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A recent survey of Europe’s highway infrastructure has concluded that almost half of Europe’s bridges are nearing the end of their design live. Work in the wider Structural Health Monitoring sector is aiming to develop reliable and cost-effective methods for verifying condition, remaining service life and safety of ageing structures. Most bridge condition assessment methods are based on deflection, acceleration or strain measurements. This paper looks at the possibility of using rotation measurements as a main parameter to identify damage. This study looks at numerical analyses of a moving point load on a one-dimensional bridge model to provide the theoretical basis of the proposed damage detection method. It is shown that when local damage occurs, even when it is remote from a sensor location, it results in an increase in the magnitude of rotation measurements. This study looks at how best to exploit this fact for damage detection. A number of damage scenarios, sensor locations, and load arrangements are investigated in this study and their influence on the ability of the algorithm to detect damage are reported.

A new type of prefabricated abutment with a weak connection is proposed. The longitudinal load (like banking force, earth pressure) distribution of this new type of prefabricated abutment was analyzed based on the hinge-joined slab method. A simplified method for calculating the stiffness parameters of the panels was introduced. The influence lines of the longitudinal load on the prefabricated abutment of an actual bridge were calculated by using the proposed theoretical method and finite element method. The comparison between theoretical calculation and simulation results shows that the theoretical calculation method proposed in this paper is correct. In order to investigate the influence of the different thicknesses of the cap beam and dimensions of prefabricated panels on the calculation error of the theoretical calculation method. The influence lines of the prefabricated abutments with different parameters were calculated theoretically and simulated. All calculation errors of the central values of influence lines were less than 20% when the thickness of the cap beam changes from 0.8 to 2.4 m, the errors were all less than 10% when the thickness of the cap beam was 1.2–1.575 m. This calculation further verified that the theoretical calculation method proposed in this paper is suitable for longitudinal load distribution of a weakly connected Prefabricated bridge abutment. It provides a reference for the design and theoretical calculation of prefabricated abutment.

Bridge weigh-in-motion (BWIM) consists of the use of sensors on bridges to assess the loads of passing vehicles. Probabilistic bridge weigh-in-motion (pBWIM) is an approach for solving the inverse problem of finding vehicle axle weights based on deformation information. The pBWIM approach uses a probabilistic influence line and seeks the most probable axle weights, given in situ measurements. To compute such weights, the original pBWIM employed a grid search, which may lead to computational complexity, especially when applied to vehicles with high number of axles. Hence, this note presents an improved version of pBWIM, modifying the manner in which the most probable weights are sought. Here, a gradient based optimization procedure is proposed for replacing the computationally expensive grid-search of the original algorithm. The required gradients are fully derived and validated in numerical examples. The proposed modification is shown to highly decrease the computational complexity of the problem.

The bridge health monitoring system is being increasingly applied to bridge structure monitoring nowadays. However, due to the limitation in monitoring means and data analysis methods, many deficiencies still exist in the analysis and utilization of the monitoring data of bridge structures. In particular, damage identification and assessment technology is far from reaching the practical stage, and this restricts the development of the overall health monitoring technology. On the basis of the analysis of the strain responses of a bridge under vehicle load by using the theory of bridge strain influence line, we put forward a bridge damage identification and evaluation method based on strain ratio. The stiffness degradation matrix of the structure is deduced using the strain ratio of the corresponding parts of the test and reference sections, and the strain ratio and stiffness degradation matrices are accurately obtained using the load effect of test vehicles under closed traffic conditions. By analyzing a large amount of monitoring data in combination with the theory of random signal analysis and statistical technology, we analyze the probability distribution of the strain ratio and perform damage identification of the test section in accordance with the change in strain ratio distribution. A rapid damage identification method for the test section under closed and open traffic conditions is also proposed. The analysis reveals that the mode of the strain ratio is unchanged when the test section does not experience damage in a certain monitoring period under traffic load. We apply this method to a bridge health monitoring system and adopt Qingyin Yellow River Bridge in Jinan as an example to verify the effectiveness of the method. Results show that the method is efficient, accurate, and universal and can realize rapid and accurate online identification and assessment of bridge damage in closed and normal traffic conditions.

