# Tension Performance of Precast Bridge Deck Longitudinal Joints with Different Configurations
## 4 Finite Element Analysis  
In this study, the optimal joint configuration obtained from the experimental analysis (J100-HB-SP) was simulated using a three-dimensional (3D) FEM to analyze its structural behavior. This analysis was conducted using the ABAQUS (2021) [37] general-purpose structural analysis software. The model constructed had the same dimensions as the test specimen, which were as follows: 1450 mm \(\times\) 1900 mm \(\times\) 240 mm. The concrete was modeled using C3D8R 3D solid elements. The implementations of the precast concrete bridge deck units and CIP joint section were executed separately; as the contact surface between the two cannot be considered as fully integral, it was modeled using a nonlinear spring element (connecting two nodes) in this study (Figure 12a). The concrete had an elastic modulus of 30,000 MPa and Poisson's ratio of 0.17, with reference to the ACI 318-19 Building Code Requirements for Structural Concrete [38]. The steel plate in the joint, rebars in the concrete, and steel bars for fixing and loading the specimen were implemented using S4R shell elements, T3D2 truss elements, and B31 beam elements, respectively. The steel plate, rebars, and steel bars had an elastic modulus of 200,000 MPa and Poisson's ratio of 0.3, with reference to the ASTM A615M Standard Specification for Deformed and Plain Carbon-steel Bar for Concrete Reinforcement [39], ASTM A572M Standard Specification for High-strength Low-alloy Columbium-Vanadium Structural Steel [40], and ASTM E8M Standard Test Methods for Tension Testing of Metallic Materials and Road bridge design standards [41; 42; 43]. Since the rebars and steel bars were embedded in the concrete, the portions of their lengths within the specimen were placed in the model using the embedded element technique. Curvature control of the model mesh was applied by setting the ratio of the mesh height to length to 1:1, and the mesh size was set to 50 mm. A structured hex was applied for the mesh geometry to prevent distortion. The total number of mesh cells was 6474 (Figure 12b). Hinges were situated at the lower ends of the fixing steel bars to provide a reaction against the applied load. In the actual tests, the steel loading plate attached to the actuator limited the vertical displacement of the precast bridge deck specimen; therefore, rollers were arranged in the orthogonal direction at the corresponding locations in the model to reflect this condition. The tension load was applied equally to the upper and lower parts of the specimen model at the loading bars (Figure 12c). The relative displacement of the joint was subsequently analyzed at the following four characteristic loads: initial cracking, extensive cracking, accelerated cracking, and final load. Figure 11: Final crack geometry in J100-HB-SP (800 kN). The numbers in the expansion represent the crack tip locations at that load (in kN). Figure 13 shows the displacement distributions obtained for the FEM under each characteristic load. Initial cracking occurred at a load of 482 kN when nonlinear behavior was first observed, and a relative displacement of 0.12 mm was observed across the joint (Figure 13a). The crack width exceeded the allowable crack width (0.3 mm) with extensive cracking at 600 kN, as the relative displacement across the joint increased beyond 0.5 mm (Figure 13b). At 750 kN, the relative displacement owing to cracking accelerated to 0.63 mm, and the interface between the precast units and joint could be clearly observed (Figure 13c). At a final load of 840 kN, the geometry of the joint was clearly visible, with a final relative displacement of 2.29 mm (Figure 13d). Notably, the final crack geometry obtained using the FEM (Figure 13d), the final crack geometry for the actual test specimen (Figure 11), and the crack development observed using the high-speed PCIe camera (Figure 10) are all quite similar. Figure 14 compares the FEM- and test-obtained load-relative displacement curves.