Considering continuous support conditions in moving force identification

A method is presented to identify moving forces on a continuous bridge. The bridge is modeled as a continuous supported Bernoulli-Euler beam and the boundary value problem of the beam is solved to get the exact mode shape functions of vibrating beam with inner supports. The bending moment responses are used to study the inverse problem in identifying moving forces on a bridge. The SVD (singular value decomposition) is used in the solution to study the inverse problem. Two time varying forces moving over the bridge are simulated to evaluate the method. White noise is added to simulated bending moment responses to study the effect of noise in moving forces identification problem for different numbers and arrangements of sensors. Results obtained from simulation study show that the method is effective in identifying moving forces and acceptable results can be obtained

Experimental study of moving force identification on a continuous bridge

This paper describes an experimental study on the identification of moving vehicle axle loads on a continuous supported bridge based on the measured bending moment responses. A bridge-vehicle system model was fabricated in the laboratory. The bridge was modeled as a three span continuous supported beam and the vehicle was modeled as a vehicle model with two-axle loads. A number of strain gauges were adhered to the bottom surface of the beam to measure the bending moment responses. Using measured bending moment responses as an input, the inverse problem was solved to identify moving loads. The moving forces were identified when considering bending moment responses from all spans of the beam and only one span respectively. The rebuilt responses were reconstructed from the identified loads as a forward problem. To study the accuracy of the method the relative percentage errors were calculated with respect to the measured and the rebuilt bending moment responses. The rebuilt bending moment responses obtained from the identified forces are in good agreement with measured bending moment responses. This indirectly shows that the method is capable of identifying moving loads on continuous supported bridges

Statistical models from weigh-in-motion data

This paper aims at formulating various statistical models for the study of a ten year Weigh-in-Motion (WIM) data collected from various WIM stations in Hong Kong. In order to study the bridge live load model it is important to determine the mathematical distributions of different load affecting parameters such as gross vehicle weights, axle weights, axle spacings, average daily number of trucks etc. Each of the above parameters is analyzed by various stochastic processes in order to obtain the mathematical distributions and the Maximum Likelihood Estimation (MLE) method is adopted to calculate the statistical parameters, expected values and standard deviations from the given samples of data. The Kohnogorov-Smirnov (K-S) method of approach is used to check the suitability of the statistical model selected for the particular parameter and the Monte Carlo method is used to simulate the distributions of maximum value stochastic processes of a series of given stochastic processes. Using the statistical analysis approach the maximum value of gross vehicle weight and axle weight in bridge design life has been determined and the distribution functions of these parameters are obtained under both free-flowing traffic and dense traffic status. The maximum value of bending moments and shears for wide range of simple spans are obtained by extrapolation. It has been observed that the obtained maximum values of the gross vehicle weight and axle weight from this study are very close to their legal limitations of Hong Kong which are 42 tonnes for gross weight and 10 tonnes for axle weight

Evaluation of dynamic loads on a skew box girder continuous bridge part I: field test and modal analysis

Field measurements were carried out to evaluate dynamic loads on an existing skew box girder continuous bridge. This paper presents the experimental procedure, the data acquisition system, the calibration test, the modal analysis and the load distribution in a transversal direction. A three-axle heavy truck was hired for use in the test to calibrate the field measurements. The static and dynamic bending moments of the tested bridge induced by the calibration truck were obtained. The relationship between the measured strain and bending moment were determined. Information on the dynamic behaviours of the bridge were obtained from an experimental and theoretical modal analysis. The influence of skewness on the static and dynamic behaviours of the bridge as well as on the load distribution in the transversal direction for the calibration truck and in-service vehicles was investigated. It was found that the influence of skew in both the static and dynamic behaviours of the bridge within the skew angle range of 0 degrees-30 degrees is very small

Evaluation of dynamic loads on a skew box girder continuous bridge part II: parametric study and dynamic load factor

Studies on dynamic loads are important for bridge engineering as well as pavement design. A large number of research studies have indicated that bridge dynamic loads increase road surface damage by a factor of 2-4. Although the field test is the best available approach to understanding actual vehicle-induced dynamic loads on bridges, according to pervious studies there is only a limited amount of field data available on skew box girder continuous bridges. This paper presents an evaluation of vehicle-induced dynamic loads, based on a field test that was carried out on a skew box girder continuous bridge as reported in a companion paper (Part I). The effects of different parameters such as the weight, speed, type, number of axles and position of vehicles on dynamic loads are investigated. Based on the statistical analysis, the use of the dynamic load factor (DLF) is proposed. The dynamic load factor obtained in this study is less than the values provided by most bridge design codes

Field tests for condition assessment and moving force identification on a skew bridge

Field tests are still one of the most important and practical methods for bridge assessment and for better understanding on bridge behaviour so far. This paper reports some preliminary results on a series of field tests that had been carried out on the Tsing-Yi South Bridge (N797) in New Territories West of Hong Kong in the April 2005. After the tested skew bridge is briefly introduced, the experimental modal analyses on the skew bridge and the hired vehicle, the corresponding calibration test of tested bridge, the subsequent moving force identification tests, and other dynamic tests are described. Some experimental results from the mentioned tests are then analyzed and discussed. In addition, some useful data were extracted from the developed data base and provided for the subsequent moving force identification, impact factor study and bridge condition assessment. The results will also be discussed

Moving axle load from multi-span continuous bridge: Laboratory study

Laboratory study on the identification of moving vehicle axle loads on a multi-span continuous bridge from the measured bending moment responses is presented. A bridge-vehicle system model was fabricated in the laboratory. The bridge was modeled as a three span continuous beam and the car was modeled as a vehicle model with two-axle loads. A number of strain gauges were adhered to the bottom surface of the beam to measure the bending moment responses. Using measured bending moment responses as an input, the corresponding inverse problem was solved to identify moving loads. The moving forces were identified when considering bending moment responses from all spans of the beam. In order to avoid the lower identification accuracy around the inner supports of continuous bridge and to improve the computation efficiency, the moving force identification from the target (one selected) span of the continuous bridge was studied. The rebuilt responses were reconstructed from the identified loads as a forward problem. To study the accuracy of the method the relative percentage errors were calculated with respect to the measured and the rebuilt bending moment responses. The rebuilt bending moment responses obtained from the identified forces are in good agreement with the measured bending moment responses. This indirectly shows that the method is capable of identifying moving loads on continuous supported bridges

Vertical displacement measurements for bridges using optical fiber sensors and CCD cameras : a preliminary study

Bridge managers all over the world are always looking for simple ways to measure bridge vertical displacements for structural health monitoring. However, traditional methods to obtain such data are either tedious or expensive. There is a need to develop a simple, inexpensive, and yet practical method to measure bridge vertical displacements. This paper proposes two methods using either optical fiber (FBG) sensors or a charge-coupled-device (CCD) camera, respectively, for vertical displacement measurements of bridges. The FBG sensor method is based on the measured horizontal strains together with the identified curvature functions obtained by a self-developed FBG Tilt sensor. CCD cameras use a large number of pixels to form an image. The CCD camera method utilizes image processing techniques for pixel identification and subsequent edge detection. A preliminary study to validate the proposed methods in laboratory was presented. The tests include applying the methods to determine the vertical displacements separately for a concrete beam and a steel beam under various loadings. The comparisons include their installations, costs, degrees of accuracy, external factors affecting the measurement, etc. It was concluded that both methods could be used for vertical displacement measurement, and they could be complementary with one another. It was suggested to further improve the two methods developed and a successful outcome will not only help to solve an important problem for bridge management, but also prepare the way for better structural health monitoring techniques