In orthotropic steel decks (OSDs), the rib-to-crossbeam joint is the most vulnerable detail that has not been drawn enough attention. The failure mode of cracks initiate from the lower weld end on rib wall is governing its fatigue performance. However, relevant detail categories are still missing in prevailing codes. This paper mainly focuses on the stress concentrations at the rib-to-crossbeam joint induced by rib distortions. A series of static load tests were first performed on a full-scale OSD specimen with different weld length between the ribs and the crossbeam. Then, corresponding numerical simulations were finished. Several possibilities that may cause the differences between the measurements and the calculations are investigated. At last, fatigue assessments based on influence lines of structural hot spot stress (SHSS) are completed. Research results reveal that the measurement results of reference points for SHSS method would be very sensitive to the exact location of strain gauges. Due to the manual welding, the deviation of strain gauge positions induced by the irregular weld shape is thought to be the main reason that causes the differences between measurements and calculations. Raising the location of cope hole terminations would decrease distortional stresses. However, the influence of this parameter on fatigue lives is rather small. The fatigue lives of points along the lower weld toe are very close. Hence, the point at the middle plane of crossbeam could be used as the reference point for fatigue assessments. Meanwhile, the center between ribs could be used as the reference transverse load position for fatigue assessments of this joint.

Purpose. To improve the fatigue life evaluating method of welded joints in railway girders based on experimental and theoretical studies of these structures operation. Methodology. The fatigue life assessment is based on the nonfailure operation probability, at which is greater than the operating time. The hypothesis of damages linear summation is used to determine the fatigue life and operating time of welded joints. Accumulated damage from the reference train is a measure of fatigue life and operating time. The amount of damage depends on the stresses and fatigue curve of a typical welded joint. Influence lines are used to determine the stresses in a construction member under moving load. The operating time of the construction member is calculated by cargo traffic mathematical modeling for the construction service life. Results. The method for assessing fatigue life is described. This method is taking into account the design features of the railway girder and the parameters of its operation. Originality. The numerical simulation of railway girder has allowed to establish the dependence of stresses on the beam web surface near the weld toe on the rigidity of stiffener fixation to beam flanges, to formulate rules for constructing bending moment influence lines, and to obtain a formula for determining stresses on the surface of the beam web under moving load. An equation is obtained for describing the fatigue curves of typical welded joints depending on the probability of joint failure. Practical value. A stochastic model for fatigue life predicting of typical railway welded girders is proposed. This model is taking into account the design features of the span and the parameters of its operation.

A real-time vehicle monitoring is crucial for effective bridge maintenance and traffic management because overloaded vehicles can cause damage to bridges, and in some extreme cases, it will directly lead to a bridge failure. Bridge weigh-in-motion (BWIM) system as a high performance and cost-effective technology has been extensively used to monitor vehicle speed and weight on highways. However, the dynamic effect and data noise may have an adverse impact on the bridge responses during and immediately following the vehicles pass the bridge. The fast Fourier transform (FFT) method, which can significantly purify the collected structural responses (dynamic strains) received from sensors or transducers, was used in axle counting, detection, and axle weighing technology in this study. To further improve the accuracy of the BWIM system, the field-calibrated influence lines (ILs) of a continuous multi-girder bridge were regarded as a reference to identify the vehicle weight based on the modified Moses algorithm and the least squares method. In situ experimental results indicated that the signals treated with FFT filter were far better than the original ones, the efficiency and the accuracy of axle detection were significantly improved by introducing the FFT method to the BWIM system. Moreover, the lateral load distribution effect on bridges should be considered by using the calculated average ILs of the specific lane individually for vehicle weight calculation of this lane.

Structural displacement monitoring remains a challenging problem, especially for long-span bridges. A ground-based microwave interferometric radar system was developed and used to obtain multipoint displacement measurements of a suspension bridge with a main span of 1200 m. First, a microwave interferometric radar system with the merits of low price, straightforward usage, and good stability and robustness was developed. The phase was obtained by performing fast Fourier transform (FFT) of the in-phase/quadrature signals and calculating the displacement according to the phase interference. Second, the radar system was used in field tests of a long-span suspension bridge, including static, ambient vibration, and moving load tests. Multipoint displacements of the bridge girder, tower, and cables were obtained, and simultaneous measurements of the multipoint displacement influence lines of the bridge girder were performed. A method that uses three reference points to measure the bridge girder displacement was proposed. Good agreements between the results from the developed radar system and those from traditional sensors, including connecting pipes and total stations, demonstrated the excellent performance of the proposed method for remote multipoint displacement measurements of long-span bridges.

