Response Of Girder Research Articles

Protocol of investigations for the preliminary assessment of the structural safety of highway overpasses

This paper presents the results of a protocol of investigations that have been carried out on 15 overpasses, located along the highway A18 in Sicily (south of Italy) and built about fifty years ago, with the aim of achieving a preliminary evaluation of the structural safety of these overpasses. The investigated overpasses are characterized by a three-span deck consisting of a reinforced concrete slab and prestressed concrete girders. The girders of the central span are simply supported by two Gerber saddles located on cantilever girders at the two ends of the same span. The safety level of the overpasses is investigated by means of different activities that include visual inspection and computation of the class of attention of the overpasses according to the Italian Bridge Guidelines for the classification and the risk management, safety evaluation and monitoring of existing bridges, laboratory and in situ tests on materials, pachometric, georadar and video-endoscopic tests on structural details, and static load tests of the overpasses. The results of the static load tests have also been used to assess the accuracy of two numerical models of the overpasses. These models are elastic but characterised by different levels of accuracy and computational burden: while the first model is the well-established and simple Courbon-Albenga method, the second is a finite element model characterised by a more refined simulation of the response of slabs, longitudinal girders and crossbeams. The results of the investigations have been critically analysed and discussed to underline the ability of the protocol to reveal possible deficiencies of the overpasses and thus identify overpasses that are liable to structural interventions or more accurate and expensive investigations.

Tensile constitutive relationship of UHPFRC from crack hinge based inverse analysis of notched beams

The structural applications of ultra-high performance fiber reinforced concrete (UHPFRC) in the construction industry can be promoted if proper constitutive models can be established for design. The various tension test methods for UHPFRC are being adopted to develop a complete stress-crack width or strain response for design. This study aims to understand the fracture behavior of UHPFRC by testing notched beams under a three-point bending configuration. This testing method helps in quality control checks and obtaining complete tension stress-crack opening behavior that can be used for design. The tensile stress-crack width response of UHPFRC is obtained using the load-CMOD response. The variables considered in this study are the volume fraction of fibers (1 % and 2 %), types of steel fibers (straight, combination of straight and hooked ended), and different cross-section dimensions (100×100×500 mm and 75×75×500 mm). A crack hinge-based inverse analysis method is used for UHPFRC to obtain the complete tensile stress-crack opening response. Stress-strain relations from inverse analysis and direct tension stress-crack opening results are compared and found to be similar. A data-driven tension stress-crack opening response UHPFRC is verified by simulating the girder's response using nonlinear finite element analysis (NFEA). Thus, the proposed inverse analysis can be used to obtain the multi-linear tensile stress-crack opening response which is adequate for capturing the structural response.

Dynamic response of girder bridges with corrugated steel webs subjected to moving loads

Girders with corrugated steel webs (CSWs), replacing traditional concrete webs in prestressed concrete box girders, exhibit a unique dynamic behavior due to the accordion effect and the thinner dimension of CSWs. The study aims to investigate the dynamic response of girder bridges with CSWs under moving loads. Utilizing the Timoshenko beam theory and modal analysis method, the analytical formula for the dynamic response, considering shear deformation and rotational inertia, was developed. The proposed analytical formula was validated through finite element simulation. Employing dimensionless parameters, a parametric analysis was conducted to examine the effects of multi-modes, loading position and shear deformation on the dynamic response of girders with CSWs. The results highlight the significant influence of the shear parameter αS and the speed parameter SE1 on the magnitude of the impact factor. Precise calculations for deflection and bending moment only require consideration of low-order modes, whereas accurate estimation of shear force requires attention to higher-order modes. In particular, a high-frequency resonance phenomenon is identified when the speed parameter SE1 and the shear parameter αS conform to the formula “πSE1αS = 1”. The suggested impact factor formulas for midpoint deflection, midpoint bending moment and end shear force have been developed and categorized into three groups based on the magnitude of the shear parameter αS.

