Stiffness Of Bridge Research Articles

Crossing cable design optimization of multi-tower cable-stayed bridge based on joint analytical method and genetic algorithm

As the length of the main span increases, the stiffness of multi tower cable-stayed bridges continues to decrease. The performance of the structure can be improved by setting crossing cables at the main span. The setting of crossing cables is a key issue in the overall design of bridges. This study presents a new optimization strategy to achieve the optimal setting of crossing cables. The developed technique combines analytical algorithm, optimization algorithm and finite element method. The anchor position, number, cross-sectional area and cable force of crossing cable are taken as variables. Firstly, an analytical algorithm is used to determine the feasible interval of the number and area of crossing cables, and then the genetic algorithm is used to search for the optimal solution within the feasible interval to obtain the crossing cable layout with minimum steel. Based on the analytical method, the feasible interval is determined, so that the population is close to the convergence point from the initial state, and the optimization efficiency is improved. The effectiveness of the proposed method is verified by four optimization problems, and the influence of the deck stiffness on the anchor position of crossing cable is discussed, which provides a reference for the setting of the crossing cables in the preliminary design stage.

An analytical method for out-of-plane stability assessment of network arch bridges

Network arch bridges typically feature inclined cables with a net configuration to support the bridge deck, therefore, improving the bridge's stiffness and reducing bending moments along the arch elements. Given their relatively slender cross-sections and large compression stresses, properly evaluating stability safety is crucial to the integrity of network arch bridges. However, because of the unique design of cable configuration, current design specifications mostly do not provide specific methods for such stability assessments. To address this gap, the study proposes a new analytical methodology that elucidates the mechanical relationship between basic design parameters and the stability performance of network arch bridges. A numerical example is conducted using finite element analysis to validate the performance of the proposed method. In addition, the influence of several design parameters on the stability factor and buckling length factor is investigated. This research further proposes a practical expression for the buckling length factor of arch ribs with nonlinear regression analysis. The results exhibit that the proposed method can efficiently and accurately evaluate the buckling stability performance of network arch bridges, and the established practical expression can facilitate designers in easily estimating the critical buckling load during the design process.

Analysis of load carrying capacity of bridges strengthened by extracorporeal prestressing after five years of operation: a case study

PurposeThe application of reinforcing old bridges by adding external prestressed steel bundles is becoming more and more widespread. However, the long-term safety performance test of the strengthening method is rarely carried out. In this paper, the bearing capacity of a 420 m prestressed concrete (PC) continuous girder bridge after five years of strengthening is analyzed.Design/methodology/approachThe bridge model of the bridge structure and strengthening scheme is established by the finite element software of the bridge. The theoretical load-bearing capacity of the bridge under the latest standard load grade is obtained by finite element analysis. The actual bearing capacity of the bridge is obtained by field test. Through the comparative analysis of theory and practice, the health state of the bridge after five years of reinforced operation is judged. The damage to the overall stiffness and external prestressing of the bridge is also analyzed.FindingsThe results of deflection and strain show that the stiffness and strength of the secondary side span and the middle span decrease slightly, and the maximum reduction of bearing capacity is 4.5%. The static stiffness of the whole bridge decreases as a result of cracks, and the maximum decrease is 21%. In the past five years, the relaxation loss of the external prestressing of the bridge is 3.31–3.97%, which is the main reason for the decrease in bearing capacity.Originality/valueThrough the joint analysis of the bridge stiffness and the loss of external prestressing, the strengthening condition of the bridge after five years of operation is effectively analyzed. The strengthening effect of the external prestressed steel beam strengthening method is analyzed, which can provide a reference for similar bridge strengthening.

Bridge damage identification based on synchronous statistical moment theory of vehicle–bridge interaction

AbstractConsidering the weak noise resistance and low identification efficiency of traditional bridge damage identification methods, a data‐driven approach based on synchronous statistical moment theory and vehicle–bridge interaction vibration theory is proposed. This method involves two main steps. First, a two‐axle test vehicle is used to collect acceleration response signals synchronously from adjacent designated measurement points while stationary. This operation is repeated to calculate the second‐order statistical moment curvature (SOSMC) difference of entire bridge points corresponding signals in different states. By comparing with the reference value, the preliminary damage location of the bridge can be obtained. Second, the first‐order modal shape curve is constructed using the second‐order statistical moment (SOSM). The refined identification of bridge damage is then based on an improved direct stiffness back calculation of the bridge's stiffness. This article proposes the synchronization theory for the first time and combines it with the statistical moment clustering method, forming an innovative approach to obtaining structural vibration modes. The effectiveness of this method has been well validated through numerical simulations with different parameters and on‐site bridge tests. The research results indicate that SOSMC indicators have better noise resistance and higher recognition efficiency in identifying damage locations, compared to modal curvature and flexibility curvature indicators. Additionally, compared to transfer rate and random subspace methods, the SOSM method results in smaller error and higher identification efficiency.

