## 3 Three-Dimensional OSD Finite Element Model  
A standard OSD model was selected to evaluate these aforementioned SHSS methods. In OSDs, the RD joint has been reported as the most vulnerable to fatigue cracking due to its direct contact with vehicular load [9; 10], but the details of this joint are not in scope of this paper. We are more focused on the implementation and the assessment of these SHSS methods at this particular joint using numerical models. It is a welded connection between a deck-plate and a longitudinal-rib, and their respective thicknesses are shown in Figure 5a,b. The OSD models were simulated and tested on a finite element method (FEM) based software Siemens NX.12.0. The OSD model consists of a deck plate, cross-beams, longitudinal-ribs, and girders. It has stress relying cut-outs with a 16.0 mm thick deck-plate and 8.0 mm thick trapezoidal longitudinal-ribs. It has six longitudinal-ribs and three cross-beams with  
Figure 4: [PERSON] and [PERSON] method for evaluation of SHSS at weld-toe with 2.0 mm CHEXA20 mesh. 600.0 mm and 4000.0 mm centre-to-centre spacing, respectively. The cross-sectional details of this OSD model are shown in Figure 5a. All the dimensions were adopted according to the guidelines given in Eurocode [22]. The properties of AISI-1005 steel were used for all the models. It is a low carbon structural steel with a modulus of elasticity of 200,000 MPa. The Poisson's ratio was taken as 0.27. The yield and the ultimate tensile strengths were 226 MPa and 321 MPa, respectively. The Eurocode fatigue load model-4 was applied to the deck-plate to assess this joint [11]. According to the given load model, the axle load should be applied on OSD as two closely spaced 150 kN wheels (i.e., 75 kN for each wheel), 2.0 m apart to accurately reflect the actual loading condition. The contact area for each wheel should be 540 mm \(\times\) 250 mm. The simply supported boundary conditions were applied at the bottom flange of the girders. Here, it is important to mention that the deck-plate was loaded transversally and the longitudinal-rib was loaded axially to produce bending and membrane stresses in the respective plates, as shown in Figure 5b. Therefore, two types of stress conditions were rendered, and their effect on SHSS methods was studied considering this joint. A detailed study was carried out to optimize the mesh size for this OSD model. The breakout modelling was adopted to increase the efficiency of the model and to reduce the cost of analysis. Figure 5: Details of the orthotropic steel deck specimen used in this study. (**a**) The cross-section of orthotropic steel deck specimen with rib-to-deck joint details. (**b**) 3D-Orthotropic steel deck specimen with breakout modelling and applied fatigue load model details. Therefore, to save the computational cost and time without compromising the accuracy of the results, the optimized mesh variation was adopted, as shown in Figure 5b, where mesh sizes are labelled in brackets. All models were simulated on Siemens NX.12, which uses NX Nastran solver. Four types of elements were used, i.e., 8 node cubic linear hexahedral (CHEXA8) and 20 node cubic parabolic hexahedral (CHEXA20) elements for 3D solid models, and 4 node cubic linear quadrangle (CQUAD4) and 8 node cubic parabolic quadrangle (CQUAD8) elements for 3D shell models. The irregular elements were not used, because large errors were observed, especially for linear elements. Different mesh variations that were used to model this RD joint are shown in Figure 6a-h. These were named considering mesh size and element type, e.g., 1-CH20 mesh variation stands for 1.0 mm 20 node cubic parabolic hexahedral solid element. Similarly, 8-CQ4 is the abbreviation of an 8.0 mm 4 node cubic linear quadrangle shell element. A minimum of three layers of elements were used over the thickness of the plate for linear (1/2-CH8) and parabolic hexahedral (1/2-CH20) elements.