Serviceability limit state of incrementally launched steel bridge I-girders

Bridge girders are subjected to repeated patch loading during incremental launching (i.e. travelling over supports). Plastic deformations are likely to occur in the girder already at the first patch loading. They influence the girder’s structural response and bring about a decrease in the ultimate resistance at subsequent patch loadings. This problem is analysed in the present paper through the serviceability limit state (SLS) of incrementally launched bridge I-girders (ILBGs). The SLS of ILBGs is a current problem since only a few studies, with contrasting conclusions and certain limitations, have been recognised in the literature. Research is limited on plate girders without longitudinal stiffeners made of structural steel. Flat slide-type launching shoes are considered in this paper.The serviceability requirement (repeatable behaviour of ILBGs) and criterion (that effective membrane strains should remain in the elastic range) are adopted from the literature. So, the serviceability resistance is adopted as a load at the start of the effective membrane plastic strains in the girder. In order to propose a practical and simple SLS design procedure, the serviceability resistance is normalised against the ultimate resistance, so a serviceability correction factor (ksls) is defined. The paper presents a parametric numerical analysis of the factor (ksls). A finite element model previously developed and validated by the author is employed to simulate a nonlinear response of patch-loaded girders. The parametric study includes 599 girders. ksls is inversely proportional to the web thickness and directly proportional to the flange thickness and the yield strength of the steel material. The load length, web depth and flange width do not influence ksls. The influence of the spacing between transverse stiffeners on ksls is negligible. Finally, by regression analysis of the results of parametric study, an original and reliable serviceability correction factor is proposed as the main objective of the research. The range when the SLS of ILBGs should be checked is also defined.

A geometrically nonlinear Hellinger–Reissner shell element for the postbuckling analysis of variable stiffness composite laminate structures

Variable stiffness (VS) composite laminates provide larger freedom to design thin-walled structures than constant stiffness (CS) composite laminates. They showed to allow the redistributing of stresses, improving buckling and post-buckling performance and, therefore, reducing material weight and costs. This work extends a recently developed mixed shell element, MISS-4C, to the postbuckling analysis of VS composite laminate structures. MISS-4C has a linear elastic closed-form solution for the stress interpolation of symmetric composite materials. Its stress field interpolation is obtained by the minimum number of parameters, making it an isostatic element. Moreover, its kinematic is only assumed along its contour, leading to an efficient evaluation of all operators obtained through analytical integration along the element contour. MISS-4C uses a corotational approach within a fast multi-modal Koiter algorithm to efficiently obtain the initial post-buckling response of VS composite laminate structures.First, the element performance is investigated by analysing a carbon fibre VS composite laminate plate subjected to compressive stresses. Numerical results obtained with MISS-4C are compared with those obtained with the MISS-4 element, showing good accuracy and a high convergence rate. Subsequently, the structural response of a glass fibre VS composite laminate girder of a short-length bridge is optimised through a multi-objective optimisation that exploits the robustness of the MISS-4C element and the efficiency of the multi-modal Koiter algorithm.

Assessment of maximum and minimum hanger forces in a triple-cable suspension bridge under live load: Analytical algorithm with manta ray foraging optimization

Triple-cable suspension bridges (TCSBs) are widely used in sea-crossing, island-linking projects with extra-long spans and ultra-wide decks. Their safe operation requires sufficient resistance of all bridge components (towers, cables, girders, and hangers) to static/dead and cyclic/live loads. Therefore, reliable assessment of maximum and minimum axial forces acting on each hanger is topical. This study proposes an analytical algorithm for assessing the internal forces and deformations of a TCSB. Specific steps and formulae for solving the coefficients are described by taking the estimation of girder response under random eccentric line loading as an example. Parameters of the suspension bridge under dead load are treated as known quantities. Actual engineering scenarios, including girder displacements along the bridge, are analyzed and discussed in detail. Basic unknown quantities are determined via governing equations under conditions of elevation differences’ closure and conservation of main cables’ unstressed lengths, yielding direct solutions for deformations of the main cables, girder, towers, and hangers. The proposed analytical model’s feasibility is verified via the finite element method. Optimal solutions to the above equations are derived by the manta ray foraging optimization (MRFO) algorithm to find the most unfavorable load distributions for all vehicle lanes of the bridge and the maximum and minimum axial forces of random hangers. Finally, the proposed method is successfully applied to a TCSB with a 1600 m main span under two operating conditions. The most unfavorable load distributions and the maximum and minimum axial forces of hangers at the mid-span and at the quarter-span point are estimated. The calculation results are compared against those obtained by the influence surface method, showing their good correlation and superiority of the proposed method in computation workload.

