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Showing papers on "Structural health monitoring published in 2002"


Journal ArticleDOI
TL;DR: In this article, the authors presented an experimental and analytical survey of candidate methods for in situ damage detection of composite materials, including delamination, transverse ply cracks and through-holes.
Abstract: Cost-effective and reliable damage detection is critical for the utilization of composite materials. This paper presents part of an experimental and analytical survey of candidate methods for in situ damage detection of composite materials. Experimental results are presented for the application of Lamb wave techniques to quasi-isotropic graphite/epoxy test specimens containing representative damage modes, including delamination, transverse ply cracks and through-holes. Linear wave scans were performed on narrow laminated specimens and sandwich beams with various cores by monitoring the transmitted waves with piezoceramic sensors. Optimal actuator and sensor configurations were devised through experimentation, and various types of driving signal were explored. These experiments provided a procedure capable of easily and accurately determining the time of flight of a Lamb wave pulse between an actuator and sensor. Lamb wave techniques provide more information about damage presence and severity than previously tested methods (frequency response techniques), and provide the possibility of determining damage location due to their local response nature. These methods may prove suitable for structural health monitoring applications since they travel long distances and can be applied with conformable piezoelectric actuators and sensors that require little power.

752 citations


Journal ArticleDOI
TL;DR: In this paper, the state-of-the-art in piezoelectric-wafer active sensors structural health monitoring and damage detection is reviewed, and two main detection strategies are considered: the E/M impedance method for near field damage detection, and wave propagation methods for far-field damage detection.
Abstract: Piezoelectric wafer active sensors may be applied on aging aircraft structures to monitor the onset and progress of structural damage such as fatigue cracks and corrosion. The state of the art in piezoelectric-wafer active sensors structural health monitoring and damage detection is reviewed. Methods based on (a) elastic wave propagation and (b) the Electro–Mechanical (E/M) impedance technique are cited and briefly discussed. For health monitoring of aging aircraft structures, two main detection strategies are considered: the E/M impedance method for near field damage detection, and wave propagation methods for far-field damage detection. These methods are developed and verified on simple-geometry specimens and on realistic aging aircraft panels with seeded cracks and corrosion. The experimental methods, signal processing, and damage detection algorithms are tuned to the specific method used for structural interrogation. In the E/M impedance method approach, the high-frequency spectrum, representative of the structural resonances, is recorded. Then, overallstatistics damage metrics can be used to compare the impedance signatures and correlate the change in these signatures with the damage progression and intensity. In our experiments, the (1 � R 2 ) 3 damage metric was found to best fit the results in the 300–450 kHz band. In the wave propagation approach, the pulse-echo and acousto-ultrasonic methods can be utilized to identify the additional reflections generated from crack damage and the changes in transmission phase and velocity associated with corrosion damage. The paper ends with a conceptual design of a structural health monitoring system and suggestions for aging aircraft installation utilizing active-sensor arrays, data concentrators, wireless transmission, and a health monitoring and processing unit.

587 citations


Journal ArticleDOI
TL;DR: The trade-offs between parametric-based modeling and non-parametric modeling of non-linear hysteretic dynamic system behavior are discussed and their implications are discussed in the context of adaptive structures and structural health monitoring.
Abstract: Adaptive estimation procedures have gained significant attention by the research community to perform real-time identification of non-linear hysteretic structural systems under arbitrary dynamic excitations. Such techniques promise to provide real-time, robust tracking of system response as well as the ability to track time variation within the system being modeled. An overview of some of the authors’ previous work in this area is presented, along with a discussion of some of the emerging issues being tackled with regard to this class of problems. The trade-offs between parametric-based modeling and non-parametric modeling of non-linear hysteretic dynamic system behavior are discussed. Particular attention is given to (1) the effects of over- and under-parameterization on parameter convergence and system output tracking performance, (2) identifiability in multi-degree-of-freedom structural systems, (3) trade-offs in setting user-defined parameters for adaptive laws, and (4) the effects of noise on measurement integration. Both simulation and experimental results indicating the performance of the parametric and non-parametric methods are presented and their implications are discussed in the context of adaptive structures and structural health monitoring.

177 citations


Journal ArticleDOI
TL;DR: In this article, a frequency-domain maximum likelihood estimator is used to automate the modal identification process and a fuzzy clustering algorithm is used for mode selection and mode-tracking.

