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International Journal of Fatigue
, Pages 129-142
The fatigue life estimation of orthotropic steel bridge decks using the finite element method is most frequently associated with the application of the structural hot spot stress approach or the effective notch stress approach, rather than the traditional nominal stress approach. The application of these approaches to a welded joint with cut-out holes in orthotropic bridge decks, where it is not easy to distinguish the non-linear stress caused by the notch at the weld toe from the stress concentration effect emanating from the hole in the detail, was investigated. The results of the finite element calculations were compared with the results of the fatigue tests which were carried out on full-scale specimens. The results of the finite element analyses revealed that the structural hot spot stresses obtained from the shell element models were unrealistically high when the welds were omitted. Moreover, the way in which the welds were represented had a substantial influence on the magnitude of the hot spot stress. The results of the analysis when using the effective notch stress approach showed that the agreement between the estimated fatigue life using this approach and the fatigue life obtained from the fatigue tests was good.
► The paper presents that complex details with holes require more accurate methods. ► Modelling technique is very important to obtain a reliable hot spot stress value. ► The welds in complex joints should be represented when using shell element models. ► Effective notch stress method yields good results despite it requires more effort. ► A more clear definition for critical cross-sections should be outline in EC3.
Stiffened, welded steel deck plates have been used for many years in steel structures due to their load-carrying capacity in proportion to their weight. This type of deck plate is common not only in steel bridges but also in other heavy fatigue-loaded steel structures, such as offshore and ship structures. An orthotropic steel bridge deck, made up of a deck plate, longitudinal ribs and cross girders, contains a number of complex welded joints which display complex behaviour. The deck plate in these structures distributes traffic loads in two directions, with different structural rigidity in the longitudinal and transverse directions . Because of this complexity in geometry and load transfer conditions, steel bridges with orthotropic decks include details that make it difficult to estimate their fatigue strength correctly. Also the complexity in orthotropic bridge decks increases if the bridge deck connections contain cut-out holes which facilitate the continues ribs passing through the cross girder and which are provided to access the crossing welds. However, the fatigue strength of these welded details becomes more critical due to the higher stress concentration caused by stiffness reduction at the section. Fatigue cracks in welded joints with cut-out holes in orthotropic bridge decks in existing bridges all over the world have been observed and reported , , , .
In general, the fatigue design and analysis of steel bridges is performed using the nominal stress approach. S–N curves with the corresponding fatigue classes are provided for a number of typical steel details in various codes. This method is based on the average stress in the section of interest, assuming elastic material behaviour and without taking account of the local stress concentration effects of the weld feature. However, the stress-raising effects originating from the macro-geometrical changes are included in the fatigue design stress calculations . In the case of large structures with complex details, such as joints in orthotropic bridge decks – in which an accurate estimation of the nominal load effects in the detail is often difficult to obtain – a local stress determination approach, which takes account of the stress-raising effects due to the geometry, might provide an accurate estimate of the load defects in the detail. Using the nominal stress in such cases can yield unrealistic results. These types of complex detail therefore require advanced fatigue life evaluation techniques based on accurate fatigue design stress calculations using the finite element method (FEM).
In this paper, the application of the most common fatigue life assessment methods using the FEM is demonstrated on an orthotropic bridge detail. The detail is a welded rib-to-cross-girder connection with cut-out holes. In addition to the structural hot spot stresses which were evaluated both experimentally and numerically using different stress determination procedures, the effective notch stress approach and the nominal stress approach were used to evaluate the fatigue life of the detail.
The use of the structural hot spot stress approach for the fatigue life assessment of welded complex structures has increased rapidly with the increasing use of the FEM. However, the result of finite element analysis (FEA) is highly mesh sensitive, as the structural hot spot stresses are often in an area of high strain gradients, i.e. stress singularities. The resulting stresses may differ substantially, depending on the type and size of elements and the procedure used to extract the values of the hot spot stresses. For this reason, a stress evaluation method is needed to obtain a relevant stress value that can be related to the fatigue strength of the detail. The International Institute of Welding (IIW) provides the most comprehensive rules and recommendations for the application of structural hot spot stress, such as element type, size and reference points. In Eurocode 3 , the method is included as an alternative fatigue life assessment method. However, the code does not provide any recommendations or instructions, relating to the application of the structural hot spot stress method, i.e. modelling and extrapolation techniques and type of hot spot points, apart from some structural details and corresponding fatigue curves.