Improved softened truss model of prestressed concrete box girders subjected to combined bending and torsion

Prestressed concrete (PC) box girder is an innovative structure that is widely used in large-span bridges. Under eccentric loads such as vehicles, PC girders are inevitably under combined bending and torsion. To study its bending-torsional behavior, a refined full-range analysis model based on the combined action softening truss model (CA-STM) was proposed, where a simple and effective solution procedure and failure criteria were provided. The equilibrium equation, initial estimation equation for torque, and material constitutive model were modified by considering the prestressing effect to improve the CA-STM. An optimized algorithm was also employed to simplify the solution procedure instead of the traditional trial-and-error method, thus increasing the solution rate and stability. The theoretical curves predicted from the improved CA-STM exhibited great agreement with the available experimental results, and the predicted cracking and ultimate loads were also close to the experimental values. Hence, the improved CA-STM can reasonably predict the full-range mechanical response and failure modes of PC box girders subjected to combined bending and torsion, which provides great support to the design evaluation of such bridges.

Experimental study on protection of prestressed concrete box girder under vehicle explosion of bridge deck

AbstractThis paper presents a study on the explosion protection of prestressed concrete box girder, which is a commonly used in concrete bridges. The explosion protection tests of four prestressed box beams were designed with 1:5 scale. In order to evaluate the explosion performance of different protective layers, steel plate, ultra‐high‐performance concrete (UHPC) layer, and composite protective layer were used to protect the box girder. The experimental results revealed that under the effect of deck explosion, local penetrating failure occurred in the top plate of the box girder, which exhibited characteristics of punching failure. The web and bottom plate of the box girder as a whole exhibited bending characteristic. Compared with the unprotected box girder, the damage of the top plate of the protected box girder was less severe, whereas the damage of the bottom plate was greater. In working conditions 2–4, the UHPC protective box girder suffered less damage to the top plate, whereas the other protective box girders suffered more. The explosion dynamic responses of the box girder were compared, and the influences of different protective layers on the explosion dynamic response of box girder were studied. Based on the box girder damage, the protective efficiency of each protective layer under near‐explosion was studied. Based on the explosion tests, three‐dimensional numerical analysis model of box girder explosion was established. The accuracy of the numerical simulations of the box girder explosion were verified by comparing with the experimental failure data. Through the numerical results, the explosive energy dissipation capacity of different protective materials was compared and analyzed. Finally, based on the dynamic response of the box girder under different working conditions, the sensitivity of the protective layer to the dynamic responses of the box girder were studied. The analysis showed that the UHPC layer was sensitive to the change of prestress and explosion damage area of the box girder but had little influence on the rebars stress and the overall response of the box girder.

Influence of strand rupture on flexural behavior of reduced-scale prestressed concrete bridge girders with different prestressing levels

In prestressed concrete (PC) bridges, high-strength prestressing steel plays a key role in the flexural response of girders. In both pre-stressed and post-tensioned PC bridge girders, damage induced by corrosion or impact of under-passing high vehicles may led to rupture of one or more strands, significantly affecting the load-carrying capacity against dead and traffic loads. This paper presents an experimental study on the response of PC girders affected by strand rupture at different locations. Four reduced-scale post-tensioned concrete girders with different levels of initial prestressing force were tested under four-point bending. Two specimens with a different level of prestress were initially tested in undamaged configuration to provide a basis for the assessment of damage effects. The other pair of specimens were intentionally damaged - having the same initial prestressing level of their undamaged counterparts - in the lower tendon to investigate their limited flexural response under different performance levels including serviceability and collapse. Damage turned into a different critical cross section outside the loading region, i.e. both cracking and collapse were attained 1.1m away from midspan. In the last section of the paper, a cross sectional analysis of the girder was developed at cracking and ultimate conditions for the prediction of damage impact on failure mechanisms, thus validating the experimental findings.

The effect of high-speed railway train on the seismic response of bridge under earthquakes

This study aims to discuss the effect of high-speed railway train on the seismic response of bridge girder under earthquakes especially pay attention to the possible response reduction to the bridge caused by vehicle, utilizing experimental and simulation methods. A 1:10 scale model for the train-track-bridge system was built and a high-speed train running test platform based on shaking table array was constructed for the seismic loading test at varying running speed. To account the effects of different earthquake characteristics, earthquakes under the four types of site soil in the far-field and near-field were selected. The vehicle was modeled in two kinds of ways to distinguish the effects of spring-mass vehicle and additional mass which means a vehicle was set with spring suspension and mass, while another with additional mass only. Through a large amount of numerical simulation dates to determine the distribution interval of specific reduction value caused by the vehicle under the earthquake. Results in running tests and numerical simulation indicate that the lateral acceleration of the bridge girder can be effectively reduced when the train is stationary. The reduced ratios were about 4%− 8% compared without train on bridges. As the speed increases, the response of bridge is generally intense and the reduction is also weakened. Similar reduction was not observed in the response of vertical earthquake excitations, and high-frequency earthquakes have adversely affected this kind of reduction. The main reason for the reduction of lateral seismic response of bridge girder in the presence of static vehicle can be attributed to the phase difference between vehicle and bridge caused by a mass damper-like action, and the additional mass cannot cause similar changes alone.