135 citations


Dissertation
01 Jan 2002
TL;DR: Spearing et al. as discussed by the authors presented the conclusions of an analytical and experimental survey of candidate methods for in-situ damage detection in composite materials and verified experimentally by using piezoelectric patches as actuators and sensors.
Abstract: Cost-effective and reliable damage detection is critical for the utilization of composite materials This thesis presents the conclusions of an analytical and experimental survey of candidate methods for in-situ damage detection in composite materials Finite element results are presented for the application of modal analysis and Lamb wave techniques to quasi-isotropic graphite/epoxy test specimens containing representative damage These results were then verified experimentally by using piezoelectric patches as actuators and sensors for both sets of experiments The passive modal analysis method was reliable for detecting small amounts of global damage in a simple composite structures By comparison, the active Lamb wave method was sensitive to all types of local damage present between the sensor and actuator, provided useful information about damage presence and severity, and presents the possibility of estimating damage type and location Analogous experiments were also performed for more complex builtup structures such as sandwich beams, stiffened plates and composite cylinders These techniques have proven suitable for structural health monitoring applications since they can be applied with low power conformable sensors and can provide useful information about the state of a structure during operation Piezoelectric patches could also be used as multipurpose sensors to test using a variety of methods such as modal analysis, Lamb wave, acoustic emission and strain based methods simultaneously by altering driving frequencies and sampling rates Guidelines and recommendations drawn from this research are presented to assist in the design of a structural health monitoring system for a vehicle, and provides a detailed example of a SHM system architecture These systems will be an important component in future designs of air and spacecraft to increase the feasibility of their missions Thesis Supervisor: S Mark Spearing Title: Associate Professor of Aeronautics and Astronautics

131 citations


Journal ArticleDOI
Nobuo Takeda1
TL;DR: In this article, a methodology for observation and modeling of microscopic damage evolution in quasi-isotropic composite laminates is presented, based on the damage observation using both an optical microscope and a soft X-ray radiography, a damage mechanics analysis is conducted to formulate the stiffness change due to transverse cracking.

94 citations


Journal ArticleDOI
TL;DR: In this article, the importance of intelligent signal processing for damage identification in composite materials is discussed, including data denoising techniques, feature extraction and selection, pattern recognition and optimal sensor location procedures.

83 citations


01 May 2002
TL;DR: The basic technical knowledge is established to evaluate whether remote surveillance of the rotor blades of large off-shore wind turbines has technical and economical potential and a cost-benefit analysis was developed, showing that it is economically attractive to use sensors embedded in the blade.
Abstract: This summary-report describes the results of a pre-project that has the aim of establishing the basic technical knowledge to evaluate whether remote surveillance of the rotor blades of large off-shore wind turbines has technical and economical potential. A cost-benefit analysis was developed, showing that it is economically attractive to use sensors embedded in the blade. Specific technical requirements were defined for the sensors capability to detect the most important damage types in wind turbine blades. Three different sensor types were selected for use in laboratory experiments and full-scale tests of a wind turbine blade developing damage: 1) detection of stress wave emission by acoustic emission, 2) measurement of modal shape changes by accelerometers and 3) measurement of crack opening of adhesive joint by a fibre optics micro-bend displacement transducer that was developed in the project. All types of sensor approaches were found to work satisfactory. The techniques were found to complement each other: Acoustic emission has the capability of detecting very small damages and can be used for locating the spatial position and size of evolving damages. The fibre optics displacement transducer was found to work well for detecting adhesive failure. Modelling work shows that damage in a wind turbine blade causes a significant change in the modal shape when the damage is in the order of 0.5-1 m. Rough estimates of the prices of complete sensor systems were made. The system based on acoustic emission was the most expensive and the one based on accelerometers was the cheapest. NDT methods (ultrasound scanning and X-ray inspection) were found to be useful for verification of hidden damage. Details of the work are described in annexes. (au)

82 citations


Journal ArticleDOI
TL;DR: This paper presents the application of wavelet analysis to identify events and changes in structural state in a bridge during and after its construction.

81 citations


Journal ArticleDOI
TL;DR: Structural health monitoring can be viewed as a problem in statistical pattern recognition involving operational evaluation, data cleansing, damage identification, and life prediction as mentioned in this paper, and it can be seen as a special case of the problem of pattern recognition.
Abstract: Structural health monitoring can be viewed as a problem in statistical pattern recognition involving operational evaluation, data cleansing, damage identification, and life prediction. In damage id...

