Bridge Deflection Research Articles

Predicting the maximum deflection and girder-end rotation of a three-tower suspension bridge under live load: An analytical algorithm

The maximum deflection and girder-end rotation of the stiffening girder for a suspension bridge are key stiffness indicators that need to be verified to secure the structure's performance during the operation. The overall vertical stiffness of a three-tower suspension bridge is significantly reduced due to the mid-tower being constrained in the horizontal direction of the main cable in the main spans with large sag-to-span ratios. Therefore, rapid and accurate evaluation of the vertical stiffness of the three-tower suspension bridge is quite problematic. Based on the deflection theory, this study proposed an analytical expression of the deflection and girder-end rotation of a three-tower suspension bridge. The deflection and girder-end rotation were used as the optimization objectives. Combining the harmony search algorithm with the “death-penalty” function approach, the most unfavorable loading conditions and corresponding maximum values were obtained. The effectiveness of the proposed method was verified by finite element modeling of an exemplary-three-tower suspension bridge. The proposed method had high accuracy, improved calculation efficiency, and wide applicability, which made it lucrative for selecting the optimal structural parameters in the preliminary design of suspension bridges. The dead-to-live load ratio, cable sag-to-span ratio, mid-tower lateral stiffness, side-to-main span ratios, cable’s axial stiffness, and deck’s flexural rigidity were further analyzed. The results indicated that increasing the dead-to-live load ratio and mid-tower stiffness was the most effective method to control maximum deflection and girder-end rotation of stiffening girders.

Damage modes and residual deflections of multi-beam hollow slab bridge under car explosions

The purpose of this study is to investigate the damage modes and residual deflection of multi-beam hollow slab bridges under car explosions. To comprehensively estimate the blast response, the failure process of the bridge with different beam numbers are cautiously simulated and compared. With the experimentally validation of the constitutive laws and the fluid–structure interaction parameters, the impact analysis software Autodyn is adopted to capture the damage mechanisms and the vibration histories. After cautious numerical simulations, local punching shear failure and global flexural failure dominate the damage modes of multi-beam hollow slab bridges. Due to the oversized impact energies and the insufficient structural resistance, overall collapse is observed in bridge with 4 or 6 beams in middle and acentric explosions. For bridge with 8 or 10 beams, the formed plastic hinges imply the large residual deflection and possible overall collapse during middle explosions. Owing to the easier energy dissipation and the smaller impact areas, limited flexural damage are discovered in bridge with 8 or 10 beams under acentric explosions. Due to the limited flexural damage and the small residual deflection of the distant beams, these beams can maintain great bearing capacity and can be repaired after explosions.

Reliability Assessment Method for Simply Supported Bridge Based on Structural Health Monitoring of Frequency with Temperature and Humidity Effect Eliminated

Structural health monitoring (SHM) has been widely used for the performance assessment of bridges, especially the methods based on dynamic characteristics. Meanwhile, bridge modal frequency is influenced significantly by environmental factors, such as temperature and humidity. Combined with SHM, a reliability assessment of bridges with the temperature and humidity effects eliminated is proposed. Firstly, the bridge deflection verification coefficient is adopted as the evaluation indicator for bridge condition, which is the ratio of deflection-measured value to deflection-calculated value. It is obtained from the relationship between verification coefficient and modal frequency through theoretical derivation. Secondly, a back propagation (BP) neural network is improved by using an artificial bee colony algorithm and employed as a surrogate model to eliminate the effect of temperature and humidity on frequency. Thirdly, a dynamic Bayesian network is applied to establish the reliability analysis model combined with the monitoring results, so that the probability distribution of bridge parameters is updated to improve the accuracy of the reliability analysis. Finally, a simply supported bridge is used as the case study, based on the proposed method in this work. The results indicate that the proposed method can eliminate the temperature and humidity effect on frequency precisely and effectively. With the effect of temperature and humidity on frequency eliminated, the bridge condition assessment can be evaluated accurately through the reliability analysis based on SHM and the dynamic Bayesian network.

