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A novel unified theory for distortion analysis of thin-walled hollow section has been proposed based on the Hellinger–Reissner variational principle to account for distortional shear deformation effects. Based on the proposed theory, a finite segment model has been developed and the method for determining the distortion functions of the cross-section has been proposed. The rationality of approaches for determining distortional shear stress has been analysed and it is concluded that Bredt’s pure distortion does not exist in the single-cell hollow section. Comparisons and analyses have been performed between the proposed theoretical model and the existing four groups of theories in distortion analysis of thin-walled hollow section. Effects of distortional warping shear stress on the shear deformation has been investigated and the results indicate that the distortional shear deformation effect results in a decrease of the distortional warping stresses and shear stresses but an increase of the transverse bending stresses. The numerical study indicates that the distortional shear deformation effects can be ignored and the first derivative of the distortion angle can be employed as the distortional warping function for the conventional hollow sections of bridge structures.

The running safety of railway vehicles on bridges can be negatively affected by earthquake events. This phenomenon has traditionally been investigated with only the lateral ground excitation component considered. This paper presented results from a numerical investigation on the contribution of vertical ground motion component to the derailment of vehicles on simply-supported bridges. A full nonlinear wheel–rail contact model was used in the investigation together with the Hertzian contact theory and nonlinear creepage theory, which allows the wheel to jump vertically and separate from the rail. The wheel–rail relative displacement was used as the criterion for derailment events. A total of 18 ground motion records were used in the analysis to account for the uncertainty of ground motions. The results showed that inclusion of vertical ground motion will likely increase the chance of derailment. It is recommended to include vertical ground motion component in earthquake induced derailment analysis to ensure conservative estimations. The derailment event on bridges was found to be more closely related to the deck acceleration rather than the ground acceleration.

Under repetitive heavy train traffic, railway steel truss bridges tend to have many fatigue related performance issues, especially at welded joints. Accurate estimation of the stress history at critical locations of welded joints under vehicle loading is important for joint fatigue design. Traditionally, vehicle loads were treated as moving static loads without considering their dynamic effects. In this study, a numerical procedure was introduced to incorporate the effect of dynamic response of the train–bridge coupled system on nodal fatigue damage. The proposed approach employs a twolevel modelling scheme which combines dynamic analysis for the full train-bridge system and detailed stress analysis at the joint. Miner rule was used to determine the cumulative fatigue damage at critical locations on the welded joint. A sensitivity analysis was conducted for different train loading configurations. It was determined that dynamic vibration negatively influences fatigue life. The calculated cumulative damage at investigated locations can more than the damage estimated using only static moving load method.

Railroad vehicle and bridge coupled lateral vibration problems are traditionally solved through detailed nonlinear models in time domain using limited samples to represent rail irregularity. Ideally, a random vibration and reliability based approach should be implemented because of the random nature of the excitation process. In this study, vehicle–bridge coupled dynamic equation was derived using the principle of virtual work utilizing a linearized wheel–rail contact equation. This simplification enables the calculation of the system random lateral responses through the pseudo-excitation method. By applying rail irregularity as random excitations to the system, this study utilized an explicit linearization method to avoid iterative solution at each time step of the integration. The results from the linearized method were validated through comparison with results obtained from Monte-Carlo simulations. By applying the linearized approach to probabilistic assessment of the vehicle–bridge system reliability, it was shown that system probability of exceedance of admissible limits increases with train speed and reduces with increased bridge self-weight. It is concluded that the proposed approach provides a viable efficient alternative to investigate the random dynamic characteristics of vehicle–bridge system especially in the lateral direction, which is dominated by the random rail irregularities.

