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For rail-cum-road bridges, when the bridge span increases and road traffic becomes dense, the coupling effect between vehicles and the bridge cannot be ignored. This paper establishes a coupled dynamic analysis model that includes four subsystems: vehicles, trains, tracks, and the bridge. In this system, each vehicle in the random traffic flow is treated as an independent entity with its own motion equations. By focusing on the deformation characteristics of the bridge, the study reveals how vehicles impact train’s running stability. Additionally, a parameter analysis is conducted to identify the key influencing parameters of random traffic flow. The results show that the movement of vehicles induces notable deformation in the bridge’s main girder, particularly increasing the amplitude of alignment with wavelengths both below 200m and above 200m at the bridge tower area, and increasing the amplitude of alignment with wavelengths above 200m at the main span. This leads to heightened train vibration acceleration and centrifugal acceleration. The maximum train acceleration while crossing the bridge is observed in the bridge tower area, increasing from 0.12m/s² in the absence of vehicles to 0.3m/s² under the condition with vehicles. Among the parameters of random traffic flow, the average vehicle weight on the bridge significantly influences the vertical acceleration of the train, showing a linear relationship.

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.

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.

We consider the dynamics of the first vibrational mode of a suspension bridge, resulting from the coupling between its roadbed (elastic beam) and the hangers, supposed to be one-sided springs which respond only to stretching. The external forcing is due to time-periodic vortices produced by impinging wind on the bridge structure. We have studied some relevant dynamical phenomena in such a system, like periodic and quasiperiodic responses, chaotic motion, and boundary crises. In the weak dissipative limit the dynamics is mainly multistable, presenting a variety of coexisting attractors, both periodic and chaotic, with a highly involved basin of attraction structure.

This paper presents a two-node catenary cable element for the analysis of three-dimensional cable-supported structures. The stiffness matrix of the catenary cable element was derived as the inverse of the flexibility matrix, with allowances for selfweight and pretension effects. The element was then included, along with the beam and truss elements, in a geometric nonlinear analysis program, for which the procedure for computing the stiffness matrix and for performing iterations was clearly outlined. With the present element, each cable with no internal joints can be modeled by a single element, even for cables with large sags, as encountered in cable nets, suspension bridges and long-span cable-stayed bridges. The solutions obtained for all the examples are in good agreement with the existing ones, which indicates the accuracy and applicability of the element presented.

When studying the vibration of a bridge–vehicle coupled system, most researchers mainly focus on the vertical vibration of bridges under moving vehicular loads, while the lateral and longitudinal vibrations of the bridges and the stochastic characteristics of the traffic flows are neglected. However, for long-span suspension bridges, neglecting the bridge’s three-dimensional (3D) vibrations under stochastic traffic flows can cause considerable inaccuracy in predicting the dynamic performance. This study is mainly focused on establishing a new methodology fully considering a suspension bridge’s vertical, lateral, and longitudinal vibrations induced by stochastic traffic flows under varied road roughness conditions. A new full-scale vehicle model with 18 degrees of freedom (DOFs) was developed to predict the longitudinal and lateral vibrations of the vehicle. An improved Cellular Automaton (CA) model considering the influence of the next-nearest vehicle was introduced. The bridge and vehicles in traffic flow coupled equations are established by combining the equations of motion of both the bridge and vehicles using the displacement relationship and interaction force relationship at the patch contacts. The numerical simulations show that the proposed method can rationally simulate the 3D vibrations of the suspension bridge under stochastic traffic flows.