Dynamic response and cumulative damage mechanism of simplified hull girders under repeated underwater explosions

The dynamic response and cumulative damage mechanism of simplified hull girders (SHGs) subjected to repeated underwater explosions were investigated in this research. Experimental and numerical investigations were conducted to gain a comprehensive understanding of the relationship between cumulative damage and explosive charge. Three series of experiments were carried out on SHGs, subjecting them to both single and repeated loading (up to five times). The analysis focused on the overall deflection values of the SHG and the local bottom plate deflection values, revealing a linear relationship with the cumulative number of occurrences. A validated finite element simulation model was employed to examine the response of the SHGs under repeated blast loading, utilizing experimental results for validation. An impact factor was established to quantify the magnitude of the explosive force, considering both the power of the explosive and the distance of detonation. The SHGs showed localized deformation at 10 impact factors, but experience pronounced cumulative effects at 14.4 and 20 impact factors. Furthermore, a consistent decline in the residual strength of the SHGs as the number of explosions increased. Following the first underwater explosion, the damaged SHG displayed an ultimate plastic bending moment of 3696.5 N m, reflecting a 16.3 % reduction compared to the unloaded SHGs. This reduction can primarily be attributed to the altered load distribution on the deformed SHGs. These findings contributed to the understanding of the cumulative damage behavior and response of SHGs exposed to repeated underwater explosions, providing valuable insights for the design and structural integrity assessment of naval vessels.

Temperature Response of Double-Layer Steel Truss Bridge Girders

Double-layer steel truss continuous girders are prone to significant temperature stress, deviation, torsion, and warping, thus causing adverse temperature structural responses, and also affecting the safety and durability of bridge structures. This paper presents an investigation on time-dependent characteristics in the temperature field and temperature response of double-layer steel truss continuous bridge girders, fully considering the shielding effect subjected to different solar radiation angles during the high-temperature season. The time-dependent thermal boundary conditions and support conditions provided for the steel truss bridge structure were determined. Subsequently, a thermal analysis model for the entire structure of double-layer steel truss continuous girders was established to attain the temperature distribution law. The research results show that significant differences occur in the position and temperature difference of temperature gradients exhibited in the vertical, horizontal, and longitudinal directions in the double-layer steel truss bridge structure. The temperature distribution pattern within the chord section is mainly influenced by the environmental temperature and solar radiation intensity, along with the heat exchange between different panels. Thereafter, a validated temperature gradient formula for the component section has been proposed. The time-dependent laws in structural displacement, stress, and rotation angle under daily temperature cycling conditions have been revealed, thereby providing a theoretical basis for the life cycle construction and safety maintenance of double-layer steel truss structure bridges.

Evaluating Shear Response of UHPC Bridge Girders Exposed to Fire

Evaluating Shear Response of UHPC Bridge Girders Exposed to Fire

Numerical method for whipping response of ultra large container ships under asymmetric slamming in regular waves

In this paper, a 3-D nonlinear time-domain hydroelastic analysis method for ship wave loads considering asymmetric slamming is proposed, and a 3-D Rankine panel method is used to solve the seakeeping problem. To accurately predict the hydroelastic response of the hull girder, the interaction between the hull structure and the flow field is considered in the body boundary condition. The motions and sectional loads of the ship are expressed by the superposition of the modal, which is obtained by modal analysis on a 3-D finite element model of the hull. After calculating asymmetric slamming loads using the Modified Logvinovich Model (MLM), the hydroelastic response of a 21,000-TEU container ship is analyzed, which incorporates the horizontal bending-torsional coupling vibration. Furthermore, the hull motion, slamming force, and section load are analyzed in detail to properly identify the mechanism of the slamming-whipping phenomenon. The results show that asymmetric slamming significantly affects the horizontal-torsional whipping response of the hull, especially when the wave encounter frequency matches the natural frequency.