Bridge weigh-in-motion systems use instrumented bridges or culverts to weigh vehicles as they pass over the structures. They also provide data to allow the calculation of several bridge performance indicators. The article starts with the basics of a bridge weigh-in-motion system and briefly describes two key bridge performance indicators, girder distribution factor and dynamic amplification factor, which are also derived from B-WIM measurements. The central part of the article focuses on monitoring of influence lines, the third key parameter that characterises the bridge performance under traffic loads. First, the method of calculating the bending moment influence lines from random heavy traffic is described. A coefficient of rotational stiffness is introduced, which defines the shape of influence lines around the supports as a linear combination of the ideal simply supported and fixed supported influence lines, to allow quantifying the influence line changes. Then the long-term monitoring of influence lines is investigated on four different single-span test bridges. The initial focus is given on the examination of the effect of temperature on the shape of influence lines. Finally, two sets of influence lines are compared on one test bridge, one from before and the other from after replacing the expansion joints and bearings. The work done so far confirms that calculating of influence lines from random vehicles with a B-WIM system is entirely feasible and that differences in their shape can be detected on single-span bridges. What remains to be investigated is the comparison of these differences to the actual damages and under which circumstances the proposed procedure can compete with or better the routine bridge inspection and the conventional monitoring techniques.

The unit influence line of a structure reflects its behaviour and changes in response to damage that may occur. An iterative algorithm is presented in this paper to obtain the shape of the instantaneous influence line of a bridge together with the relative axle loads of trucks passing overhead. One great advantage of this approach is that the need for sensor calibration with pre-weighed trucks can be avoided. The only initial information needed are the measurement data and a preliminary estimate of influence line based on engineering judgement. The concept of a so-called population unit influence line is also presented. This is an influence line that is found from a population of trucks instead of a single vehicle. An illustrative example is presented, where strain data have been collected on a reinforced concrete culvert. As well as the robustness of the proposed algorithms, the influence of temperature on the results is demonstrated. The sensitivity of the population influence line to temperature shows that it is likely to be equally sensitive to loss of stiffness in the structure.

This paper presents a method of developing digital twins (DTs) of road bridges directly from field measurements taken under random traffic loading. In a physics-based approach, the full th...

This paper addresses a new damage detection method for simply supported and continuous bridge structures based on combined influence lines for deflections and rotations and weigh-in-motion devices. The real structural behaviour of the superstructure is captured by sensors that measure vertical displacements at midspans and rotations at each support. Information on speed and weight of vehicles in transit are provided by weigh-in-motion devices placed at the beginning and at the end of the bridge. An optimization technique based on genetic algorithm and developed in a Matlab environment identifies the flexural stiffness distribution that best fits the experimental data. The comparison between the identified flexural stiffness distribution and the nominal one, or that obtained by previous identification, allows to verify the existence and the position of single or multiple damages. The capabilities of the proposed method was proved by means of three numerical simulations on a simply supported prestressed concrete I-beam bridge, on a three-span continuous prestressed concrete box bridge and on a four-span continuous steel-concrete composite bridges. Moving loads were considered to generate synthetic displacement and rotational distributions for different load positions. Changes in the flexural stiffness as small as 20% for finite elements with a length of 0.5 m or 10% for finite elements with a length of 2.0 m were successfully identified with a root-mean-square-error of less than 2.72%. The simulations produced evidence of benefits, in terms of damage identification, provided by the combined use of different types of influence lines with the maximum error in the stiffness identification that reduced from 3.40 to 2.64%.

With an increase in bridge service time, damage will inevitably occur. Accurately identifying damage is of great significance to the operation and maintenance of a bridge. To realize a freq...

Traffic monitoring, including the estimation of axle and gross vehicle weights of passing trucks over bridges plays an important role in the determination of actual service loads. Knowledge of thes...

Structural health monitoring has garnered attention as a method to quantitatively evaluate damage to road bridges, and various dynamic and static damage detection methods have been proposed recently. However, few damage detection methods focus on the displacement shapes of road bridge decks. In this study, a damage detection approach is proposed using Displacement-Based Index (DBI) and Grey Relational Coefficient (GRC), in which displacement influence lines of deck slabs are used as inputs in the evaluation procedures. Parametric studies were performed by changing the damaged positions and boundary conditions of a full-scale bridge model to examine their possible effects on the performance of the proposed method. The results indicated that either approach could properly detect damage in the simulation model. In addition, because the proposed method was insensitive to damage away from the measurement position, it was clarified that damage detection could be performed accurately by installing multiple displacement meters at appropriate intervals.

Current design live load model for bridges are mainly for short to medium span bridges. For these bridges, one very heavy truck or a few heavy trucks may give the maximum load effects. However, for long span bridges, due to long lengths of the effective influence line, different scenarios should be considered for the bridge design. Long span bridges mainly have cable- supported structures and steel girder and deck. This paper deals with the development and application of the live load model for long span steel cable bridges considering traffic congestion scenarios. New live load model was proposed based on long-term weigh-in-motion truck weight data and various traffic congestion scenarios. Weigh-in-motion data have been collected at the location near industrial complex so that the sufficient number of loaded trucks can be measured. For the accuracy of long-term data, temperature compensation had been applied by considering the front axle weights of trucks. Traffic congestion scenarios utilizes the normal sequences of trucks arriving at the bridge with the minimum headway distances between trucks and other vehicles. One, two and four lanes scenarios are developed and used in this study. Proposed new live load model consists of four-axle truck with total weight of 510 kN and uniformly distributed load in which its magnitude is decreased as the length of the effective influence line increases. The load effects of the proposed model are compared with other well-known load model in the world for long span steel cable bridges with different span lengths.