73 citations


Journal ArticleDOI
TL;DR: In this paper, the use of embedded piezoelectric-wafer active-sensors for in-situ structural health monitoring of thin-wall structures is presented, and experiments performed on aircraft-grade metallic specimens of various complexities exemplified the detection procedures for near-field and far-field damage.
Abstract: The use of embedded piezoelectric-wafer active-sensors for in-situ structural health monitoring of thin-wall structures is presented. Experiments performed on aircraft-grade metallic specimens of various complexities exemplified the detection procedures for near-field and far-field damage. For near-field damage detection, the electro-mechanical (E/M) impedance method was used. Systematic experiments conducted on statistical samples of incrementally damaged specimens were followed by illustrative experiments on realistic aging aircraft panels. For far-field damage detection, guided ultrasonic Lamb waves were utilized in conjunction with the pulse-echo technique. Systematic experiments conducted on aircraft-grade metallic plates were used to develop the method, while experiments performed on realistic aging-aircraft panels exemplified the crack detection procedure.


Journal ArticleDOI
TL;DR: In this article, a spectral finite element model consisting of a damaged spectral element is used for model-based prediction of the damaged structural response in the frequency domain, and a genetic algorithm (GA) specially tailored for damage identification is derived and is integrated with finite-element code for automation.
Abstract: An efficient strategy for identification of delamination in composite beams and connected structures is presented A spectral finite-element model consisting of a damaged spectral element is used for model-based prediction of the damaged structural response in the frequency domain A genetic algorithm (GA) specially tailored for damage identification is derived and is integrated with finite-element code for automation For best application of the GA, sensitivities of various objective functions with respect to delamination parameters are studied and important conclusions are presented Model-based simulations of increasing complexity illustrate some of the attractive features of the strategy in terms of accuracy as well as computational cost This shows the possibility of using such strategies for the development of smart structural health monitoring softwares and systems

Journal ArticleDOI
TL;DR: In this article, an approach based on the Damage Location Vector (DLV) method is proposed to handle the ambient vibration case. But, in many cases, there is no easy way to measure these inputs - or alternatively to externally excite the structure.
Abstract: In recent years, Structural Health Monitoring (SHM) has emerged as a new research area in civil engineering. Most existing health monitoring methodologies require direct measurement of input excitation for implementation. However, in many cases, there is no easy way to measure these inputs - or alternatively to externally excite the structure. Therefore, SHM methods based on ambient vibration have become important in civil engineering. In this paper, an approach is proposed based on the Damage Location Vector (DLV) method to handle the ambient vibration case. Here, this flexibility-matrix-based damage localization method is combined with a modal expansion technique to eliminate the need to measure the input excitation. As a by-product of this approach, in addition to determining the location of the damage, an estimate of the damage extent also can be determined. Finally, a numerical example analyzing a truss structure with limited sensors and noisy measurement is provided to verify the efficacy of the proposed approach.

Proceedings ArticleDOI
29 Oct 2002
TL;DR: In this paper, the authors describe the installation and testing of a large-scale fiber optic sensor network on the British Trimaran Research Vessel (RV Triton) in the North Atlantic.
Abstract: Systems Planning and Analysis, Inc., under sponsorship from the United States Navy, Office of Naval Research (ONR), has developed a structural health monitoring system for large-scale structures, based on fiber Bragg grating (FBG) sensors. The application of this new structural health monitoring system to US Navy vessels will reduce maintenance costs by allowing for scheduling of need-based maintenance, increase fleet operational availability, and ship survivability by providing ship operators real-time information concerning the state of the ship structure. Central to the monitoring system is an instrumentation unit capable of detecting signals from hundreds of FBG sensors with sampling rates approaching 2 kHz. The instrumentation is based on SPA's proprietary Digital Spatial Wavelength Domain Multiplexing (DSWDM) technology developed under this effort. DSWDM technology is electro-optics based and has been shown to provide significantly higher sampling rates than comparative FBG interrogation technologies. The baseline system interrogates more than 120 sensors along eight fiber channels. The prototype High Speed-Fiber Optic Interrogation System (HS-FOIS) also possesses a number of advantages intrinsic to optical fiber sensors as compared to conventional strain sensor systems. These advantages include extremely low installed weight and volume, immunity to electromagnetic interference and corrosive environments, and low signal attenuation and drift. This paper describes the installation and testing of a large-scale fiber optic sensor network on the British Trimaran Research Vessel (RV) Triton. In this on-going project with the Naval Surface Warfare Center, Carderock Division (NSWCCD) and the British Defence Science and Technology Laboratory (formerly DERA), Systems Planning and Analysis, Inc. (SPA) recently completed the installation and at-sea testing of an integrated hardware/software structural monitoring system. The rough sea trials of the RV Triton was conducted in early February 2002 in the North Atlantic. This paper describes the fiber optic Bragg grating sensor network comprising of 51 sensors, the interrogating system, and the processing algorithms used to simultaneously record strain data at both high- and low-speed frequencies, including triggering of the high-speed channels. This paper also details the sensor layout and installation process with emphasis on lessons learned during this procedure. The test procedure and sample data results are presented. Finally, conclusions on the presented data and implications of the structural health monitoring system for future naval vessels are discussed.