Compared with medium and small span bridges, very limited attention has been paid on the research of the impact coefficient of long-span railway bridges. To estimate the impact effects of long-span railway bridges subjected to moving vehicles, a real long-span railway cable-stayed bridge is regarded as the research object in this study, and a coupled model of vehicle-bridge system is established. The track irregularities are taken as the system excitation and the dynamic responses of the vehicle-bridge system are calculated. The impact effects on main girder, stayed cable, bearings, and bridge tower are discussed at various vehicle speeds. The results show that different components of the long-span railway cable-stayed bridge have different impact coefficients. Even for each part, the impact coefficient is also different at different local positions. It reveals that the impact coefficients in the actual situation may have significant differences with the related code clauses in the present design codes.

Using nonlinear numerical methods, the structural systems of cables system, stiffening beams, pylons, and bearing systems are comparatively analyzed. This study demonstrates the technical feasibility of suspension bridges with a 3,500 m main span and Carbon Fiber Reinforced Plastic (CFRP) main cables. Using fine finite element structural simulation, the parameter sensibility of a suspension bridge structural system with a 3,500 m main span and CFRP main cables is analyzed, and the influence of structural parameters on the static and dynamic performance of super-long span suspension bridges is discussed. In combination with numerical analysis of a structural system model, the optimum structural system of a suspension bridge with a 3,500 m main span and CFRP main cables is determined. The physical model is set up to allow theoretical measurements of the anchorage, sliding, and bending moment of the CFRP main cable strands as well as static load and fatigue testing. A bond-type anchorage that can be applied to real bridges is developed, which has an anchorage efficiency coefficient of 100%. The sliding resistance and bending performances are verified: the frictional coefficient between CFRP main cable strand and saddle is about 0.5, the frictional coefficient between the CFRP main cable strand and clamp is up to 0.331, the bending strength of the CFRP wire at the saddle point is over 90% of its tensile strength, and there is almost no bending problem at the clamp. A bridge prototype design is produced based on the test results.

With crosswind actions, the wind loads on trains can change dramatically as the trains pass through the wake of bridge towers or when two trains pass each other, which will influence the stability of trains and the comfort of passengers. Taking advantage of the developed testing system of a wind tunnel test rig with moving train models, a three-car train model and a single-car train model were used to simulate rail vehicles and road vehicles, respectively. Sudden changes in the aerodynamic forces were measured when the train was passing through the bridge tower or when two trains were passing each other, and the effects of wind speed, train speed, rail positions of trains, and train types on the train’s aerodynamic coefficients were investigated. The analysis showed that for these studied cases, the aerodynamic coefficients of trains all have sudden changes. However, train-induced wind can weaken the sudden change of a train’s aerodynamic coefficients and lengthen the sudden-change region of wind shielding. The effect of sudden changes of wind loads acting on the road vehicle is more obvious than that on the rail vehicle.

Gusset plate anchorage devices are widely used in long-span cable-stayed bridges with steel girders because the force in the cable can be transferred directly to the main girder via the gusset plate, which is very convenient for inspection and maintenance. The disadvantage is the severe stress concentration between gusset plate and steel tube, and the cruciform joint between gusset plate, top flange and web of main girder. This paper presents the static analysis of and experimental research into a gusset plate anchorage device. The magnitude and stress distribution of each load case were analysed very carefully, and the stress history of typical points was also monitored to indicate the structural behaviour. Under the load of the maximum design cable force, the anchorage device exhibits linear elastic behaviour on the whole. The von Mises stress at some monitored points reaches the yield stress when the load is 1.28 times the maximum design cable force. Ultrasonic inspection of the test model revealed no strength cracking or plate buckling, which indicates that the safety margin of the anchorage device is sufficient and complies with the requirements of bridge design code. By comparing calculations and test results it could be proved that FEM can be utilized for the structural analysis of gusset plate anchorage devices and that the calculation accuracy exceeds 70 % for most monitored points.