Numerous long-span suspension bridges have been built worldwide over the past few decades. To ensure the safety of such bridges and their users during the bridge service life, several bridges have been equipped with Structural Health Monitoring Systems (SHMSs), which measure dynamic bridge responses and various loading types on-site. Integrating SHMS and damage detection technology for condition assessment of these bridges has become a new development trend. Recent studies have proven that stress influence line (SIL)-based damage indices achieve excellent damage detection performance for a long suspension bridge. However, an accurate and prompt manner of identifying the SIL of a long suspension bridge is important to facilitate the development of the SIL for an effective damage index. Identifying the SIL from field measurement data under in-service conditions has several advantages over the traditional static loading test. This study proposes and develops a new SIL identification method by integrating the least squares solution and Weighted Moving Average (WMA) based on the measured train information and the corresponding train-induced stress time history. The efficacy of the proposed method is validated through its application to Tsing Ma Bridge (TMB). The good agreement between the identified and baseline SILs for a typical diagonal truss member verifies the effectiveness of the proposed method. Furthermore, robustness testing is performed by identifying SIL on the basis of information on different trains and train-induced stress responses and by identifying the SIL of different types of bridge components. Results indicate the feasibility of the application of the proposed approach to SIL identification for long-span bridges.

The passive control using winglets has been considered to be an alternative solution for control of flutter and buffeting responses of long suspension bridges. This method is aimed at not only developing lightweight, reduced-cost stiffening girders without adding stiffness for aerodynamic stability, but also avoiding problems from malfunctions caused by the control and energy supply systems of active control devices by winglets. This paper presented a mechanically controlled approach using the winglets, for which a two-dimensional bridge deck model was numerically and experimentally studied. In addition, numerical research on the flutter and buffeting passive control of a 3000m span suspension bridge was carried out. The result showed that the flutter speed of the suspension bridge increases, whereas the buffeting response decreases, through the implementation of the winglets.

This study proposes an approach to set up a continuum full bridge model with spatially inclined cables based on the Hamilton principle. The dynamic governing functions, considering the geometric non-linearities of cables and deck, represent simultaneously the vertical motion of deck and vertical–horizontal motion of cable. With the comparison of the modal properties obtained from the model to those from the accurate model, results show that the proposed model is capable of accurately simulating the modal properties. The primary resonance responses and corresponding frequency-response curves are obtained through the multiple-scale-method. A finite element (FE) model is established, and the corresponding non-linear dynamic analysis in time domain is conducted. Comparing the results from two models, it can be checked that the proposed model is reliable. According to the results of the proposed model, it is found that the second-order shape functions (SOSFs) play a significant role in the system response. Once the non-linear vibration of the bridge becomes significant only considering the excited mode with using the classical Galerkin decomposition cannot correctly predict the structure response. The SOSFs can be classified into stationary and vibrating components. The vibrating component can deviate the time-series of response from the harmonic wave, and the stationary component directly determines the mean value of the time-series.

Flexible suspension bridges are susceptible to aerodynamic instability phenomena. In this paper, the torsional divergence is addressed in terms of underlying mechanism, 3D and turbulence effects. A 3D generalized analytical model is first established by reasonable simplification of the model. Comparisons among results from different models are performed. The mechanisms of symmetric and asymmetric torsional divergence are explored. Finally, the 3D and turbulence effects are investigated. The results show that the proposed 3D generalized model is feasible for estimating the critical wind speed of asymmetric torsional divergence, and its computational accuracy is higher than the method provided by the code. The effects of turbulence on torsional divergence are multifaceted: the buffeting response due to wind fluctuations can significantly reduce the aerostatic stability of the bridge, resulting in a much lower critical wind speed than that in a smooth flow; the threshold of divergence is ambiguous and the instability is intermittent; further, the left and right quarter span sections largely vibrate in opposite directions during asymmetric torsional divergence.