A method for distributed detection of damage along the lengths of multi-span continuous Bridges is introduced. It is based on monitoring the distributed strains along the length of the bridge by using Brillouin scattering based optical fiber sensors. Identification of damage beyond the signal to noise limits of the instrument is achieved by normalization of the measured distributed strains during multiple positions of a truck with respect to the theoretical influence line of the bridge. Formulation of the method leads to the introduction of a damage index for identification of microcrack locations along the spans of the Bridge. Effectiveness of the proposed method was evaluated by load testing of a five span continuous precast post-tensioned concrete box girder bridge. Locations of detected microcracks by the distributed sensor system were further verified by visual inspections.

Collecting the information of traffic load, especially heavy trucks, is crucial for bridge statistical analysis, safety evaluation, and maintenance strategies. This paper presents a traffic sensing methodology that combines a deep learning based computer vision technique with the influence line theory. Theoretical background and derivations are introduced from both aspects of structural analysis and computer vision techniques. In addition, to evaluate the effectiveness and accuracy of the proposed traffic sensing method through field tests, a systematic analysis is performed on a continuous box-girder bridge. The obtained results show that the proposed method can automatically identify the vehicle load and speed with promising efficiency and accuracy and most importantly cost-effectiveness. All these features make the proposed methodology a desirable bridge weigh-in-motion system, especially for bridges already equipped with structural health monitoring system.

This paper presents finite element model (FEM) based virtual load rating method for accurately and efficiently evaluating the bearing capacity of taxiway bridge in the field under aircraft taxiing. A dynamic load coefficient of aircraft loading was first developed considering deck pavement roughness and aircraft lift force. The in situ responses of taxiway bridges under 10 aircraft were collected using instrumentation system with acceleration sensor, strain sensor, and inclinometer. The modal frequency, strain influence lines, and deflections of taxiway bridge were obtained from FE analysis and in situ test. An optimization objective function in terms of fundamental frequency and strain influence lines was formulated to ensure convergence and effectiveness in the model updating process, wherein the bending stiffness, density and boundary conditions of the structures are selected as the design variables. The weighted-average method of model updating parameters was proposed considering the differences in the obtained parameters under different loading conditions. The analysis results of updated FE model were validated using static loading test conducted on taxiway bridge. Finally, the proposed virtual load rating method was applied to Taxiway Bridge V in Guangzhou Baiyun International Airport (CAN).

In this article, the condition assessment of a cable-stayed bridge using remote sensing is presented. The displacement influence line (DIL) of the bridge under the live load tests is measured for a...

Dynamic strain-based methods are promising for bridge status assessment; however, the influences of vehicle parameters variations on their capabilities for damage identification are usually indeterminate. In this paper, parametric study for highway bridge rapid assessment method is conducted under moving vehicle loads, which is based on the distributed macro-strain envelope line. First, the relationship between the average bending stiffness and macro-strain history is studied according to the theory of the strain influence line. To determine the influence of different vehicle parameters (velocity, weight and axle numbers) on the method, a 1:10 scale model of a bridge-vehicle system is established for the parametric experimental study. A type of long-gauge Fiber Bragg Grating (FBG) sensor is used in the experiment. The empirical mode decomposition method (EMD) is applied to extract the static macro-strain component, and the maximum values of the static macro-strain histories are accumulated as the long-gauge strain envelope line. The experimental results show that the proposed method not only effectively identifies the location of damage but also damage extent and is not affected by the parameters of the vehicle. This method has engineering significance in bearing capacity evaluation and post-bridge structure reinforcement design.