In a welded joint, the critical points at which the fatigue cracks are most likely to initiate and propagate are usually located at the weld toes. These points are referred to as the “hot spot points” and are shown in Fig. 1, as defined by Niemi and Fricke , , , . The calculated stress at such a point is called “structural hot spot stress”. According to the definition of the structural hot spot stress approach, the calculated stresses or measured strains include all the stress-raising effects of the structural detail but exclude the stress concentrations due to the weld itself.
Researchers have attempted to develop alternative methods for determining the hot spot stress that is intended to be “mesh-insensitive”. The concept of a linearised structural stress distribution over the plate thickness has been modified by researchers headed by Dong at the Battelle Institute , ,  in order to fit better fatigue results from different connection types and sizes into a single hot spot stress S–N curve. Another new concept of determining structural stress based on assuming the computed stress value at a depth of 1mm below the surface at the weld toe in the direction of the expected crack path has been proposed by Xiao and Yamada .
Another fatigue life assessment approach in conjunction with the use of the FEM is the effective notch stress method which is based on the computed highest elastic stress at the fatigue-critical point. The method was proposed by Radaj et al.  who took account of stress averaging in the micro-support theory with a fictitious radius of 1mm in plate thicknesses of 5mm and above . For smaller plate thicknesses, Zhang and Richter  has proposed the use of a fictitious radius of 0.05mm, which is based on the relationship between the stress-intensity factor and the notch stress , , . The effective notch stress approach is included in IIW recommendations as an alternative fatigue life assessment method.
The method – which is applicable for 2D plane and 3D solid element models – requires that the detail geometry is modelled accurately. For welded details with orthogonal components, 3D solid element models are generally preferred than 2D plane element models due to the details complexity. An example of such details in bridge structures can be found in orthotropic bridge decks. In this study, one of the aims of using the effective notch stress approach is to investigate the applicability of this approach for orthotropic bridge decks with open ribs. Another aim is to compare the fatigue life of the test specimens with the design curves used for the most common fatigue life assessment methods.
In order to estimate the fatigue life of orthotropic bridge decks with longitudinal open ribs, the test specimens with a commonly used open ribs type have been chosen. These test specimens have been designed and loaded to simulate the crack behaviour at the intersection of the cross girder and longitudinal open ribs.
Finite element analyses
One of the aims of the study reported in this paper was to investigate the feasibility and accuracy of the fatigue life assessment methods using the FEM for orthotropic bridge deck details, especially the structural hot spot and the effective notch stress approach. These methods require different modelling techniques and procedures to obtain reliable stress values at fatigue-critical points. Various finite element models were therefore generated to compare the applicability and accuracy of
Discussion of results
In order to compare the fatigue life of the test specimens with the recommended design S–N curves used for different fatigue life assessment methods, the results are plotted in an S–N diagram, as shown in Fig. 24. Since the effective notch stress method is not included in Eurocode 3, the design curve of FAT225 recommended by the IIW is used here. As shown in this figure, it is obvious that the results produced by the effective notch stress method and the results produced by the structural hot
In this paper, the applicability of the most common fatigue life assessment methods using the FEM was investigated on an orthotropic bridge detail. Fatigue tests, as well as various modelling techniques, were included in the study. The experimental results showed that the fatigue life of complex welded structures, such as orthotropic bridge decks with open rips, estimated by the structural hot spot stress method or the effective notch stress method, yields a better estimation, even though the
This investigation within the framework of the research project (Brifag – Bridge Fatigue Guidance) is being carried out with a financial grant from the Research Fund for Coal and Steel (RFCS) of the European Community and the Swedish Transport Administration, Granted under Contract No. RFSR-CT-2008-00033. The authors would like to express their appreciation to Prof. C.M. Sonsino (Germany) for his review.