The Levitation Characteristics of HTS Bulks Under the Effect of Bridge Deflection Coupled with Random Excitations

The Levitation Characteristics of HTS Bulks Under the Effect of Bridge Deflection Coupled with Random Excitations

Drive-by deflection estimation method for simple support bridges based on track irregularities measured on a traveling train

Bridge deflection under train passage is a typical index of the bridge’s structural performance that can be measured from the ground with considerable effort and expense. This study develops a novel drive-by bridge deflection estimating method based on track irregularities measured on a moving train as a significantly efficient bridge deflection measuring method. First, theoretical analysis demonstrates that the difference in track irregularities observed by the first and last vehicles of a train is proportional to the bridge deflection that the train travels through when the dynamic response of the bridge is small and quasi-static response is predominant. Furthermore, it is stated that the proportionality coefficient is only determined by the train wheelset arrangement and the bridge span. Based on the different peaks of track irregularities observed at the first and last vehicle of a train, a unique method for estimating bridge deflection after canceling the track irregularity components other than bridge displacement has been devised. The accuracy verification by vehicle-bridge interaction simulation shows that the proposed method can be applied to track irregularities measured by a traveling train at a speed of <150 km/h with a standard deviation of <0.2 mm measurement error. Finally, the proposed method is applied to actual railway track irregularities as measured by the first and last vehicles of a train traveling at ∼ 100 km/h. The maximum deflections of five bridges estimated from the track irregularity are shown to be in good agreement with the on-site deflection measurement results, which were separately performed, with an error of <10%.

Measurement method and recent progress of vision-based deflection measurement of bridges: a technical review

The deflection that can reflect the vertical stiffness of a bridge plays an important role in the structural evaluation and health monitoring of bridges. In the past 20 years, the bridge deflection measurement methods based on computer vision and photogrammetry have been gradually applied to the field measurement due to the advantages of noncontact measurement, simple experimental setup, and easy installation. The technical research progress of vision-based bridge deflection measurement is reported from four aspects: basic principles, measurement methods, influencing factors, and applications. Basic principles mainly include camera calibration, three-dimensional (3D) stereo vision, photogrammetry, feature detection, and matching. For measurement methods, the single-camera two-dimensional measurement, the dual-camera 3D measurement, the quasistatic measurement based on photogrammetry, the multipoint dynamic measurement based on the displacement-relay videometrics and the deflection measurement based on UAV platform are introduced, respectively. In the section of influencing factors, this part summarizes the work of many researchers on the effects of camera imaging factors, calibration factors, algorithm factors, and environmental factors on measurement results. The field measurement results at different measurement distances and measurement accuracy based on these are presented in terms of applications. Finally, the future development trends of vision-based bridge deflection measurement are expected.

Analysis of influence of concrete stiffness reduction on mid-span deflection of PC box girder bridge

At present, the concept of bridge preventive maintenance has been widely used. In order to find the right time for PC bridge maintenance and make better maintenance decision, it is necessary to predict the service performance of PC bridge. In this paper, the service performance of PC bridge is divided into several indexes, and the fuzzy neural network method is used to calculate these indexes data. Taking shangtan bridge as an example, the maximum relative error between the measured value and the predicted value is found to be within 5%, which meets the accuracy requirements. The feasibility of this method is verified and provides guidance for the future decision-making of bridge maintenanc.

Bridge Load Testing as Per IRC SP 51

Abstract: Bridge load testing is popular means of demonstrating bridge’s capability to carry safely design loads. It is commonly used to determine the issues which cannot be resolved by only visual inspection or analysis. This paper deals with the study of load testing of major Bridge on River of 17.20 meter span Between Pier P5 and Pier P6. Under this project bridge was loaded with vehicular loading and tested for design load. Deflection of bridge is measured by dial gauges and recorded for bridge analysis. This study consists preparation of load test on bridge for deflection load as per IRC SP 51(2015) and how load testing is carried out by visual inspection, by applying vehicular loading or dynamic loading , its behaviour under loading and unloading conditons, behavior of bridge under the different temperatures to check how bridge is going to behave under weather conditions , maximum permissible deflection of girders , total deflection of girders, total recovery and percentage recovery of deflections after removal of load and comparison between theoretical deflections and actual deflections to find out testing bridge capability and its structural integrity. Keywords: Bridge Load Test, Dial Gauge, vehicles, Loading, Unloading, Deflection, Design load, Temperature effect, Temperature correction, Total recovery, Total Deflection, Theoretical Deflection, Percentage recovery.