This study proposes a new damage identification technique for condition assessment of bridge structures. The method is based on the concept of rotation influence line (RIL) at the bridge bearing locations, and solely relies on measurements obtained from two points at either end of the bridge e.g., RILR and RILL. The sensitivity of the rotation measurement to damage is first investigated using a 1-D simply supported beam model and it is demonstrated that unlike conventional strain measurements, the rotation measurement is capable of providing useful information about damage even though it is far from the measurement point. Further, an existing cable-stayed bridge is considered to validate the capability of RIL in damage identification. A comprehensive three-dimensional finite element model (FEM) of the bridge is established and calibrated using the measured static and dynamic responses. Numerous field tests are conducted on this large-scale structure to extract static and dynamic characteristics, including natural frequencies, mode shapes and influence lines (ILs). Sixteen hypothetical damage scenarios are induced in the numerical model, including symmetric and asymmetric cases of cable loss. A damage index based on the normalised discrepancy of RIL between the benchmark state and an unknown state is introduced and through extensive investigations it is demonstrated that regardless of damage location, either RILR or RILL (or both) can successfully identify the induced damage in all of the sixteen damage scenarios. In contrast, the success of strain-based measurement is highly dependent on the closeness of damage to the sensor location, thus a much higher number of strain gauge sensors is required not to misidentify damage. The contribution of this work is four-fold. First, a novel and robust damage identification technique based on RIL is proposed which has not been reported in the literature. Second, the method solely relies on two measurement points e.g., two tilt meters at either end of the bridge and it is capable of identifying damage, even far from the sensor location. Third, the validation of the technique is demonstrated through extensive numerical and field test investigations on a statically indeterminate cable-stayed bridge structure. Finally, it is demonstrated that the conventional strain-based measurement is very likely to misidentify cable damage even with extreme case of cable loss.

Computer vision applications are frequently selected for short-term monitoring of bridges. The availability of high resolution and frame rate consumer-grade cameras such as action cameras makes the computer vision-based monitoring an attractive and affordable option. This paper presents findings from monitoring deformations of a steel girder footbridge subjected to cyclist loads captured with an action camera. A modified GoPro action camera with a zoom lens was located 35 m from the centre of the bridge. High resolution (720 × 1080 pixel) and high frame rate (240 fps) videos were recorded during cyclist crossings. Image processing, measurement denoising, vertical deflection interpretation and influence line (bridge signature) derivations are presented and discussed. Both static and dynamic responses are identifiable (discernible in vision measurements) and even tiny (a fraction of a millimetre) vertical deflections can be accurately computed from videos collected with the action camera.

The influence line is an important static property in bridges. The shape and magnitude of the girder bridge influence line contain stiffness information for the bridge supports and beam. Th...

The framework security of a bridge is essential as a critical component of traffic engineering. Even though the bridge structure is damaged to various degrees due to various reasons, the bridge will be wrecked when the damage reaches a particular level, suggesting a negative influence on people’s lives. Based on the current situation and existing problems of structural damage identification of bridges, a structural damage identification technology of continuous beam bridges based on deflection influence lines is proposed in this paper in order to keep track of and always detect broken bridge elements, thereby extending the bridge’s service life and reducing the risk of catastrophic accidents. The line function expression of deflection impact on a multi-span continuous beam bridge was first obtained using Graphic Multiplication theory. From the theoretical level, the influence line function of the continuous beam bridge without extensive damage was computed, and a graph was generated. The photographs of the DIL as well as the first and second derivatives, the deflection influence line distinction and its first and second derivatives, and the DIL distinction and its first and second derivatives of a continuous beam bridge in a single position and multi-position destruction were fitted in this paper. Finally, after comparing multiple work conditions and multiple measuring points, it was found that the first derivative of deflection influence line difference had the best damage identification effect. The design was completed and tested, which had verified the feasibility of this theory.

A new method was proposed for the damage identification of box girder bridges under moving load, wherein the difference of strain influence line (DSIL) was taken as an index to represent the long-gauge strain difference before and after damage. The damage identification theory based on long-gauge strain influence lines was derived for box girder bridges with shear lag effect under consideration, and a regularized index DSIL was proposed for the quantitative identifications of damage location and extent. A series of experiments were carried out to study the influences of speed, vehicle type, and vehicle weight on the damage identification, and the experimental data were obtained by long-gauge fiber Bragg grating strain sensors. Moreover, numerical simulations were performed to confirm the method. The experimental and numerical results show that the method can locate the damage accurately, and quantitatively identify the damage extent under different working conditions. The experimental damage extent is generally slightly higher than the theoretical, with an average identification error smaller than 5%. Additionally, the relative error of damage extent is smaller than 3% under different working conditions. Thus, the effectiveness of this method was verified.