Journal ArticleDOI
TL;DR: In this paper, the effect of a typhoon on fatigue damage in steel decks of long-span bridges was investigated by using on-line strain data acquired from the structural health monitoring system permanently installed on the bridge.

Journal ArticleDOI
Chi-Young Ryu1, Chang-Sun Hong1
TL;DR: In this paper, an improved fiber bragg grating (FBG) sensor system using a wavelength-swept fiber laser which exhibits high output power for several sensor arrays is presented.
Abstract: Fiber Bragg grating (FBG) sensors based on the wavelength division multiplexing technology are ideally suited for structural health monitoring. In many applications, it is desirable to form several arrays of optical fiber sensors to monitor the response of structures. In the present study, we constructed an improved FBG sensor system using a wavelength-swept fiber laser which exhibits high output power for several sensor arrays. A fiber cavity etalon was also fabricated for the calibration of the nonlinear output wavelength of a laser and for scaling the information in the wavelength domain for signal processing. The constructed FBG sensor system with the fiber cavity etalon and a reference FBG was applied for strain measurements of a laminated composite panel under axial compressive loading. In order to monitor the structural strain in real time, the signal-processing program was constructed using LabVIEW software for storing and visualizing data from the FBG sensors. Experiments showed that the constructed FBG sensor system and the real-time signal-processing program could successfully monitor the strain of composite laminates. This improved FBG sensor system could be useful for large structures which require a large number of sensor arrays.

Proceedings ArticleDOI
TL;DR: This paper discusses basic concepts, design issues, and preliminary performance of wireless sensors, including a temperature-threshold indicator and a chloride-th threshold indicator.
Abstract: Wireless sensors can be realized by integrating a sensor with a passive commercial radio-frequency identification (RFID) chip. When activated, the chip responds with a digitally encoded signal that not only identifies the sensor but also contains information about the sensor state. Two devices have been developed to date: a temperature-threshold indicator and a chloride-threshold indicator. This paper discusses basic concepts, design issues, and preliminary performance.

Proceedings ArticleDOI
01 Nov 2002
TL;DR: A dynamic impedance model derived from the Euler-Bernoulli beam theory was developed to investigate the influence of in-situ stress on the dynamic and electro-mechanical response of a smart beam interrogated by a pair of symmetrically bounded, surface-bonded piezoceramic (PZT) transducers.
Abstract: In the beginning, the electro-mechanical (EM) impedance method for structural health monitoring was recognized as a means of structural in-situ stress monitoring and measurement. Consequently, theoretical analysis based on the EM impedance method as a tool for in-situ stress identification in structural members was presented. A dynamic impedance model derived from the Euler-Bernoulli beam theory was developed to investigate the influence of in-situ stress on the dynamic and electro-mechanical response of a smart beam interrogated by a pair of symmetrically bounded, surface-bonded piezoceramic (PZT) transducers. Numerical simulation was performed for a laboratory sized smart beam subjected to a multitude of axial loads at the ends. It was found that natural frequency shifts takes place in the presence of in-situ stress. Furthermore, these shifts, which are linearly related to the magnitude of applied load, is directly reflected in the point-wise dynamic stiffness response. However, in terms of the electro-mechanical response, which can be measured directly, the shift of peaks of the EM admittance signature is not directly indicative of the natural frequency shifts. This arises as an inverse problem in engineering, which cannot be deciphered using direct approach. Back calculation of the in-situ stress using genetic algorithm (GA) was proposed.