Design and optimization analysis of pylon open lower corbel

This study, centered around the engineering context of the Wuxue Yangtze River Bridge, addresses the challenge of significant temperature-induced secondary internal forces in the short lower tower column. A novel open lower corbel tower scheme is proposed as a solution. Firstly, comprehensive finite element models are established for both the open lower corbel pylon scheme and the traditional lower continuous beam pylon scheme. These models are employed for finite element analysis to derive bending moments and displacements of the bridge pylon under various loads, including permanent, vehicle, temperature, and wind loads. Subsequently, considering internal force distribution and stiffness, a comparative assessment is made between the open lower corbel cable pylon scheme and the traditional lower continuous beam cable pylon scheme. The findings reveal that the open corbel structure bridge pylon exhibits lower transverse bending moment values under the influence of permanent load, vehicle load, temperature load, and wind load. This reduction is advantageous for mitigating the issue of significant temperature-induced secondary internal forces in the bridge pylon. Additionally, the transverse bridge stiffness of the open lower corbel cable pylon scheme is found to be on par with that of the lower continuous beam cable pylon scheme. Moreover, topology optimization of the original corbel design is accomplished using the relative density method. The computational results demonstrate that the corbel’s stress and deformation under vertical loads meet code requirements. These research findings offer valuable insights for the design and construction of similar projects.

Study of the Impact of Varying Inclination Angles of Arch Ribs on the Seismic Behavior of Half-Through Steel Basket-Handle Arch Bridge

In the present study, multiscale finite element (FE) models of half-through steel basket-handle arch bridges were established. The eigenvalue analyses were conducted to explore the dynamic characteristics of the arch bridges based on the FE models. In addition, a parametric analysis was carried out to investigate the impact of the inclination angle of the arch rib (0°, 4°, and 7°) on the longitudinal and transverse seismic performances of arch bridges. The results show that with the increase in inclination angle, the out-of-plane stiffness of half-through steel basket-handle arch bridges increases, resulting in the natural period of the structure becoming shorter from 3.09 s to 2.93 s. Adjusting the inclination angle appropriately has a beneficial impact on the overall seismic performance of the structures, affecting both displacement and internal forces, in which the most significant improvements include a 42.8% decrease in displacement and a 62.6% reduction in internal forces. Adjusting the inclination angle can cause the arch springing and transverse brace to undergo larger plastic deformation. It is advisable to judiciously enlarge the sectional dimensions and enhance the material strength of both the arch springing and the transverse bracing in seismic designs.

Distributed stiffness assessment of bridges based on macro-strain envelope curve under moving trainloads

Due to the limited gauge length of traditional strain gauges, the bridge strain influence line cannot be obtained from actual measurement, rendering the evaluation of the longitudinal stiffness distribution of bridges by monitoring results a difficult task. To address this issue, a distributed long-gauge strain sensing technology was used to evaluate the stiffness of high-speed railway bridges. Firstly, the distributed macro-strain influence line of bridges under train load was derived, followed by the clarification of the mechanical relationship between the longitudinal stiffness of railway bridges and the distributed macro-strain of the bridges. Then, a stiffness evaluation method was proposed based on the distributed macro-strain time history envelope curve. Secondly, the feasibility of the method was verified through finite element simulations. By establishing a refined dynamic macroscopic strain calculation model for railway bridges, the proposed method was explored for the accuracy and feasibility of bridge stiffness under different damage conditions. Finally, a real bridge verification test was conducted on a bridge on the Shanghai-Kunming Railway, and the test results showed how the thickness of the bottom plate would vary with the bridge span in the bridge design.