According to federal law, routine commercial vehicles must adhere to certain limits on their load configuration in order to operate legally on interstate highways. However, states may allow for heavier or different load configurations provided that bridges on the state and county highway system are load rated and, if necessary, posted with vehicles that appropriately represent these loads. The state of Indiana allows several classes of vehicles to operate with loads that exceed federal limits, and, presently, several LFD design loads are used to represent these exceptions as state legal loads. This study evaluates the MBE rating loads for their ability to encompass Indiana’s exception vehicles and recommends a set of state rating loads which can replace the current state legal loads and, combined with the MBE rating loads, satisfactorily encompass the load effects due to these exceptions. Comparing moment and shear envelopes on a representative set of bridges, the MBE rating vehicles were found to be insufficient for representing Indiana’s exception vehicles. Three new rating loads are proposed which encompass the exception vehicles efficiently and represent realistic legal loads. Conversely, acceptable HS-20 rating factors are also provided as an alternative to the adoption of these new vehicles. These rating factors, all 1.0 or greater, can ensure a similar level of safety by requiring a specific amount of excess capacity for the HS-20 design load.

This chapter is devoted to the analysis of statically determinate multispan beams subjected to fixed and moving loads. Methods for generation of beams and load path, construction of internal force diagrams, construction of influence lines and theirs application are discussed. Also analysis of plane frame subjected to fixed load is presented.

In this study, an influence line of girder deflection of the bridge was calculated for the initial calibration of Bridge Weigh-in-Motion (B-WIM). The deflection responses were obtained from the proposed integration process using the baseline correction. Optical flow analysis was applied using a video camera to adapt to the variable vehicle speed and precisely measure the location of vehicles on a bridge. A foreground mask using the Gaussian mixture model and a Kalman filter was then applied to identify the vehicles. A calibration process of B-WIM was proposed using the iteration process to optimize the influence line of deflection using local buses in regular traffic. Finally, the axle weights of a weight-known test truck were analyzed by monitoring with the video camera and acceleration sensor. Compared with conventional B-WIM methods, the proposed method has demonstrated higher adaptability in variable vehicle speed.

In the identification of bridge damage in the series of deflection-affecting lines, noise signals due to axle coupling often occur. Removing these noise signals has become a key technique for effectively identifying damage. Taking the main line bridge of a overpass project in Fuzhou City of Fujian Province as an example, we collected the deflection a data of the bridge by using HPON-X target-free bridge deflectometer and used YOLOv3 algorithm for deep learning of the vehicle load position. The data were measured and studied by using DB9 wavelet de-noising method. The research shows that this method can greatly reduce the influence of vehicle bridge interaction on deflection influence line, and can enhance the accuracy and speed of bridge damage detection.

General rules for determining the internal forces in case of fixed loads, which act on the rod structures and known to reader from the course Mechanics of Materials, are reminded. Concepts of influence lines and direct/indirect load application are introduced. All influence lines for simplest structures (one span simply supported and cantilevered beams) are constructed using analytical expressions for required factor. Applications of influence lines for fixed and moving loads are discussed.

This chapter is devoted to the analysis of statically determinate three-hinged arches, subjected to fixed and moving loads. Analysis of an arch in the case of fixed loads implies determination of reactions of supports and construction of internal force diagrams. Analysis of an arch in the case of moving load implies construction of influence lines for reactions, thrust, and internal forces.

The stress and deflection effects of the line changes before and after the bridge damage are used as indicators to evaluate the bridge damage and the initial damage site. Then a method of combining information is proposed to improve the accuracy of the damage site. Three-span continuous reinforced concrete was used in the analysis. According to the test, the effectiveness of damage identification based on the damage change of the influence line and the feasibility of the damage location method based on multi-sensory information fusion are confirmed.

Article describes modeling processes influencing the lines in rods load truss of the bridge crane in Mathcad system: for the rods of the top belt of a truss; for the rods of the bottom belt of a truss; for diagonal and vertical rods of a truss at various section of the load truss; algorithm and a program complex for automation of modeling and graphical representation influence lines and maximum their values. The proposed modeling procedures of the influence lines in any section of a load truss make it possible to reduce time and cost for these calculations’ performance at least in ten times and to carry out the research on load truss parameters, rods parameters and materials change effectively.

The measurement of track substructure deflections is an important parameter for the determination of structural capacity, identification of track problem areas and evaluation of overall track condition. This paper describes a mechanistic-empirical method by which elastic moduli of railway formation layers can be determined from substructure deflections under transient train loading. The method was founded on surface deflection theory from falling weight deflectometer (FWD) analysis. Finite element (mechanistic) analysis and field data (empirical) from railway substructure deflections obtained from multi-depth deflectometers (MDDs) were used to assess the validity of the mechanistic-empirical method by comparing measured and modelled railway substructure responses. The results indicate that substructure deflections and stresses are affected by the complex superposition of different bogie loading configurations on a particular superstructure. The load distribution in the railway substructure does not follow a 45° influence line as commonly assumed in surface deflection theory. On the contrary, railway equilibrium influence lines are significantly influenced by the structural capacity of the formation layers and in-situ subgrade. The predictions offered by this method strongly agree with the long-term formation peak strains measured by MDDs and this method was determined suitable for evaluation of formation structural capacity due to good agreement between measured and estimated elastic moduli of formation layers.