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Eng Fail Anal
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Int J Fatigue
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Int J Fatigue
(2012)(Video) [midas FEA webinar series] Modeling and analysis of steel bridge orthotropic deck
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Int J Fatigue
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Int J Fatigue
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Int J Fatigue
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Int J Fatigue
Int J Fatigue
- Research on fatigue performance and optimal design of steel-UHPC composite slab
To study the crack resistance of UHPC (Ultra-High Performance Concrete) in the negative moment region of the steel-UHPC light composite bridge deck and the performance of fatigue-prone details around the arc-shaped notch, a full-scale two-span model with double U-ribs was fabricated according to the prototype of a steel box girder and subjected to six million fatigue load cycles. In parallel with the fatigue test, a numerical model (M1) was developed in ANSYS. Using the numerical model M1, three factors affecting the composite deck mechanical performance were analyzed, including the thickness of the UHPC layer, the amount of reinforcement placed in the UHPC layer, and the shear studs spacing. Combined with the reliability theory and Miner’s cumulative damage model, the fatigue reliability of the arc-shaped notch welding details was analyzed using another segmental numerical model (M2). The test results revealed no fatigue cracks around the arc-shaped notch of the diaphragm and the surface of UHPC layer after six million loading cycles. Furthermore, there was no delamination between the UHPC and the steel plate. The numerical simulation results indicate that the upper surface tensile stress for thin UHPC increases with the reduction in the shear studs spacing, however, there is an opposite trend for thicker UHPC. Moreover, the thicker the UHPC is, the more significant the influence of the reinforcement mesh spacing on the extreme tensile stress of the UHPC upper surface is. The calculation results of the segmental numerical model showed that the fatigue detail of the arc-shaped notch welded joints on the transverse rib (clear height of 0.9m) base metal could not meet the design requirements. Based on the analysis of the relationship between the reliability index and UHPC thickness and the transverse rib clear height, it has been found that the detail of the arc-shaped notch welded joints on the transverse rib base metal could achieve infinite fatigue life without changing other design parameters except for the transverse rib clear height.
- An experimental investigation into fatigue behaviors of single- and double-sided deck-U rib welds in orthotropic bridge decks
2022, International Journal of Fatigue
In this study, the fatigue resistance properties of single- and double-sided welded joints in OBD are investigated using the traction structural stress method by conducting experimental and numerical investigations. Full-scale fatigue specimen tests are conducted to analyze the fatigue property validations and failure modes, considering the effects of length scale, residual stress relaxation, angular misalignment corrections, and stress ratio. Double-sided welded joints have been found to fail at the interior weld toe with the propagation direction of deck thickness, and the prediction results will be more accurate considering the effect factors of angular misalignments and stress ratio. The specific united master S-N curve for the fatigue performance prediction of single- and double-sided welded joints in OBDs is recommended with the combination of fatigue test data.
- Interface stress analysis and fatigue design method of steel-ultra high performance concrete composite bridge deck
Orthotropic steel-UHPC composite deck consists of orthotropic steel deck and ultra-high performance concrete (UHPC) layer. The shear force transferred by shear studs at the interface between steel deck and the UHPC layer is a key in fatigue design. Based on the finite element (FE) whole model analysis of composite deck, the detailed submodels of composite deck segments with single stud and single row studs were established respectively. It aimed to investigate the interface stress distribution and slip behavior of steel-UHPC composite deck under negative bending moment, and explore the failure mechanism of short headed stud. In term of shear force relationship, considering likely influences such as location and pattern of loading, flexural stiffness of the composite deck and stud arrangement, the whole model analysis results were compared with the submodel analysis results, and a fitting formula of shear relationship between the two models was proposed. A formula for fatigue design of short headed stud in orthotropic steel-UHPC composite deck was also proposed. In respect to the longitudinal and transverse shear force distribution of studs, composite deck stiffness, hot spot stress of fatigue-prone details of steel bridge deck and the maximum stress level of UHPC layer, the evaluation method of stud arrangement was proposed. The calculation results were assessed and compared with the stud layout schemes of three actual steel-UHPC composite decks, and the effectiveness of the design formula was validated.(Video) Application of finite element methods to model masonry arch bridges
- ESS-based probabilistic fatigue life assessment of steel bridges: Methodology, numerical simulation and application
2022, Engineering Structures
The selection of an appropriate S-N curve for a specified type of welded joints is an essential part for the fatigue reliability assessment of steel bridges by means of a stress-life approach. However, this is still a challenging issue in the real engineering applications due to the complexity of the structural components and the lack of the available numbers and types of S-N curves. In this study, a generalized fatigue reliability model based on equivalent structural stress (ESS) is proposed, which has the merit of taking no account of the selection of the S-N curve. An ESS-based probabilistic S-N formulation is first derived by introducing a probability index to the expression of the S-N curve. Then, the fatigue reliability model, which incorporates the random variables of the ESS range, the number of cycles and material properties, is deduced by combining the Miner’s rule. Numerical case studies and sensitivity analyses on the effects of the ESS range, the number of cycles and the growth in traffic volume are performed to evaluate the practicability and the effectiveness of the proposed fatigue reliability model. Finally, the proposed method is applied to an instrumented steel arch bridge with the aid of field dynamic strain data. The fatigue failure probability and the fatigue reliability index versus fatigue life are achieved through random samples generated by means of the Monte Carlo (MC) simulation on the basis of the joint probability density function (PDF) of random variables. The results show that the proposed method provides a viable way of resolving the difficulty in selecting a suitable category for the evaluation of the probabilistic fatigue life of the welded details in steel bridges. In addition, it can be found that both the PDF of stress spectrum and the growth of traffic volume are sensitive to the failure probability and reliability index obtained by the proposed fatigue reliability model.