To account for the influence of winglet’s arrangement length and installing position along the longitudinal direction of bridge deck, as well as actuators quantities on flutter control effect, a three-dimensional model of deck-winglet system was been derived in state space domain, and a model reduction method was also discussed to enhance control efficiency. Then, a suspension bridge with a main span of 3000m was used to investigate the control effect of active winglets, and to explore the influence of winglet length and actuator quantity on flutter control effect. Finally, the flutter and buffeting performance of winglet itself was investigated. The simulation results shows that the modes involved in flutter analysis should be determined according to mode-energy participation ratio. When installing a pair of winglets whose width is 10% of bridge deck, the critical wind speed of bridge deck may be twice of a non-controlled condition. In addition, the critical wind speed increases by increasing the length of winglets and actuator quantity. However, the critical wind speed may remain constant once the winglet length and actuator quantity exceed a critical value. By ensuring the critical wind speed of winglet itself is higher than bridge deck, winglet’s width should be less than 10% of bridge deck’s width, and the independent length winglet is proposed to be shorter than 15% of the length of center span of bridge deck.

Asymmetric stiffness in transverse direction of suspension bridge can be easily induced by many causes during its long-term service. Such phenomenon may cause the coupling effect between vertical and torsional vibrations. A cross-section model of suspension bridge with seven-degree of freedom is proposed, to investigate the asymmetry effect on the dynamic behavior of the system. Corresponding modal analysis is firstly carried out. Results show that the asymmetric stiffness will induce veering phenomenon when natural frequency loci of vertical and torsional modes approach each other. In the veering region, mode hybridization phenomenon can be observed between these two modes. In addition, asymmetry-induced nonlinear vibration of hybrid vertical and torsional modes is studied using the extended incremental harmonic balance method. The effect of asymmetry extent is also investigated in this study. Results show that both hybrid modes can be excited by either the vertical or torsional excitation. Moreover, the energy can be transferred between these two modes, because of the nonlinear stiffness introduced by the significant swaying motion of hanger and cable.

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${}^{\circ }$ 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.

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.

The wind field environment in mountainous zones is complex. If the wind field characteristics are regarded as stationary and Gaussian, the inaccurate response results of the structure will be obtained. In this paper, a fatigue evaluation method of steel truss suspension bridge members under non-stationary and non-Gaussian buffeting is proposed. This approach can solve the fatigue evaluation problem of steel truss suspension bridge members under mountain wind. Firstly, the normal wind speed (stationary and Gaussian) is obtained by the harmonic wave synthesis method. The wind speed considering non-stationary characteristics is obtained by adopting time-varying power spectrum. Secondly, through non-linear translation, the wind speed considering non-stationary characteristics is transformed into wind speed considering both non-Gaussian and non-stationary characteristics. Finally, combined with the Palmgren–Miner rule, the effects of three different buffeting responses on fatigue damage of suspension bridge members are studied. They are traditional buffeting response, buffeting response considering non-stationary characteristics and buffeting response considering both non-stationary and non-Gaussian characteristics. The results indicate that the fatigue damage of the main cable of the suspension bridge is the biggest at the mid-span. Under the same wind speed, considering two characteristics, the component fatigue damage will further increase.

The success of Suramadu Bridge construction is an achievement in the world of Indonesian construction. Suramadu Bridge crossing the seas connecting Java Island with Madura Island. Indonesia is now looking ahead with plans to build a larger bridge which will connect Sumatera and Java called the Sunda Strait Bridge. Sunda Strait Bridge will stretch along 30 km with two suspension bridges, each main span approximately will be 2.5 km long, as its main bridge. Conditions and natural phenomena around Sunda Strait Bridge construction site such as the presence of vault, plate and Anak Krakatau Volcanic near it will be a challenge for the Civil Engineers not only in Indonesia but also worldwide.

This paper describes the analysis of the calibration procedure of a computational optical system applied in the dimensional monitoring of the 25^th of April suspension bridge (P25A) in Lisbon (Portugal). The analysis includes the displacement optical measurement approach, the calibration method, the reference standard prototype and the experimental setup. The evaluation of the measurement uncertainty is described, including input measurement uncertainty contributions related to the experimental design and the use of Monte Carlo numerical simulation as tool for determination of the measurement uncertainty related to the calibration test, as well as a sensitivity analysis to identify the major sources of uncertainty. Conclusions are drawn about the suitability of the calibration method and reference standard prototype.