Model-assisted clustering for automated operational modal analysis of partially continuous multi-span bridges

Long multi-span bridges represent a broad section of the civil roadway infrastructure. Despite being so common, their condition-based maintenance through vibration-based Structural Health Monitoring (SHM) has been scarcely investigated in the literature. The dynamic identification of such structures through Operational Modal Analysis (OMA) is especially challenging due to of their quasi-periodic nature and the common existence of weak inter-span coupling. Even when designed following an isostatic scheme, there always exists a certain degree of coupling between spans due to the continuity of the deck, the pavement and imperfect expansion joints. Hence, the modal poles of the spans typically appear as dense clusters with closely spaced frequencies and mode shapes with similar wavelengths, which significantly hinders the identification of physical poles through stabilization diagrams. In this light, this paper proposes a model-based machine learning approach to conduct and interpret the OMA results of partially continuous multi-span bridges. The proposed method is a hierarchical clustering approach that leverages on the analytical solution of the vertical free vibration response of multi-span girders with weak inter-span rotational coupling, allowing the estimation of the modal features of any bridge configuration ranging from simply supported to perfectly continuous conditions. Detailed parametric analyses and discussions are presented to appraise the correlation between the inter-span rotational coupling and the clustering of the modal poles of multi-span bridges, as well as the influence of damage conditions of varying severity and extension. On this basis, a model-based cut-off distance threshold for hierarchical clustering of stable poles is proposed to assist the automation of the global OMA of multi-span bridges. The developed formulation is tested in a real-world in-operation seven-spans reinforced concrete girder bridge, the Trigno V Bridge in Italy.

Experiment study on vortex-induced vibration of a twin-box girder with large cantilever plates

Due to their good aerodynamic stability performance, twin-box girders are frequently adopted in long-span cable-supported bridges. However, they are also susceptible to vortex-induced vibration (VIV) since the central slot changes the flow patterns around a bridge girder. In this paper, the VIV performance of a twin-box girder with large cantilever plates was investigated through wind tunnel tests of sectional models with 1:75 and 1:30 scale ratios. Furthermore, the effects of increasing the damping ratio and installing various conventional aerodynamic countermeasures such as guide vanes, grid plates, and central stabilizers on VIV suppression of the twin-box girder were investigated. A new type of aerodynamic countermeasure named the L-shaped windshield was proposed to suppress the VIV response of the twin-box girder to an acceptable level. The results indicated that significant vertical VIV occurred for the twin-box girder, and increasing the damping ratio and installing conventional aerodynamic countermeasures could not suppress the VIV response of the twin-box girder effectively. The attachments obviously worsened the vertical VIV performance of the twin-box girder, and the attachments on the upper surface showed a more significant effect. It was further demonstrated that the L-shaped windshield is an effective countermeasure that can completely suppress the vertical VIV of the twin-box girder by greatly reducing the motion-induced vortexes in the central slot with the help of low turbulence in the turbulent flow field.

Development of a bidirectional rocking isolation bearing system (Bi‐RIBS) to control excessive seismic response of bridge structures

AbstractA bidirectional rocking isolation bearing system (Bi‐RIBS) is proposed to provide seismic protection for bridge structures. By using the 3‐D rocking motion of the Bi‐RIBS, this system acts as a mechanical fuse to limit the maximum force transmitted to the bridge piers and as a restoring component to control an excessive girder response. Possible applications in bridge structures were discussed. A simple analytical model was established to characterize the dynamics of an example bridge featuring such a Bi‐RIBS. A series of dynamic analyses were performed by using the proposed model to investigate the effects of several factors on controlling the seismic responses of the bridge, for example, the design parameters of Bi‐RIBS including inclined angle and size, the damping property at the support interface, and the mass ratio. The peak ground accelerations of the bidirectional ground motion record were scaled to various levels to evaluate the maximum performance indices of the bridge structure and the response control effectiveness of the Bi‐RIBS compared to the uncontrolled counterparts. The simulation results demonstrated that the proposed Bi‐RIBS could effectively control the maximum pier displacement while keeping the bearing from overturning if suitable parameters were selected. In particular, the control effectiveness on the maximum pier response becomes more significant as the seismic intensity increases, due to its distinctive negative stiffness property.