Railway Bridge Condition Monitoring Using Numerically Calculated Responses from Batches of Trains

This study introduces a novel method to determine apparent profile of the track and detect railway bridge condition using sensors on in-service trains. The concept uses a type of Inverse Newmark-β integration scheme on data from a batch of trains. In a self-calibration process, an optimization algorithm is used to find vehicle dynamic properties and speed. For bridge health monitoring, the apparent profile of the bridge is first determined, i.e., the true profile plus components of ballast and bridge deflection under the moving train. The apparent profile is used, in turn, to calculate the moving reference deflection influence line, i.e., the deflection due to a moving (static) unit load. The moving reference influence line is shown to be a good indicator of bridge stiffness. This numerical approach is assessed using an elaborate finite element model operated by an independent research group. The results show that the moving reference influence line can be found accurately and that it constitutes an effective indicator of the condition of a bridge.

Wireless SmartVision system for synchronized displacement monitoring of railroad bridges

AbstractThe deflection of railroad bridges under in‐service loads is an important indicator of the structure's health. Over the past decade, an increasing number of studies have demonstrated the efficacy of using vision‐based approaches for displacement tracking of civil infrastructure. These studies have relied primarily on external processing of manually recorded videos of a structure's motion to estimate displacements. To date, vision‐based techniques applied to long‐term structural health monitoring have yet to be proven effective as an alternative to the traditional displacement measurement methods, such as linear variable differential transformers. This paper proposes a wireless SmartVision system (WSVS) that uses edge computing to directly output bridge displacements that can be sent to the end user. The system estimates displacements using both target‐free and target‐based approaches. A synchronized sensing framework is developed for multipoint displacement estimation using several wireless vision‐based nodes for full‐scale displacement‐based modal analysis of structures. Pose estimation using an AprilTag, a fiducial marker, is employed with a modified algorithm for improved displacement tracking of targets installed on a bridge, yielding subpixel accuracy. The robustness of the results in field conditions is enhanced by linking a tracking quality factor to each timestamp to handle vision‐related uncertainties. To meet the need for precise error metrics evaluation, an inexpensive cyber‐physical setup using a synthetic testing environment is also developed in this study. Following laboratory validation, field tests on a cable‐stayed pedestrian bridge were performed to demonstrate the efficacy of the proposed WSVS.

Scanning of Bridge Surface Roughness from Two-Axle Vehicle Response by EKF-UI and Contact Residual: Theoretical Study.

The scanning of bridge surface roughness by the test vehicle is a coupled and non-stationary problem since the bridge deflection caused by vehicles will inevitably enter into the vehicle response. To this end, a two-step procedure is proposed to retrieve the bridge surface profile from the noise-contaminated responses of a two-axle vehicle moving over bridges. Central to this is the elimination of the bridge deflection from the estimated unknown input to the test vehicle system. First, the extended Kalman filter with unknown inputs (EKF-UI) algorithm is extended to formulating the state-space equations for the moving vehicle over the bridge. Analytical recursive solutions are derived for the improved vehicle states and the unknown input vector consisting of the vehicle–bridge contact displacement and surface profile. Second, the correlation between the cumulated contact residuals and contact displacements for the two axles is approximately defined by using the vehicle’s parameters and location on the bridge. Then, the surface profile is retrieved from the unknown input by removing the roughness-free contact (bridge) displacement, calculated with no prior knowledge of bridge properties. The efficacy of the proposed procedure was validated by the finite element method and demonstrated in the parametric study for various properties of the system. It is confirmed that the retrieved bridge surface profile is in excellent agreement with the original (assumed). For practical use, the vehicle is suggested to run at a not-too-high speed or in a too noisy environment. The proposed technique is robust with regard to vehicle mass and bridge damping.

Representation of In-Service Performance for Cable-Stayed Railway-Highway Combined Bridges Based on Train-Induced Response's Sensing Data and Knowledge.

Real-time representation of the current performance of structures is an important task for perceiving potential danger in in-service bridges. Methods driven by the multisource sensing data of structural health monitoring systems are an effective way to achieve this goal. Due to the explicit zero-point of signals, the live load-induced response has an inherent advantage for quantitatively representing the performance of bridges. Taking a long-span cable-stayed railway–highway combined bridge as the case study, this paper presents a representation method of in-service performance. First, the non-stationary sections of train-induced response are automatically extracted by wavelet transform and window with threshold. Then, the data of the feature parameter of each non-stationary section are automatically divided into four cases of train load according to the calculational theory of bridge vibration under train effect and clustering analysis. Finally, the performance indexes for structural deformation and dynamics are determined separately, based on hierarchical clustering and statistical modeling. Fusing the real variability of massive data from monitoring and the knowledge of mechanics of theoretical calculations, accurate and robust indexes of bridge deflection distribution and forced vibration frequency are obtained in real time. The whole process verifies the feasibility of the representation of bridge in-service performance from massive multisource sensing data. The presented method, framework, and analysis results can be used as a reference for the design, operation, and maintenance works of long-span railway bridges.