- On the fatigue behavior of duplex and high-strength welded cruciform joints
2021, Engineering Structures
This paper presents outcome of a research which investigates the fatigue behaviour of duplex stainless steel grade (EN 1.4162) via cyclic tests on welded cruciform joints and base plates. A database of experimental tests for similar high-strength steel details was also collated from the literature. The obtained experimental S-N curve was then compared to the current European design ones and re-evaluated according to the hot spot stress method. A good agreement was observed between the studied detail performance and the collated reference data. Improvement to the fatigue design rules for the studied duplex and similar high-strength steel details is then proposed.
- On the applicability of the hot spot stress method to high strength duplex and carbon steel welded details
2021, Engineering Failure Analysis
In this paper, the applicability of the hot spot stress method (HSSM) to the study of fatigue behaviour of welded details made of high-strength stainless or carbon steel is investigated. To that purpose, a broad database of fatigue test results was collated from the literature for transverse stiffeners, butt welds and cope holes which are frequently present in highway girder bridges. For each set of test results, the hot spot stress range was evaluated using finite element (FE) models. The fatigue resistance using the HSSM was then computed and compared to that obtained using the well-known nominal stress method (NSM). It is concluded that the HSSM yields less conservative results than the NSM leading to more economic design of the covered range of high-strength steel welded details.
Research articleFatigue evaluation of rib-to-deck welded joint using averaged strain energy density method
Engineering Structures, Volume 177, 2018, pp. 682-694
This paper investigates the feasibility of an averaged strain energy density (SED) method for fatigue evaluation of rib-to-deck weld joint in orthotropic steel deck. The effect of weld geometry on fatigue resistance of rib-to-deck joint is evaluated. The analysis results of the presented average SED method are validated against fatigue testing data and compared with the results of the conventional hot-spot stress and effective notch stress methods. A W-N curve is derived using the averaged SED method and used for evaluating the fatigue strength of rib-to-deck welded joints. The averaged SED method is also used to investigate the effect of weld geometrical variables on the fatigue failure mode transition, and the fatigue strength of full-scale orthotropic steel deck specimens. The results indicate that the averaged SED method provides superior ability in evaluating fatigue resistance and failure mode of rib-to-deck welded joint.
Research articleHot spot stress analysis on rib–deck welded joint in orthotropic steel decks
Journal of Constructional Steel Research, Volume 97, 2014, pp. 1-9
Orthotropic steel decks are used in beams and cable-supported bridges. Fatigue cracks of the vertical rib–deck welded joint have been found in some of the bridges. In this paper, the structural hot spot stress (SHSS) approach is applied to evaluate the rib–deck fatigue. Refined solid models are built using a multi-sub-model technique. Stress around the weld tip is analyzed and effects of the weld profile, the weld toe radius and mesh size are discussed. The SHSS is analyzed using the surface stress extrapolation method, the stress linearization method and the 1mm stress method. Fatigue strength of the joint based on the SHSS is proposed. Results of this study show that the refined multi-sub-model considering the weld detail can reflect the mechanical behavior of the rib–deck joint. Variation of the SHSS by the three methods decreases to less than 10% and a convergent SHSS is achieved using the refined models. The derived fatigue strength for the rib–deck joint using the SHSS of the refined models is close to FAT100. A more precise fatigue strength prediction can be achieved using the refined model while the coarse models result in a conservative design.(Video) Crush Zone FEA Tutorial
Research articleA comparative study of different fatigue failure assessments of welded bridge details
International Journal of Fatigue, Volume 49, 2013, pp. 62-72
Five different welded joints frequently used in steel bridges have been selected to investigate the accuracy and applicability of three fatigue assessment methods. The first method, also categorised as the global method, is the nominal stress method, while the more advanced methods are the hot spot and the effective notch stress methods. Solid element based finite element models for welded bridge details were created by following the modelling requirements of each fatigue assessment method. A statistical evaluation based on the results of the finite element analyses and the fatigue test data collected from the literature was performed to determine the mean and characteristic fatigue strength. In addition, the standard deviation for each data series was also determined to conclude how well each method describes the fatigue strength of each welded detail. A method with a lower standard deviation is regarded as more accurate. Moreover, the evaluated results from each method were compared with the recommended fatigue strength values in the Eurocode 3 (EN 1993-1-9:2005) and IIW codes. In the light of the test results in this study, it appears that the codes are in reasonable agreement with the test data, even though a few examples of the opposite occurred. The conclusion based on the revised results in this article indicates that the nominal stress method yields satisfactory results, despite its simplicity. When considering the effort involved in creating FE models for numerical analysis, it seems clear that the choice of the nominal method is fairly acceptable.
