# Numerical Study on the Bending Performance of Steel-Ribbed Composite Slabs for Substations
## 3 Finite Element Modeling
### Establishment of Finite Element Models  
The finite element (FE) models of the composite slabs are established using the Abaqus software [23]. The concrete parts and steel ribs are modeled using solid elements C3D8R. The rebars and prestressing steel are modeled with truss elements T3D2. The material parameters for steel and concrete components are shown in Table 1.  
The constitutive model for concrete employs the concrete damage plasticity (CDP) model built into the Abaqus software, with the required parameters specified in Table 2. The dilation angle in the table describes the plastic strain due to shear stress after the elastic phase. The flow potential eccentricity is 0.1, which implies that the material has almost the same dilation angle over a wide range of confining pressure stress values. The parameter \(f_{b0}/f_{c0}\) is the ratio of biaxial to uniaxial compressive yield stresses, denoting the characteristics of the failure function. The viscosity parameter is employed in viscoplastic regularization equations to achieve convergence. These parameters define the material's behavior under different loading conditions and are crucial for the accurate simulation of concrete behavior. The responses of concrete to uniaxial loading in compressive and tensile behavior are shown in Figure 5a-d. It should be noted that creep and shrinkage effects in the concrete are not considered herein. For rebars and prestressing steels, the bilinear model is adopted to demonstrate elastic and plastic stages, as shown in Figure 5e,f. The reduction rate in the elastic modulus during the plastic stage is 0.01 of that in the elastic stage. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component** &
\begin{tabular}{c} **Young’s Modulus** \\ **(MPa)** \\ \end{tabular} & **Poisson’s Ratio** & **Yield Stress (MPa)** \\ \hline Prestressing steel & 206,000 & 0.3 & 1570 \\ \hline Rebar & 206,000 & 0.3 & 400 \\ \hline Steel rib & 206,000 & 0.3 & 235 \\ \hline Concrete & 32,500 & 0.2 & 2.4/26.8 1 \\ \hline \hline \end{tabular} \({}^{\dagger}\)Cracking/ultimate compressive strength for concrete.  
\end{table} 
Table 1: Material properties. The FE models of steel-ribbed composite slabs A and B are shown in Figures 6 and 7, respectively. The reinforcement (rebar and prestressing steel) is embedded in the precast base slab. The interaction between the precast base slab and the post-cast concrete layer is set as \"tied\" without any relative slip. Two strips of rigid cushion blocks are placed under the ends of the slab perpendicular to the direction of the steel ribs to prevent local failure. The reinforcement mesh size is approximately 20 mm. For the precast base slab and post-cast concrete layer, the mesh sizes are 20 \(\times\) 20 \(\times\) 20 mm and 20 \(\times\) 20 \(\times\) 22 mm, respectively, aligning with the reinforcement mesh size. The steel ribs and upper concrete flange are modeled with mesh sizes of 1 \(\times\) 10 \(\times\) 20 mm and 20 \(\times\) 50 \(\times\) 50 mm, respectively. A coarser mesh size of 50 \(\times\) 50 \(\times\) 50 mm is applied to the rigid cushion blocks. Simply  
Figure 5: Constitutive models: (**a**) Response of concrete in compression; (**b**) Concrete compressive damage; (**c**) Response of concrete in tension; (**d**) Concrete tensile damage; (**e**) Response of rebar in tension; (**f**) Response of prestressing steel in tension. supported boundary conditions are defined along the centerline of the bottom surface of the cushion blocks. The FE models of the double-spliced, triple-spliced, and cast-in-place monolithic composite bidirectional slabs are shown in Figures 8-10, respectively. The joint of the spliced slabs is defined as \"hard\" contact and allows separation, with the tangential friction coefficient set to 0.8. Rigid cushion blocks are placed under the edges of the slab for bidirectional loading. Simply supported boundaries are set on the center line of the bottom surface of the four-sided cushion blocks.