01 Jan 2002
TL;DR: In this article, a survey of candidate methods for in-situ damage detection of composite materials is presented, including linear wave scans on narrow laminated specimen, sandwich beams, and built-up structures such as composite plates with stiffeners and a cylinder.
Abstract: * Cost-effective and reliable damage detection is critical for the utilization of composite materials. This paper describes part of an experimental and analytical survey of candidate methods for in-situ damage detection of composite materials. Optimal piezoceramic actuator geometry and driving parameters were developed from the Lamb wave equations. Results are then presented for the application of this Lamb wave technique to graphite/epoxy specimens containing representative damage modes. Linear wave scans were performed on narrow laminated specimen, sandwich beams, and built-up structures such as composite plates with stiffeners and a cylinder. Lamb wave techniques have been proven to provide more information about damage type, severity and location than previously tested methods (frequency response techniques), and may prove suitable for structural health monitoring applications since they travel long distances and can be applied with conformable piezoelectric actuators and sensors that require little power.

Proceedings ArticleDOI
22 Apr 2002
TL;DR: In this paper, the authors present an experimental and analytical survey of candidate methods for in-situ damage detection of composite materials using piezoceramic sensors (PZT).
Abstract: Structural Health Monitoring (SHM) denotes a system with the ability to detect and interpret adverse “changes” in a structure in order to improve reliability and reduce life-cycle costs. The greatest challenge in designing a SHM system is knowing what “changes” to look for and how to identify them. The characteristics of damage in a particular structure plays a key role in defining the architecture of the SHM system. The resulting “changes,” or damage signature, will dictate the type of sensors that are required, which in-turn determines the requirements for the rest of the components in the system. The present research project focuses on the relationship between various sensors and their ability to detect “changes” in a structure’s behavior. This paper presents part of an experimental and analytical survey of candidate methods for in-situ damage detection of composite materials using piezoceramic sensors (PZT). Results are presented for the application of modal analysis, Lamb wave, acoustic emission and strain monitoring techniques to quasi-isotropic graphite/epoxy specimens containing representative damage modes, including delamination, transverse ply cracks and through-holes.

Journal ArticleDOI
TL;DR: In this paper, the authors present experimental results on thermomechanical behavior of Extrinsic Fabry-Perot Interferometric fiber optic strain sensors (EFPI-FOSS).
Abstract: This paper presents experimental results on thermomechanical behavior of Extrinsic Fabry-Perot Interferometric fiber optic strain sensors (EFPI-FOSS). The objective of this study was to determine the accuracy, strength characteristics, and durability properties of both bare (nonembedded) EFPI sensors, and embedded optical fiber sensors in either a neat resin or aerospace grade composite laminate. Experimental results suggest that the embedded EFPI sensors provide reliable strain measurements for values exceeding 10,000 μ∊ under static loading conditions. A major portion of this study focused on evaluating the long term tension–tension fatigue behavior of optical fiber sensors. Test data suggest the EFPI sensors provide reliable data up to 1 million cycles at fatigue strain levels below 3,000 μ∊. For fatigue strain levels above this value, failure of the fiber optic sensor was observed. While the sensor failed it did not influence the strength and fatigue life of the composite coupons. Considering the desi...

Journal ArticleDOI
TL;DR: In this article, the use of fiber bragg gratings (FBGs) in structural health monitoring is reported. But the results obtained followed the same trend as that expected from concrete structures subjected to loading tests.
Abstract: In this paper we report on our results for the applications of fibre Bragg gratings (FBGs) in structural health monitoring. Multiplexed FBG-based strain sensors were fixed onto the reinforced bars (rebars) in concrete structures to determine the strain changes at different locations within the structures during loading and unloading tests. A similar set of FBG-based strain sensor arrays was also mounted onto the surface of the structures for the purpose of comparison. At the same time an FBG-based sensor array optimized for temperature measurement was also distributed alongside the strain sensors to obtain the temperature information, as well as to compensate for the temperature-induced wavelength shifts on those FBG strain sensors. The results obtained followed the same trend as that expected from concrete structures subjected to loading tests.


Journal ArticleDOI
TL;DR: In this paper, the applicability of the sensitivity-based method is extended to the domain of operational modal analysis (output-only measurements) by using a new method for the correct rescaling of operational mode shape estimates that neither requires forced vibration testing nor finite element modelling.