Research articleExperimental study on fatigue failure of rib-to-deck welded connections in orthotropic steel bridge decks
International Journal of Fatigue, Volume 103, 2017, pp. 157-167
The rib-to-deck (RD) welded connections are the most sensitive locations to encounter the fatigue failure in orthotropic steel decks (OSDs), and numbers of fatigue cracks arising from these areas have been found in existing OSD bridges. This research focus on the fatigue cracking process, fatigue characteristics as well as failure mechanics of RD connections under cyclic loading. Six full-scale RD welded joints were fabricated, and two load cases of centric and eccentric loading were considered. Static loading was first conducted with aims of measuring elastic strain distributions at potential hot spots. Structural hot spot stresses at weld toes as well as stress concentration factors (SCFs) were linearly extrapolated by using the recorded strains, based on which critical locations were identified. High-cycle repeated loading was subsequently implemented, from which the fatigue crack initiation and propagation process, fatigue failure mode, characteristic fatigue life, as well as degradation of vertical rigidity, were obtained. Four stages of crack propagation were mainly observed, and the remaining fatigue lives after the crack reached the deck edge were short to be neglected. Variations of crack dimensions including the longitudinal length and the depth in the plate thickness were also revealed. Comparison between experimental numbers of cycles and standard S-N formulae indicates that the FAT 100 curve provided in the IIW fatigue recommendation could be conservatively used to estimate the fatigue resistance of such rib-to-deck welded connections composed of 16mm thick deck plates and 80% PJP welds.
Research articleExperiment on fatigue behavior of rib-to-deck weld root in orthotropic steel decks
Journal of Constructional Steel Research, Volume 119, 2016, pp. 113-122
This study experimentally investigated the fatigue behavior of the weld root in orthotropic steel decks stiffened with U-ribs in relation to the loading conditions and welding details. To examine the structural response and local stress near the welded joint, field loading tests, measurement of residual stress, and fatigue tests were carried out. A total of 12 specimens were manufactured, and the fatigue tests were performed by simulating the double tire loading of an actual vehicle. The welding residual stress distribution at the root was examined to understand the mechanism of root crack initiation and propagation behavior. Thus, fatigue behavior of the root crack was investigated and evaluated by considering different stress ratios and weld penetration rates. Based on the fatigue test results and crack patterns, it was revealed that both tensile stress and stress range could affect the root crack initiation. However, the tensile stress rather than the magnitude of stress range would be the effective stress after a crack initiated, and it was seen to be an important factor for root crack propagation. In addition, a penetration rate in the range of 0% to 75% was beneficial for fatigue durability of this structural detail.
Research articleExperimental investigation for structural parameter effects on fatigue behavior of rib-to-deck welded joints in orthotropic steel decks
Engineering Failure Analysis, Volume 79, 2017, pp. 520-537
Various fatigue cracks occurred in orthotropic steel decks have been reported in the last decade. The fatigue cracks initiated at the weld root of the fillet weld of rib-to-deck plate were investigated in this study. The fatigue behaviors were investigated by performing 19 full-scale fatigue tests, which conducted on six types of orthotropic steel decks with different structural parameters. The fatigue cracking patterns and their influence factors were discussed by comparing the crack propagation angles, crack lengths and depths of the cracked section. Meanwhile, the cracking mechanism and stress responses around root tip were analyzed by establishing elastic finite element models, and verify with fatigue tests results. The results of the experimental analysis demonstrated that fatigue cracks did not occur where the stress ranges were purely compressive, it was considered the welded joint might under the low tensile residual stress so that the effective stress range was reduced. Similarly, the magnitude of tensile stress range would play a decisive role during the root crack propagation. It was found that increasing the penetration rate had the beneficial effect of preventing root cracking. There was also a significant improvement in the fatigue durability when the deck plate thickness was increased from 12mm to 16mm. Finally, some special treatments in welded joint such as: the grinding at weld toe could avoid crack at toe but might lead to a deeper root crack, and the press straighten could be an effective treatment for preventing root cracks propagating in depth.
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