PSI - Issue 63

Jiří Brožovský et al. / Procedia Structural Integrity 63 (2024) 1– 6

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tasks it is usually necessary to deal with complex details and geometries and with three-dimensional stress states (e.g. in standard EN 1993-1-9, when calculating the fatigue strength for nominal stress ranges, typical categories of details are used, e.g. [3]). Analytical formulae are usually derived for well-described situations with one-dimensional or two dimensional stress states. It is thus necessary to verify that the used analytical formula is only applied in situation which is compatible with geometry and stress state for which it was derived. One of possible approaches for such verification is use on numerical modelling to study actual stress state of the studied structural detail, e.g. [4]. The goal of the presented work was thus to study stress state of a detail of real bridge structure in order to decide if the developed analytical formulae can be applied in this case. Nomenclature size (length) of the fatigue crack width of steel flange under tension in bending Young's modulus of elasticity for tension or axial compression ��� Calibration function for fatigue crack propagation Poisson's ratio � normal stress in the direction � normal stress in the direction � normal stress in the direction (in the direction of the main beam axis) The studied detail is on a real steel bridge which is a part of highway system in Slovakia. In [5], this detail in the welded connection of the steel crossbar to the stringer (detail category according to EN 1993-1-9 is No. 125 according to table 8.2 for welded built-up sections with continuous longitudinal welds) is assessed stochastically using the DOProC probabilistic method, described in detail in, e.g., [6]. This probabilistic fatigue damage modeling of a cyclically stressed bridge structure is based on linear fracture mechanics [7], [8], and the resulting failure probability is used to design a bridge inspection system focusing on fatigue damage, similarly as in [9]. For the crack propagating from the edge of the analysed detail of the steel part of the bridge, the calibration function for bending (applies to the calculation of the stress in the weakened section [10]) was used: ��� � 1.122 � 1.4 ∙ � � � 7.33 ∙ � � � � � � 13.08 ∙ � � � � � � 14.0 ∙ � � � � � . (1) The analytical formula (1) contains 2 parameters: length of the fatigue crack and flange width . Using this calibration function leads to more conservative results compared to the usage obtained in the laboratory [11]. However, the question remains whether this analytical relationship is valid for the solved problem given the initial assumption of a uniform course of the normal stress in the tensioned flange. For this reason, the following numerical study was The computational model was created with use of the uFEM software developed at the VSB-TUO [12] and was based on the geometry detailed in [5]. The bridge was numerically modelled in 2 steps for the purpose of presented numerical analysis: as a 3D beam problem in order to study its global behavior and then the specific detail and its surroundings were modelled with use of 3D finite elements. The global beam model was in the form of continuous beam which was modelled with use of 3D beam elements. The model respected geometry (curvature and inclination) of bridge axis and the supports were placed in places of real supports. The idealized cross-section of the beam had the parameters computed on basis of the reals structure cross-section. The finite element model had 120 beam elements. The boundary conditions and loads were defined on basis of the results obtained from the beam model. In this numerical study, the effect of welds at the connection point was not considered. The bridge detail was then modelled as a linear elastic problem because the global stress state of the bridge was originally designed to be in the elastic range. Moreover, fatigue analysis requires that the global behavior of the model performed to verify the validity of this approach. 2. Problem definition and initial considerations