Transverse Analysis of Box Girders with Corrugated Steel Webs

The utilisation of box girders with corrugated steel webs (CSWs) represents an innovative approach to bridge superstructure design that has garnered substantial popularity worldwide, with a notable prevalence in both Asia and Europe. Compared with traditional box girders, they avoid web cracking, improving the prestressing efficiency and bridge spanning ability. As an innovative box girder, a corrugated web can increase the cantilever length and transverse stiffness, and at the same time, it reduces the dead weight of the bridge deck. However, little research has been conducted on the mechanical properties of this novel spine-like box girder with CSWs, especially its transverse performance, although it has been used in many applications. In this paper, the effect of the web form on the behaviour of box girders is introduced. Therefore, three representative three-dimensional (3D) finite-element models (i.e., corrugated web box girder, flat web box girder, and ordinary equivalent concrete web box girder) have been established to quantitatively investigate the influence of corrugated web stiffness on transverse stress under the action of gravity and vehicle loads. Generally, significant differences in the mechanical performance of box girders with CSWs have been observed compared with conventional box girders with concrete webs. Additionally, parametric studies to investigate the influences of the corrugation dimensions (in term of the corrugation height, web thickness, panel width, web height and elastic modulus) on the transverse stiffness of such bridges are analyzed. The results show that a new stiffness formula can be put forward to consider the effect of web height, and a high-strength steel web needs to be developed urgently for box girders with CSWs in the near future. Overall, the results of this investigation can be used as a reference for transverse designing and segmental construction of similar projects.

Vertical stiffness limit of 400 km/h high-speed railway simple-supported bridge considering excitation randomness

Vertical stiffness of the bridge is of paramount importance in guaranteeing optimal driving performance for high-speed railway (HSR) trains. Initially, the Auto Regression and Moving Average model with eXogenous input (ARMAX) model is employed as the surrogate model for the train-bridge (TB) coupling system. Then, the framework for analyzing vertical bridge stiffness is proposed employing the surrogate model, and the relationship between the train response affected by excitation randomness and the vertical stiffness indicators of the bridge is established. Finally, the influence of various factors such as train speed, train type, car body mass, and bridge span on stiffness limit of 400 km/h HSR simple-supported bridge (SSB) is examined. The results indicate that the surrogate model offers a notable advantage in computational efficiency, while maintaining a satisfactory accuracy in predicting the train response. With higher train speeds, lighter car body masses, and longer spans, the demand for stricter bridge stiffness limits becomes more pronounced. Based on the driving performance of the train types analyzed, the recommended stiffness limit is proposed for the prestressed concrete simply supported beam (SSB) bridges used in HSR, with a span length of less than 40 m and operating at a speed of 400 km/h.

Node-based wave analysis method for the dynamic response and stiffness of long-span cable-stayed bridges

For dynamic analysis of long-span cable-stayed bridges (LCB) with high flexibility and long force transmission paths, wave analysis method offers unique advantages over modal analysis. However, conducting wave analysis for the entire LCB poses challenges due to the modeling complexity and the substantial computational cost associated with solving numerous wave equations. Therefore, a simple analytical approach for wave analysis of LCB is proposed, which entails the discretization of the entire bridge into waveguides and the subsequent recombination of the regularized local wave propagation models. The feasibility and strategy of solving the global propagation function using local double coordinate systems and specific node-based local wave propagation models are demonstrated. Additionally, based on the geometric and mechanical configuration of nodes in the LCB, local wave scattering and propagation models corresponding to the four standardized nodes types are proposed. A unified Node-Based Wave Analysis (NWA) method for LCB is developed, considering the viscoelastic behavior of cable-stayed beams according to the Kelvin-Voigt model to enhance structural realism. The reasonable damping coefficient in bridge is determined by means of theory and dynamic in situ test of three bridges. Finally, an extended case study is conducted on a typical two-pylon cable-stayed bridge, focusing on the impact of moving loads and material properties on wave characteristics. The results demonstrate the reliability of the proposed NWA method in predicting wave energy distribution, highlighting the suitability of wave analysis for dynamic analysis of LCB. In comparison to undamped structures, it has been found that the presence of damping results in a pair of additional flexural waves with a new dispersion relation in cable-stayed bridges. Furthermore, the study reveals the stiffness enhancement mechanism associated with wave dispersion characteristics in cable-stayed bridges.