As a new high-strength material, carbon-fiber-reinforced plastic (CFRP) cable provided an opportunity for bridge structures to achieve span limits that were not possible or economical in the past. Based on existing conceptual studies on ultralong-span bridges using CFRP, a new partially earth-anchored cable bridge (PEAC bridge) system was proposed in this study. The PEAC bridge system addresses existing challenges of applying CFRP to traditional suspension and cable-stayed bridge systems, while maintaining large spanning capacity. Through a detailed comparative study on traditional and proposed long-span systems, the performance of a PEAC bridge under static and dynamic loading was evaluated. The span limit of the PEAC bridge system was calculated based on the strength of material and cost considerations.

The lateral vibration of railway bridges induced by moving trains has traditionally been solved through numerical integration. Although it provides practical prediction, the numerical approach does not explicitly reveal the underlying driving mechanism of the train–bridge interaction. In this paper, a closed-form solution is derived for the lateral vibration of a simply supported bridge subjected to hunting forces from running wheel sets. Through complex Fourier expansion, this solution leads to the formulation of three influential factors with explicit physical meanings, namely, the effective unit moving load on the bridge, the arrangement of all moving wheel sets, and the frequency response function of the bridge. On the basis of these factors, a simplified formula to estimate the maximum vibration of the bridge is proposed. The closed-form solution and the simplified formula are validated through comparison with results from numerical integration. The resonance conditions of the bridge due to m...

An analytical model for dynamics of wind–vehicle–bridge (WVB) systems is presented in this paper in the time domain with wind, rail vehicles and bridge modeled as a coupled vibration system. The analytical model considers many special issues in a WVB system, which include fluid–solid interaction between wind and bridge, solid contact between vehicles and bridge, stochastic wind excitation on vehicles and bridge, time dependence of the system due to vehicle movement, and effect of bridge deck on vehicle wind load and vice versa. The models of wind, vehicles and bridge are presented with wind velocity fluctuations simulated using the simplified spectral representation method, with vehicles modeled as mass–spring–damper systems, and with bridge represented by a finite element model. The interactions between wind and bridge are similar to those considered in conventional buffeting analysis for long span bridges. In considering difficulties in measuring aerodynamic coefficients of moving vehicles on bridge deck, the cosine rule is adopted for the aerodynamic coefficients of moving vehicles to consider yaw angle effect, and expressions of wind forces on moving vehicles are then derived for engineering application. To include mutual effects of wind loads, aerodynamic parameters of vehicles and bridge deck are measured, respectively, using a composite section model test and a specially designed test device. The dynamic interaction between vehicle and bridge depends on both geometric and mechanical relationships between wheels of vehicles and rails on the bridge deck. The equations of motion of the coupled WVB system are derived and solved with a nonlinear iterative procedure. A cable-stayed bridge in China is finally selected as a numerical example to demonstrate dynamic interaction of the WVB system. The results show the validity of the present model as well as wind effects on the rail vehicles and the bridge.

The spectral representation method has been greatly developed as the performance of computer was enhanced. For the time-domain analysis of long cable-stayed bridge, it is required to simulate wind velocity histories at many points arranged on the overall bridge. However, the number of these points is usually so large that the spectral representation method obviously becomes computationally prohibitive. In this paper, a practical method is introduced to simplify stochastic wind velocity field for long cable-stayed bridges. According to the properties of both the structural type and the vibration mode of long cable-stayed bridge, and considering the correlation characteristics of natural wind, an overall three-dimensional (i.e. three components of natural wind) wind velocity field of a long cable-stayed bridge can be simplified into many one-dimensional (i.e. just one component) wind velocity fields, respectively, along pylons and deck. The wind fluctuation along each pylon can be simulated independently by omitting the wind velocity correlation between one pylon and another. Using the explicitly expressed Cholesky's decomposition of the cross-spectral density matrix, the wind velocity field along the deck can be simulated relatively fast. The FFT (Fast Fourier Transform) technique is adopted to further improve the computational efficiency. As an example, the stochastic wind field of a three-pylon cable-stayed bridge is simulated. The spectrum and correlation characteristics of the simulated samples are checked, which demonstrates that the simulation results agree with the corresponding targets.