To ensure the safety of cable-stayed bridges, a long-term condition evaluation method has been proposed based on dead load–induced cable forces. To extract dead load–induced cable forces under random vehicle loadings, a novel approach is first developed by integrating influence lines with monitoring data. Then, based on the extracted dead load–induced cable forces, the evaluation algorithm for stay cable systems is presented. In the assessment algorithm, uniform and non-uniform characteristics are taken into account. Finally, the Third Nanjing Yangtze River Bridge, a typical large span cable-stayed bridge, is used to illustrate the effectiveness of the proposed methodology. As a result, the maximum relative error in extraction of dead load–induced cable forces accounts for 4.78% within the studied five stay cables. The precision of the extraction method is acceptable for practical applications since the relative error is less than 5%. Moreover, the bridge is continuously assessed using the dead load–induced cable forces for 5 years. Eliminating the influence of vehicle loadings, the condition of the bridge gradually degrades with time but still remains in good condition. The study not only provides a long-term condition evaluation method for stay cable systems but a dead load–induced extraction approach under random vehicle loadings, which will help bridge owners know well the condition of bridges to make appropriate maintenance decisions.

The purpose of this paper is to provide a new method for analyzing and evaluating the fatigue crack closure load and estimating the life of engineering components using RICC (Rigid-Insert Crack Closure Model), non-destructive replica technique, and a new sample. For this purpose, first, the method of solving the RICC model has been changed from linear approximation to nonlinear state and therefore, a significant improvement in the accuracy of the model results has been achieved. Then, using the model, a new formulation for the influence line in the points of sample is obtained, which has a significant accuracy. The formulation of the RICC model results in a set of equations that can help to determine the closure load and the characteristics of the load-displacement diagram using the residual crack mouth opening displacement in zero load (residual CMOD), which is the only empirical input parameter of Model. The new formulation method has been applied to a standard sample that has the same conditions as a real instance. The amount of residual crack openness in zero load (crack residual displacement) was measured using the replica technique and COD-gage simultaneously on a standard sample and were investigated using the obtained relationships and the accuracy of the outcomes. To prove the reliability, model results have been investigated through doing the experimental tests on aluminum alloys. Finally, the results obtained from the proposed relationship for the analysis and evaluation of the crack closure load and fatigue life were compared with the experimental results, which showed acceptable results.

In order to analyze the integral forced performance of external prestressing and carbon fiber reinforced beam, the analytical solution of the carbon fiber-concrete composite beams under the vertical concentrated load and external prestressing was derived in this article based on the classical theory of elasticity and contact. The deflection curve equation and the transverse distributing influence lines of simply supported beam after the joint reinforcement were obtained based on the eccentric compression method, and the results of simply supported beams with or without joint reinforcement were compared. The results show that the integral forced performance of external prestressing and carbon fiber reinforced beam was effectively improved, and the new calculation method of transverse distribution factors has a practical value.

Conventional bridge weigh-in-motion (BWIM) uses a bridge influence line to find the axle weights of passing vehicles that minimize the sum of squares of differences between theoretical and measured responses. An alternative approach, probabilistic bridge weigh-in-motion (pBWIM), is proposed here. The pBWIM approach uses a probabilistic influence line and seeks to find the most probable axle weights, given the measurements. The inferred axle weights are those with the greatest probability amongst all possible combinations of values. The measurement sensors used in pBWIM are similar to BWIM, containing free-of-axle detector (FAD) sensors to calculate axle spacings and vehicle speed and weighing sensors to record deformations of the bridge. The pBWIM concept is tested here using a numerical model and a bridge in Slovenia. In a simulation, two hundred randomly generated 2-axle trucks pass over a 6 m long simply supported beam. The bending moment at mid-span is used to find the axle weights. In the field tests, seventy-seven pre-weighed trucks traveled over an integral slab bridge and the strain response in the soffit at mid-span was recorded. Results show that pBWIM has good potential to improve the accuracy of BWIM.

In the paper a general and direct method for implementation of influence lines in finite element software is provided. Generally influence lines are applied to identify the most critical location and combination of live loads in civil engineering structures. The proposed method is based on the Muller-Breslau principle and the basic idea is to equate discontinuous displacement fields with consistent nodal forces, thus obtaining influence functions only applying a single load case without changing the geometry or boundary conditions of the finite element model. Initially the method is developed by means of some illustrative beam problems, where the consistent nodal forces for angular, lateral and axial displacement discontinuities for a Bernoulli-Euler beam element are derived. Finally it is shown that the method is fully general and efficient in identifying the influence functions of generalized stresses in e.g. plates and shells.

