The phenomenon of fatigue in orthotropic steel deck (OSD) bridges is a predominant problem because of complexity of the prediction methods. In the past, many researchers have studied the fatigue behaviour of various details in OSDs via both experiments and Finite Element Modelling (FEM). In the present research, the connection of open stiffener to crossbeam at the location of cope hole in OSDs has been be studied. Structural hot-spot stress method using surface stress extrapolation has been used to investigate the cracks in stiffener in the longitudinal direction and cracks in crossbeam. FEM is extensively used for analysing OSDs. In engineering applications, 2D shell elements are widely used instead of 3D solid elements for analysis due to less computational cost. The welds are generally not modelled with shell elements for fatigue assessment of welded structures. In this study, large difference of SHSS is obtained by shell and solid elements for both simple and complex fillet welded details and also for the OSD. This difference in structural hot-spot stress (SHSS) is reduced by the application of three weld modelling techniques with shell elements: (i) the IIW approach, (ii) the Eriksson’s approach and (iii) a combination of IIW and Eriksson’s approaches. All the three methods are based on increasing the thickness of shell elements at the weld region which are easy to be applied in practice. The dependence of SHSS on mesh size and element type is also investigated in this thesis. A parametric study is performed first on simple and then on complex fillet welded details to check whether the weld modelling technique can be applied to different geometries, loading and boundary conditions. The solid element model of the complex detail is first validated with experimental strain measurements. Then, SHSS values from other numerical models are compared with the solid model. Representative load cases are investigated initially followed by load combinations. The weld modelling method with shell elements gives good consistency in the ratio of hot-spot stress compared to the solid element model for these details. The deformations are also investigated for all load cases and load combinations. The combined weld modelling technique (iii) with shell elements replicated the weld stiffness of the solid model for both in-plane and out-of-plane load cases. As a final step in checking the consistency of SHSS ratios between shell elements with welds and solid elements in the application of OSD, a parametric investigation is performed. This study involved two geometric variants of OSD with different load positions. These two variants were based on the design of existing bridges in The Netherlands with relatively thin plate and newly designed ones with thicker plates. The parametric study is divided into two parts. The first part is based on representative load cases. The second part is based on SHSS influence lines for determination of critical loading positions having maximum and minimum hot-spot stress. For both these studies, the weld modelling approaches with shell elements gave a good match of SHSS compared to the solid models. The SHSS results from the shell model with weld are more consistent compared to the regular shell model without weld. From the preliminary parametric study on OSD, it is found that after weld modelling with shell elements using the combined approach of IIW and Eriksson, less scatter is observed in the SHSS ratios. The coefficient of variation (CV) in SHSS ratio for crossbeam is 6.8% and that for stiffener is around 5.1% which is low. The SHSS values are computed based on the stress perpendicular to weld toe. From the detailed parametric study, the mean value of SHSS ratio is 1.07 (range: 0.99-1.15) for the crossbeam and 1.02 (range: 0.98-1.10) for the stiffener. The CV of SHSS ratio is 5.4% for the crossbeam and 4% for the stiffener. The stress profiles are also investigated at the critical locations of OSD. The shell model with the combined weld modelling approach is in good agreement with not only SHSS but also with the stress at a distance far away from the stress concentration when compared to the solid model. The deformations are also very similar for both the numerical models. Thus, it is concluded that the combined weld modelling technique using the IIW and the Eriksson’s approach with shell elements could be used for accurate fatigue life assessment using hot-spot stress method where the measure of accuracy is with respect to the solid element model.