01 May 2002
TL;DR: In this paper, a description of the sensor schemes and the non-destructive testing (NDT) methods that have been investigated in this project is given and the advantages and disadvantages of different schemes are discussed.
Abstract: This annex provides a description of the sensor schemes and the non-destructive testing (NDT) methods that have been investigated in this project. Acoustic emission and fibre optic sensors are described in some detail whereas only the key features of well-established NDT methods are presented. Estimates of the cost of different sensor systems are given and the advantages and disadvantages of the different schemes is discussed. (au)

Proceedings ArticleDOI
12 Jul 2002
TL;DR: In this paper, the authors present the conclusions of an experimental and analytical survey of candidate methods for in-situ damage detection in composite structures, including modal analysis, Lamb wave, acoustic emission and strain based methods.
Abstract: Cost-effective and reliable damage detection is critical for the utilization of composite materials. This paper presents the conclusions of an experimental and analytical survey of candidate methods for in-situ damage detection in composite structures. Experimental results are presented for the application of modal analysis and Lamb wave techniques to quasi-isotropic graphite/epoxy test specimens containing representative damage. Piezoelectric patches were used as actuators and sensors for both sets of experiments. Modal analysis methods were reliable for detecting small amounts of global damage in a simple composite structure. By comparison, Lamb wave methods were sensitive to all types of local damage present between the sensor and actuator, provided useful information about damage presence and severity, and present the possibility of estimating damage type and location. Analogous experiments were also performed for more complex built-up structures. These techniques are suitable for structural health monitoring applications since they can be applied with low power conformable sensors and can provide useful information about the state of a structure during operation. Piezoelectric patches could also be used as multipurpose sensors to detect damage by a variety of methods such as modal analysis, Lamb wave, acoustic emission and strain based methods simultaneously, by altering driving frequencies and sampling rates. This paper present guidelines and recommendations drawn from this research to assist in the design of a structural health monitoring system for a vehicle. These systems will be an important component in future designs of air and spacecraft to increase the feasibility of their missions.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a continuous sensor for detecting vibration and stress waves in a cantilever bar with an active fiber composite material or piezoceramic wafers.
Abstract: The concept of a continuous sensor for detecting vibration and stress waves in bars is investigated in this paper. This type of sensor is a long tape with a number of sensing nodes that are electrically connected together to form a single sensor with one channel of data output. The spacing of the sensor nodes can be designed such that the sensor is capable of detecting acoustic emissions (AEs) occurring at any point along the length of the sensor. An active fiber composite material or piezoceramic wafers can be used as the active element of the sensor. The characteristics of this new type of sensor were investigated by a simplified simulation and through experiments. The scope of the simulation is primarily to determine the characteristics of the new type of sensor that is proposed and the simulation is not intended to model the complex dispersion characteristics of guided waves in bars. The sensor was modeled as being integrated within a uniform cantilever bar to measure longitudinal stress wave propagation. Damping was included in the model to attenuate the wave as it travels. The sensor was connected to an electrical tuning circuit to examine the capability to filter out undesirable noise due to ambient vibration that would occur in practice. The elastic response of the bar was computed in closed form, and the coupled piezoelectric constitutive equations and electric circuit equations were solved using the Newmark-Beta numerical integration method. Strain, vibration, and wave propagation responses were simulated and results indicate that damage to the bar can be detected by recognizable changes in the sensor output as the wave propagates along the bar and passes over each sensor node. Experiments were performed to verify the concept of the continuous sensor on a composite bar. The testing showed the continuous sensor can replace four or more individual sensors to detect AEs and thus may be a practical method for structural health monitoring.

01 May 2002
TL;DR: In this article, a unified approach on determination of the effective stress range based on equivalent law of strain energy and fatigue damage model, so as to provide an efficient approach for accurately assessing effective fatigue stress of existing bridge under traffic loading.
Abstract: This paper presents a unified approach on determination of the effective stress range based on equivalent law of strain energy and fatigue damage model, so as to provide an efficient approach for accurately assessing effective fatigue stress of existing bridge under traffic loading. A new theoretical framework to relate variable- and constant-amplitude fatigue is proposed in this paper. Different formulation for calculating effective stress range can be derived by the proposed theory, which include the effective stress range by the root mean square, by Miner's law and a new effective stress range based on the nonlinear fatigue damage model. Comparison of the theoretical results of fatigue damage under the effective stress range of the variable-amplitude stress spectrum and experimental data of fatigue damage under realistic traffic loading has confirmed the validity of the proposed theory. As a way to relate variable-amplitude fatigue data with constant-amplitude data, the effective stress range provides the most convenient way for evaluating fatigue damage under variable-amplitude loading. The proposed theory is then applied to provide an efficient approach for accurately assessing fatigue damage of existing bridges under traffic loading, in which online strain history data measured from bridge structural health monitoring system is available. The proposed approach is applied to evaluate the effective stress range for the purpose of the fatigue analysis of a deck section of a long-span steel bridge-the Tsing Ma Bridge in Hong Kong.