An approach for identification of bridge bending stiffness distribution using improved Gaussian peak function

Bridge damage and bending stiffness deterioration can lead to a decrease in the bearing capacity of a bridge, posing significant safety concerns. To ensure the safe operation of bridges, it is crucial to accurately identify bending stiffness deterioration and assess the bridge performance. The bridge influence line (IL), which reflects the deterioration of bending stiffness, was widely used in the assessment of bending stiffness deterioration. Existing IL-based methods mostly assume a uniform reduction in bending stiffness for identification. In reality, the deterioration of bridge bending stiffness is far more complex, which causes difficulty in accurately identifying the bending stiffness distribution using the uniform reduction model. This paper proposes a novel method for identifying bridge stiffness distribution using an improved Gaussian peak function model. The improved model incorporates additional parameters, allowing for considering a wider range of stiffness variation and thus addressing the limitations of traditional models. The parameters of the improved Gaussian peak function model are estimated by minimizing the residual between the predicted deflection influence line (DIL) and the actual DIL using the Levenberg-Marquardt (LM) algorithm. This approach enables the accurate identification of bending stiffness distribution without baseline information. Numerical simulation and laboratory experiment are used to verify the effectiveness of the proposed method in identifying bridge bending stiffness distribution. A comparison between the identified and actual bending stiffness distribution curves under various forms of damage assesses the applicability of the proposed method.

Research on the Mechanical Performance of a Mountainous Long-Span Steel Truss Arch Bridge with High and Low Arch Seats

The Loushui River Bridge is a mountainous long-span steel truss arch bridge with high and low arch seats. The design and construction of the bridge follow the principle of minimizing environmental damage and promoting sustainable development. In this article, the mechanical performance of this bridge is investigated experimentally and numerically at both the construction and operation stages. A series of validated finite element models were established for linear and nonlinear analyses by introducing geometric imperfections, geometric nonlinearities, and material nonlinearities. Then, several optimized models based on different types of design are compared with the original structure. The results indicate that the stability of the asymmetric bridge met the design requirements in both the construction and operation stages. However, the lateral stability and stiffness of the asymmetric bridge are weak due to the wind hazard that occurred in its mountain ravine. The out-of-plane instability from the short half-arch is the dominant failure mode, and the weakest area is where the arch ribs intersect with the bridge deck. It can be solved by adding more cross bracings without affecting the clearance above the bridge deck or by improving the material intensity of the arch.

Analysis of Train-Track-Bridge Coupling Vibration Characteristics for Heavy-Haul Railway Based on Virtual Work Principle.

This paper introduces an innovative model for heavy-haul train-track-bridge interaction, utilizing a coupling matrix representation based on the virtual work principle. This model establishes the relationship between the wheel-rail contact surface and the bridge-rail interface concerning internal forces and geometric constraints. In this coupled system's motion equation, the degrees of freedom (DOFs) of the wheelsets in a heavy-haul train lacking primary suspension are interdependent. Additionally, the vertical and nodding DOFs of the bogie frame are linked with the rail element. A practical application, a Yellow River Bridge with a heavy-haul railway line, is used to examine the accuracy of the proposed model with regard to discrepancy between the simulated and measured displacement ranging from 1% to 11%. A comprehensive parametric analysis is conducted, exploring the impacts of track irregularities of varying wavelengths, axle load lifting, and the degradation of bridge stiffness and damping on the dynamic responses of the coupled system. The results reveal that the bridge's dynamic responses are particularly sensitive to track irregularities within the wavelength range of 1 to 20 m, especially those within 1 to 10 m. The vertical displacement of the bridge demonstrates a nearly linear increase with heavier axle loads of the heavy-haul trains and the reduction in bridge stiffness. However, there is no significant rise in vertical acceleration under these conditions.

Damping and tuning of inerter-based dampers for cable vibration mitigation considering girder vibrations

As the spans of cable-stayed bridges increase, and with the use of steel towers and girders, bridge stiffness decreases, the bridge frequencies approach the frequencies of the cables. The effect of girder–cable coupling vibrations cannot be ignored in cable vibration control. This study focuses on the performance of inerter-based dampers (IBDs) in cable vibration control when considering girder vibrations. Two types of IBD, a viscous inerter damper (VID) and a tuned inerter damper (TID), are studied. The system dynamics are formulated through complex modal analysis. Damping effects of the VID and TID are evaluated and optimized based on the complex frequency loci of the damped system. The results indicate that the control performance of the VID and TID for the target cable mode is drastically reduced when the ratio between the girder and target cable frequencies is approximately 1. The effects of the girder–cable coupling vibration on the optimal parameters and control performance of the VID and TID for the target cable mode are found to be significant even when the girder-cable frequency ratio is not close to 1, and the effect can be increased for a smaller girder–cable mass ratio. The different evolution characteristics of the girder–cable coupling effect are revealed by comparing the designs and performances of the VID and TID. The effectiveness of the VID and TID to control the system model considering dynamic cable force and cable sag is verified using a numerical model.