Transverse Connectivity and Durability Evaluation of Hollow Slab Bridges Using Surface Damage and Neural Networks: Field Test Investigation

Prefabricated concrete hollow slab bridges are widely used in short- and medium-span highway bridges in China due to the advantages of high production quality, installation convenience, and low construction cost. Field investigation shows that severe hinge joint damage occurred during the service life, and mechanical performance of the bridges also deteriorated with the weakened joints. It is important to accurately evaluate the performance of hollow slab bridges to ensure the safety of the highway system. In this paper, transverse connectivity and durability of the concrete hollow slab bridges are investigated in a field test using the surface damage and neural networks. Hollow slab bridges in the Wu-He highway system were taken as the background bridge. Surface damage was visually checked and statistically analyzed. Static load test was conducted to evaluate the transverse connectivity of the hinge joints based on the girder responses. The hollow slab bridges were then demolished, and a total of 75 concrete girder segments were cut off. Durability of the girders was evaluated based on the conditions of concrete and rebars, and the analytic hierarchy process along with the fuzzy comprehensive evaluation method was employed. Results showed that there were two main types of the defects in the hollow slab bridges, i.e., the transverse cracks on the bottom plates of the girders and the longitudinal cracks in the hinge joints. The distribution of the deflection of each girder was non-uniform due to the weakening of the transverse connectivity, and the girders in the background bridges were within the moderate deterioration condition after 25 years’ service life. An evaluation method of the hollow slab girders using the neural networks and surface damage was verified by the field test data. The maximum crack width at different locations of the bridges was used in the input layer of the neural network, and the hinge joint damage or the durability was considered as the output results. The prediction error of the method in the test set was within 15.0% for the hinge joint damage and within 40% for the durability result of the girder, indicating the feasibility of the evaluation method.

The Multi-Functional Modelling Shear Lag Method for Accurate Calculation of Static Response and Accordion Effect of Improved Composite Box Girders

The composite box girder with corrugated web and steel bottom plate (CW-SBS) is a kind of improved steel-concrete structures. The design of CW-SBS box girders needs the accurate method to calculate the working response and accordion effect in consideration of the self-stress equilibrium condition of shear lag warping stress and shear deformation. This study proposes the multi-functional modelling shear lag (MFMSL) method which adopts the four longitudinal displacement difference functions to model the variation of shear lag in the CW-SBS box girders with different wing slab widths and thicknesses. Therefore, MFMSL is a method to calculate the static response and accordion effect of the CW-SBS composite box girders. Structural differential equations based on the energy-variation principle present that the MFMSL method effectively improves the calculating accuracy of the CW-SBS box girder static response, which can be verified by both experimental and simulative results. Also, the MFMSL method demonstrates that the accordion effect of the CW-SBS box girder is stronger than that of the traditional composite box girder and closely relates to the load distribution. Hence, the proposed method further lays the foundation for the analysis and design of CW-SBS box girders.

Reduced-Order Model Based on Volterra Series for Aerodynamics of the Bridge Deck Section and Flutter Critical Wind Speed Prediction

This study proposes a novel reduced-order model (ROM), based on the Volterra series, for the aerodynamic force of the bridge deck section. Moreover, the ROM of the aerodynamic force of the streamlined box girder section of the Great Belt East Bridge (GBEB) is identified with computational fluid dynamic (CFD) simulations. Furthermore, an analysis method combining ROM aerodynamic force and Newmark-β integration is established to simulate the aeroelastic responses of the bridge deck section. Finally, the wind-induced vibration responses of the GBEB section are calculated near the flutter critical wind speed based on the Volterra series-based aeroelastic analysis and the fluid–structure interaction (FSI) numerical simulations in ANSYS Fluent, respectively. Moreover, to verify the applicability of the proposed method, the aeroelastic responses of the main deck section with the crash barriers of Lingdingyang Bridge (LDYB) are also simulated via the Volterra model and Newmark-β integration near the flutter critical wind speed. The results show that the first-order truncated Volterra model established in this study can accurately capture the aerodynamic response of the main girder, and the results are in good agreement with those of the CFD numerical simulation under forced vibration. Furthermore, the proposed method combined with ROM aerodynamic force and Newmark-β integration can effectively calculate the FSI of the bridge girder. The numerical results of the flutter critical wind speed and flutter frequency of GBEB and LDYB are consistent with the numerical results by the FSI method based on ANSYS Fluent and the existing numerical and experimental results, respectively.