The orthotropic steel deck (OSD) is nowadays commonly used due to its advantages, such as its lightweight, short construction time, and high capacity to bear the loads. However, fatigue cracks occur in different welded connections in the OSD. In this study, the rib to-deck-plate connection at the crossbeam conjunction has been analysed. This connection has been considered as a very critical connection due to the high-stress concentration under local wheel loading. In addition, the crack initiating at the weld root and propagating through the deck plate thickness cannot be visually inspected until surface cracks appear when the overlay is removed for the investigation. In the Netherlands, deck plate cracks at rib-to-deck plate connections at the crossbeam constitute a significant proportion of investigated cracks. In this thesis, a numerical investigation of the aforementioned cracks is carried out. First, XFEM is applied to study fatigue crack propagation using compact tension (CT) specimens. Commercial FE software package Abaqus® is used to build 2D and 3D CT models. The corresponding fatigue crack propagation is calculated in the direct cyclic step with strain energy release rate calculated using the virtual crack closure technique (VCCT). A good match is found between analytical calculation and 2D XFEM modeling. For 3D fatigue crack propagation, the number of cycles calculated from the automated crack propagation approach, using the low cycle fatigue step provided by Abaqus®, shows high sensitivity to element sizes, specifically the used element sizes through the thickness of the CT. Second, 3D crack propagation is applied to OSD with a 20 mm deck plate. For this detail, the fatigue crack initiation under compressive stress states is caused by the local loading on the deck plate. A hypothesis of changing the loading sign from compression to tension to subject the initial crack zone to tension is proposed so that this type of crack can propagate using automated XFEM. This assumption is made because high residual stresses normally exist in the welded connections and fatigue crack can propagate even under compressive stresses induced by loading. Before carrying out crack propagation calculation using VCCT, the stationary crack states were analysed using FEM and XFEM for cracks inserted with different angles. The SIFs obtained from FEM and XFEM are the same; in addition, that the SIF obtained when the detail is loaded in tension or compression has the same absolute value. Subsequently, the propagating crack analysis is carried out as a small initial crack with a depth of 0.5 mm is inserted and Paris’ law parameters C and m of 1∙ 10-13 and 3.0 were selected respectively. The obtained results of strain evolution as a function of loading history came close to that from the experiment with a difference of 7.75% for the initial strain value and 10.95 % for the maximum one. Moreover, the predicted crack shape, angle, and rate were all validated with similar crack shapes obtained from experiments in various literature. As for the crack propagation behaviour in the thickness direction, the crack arresting took place at around 75% of the deck thickness and an angle with the vertical axis of around 30o. Finally, the deck thicknesses of 16 mm and 10 mm were considered. Their results converged in terms of the crack propagation behaviour with real test specimens from the literature. It is also found that the 16 mm and 20 mm cases had a common crack propagation behaviour in the thickness direction as the crack arrest occurred at around 75% of the deck thicknesses, while for the 10 mm deck case the crack developed more dangerously by penetrating through the deck plate leading to a through-thickness crack. The approach proposed by this thesis proved to be valid for predicting the crack behaviour for the considered OSD deck plate thicknesses. Thus, the structural integrity of the detail can be assessed. This proved that for the 16 mm and 20 mm deck plates, the structural integrity is acceptable, while the 10 mm deck safety is not confirmed.