Analytical Solution for Longitudinal Anti-Push Stiffness of the Middle Tower of Cross-Cable Multi-Tower Cable-Stayed Bridge

The Queensferry Crossing in Scotland is the first multi-tower cable-stayed bridge with crossed cables in the world. This means that the conceptual design of a cross-cable multi-tower cable-stayed bridge has become a reality. In this paper, the cross-cable action mechanism is studied deeply. Suppose that the small displacement amount at the top of the side tower is ignored. The deformation coordination principle is used twice to analyze the relationship between the horizontal external force and the top displacement amount of the middle tower. Thus, derive the formula for estimating the anti-push stiffness of cross cables to the middle tower of the multi-tower cable-stayed bridge under the influence of the stiffness of the tower and beam. A numerical example is given to verify this. The research results show that the error between the analytical solution and the finite element solution is less than 8%, which meets the conceptual design requirements of cross-cable multi-tower cable-stayed bridges. The cross cables can reduce the deflection of the main beam and improve the stiffness of the bridge. After setting 10 pairs of cross cables, the displacement amount of the middle tower decreases by as high as 51%. The stiffness of the multi-tower cable-stayed bridge increases with an increase in the number of cross cables, but the increasing trend of stiffness gradually slows down. Increasing the stiffness of the tower or beam can improve the structural stiffness to a certain extent, but the effect is much less potent than that of the cross cable in the middle span.

Bridge distributed stiffness identification of continuous beam bridge based on microwave interferometric radar technology and rotation influence line

Continuous beam bridges are a widely used and prevalent type of bridge. As material properties degrade over time, the bridge stiffness decreases, leading to a reduction in bearing capacity. Accurate identification of bridge stiffness is crucial for safe operation, but there are few studies on identifying the stiffness of continuous beam bridges. This paper proposes a novel method to identify regional stiffness distribution using microwave interference radar technology and rotation influence lines. Firstly, the regionally distributed multi-point displacement influence lines (DILs) are procured via an innovatively designed lightweight radar device and the multi-point rotation influence lines (RILs) can be subsequently derived through a difference method. Utilizing the derived multi-point RILs, the continuous beam is decoupled into multiple-span simple beams featuring additional moment couples. Then the moment envelope area (MEA) can be computed by integrating the superposition principle and the curvature envelope area (CEA) can be determined using multi-point DILs. Finally, the bridge distributed stiffness can be obtained by combining the MEA and CEA of the monitored area. To verify the validity of the proposed method, a laboratory experiment involving a continuous beam is conducted to identify its’ bridge distributed stiffness (BDS).

Improvement in the Seismic Performance of a Super-Long-Span Concrete-Filled Steel-Tube-Arch Bridge

The applicability of current seismic-performance-improvement technologies needs to be studied. This research took a super-long-span CFST arch bridge with a total length of 788 m as the object on which to perform a non-linear time-history analysis and a seismic-check calculation according to the seismic response, so as to reveal the seismic weak points of the arch bridge. After the completion of the bridge’s construction, we arranged and utilized the stayed buckle cables (SBCs) reasonably. The seismic performance of the super-long-span CFST arch bridge was improved through friction-pendulum bearings (FPBs) and SBCs. The research shows that FPBs can solve the problem of the insufficient shear resistance of bearings, and SBCs can address the problem whereby the compressive stress of the transverse connection of the main arch exceeds the allowable stress. Moreover, SBCs can increase the transverse stiffness of arch bridges and reduce their seismic responses. Finally, a combination of FPBs and SBCs was adopted to improve the overall seismic performance of the arch bridge and obtain the best seismic-performance-improvement effect.