In this paper, a reliable but simple identification method, here called the weighting ensemble least-square method (WELS), has been developed to extract all eight flutter derivatives of bridge deck from free vibration records. For every wind speed, free vibration test of section model is generally repeated several times in order to obtain more reliable parameter estimates. In the WELS method, many free vibration records at the same wind speed are regarded as an ensemble. The common mode parameters are then identified simultaneously from the ensemble data. The parameter fit is obtained by a nonlinear least-square method. Weighting factors are proposed to make each experiment record with the same weight in total residual error analysis. The ensemble composed of many records can reduce the effect of the colored noise of few records on the convergence of least-square iteration process. The flutter derivatives of two section models are identified to indicate the reliability and effectiveness of the WELS method.

Applying carbon fiber-reinforced plastic (CFRP) materials for long span bridge, especially for earth anchored stay-cabled bridge (PEA bridge) has been proposed in this paper. The influence of tower heights on the static responses of the PEA bridge had been investigated. It was shown that PEA bridge with lower tower which has less stiffness resulted in larger horizontal forces on the anchorage. The PEA bridge can avoid challenges of the application of CFRP to the main cable of the suspension bridge, such as, bending, shear and lateral compression at suspender connections and tower saddles. Compared with the other suspension bridge, the PEA bridge shows slightly higher vertical stiffness. The limit span of the PEA bridge was inferred the same as the suspension bridge.

In order to evaluate the dynamic response of the train running on long-span cable-stayed bridges under uniform seismic excitations, a time-domain framework of analysis for the train–bridge system is established. The rail irregularities are treated as internal excitation and seismic loads as external excitation considering the inertia forces induced by the 3D seismic waves. The vehicles are modeled as mass-spring-damper systems, and the cable-stayed railway bridge is simulated by finite elements. A comprehensive analysis of the train–bridge system subjected to earthquake is conducted, focused on the effect of seismic ground motions on the dynamic response of the running train. Four kinds of seismic waves, each with three components, are simulated, with their spectral characteristics taken into account. To consider the stochastic characteristic of actual seismic waves, the effect of the incident angle and occurrence time of earthquakes on the bridge and vehicles is analyzed. Moreover, the earthquakes with various occurrence probability levels are also studied and the safety of the train running under the seismic action is evaluated, which may be used as the operation reference for the railway authority. The results demonstrate that the seismic ground motions have significant effects on the dynamic response of railway vehicles running on the long-span cable-stayed bridge under various spectrum characteristics, incident angles, occurrence times, and occurrence probabilities.

The Pseudo-Excitation Method (PEM) is applied in the non-stationary stochastic analysis of simple supported girder bridge. Vehicle system and bridge system are considered separately and these two systems are linked together by the displacement compatibilities and the force balance. Maximum and minimum responses are obtained based on 3 σ principle and the variation trend of the system responses at the different vehicle velocity is discussed. The results show that car body vertical responses have large randomness, but vertical responses in the bridge mid-span and vertical wheel/rail force are influenced by deterministic load.

An experimental and analytical study was conducted to investigate the static performance of steel plates strengthened with pre-stressed CFRP (carbon fiber-reinforced polymer) in uni-axial tension. A linear elastic theoretical model was presented to predict the stress distribution of reinforced specimens. Static testing was performed on the double edge notched specimens strengthened by CFRP laminates at different pre-stressing levels. The theoretically predicted results were in good agreement with the experimental results. The results show that pre-stressed CFRP laminates had a large impact on the specimen’s strength but resulted only in a moderate increase of its stiffness. An eccentricity due to pre-stressing was observed leading to bending effects which result in a non-uniform stress distribution. The test results indicated that the long-term pre-stress losses due to static and fatigue loading were slight because of the excellent mechanical properties of CFRP laminates. Therefore, the total pre-stress losses could be simplified as the short-term pre-stress losses with considering a safe factor.

