Modelling and fatigue life assessment of orthotropic bridge deck details using FEM (2022)


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International Journal of Fatigue

Volume 40,

July 2012

, 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.

(Video) [midas FEA] 3D FEA for Bridges


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 [1]. 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 [1], [2], [3], [4].

In general, the fatigue design and analysis of steel bridges is performed using the nominal stress approach. SN 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 [5]. 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 [6], 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 [7], [8], [9], [10]. 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 [12], [13], [14] in order to fit better fatigue results from different connection types and sizes into a single hot spot stress SN 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 [15].

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. [16] who took account of stress averaging in the micro-support theory with a fictitious radius of 1mm in plate thicknesses of 5mm and above [17]. For smaller plate thicknesses, Zhang and Richter [18] 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 [19], [20], [21]. 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.

Section snippets

Fatigue test

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 SN curves used for different fatigue life assessment methods, the results are plotted in an SN 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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    (Video) [midas FEA webinar series] Modeling and analysis of steel bridge orthotropic deck

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