A novel damage identification method for concrete continuous girder bridges based on spatially-distributed long-gauge strain sensing is presented in this paper. First, the variation regularity of the long-gauge strain influence line of continuous girder bridges which changes with the location of vehicles on the bridge is studied. According to this variation regularity, a calculation method for the distribution regularity of the area of long-gauge strain history is investigated. Second, a numerical simulation of damage identification based on the distribution regularity of the area of long-gauge strain history is conducted, and the results indicate that this method is effective for identifying damage and is not affected by the speed, axle number and weight of vehicles. Finally, a real bridge test on a highway is conducted, and the experimental results also show that this method is very effective for identifying damage in continuous girder bridges, and the local element stiffness distribution regularity can be revealed at the same time. This identified information is useful for maintaining of continuous girder bridges on highways.

The benchmark of a simply supported beam with damage and bending fuzzy stiffness consideration is established to be utilized for damage detection. The explicit expression describing the Rotational Angle Influence Lines (RAIL) of the arbitrary section in the benchmark is presented as the nonlinear relation between the moving load and the RAIL appeared, when the moving load is located on the damage area. The damage detection method is derived based on the Difference of the RAIL Curvature (DRAIL-C) prior to and following arbitrarily section damage in a simply supported beam with bending fuzzy stiffness consideration. The results demonstrate that the damage position can be located by the DRAIL-C graph and the damage extent can be calculated by the DRAIL-C curve peak. The simply supported box girder as a one-dimensional model and the simply supported truss bridge as a three-dimensional model with the bending fuzzy stiffness are simulated for the validity of the proposed method to be verified. The measuring point position and noise intensity effects are discussed in the simply supported box girder example. This paper provides a new consideration and technique for the damage detection of a simply supported bridge with bending fuzzy stiffness consideration.

With increasing service times and performance deteriorations, the cost of inspecting and maintaining aged bridges increases dramatically, and becomes a massive challenge. There is an urgent need to explore a cost-effective and rapid evaluation method for determining the load capacities of large quantities of short/medium-span bridges. In this study, an influence line-based moving load test method was proposed for a rapid bridge capacity evaluation. The influence line of the bridge was initially extracted using the moving load test. The ratios of the maximum amplitude and total area between the actual and theoretical influence lines were defined as the capacity evaluation indices for the bridge. Based on numerical validations of three typical deterioration conditions, the proposed evaluation indices were proven to be equivalent to the conventional static evaluation index. In addition, in-situ static load and moving load tests were conducted to verify the effectiveness of the proposed method. The results show that relative to the static evaluation index, the proposed indices have a maximum difference of 1.5% in the numerical validations and 2.2% in the in-situ tests, indicating that the proposed method is accurate and more effective for future short/medium-span bridge capacity evaluation.

This paper deals with accuracy and long-term stability of bridge weigh-in-motion (B-WIM) systems. Research focused on four improvements, developed within two research projects financed by the Europ...

The bridge influence line (IL) is widely used in structural evaluation, damage identification, model updating, and other applications. The IL curve of an existing bridge is usually different from its designed value. It is crucial, yet challenging, to detect the actual bridge IL by measurement. In this paper, a fitting method is proposed for extracting the bridge IL from the dynamic response induced by a passing vehicle. Based on the theoretical mechanism of bridge IL under different boundary conditions, along with the features of bridge vibration, a piecewise polynomial and a series of harmonic sinusoids are established to describe the IL of the measured point and the fluctuation part of the bridge response, respectively. A mixed function obtained by linear superposition of these factors is utilized to fit the bridge dynamic response. The coefficients of the piecewise polynomial can be extracted by a least-square calculation; and subsequently, the actual IL curve of the measure point of the bridge is obtained. Numerical examples of vehicle-bridge models are adopted to validate the fitting method of IL extraction proposed in this paper, and to illustrate the efficiency by comparing it with the existing direct inverse calculation method. The validity and feasibility of this method are also demonstrated by both a laboratory experiment and a field test.

This paper presents a two-step approach for structural damage identification in beam structure using the influence line and bird mating optimizer (BMO). Local damage is simulated as the reduction of the elemental Young’s modulus and mass of beam element. The technique for damage localization based on influence line and its derivatives before and after damage for beam structure was outlined. An objective function comprised of dynamic acceleration is utilized for BMO algorithm. The dynamic response data under external force is calculated by Newmark integration method. Numerical examples of a simply supported beam was investigated. Effect of measurement noise is studied. Studies in the paper indicate that the proposed method is efficient and robust for identifying damages in beam structures.