A Probabilistic Model for the Amplification of the Vibration Response of Railway Bridges Due to Random Track Unevenness in High-Speed Traffic

In combination with the moving train, track irregularities have a significant influence on the structural response of railway bridges. Compared to the ideal case of perfect track geometry without any irregularities, an amplification of the response is observed. This paper proposes a probabilistic model to predict this dynamic response amplification of railway bridges due to random track irregularities when subjected to high-speed trains. The developed regression model, based on a parametric numerical study, provides the mean and standard deviation of the dynamic response amplification separately for bridge deflection and acceleration, since large differences are found for these vibration variables. Depending on the span, mass, fundamental frequency, and damping coefficient of simply supported bridges, dynamic response amplification statistics are approximated for a range of train speeds and different track qualities. The proposed model estimates the dynamic response amplification due to random track irregularities at predefined exceedance probabilities, and a customized amplification factor is determined that is consistent with the semi-probabilistic safety concept used in structural design. An application example shows the superiority of this model compared to the commonly used code-based approach.

Improved Data-Driven Stochastic Subspace Identification with Autocorrelation Matrix Modal Order Estimation for Bridge Modal Parameter Extraction Using GB-SAR Data

With the advantage of non-contact measurement, ground-based synthetic aperture radar (GB-SAR) has been widely used to obtain the dynamic deflection of various bridges. Data-driven stochastic subspace recognition (Data-SSI), a popularized time-domain technique, is commonly used for modal parameter identification of bridges. To improve the computational efficiency and accuracy of the Data-SSI method for bridge modal parameter estimation using GB-SAR, this paper proposes an improved Data-SSI method. First, boxplot data filtering is applied to screen out the error points to generate a Hankel matrix. Second, the Hankel matrix compression method is presented to reduce the ill-conditioned vectors in the column vectors of the Hankel matrix to improve calculation efficiency. Finally, the exact modal order (EMO) modal estimation algorithm based on the autocorrelation matrix is adopted to reduce the generation of false modes and improve the calculation efficiency. The results of simulation and field experiments show that the natural frequency values for the improved Data-SSI method are 2.3208 and 2.3189 and the damping ratio coefficient values are 8.10 and 8.08, under windows 1 and 2, respectively. The operation times using the improved Data-SSI method are 2.02 s and 7.61 s under windows 1 and 2, respectively. This proves that the proposed improved Data-SSI method has higher accuracy and computational efficiency.

Maximum deflection of simple span steel box girder bridge using stress data

The Structural Health Monitoring System is part of tool and method for bridge operation and maintenance to make sure that the bridge is in good condition. Deflection is one of the main parameters to be measured and various methods has been introduced to measure deflection. Accuracy and economically are two main aspects when selecting the method for determine the real time deflection. This study presents a method of determining the maximum deflection of simple span continuous bridge using strain data obtained from a strain gauge sensor for simple span steel box girder bridge. Initial data were obtained from FEM simulations under various load conditions to obtain the maximum deflection value and the strain value. Linear regression and quadratic regression were carried out to obtain the relationship between the strains data and the maximum deflection. The accuracy of the maximum deflection value is then compared with the results of the analysis using FEM. It was found that the accuracy is about 91.16 % for quadratic regression and 9.07 for linear regression 90.93 %.

Bayesian inference for predicting the long-term deflection of prestressed concrete bridges by on-site measurements

Predicting the long-term deflection of prestressed concrete bridges (PSCB) by the deterministic models is subject to significant epistemic uncertainties, and the Bayesian statistics provide a practical way to make more reliable prediction by use of the long-term measurements. In this paper, a comprehensive Bayesian inference frame was built, in which the model parameters associated with creep, shrinkage, dead load and prestress level were updated by the Bayesian inference of the deflection measurements. A 3-D time-dependent finite element model was constructed, based on which a surrogate model was built to enhance computation efficiency. The Markov Chain Monte Carlo (MCMC) algorithm was adopted to approximate the manifold of the posterior distribution. In the case study, two sets of deflection of the case bridge were utilized to perform the Bayesian inference in a sequential manner. The results revealed that the updated models could produced better fit to the measurements than the deterministic model, while the variance of the prediction was significantly reduced. The updated model revealed changing trends of the time-dependent deflection, which characterizes a later-age acceleration from the initial moderate trend. Based on the updated models, the time-dependent reliability associated with the limit states defined by deflection limits was computed. For such a task, the MCMC-based pre-sampling and the quasi-optimal importance sampling were adopted to reduce the variance of the computation.

