are developed due to the effects of cable geometry and elasticity, and this reduces the effect of the tower-girder-connected damper. Excluding these modes, the damper effect on a suspension bridge is similar to that on a tension beam with the same beam stiffness and horizontal tension forces.

A Study on Post-Flutter Characteristics of a Large-Span Double-Deck Steel Truss Main Girder Suspension Bridge

To investigate the nonlinear flutter characteristics of long-span suspension bridges under different deck ancillary structures and configurations, including those with and without a central wind-permeable zone, as well as to analyze the hysteresis phenomenon of a subcritical flutter and elucidate the mechanisms leading to the occurrence of nonlinear flutter, this paper studies first the post-flutter characteristics of the torsion single-degree-of-freedom (SDOF) test systems and vertical bending–torsion two-degree-of-freedom (2DOF) test systems under different aerodynamic shape conditions are further analyzed, and the role of the vertical vibration in coupled nonlinear flutter is discussed. The results indicate that better flutter performance is achieved in the absence of bridge deck auxiliary structures with a central wind-permeable zone. The participation of vertical vibrations in the post-flutter vibration increases with the increase in wind speed, reducing the flutter performance of the main girder. Furthermore, the hysteresis phenomenon in the subcritical flutter state is observed in the wind tunnel experiment, and its evolution law and mechanism are discussed from the perspective of amplitude-dependent damping. Finally, the vibration-generating mechanism of the limit oscillation ring is elaborated in terms of the evolution law of the post-flutter vibration damping.

Load-bearing behaviors of the composite gravity-type anchorage: Insights from physical model and numerical tests

Gravity-type anchorages (GTAs) have been extensively applied in large-span suspension bridges across the globe, but the load-bearing performance of composite GTA is not yet fully investigated. Here, the comprehensive load-bearing performance of GTA is investigated using a combination of physical modelling and numerical modelling methods, considering the impact of anchorage’s burial depth, notched sill, and pile. Six model tests are first conducted using a self-reversing force loading equipment, including flat bottom anchorage, notched sill anchorage, and notched sill anchorage with pile. Each type of anchorage is tested under two different burial depth conditions. The failure process, anchorage displacement, cable tension force, and the internal strain field of the foundation, were examined during the model tests. Additionally, through the numerical simulations, the evolution characteristics of contact stresses and load sharing ratio associated with various forms of anchorage are discussed. The results indicate that the anchorage’s burial depth and pile significantly impact on anchorage’s bearing capacity. The presence of the notched sill can change the distribution of contact stress between the anchorage and foundation, which can still resist the horizontal force until the foundation before the notched sill occurs shear failure. The failure process of the anchorage-foundation system was divided into four stages: stable bearing, sliding, sliding and overturning, and failure stage. The anchorage starts overturning with the applied load reaching to 3*Tm, except for the flat bottom anchorage of shallow burial depth condition. Under the same conditions, the greater the anchorage’s burial depth, the smaller the load shared by the friction between the anchorage bottom and foundation, the greater the load shared by the notched sill and foundation before the anchorage. In addition, the load shared by pile continuously increasing as the anchorage starts overturning. The findings from this study can provide a theoretical basis and valuable insights for the optimization design of GTA.