Structural stiffness evaluation of suspension bridge based on monitoring data

For long-span suspension bridges, the structural deformation is significantly influenced by the environment. Therefore, evaluating the structural stiffness of suspension bridges is crucial. This paper takes a certain long-span suspension bridge over the sea as an example to discuss different methods for evaluating the structural stiffness of suspension bridges. A three-dimensional finite element model is established, and influential lines at key locations are extracted. The fitting accuracy of vertical deformation and environmental temperature data under different time windows is analyzed based on GPS deformation monitoring data. Furthermore, the spatial distribution of the maximum and minimum values of bridge deformation caused by vehicle loads is statistically analyzed. The results indicate that the displacement extreme value coefficient at the mid-span of the suspension bridge is relatively large compared to other locations. The measured displacement envelope curves are within the theoretical envelope curves, demonstrating good overall stiffness performance of the bridge. The research methodology in this paper accurately evaluates the overall structural stiffness of the suspension bridge, providing strong support for ensuring the safe operation of the bridge.

An autonomous and heuristic approach for extracting bridge frequencies from passing vehicles

The Federal Highway Administration (FHWA) recognizes a need for cost-effective and practical structural health monitoring (SHM) techniques to manage the bridge network. System identification (SI) techniques are the first step in developing SHM frameworks to extract bridge dynamic properties (natural frequencies, damping ratios, and mode shapes). One promising indirect SI technique uses accelerometer-instrumented vehicles to measure the dynamic properties of bridges, such that a few instrumented vehicles could economically monitor a large network of bridges. This study proposes an autonomous framework called autonomous peak picking variational mode decomposition (APPVMD), which leverages an ensemble of signal processing techniques and heuristic models to autonomously extract bridge frequencies from instrumented vehicles. The proposed framework does not require prior information or model-informed training. The framework is tested on four vehicles and 39 unique bridge classes using finite element (FE) models to assess the feasibility of deploying it into practice. The results of this study indicate that the algorithm can make successful bridge frequency extractions in more than 69.2% of the bridge cases using any vehicle and a maximum value of 97.4% using an SUV, while considering the effects of road surface roughness. The influence of bridge stiffness, mass, and span length on the algorithm’s success rate is discussed. It is concluded that flexural rigidity and span length play a significant role in the accuracy of APPVMD. The combined effects of bridge inertia and damping cause heavier bridges to have a higher amplitude signal for a longer duration, increasing the algorithm’s successful detection rate of bridge frequency. Next, the authors examine the effect of reducing the tire stiffness in the truck model on the success of the APPVMD algorithm. The customized truck outperformed the original truck and the SUV by successfully extracting the bridge frequencies of 97.4% of the bridge cases and by having more bridge frequencies predicted in a higher confidence region than the SUV. In addition, the customized truck model is used to verify the APPVMD’s robustness to large levels of sensor noise. Even at significant levels of white noise (1% SNR), as the success rate for bridge frequency extraction using the customized truck only drops to 84.6%. Finally, the influence of vehicle speed on the APPVMD algorithm’s effectiveness is studied. Generally, slower speeds resulted in more successful predictions of bridge frequency, but minor improvements in the accuracy of the frequency predictions were observed at slightly increased velocities, 13.4 m/s (30 mph) and 17.9 m/s (40 mph), but a reduction in accuracy was observed at higher velocities, 22.3 m/s (50 mph).

Curvature envelope area based rapid identification method of bridge distributional element stiffness using microwave interference radar

The bearing capacity of a bridge mainly relies on its own stiffness, while, at present, it remains a challenge to identify the bridge stiffness rapidly. In this paper, a rapid and innovative identification method of bridge distributional element stiffness (BDES) is proposed based on microwave interference radar technology and curvature envelope area (CEA). The main contributions of the work are as follows: (1) Taking advantage of multi-point displacement synchronous measurement, the self-developed microwave inference radar makes possible the acquisition of rotation influence lines (RILs) through the measured multi-point displacement influence lines (DILs). (2) Based on the one-to-one accurate correspondence between CEA, moment envelope area (MEA) and stiffness (“point-to-point” matching), and using the essential relationships among CEA and rotation, the bridge stiffness can be derived by using the DILs and the MEA calculated from the calibrated moving load (“point-to-line” matching). (3) Due to the radar feature of synchronous observation over a large area and referring to the proposed stiffness identification method, the BDES of the monitored area can be further obtained (“line-to-surface” matching). The proposed bridge identification method was applied at a laboratory experiment to identify the BDES of a steel beam for both undamaged and damaged conditions, and the results support the feasibility of the proposed method in BDES identification.