Sensor data-based probabilistic monitoring of time-history deflections of railway bridges induced by high-speed trains

Structural condition monitoring of railway bridges has been emphasized for guaranteeing the passenger comfort and safety. Various attempts have been made to monitor structural conditions, but many of them have focused on monitoring dynamic characteristics in frequency domain representation which requires additional data transformation. Occurrence of abnormal structural responses, however, can be intuitively detected by directly monitoring the time-history responses, and it may give information including the time to occur the abnormal responses and the magnitude of the dynamic amplification. Therefore, this study suggests a new Bayesian method for directly monitoring the time-history deflections induced by high-speed trains. To train the monitoring model, the data preprocessing of speed estimation and data synchronization are conducted first for the given training data of the raw time-history deflection; the Bayesian inference is then introduced for the derivation of the probability-based dynamic thresholds for each train type. After constructing the model, the detection of the abnormal deflection data is proceeded. The speed estimation and data synchronization are conducted again for the test data, and the anomaly score and ratio are estimated based on the probabilistic monitoring model. A warning is generated if the anomaly ratio is at an unacceptable level; otherwise, the deflection is considered as a normal condition. A high-speed railway bridge in operation is chosen for the verification of the proposed method, in which a probabilistic monitoring model is constructed from displacement time-histories during train passage. It is shown that the model can specify an anomaly of a train-track-bridge system.

Development of Railway Bridge Deflection Detection System Based on NI-cDAQ Inclinometer

Aiming at the limitation of the traditional deflection test method by the field application of railway bridge inspection, the paper develops a data acquisition and analysis system for bridge deflection inspection. The system is based on NI-cDAQ series acquisition equipment and the LabVIEW programming software development environment. Through the industrial Modbus bus protocol, it is possible to integrate the inclinometer, data acquisition equipment and other hardware acquisition equipment with the application software through the computer, and establish a complete set of practical instrument equipment and dynamic deflection detection process to achieve high speed, high precision and multi-channel acquisition Bridge deflection information. Combined with field tests for verification, the results show that the real-time collection and transmission of various parameters of the system can run for a long time under complex field conditions, with stable work and reliable data.

Research on Multi-Point Detection Method of Dynamic Deflection of Super Long-Span Bridge Based on Chain Laser Model

Research on Multi-Point Detection Method of Dynamic Deflection of Super Long-Span Bridge Based on Chain Laser Model

OPERATION OF PRE-STRESSED SPAN BEAMS OF BRIDGE CRANES TAKING INTO ACCOUNT LOAD COMBINATIONS

The paper considers issues related to increasing the bearing capacity of span beams of bridge cranes by means of prestressing. It is known that the work of the span structure of the crane with pre-stressed beams takes place under the same conditions, modes and capacities as conventional cranes. The load-bearing capacity of their span structures must be provided with high strength and rigidity in two planes – the main vertical plane and the horizontal one. However, studies of the stress-strain state of the crane with a pre-stress bridge operating in the horizontal plane were not performed. The peculiarity of this question is the development of a new mathematical model of the pre-stressed main beam, as well as obtaining the equation of the deflection curve of this beam when working in a horizontal plane. An analysis of its stress-strain state in the plane of the load suspension, as well as the simultaneous action of vertical and horizontal forces. This analysis allowed establishing the effect of horizontal inertial loads on the deformed state of the pre-stressed bridge. It is established that when operating a bridge crane with cargo in the middle of the span, the deflections of the span beam do not go beyond the regulatory deflections of a conventional crane bridge, which has a positive effect on the deformed condition of the main beam and facilitates the crane as a whole. The results obtained in this work can be further used for the design of bridge cranes with pre-stressed span beams in order to increase their load capacity, extend their service life without dismantling. Also for improvement of operating designs and engineering means of calculation, both at design stages, and in the conditions of real operation.