Because of its main advantage of simplicity, practicality, lower computational cost and relative good results Pushover analysis (POA) has become an effective analytical tool during the last decade for the seismic assessment of buildings. But such work on bridges has been very limited. Hence, the aim of this study is to adapt POA for nonlinear seismic analysis of girder bridges, and investigate its applicability in the case of an existing river‐spanning approach bridge. To three different types bridge models the nonlinear POA, which adopts fiber model nonlinear beam‐column element based on flexibility approach, with return period about 2500 years is carried out. It can be concluded that POA is applicable for bridges, with some shortcomings associated with the method in general, even when it is applied for buildings. Finally the applicable selection for monitoring point and lateral load pattern is suggested according to dynamic characteristic of girder bridges.

By using the vehicle-bridge coupling dynamics method, the dynamic model and equations for both the vehicle and bridge are established for predicting dynamic responses of Nanjing Yangtze-River bridge subjected to moving high-speed train. The coupling vibration responses of vehicle-bridge system under moving high-speed trains are calculated and analyzed in details. Numerical results show that, under ICE3 running at the speed of 160 km/h∼360 km/h, the maximum value of vertical and lateral displacements of the middle of main span are only 26.79 mm and 2.10 mm respectively, the ratio of deflection to span is only 1/12542. The maximum values of vertical and lateral accelerations of bridge are 0.39 m/s² and 0.29 m/s². The maximum values of the derailment coefficient, the wheel-set decrement ratio, the wheel unloading rate, the acceleration, are smaller than the values specified by Chinese code. The vertical and lateral Spering index of vehicle reach excellent and good respectively. Vertical and lateral rigidity of Nanjing Yangtze-River bridge can satisfy the safety and comfort of running high-speed train.

This paper focuses on the experimental study on the pre-stress losses of pre-stressing carbon fiber reinforced polymer (CFRP) plates bonded on damaged steel structures. Both pre-tensioned and post-tensioned members are theoretically and experimentally analyzed. The results show that, firstly the instantaneous pre-stress losses due to elastic deformations are up to 50% of the initial pre-stress for the steel plates strengthened with CFRP plate pre-stressed by the pre-tensioned method. The longer length of CFRP plate reduces the instantaneous pre-stress loss significantly. Because of the small value of the long-term pre-stress losses in the test, the approximate estimates of total pre-stress losses can be simplified as the instantaneous pre-stress losses with considering a safety factor. Secondly for the steel girders strengthened with pre-stressing CFRP plate by the post-tensioned method, the effective pre-stress of girder specimens are directly controlled by the anchorage set, and both the instantaneous and long-term pre-stress losses are slight. However, the anchorage set with jacking system is rather complicated and difficult to design. From the view of pre-stress losses, the post-tensioned method is more effective than the pre-tensioned method.

The characteristics of tensile anchor plate anchorage structure are described. Then, by combining finite element method (FEM) analysis results with the results obtained from full scale model test under static load on tensile anchor plate in cable-girder anchorage zone of Guangzhou Dongsha Bridge, the stress distribution and mechanical behavior of anchorage system are analyzed. B is the thickness of tensile anchor plates and R is the radius at the end of fillet welds between the tensile anchor plate and the tensile anchor tube. The influences of B and R on the stress distribution of tensile anchor plate are researched, and the rationality of the design is proved. The study results are beneficial to the design of a similar bridge.

Pushover analysis (POA) has become a popular tool for evaluating the seismic behaviour of structures. But such work has hitherto focused mainly on buildings, while corresponding work on bridges has been very limited. Hence, the aim of this study is to investigate influence factors of POA based on girder bridges. To three different types bridge models which are based on river- spanning approach bridge as the engineering background the elastic POA with return period about 500 years and the nonlinear POA with return period about 2500 years are carried out respectively. Then the effects of the monitoring point and lateral load pattern on the calculating accuracy of POA are studied extensively. Finally the applicable selection for monitoring point and lateral load pattern is suggested according to structural dynamic characteristic.