# Pushover Analysis on Infill Effects on the Failure Pattern of Reinforced Concrete Frames
## 2 Numerical Modeling  
Three-dimensional validation models have been developed using ABAQUS (Dassault Company, Providence, Rhodes Island, USA). A damaged plasticity model is applied to simulate the cracking behavior of the concrete. Concrete and reinforcement element types are C3D8R and T3D2, respectively. Reinforcement is embedded into the concrete in the model. The main element size is 50 mm. The loading program is low frequency cyclic loading and the loading path can be found in [23]. Figure 1: Short column failure. Figure 2: Failure of an infill wall and the surrounding frame. The displacement of the test is from 0.1% story drift to 4.2% story drift. The loading increment follows \(\pm\)3 mm (0.1%), \(\pm\)6 mm (0.2%), \(\pm\)9 mm (0.3%), \(\pm\)12 mm (0.4%), \(\pm\)17 mm (0.6%), \(\pm\)23 mm (0.8%), \(\pm\)29 mm (1%), \(\pm\)36 mm (1.25%), \(\pm\)43 mm (1.5%), \(\pm\)58 mm (2%), \(\pm\)72 mm (2.5%), \(\pm\)86 mm (3%), \(\pm\)101 mm (3.5%), \(\pm\)110 mm (4%), and \(\pm\)120 mm (4.2%). The full Newton Raphson solution technique is used in the analysis. The unbalanced force convergence criterion and the displacement criterion are used in the simulation. The convergence standard of the unbalanced force is 5 \(\times\) 10\({}^{-4}\). The comparison of the skeleton curves of RC-2 in [23] is shown in Figure 3. The comparison characteristic displacement and load are summarized in Table 1. The analysis results show that the Finite Element Analysis (FEA) data fit the experimental results well and can be used to conduct parametric analyses. The pushover model is extended based on the experiment frame RC-2 and is also scaled 1:2.5. The model is 1 bay \(\times\) 2 bay with one story. The plan dimension is 2.4 m \(\times\) 3.2 m. The height of the model is 1.44 m. The cross-section dimension of the column and beam are 160 mm \(\times\) 160 mm and 100 mm \(\times\) 200 mm, respectively. The thickness of the slab is 50 mm. Constitutive equations of steel and concrete are shown in Equations (1)-(9) [24]. Constitutive equations of steel:  
\[\sigma_{s}=\left\{ \begin{array}{l}E_{s}\varepsilon_{s},\varepsilon_{s} \leq\varepsilon_{y}\\ f_{y,r},\varepsilon_{y}<\varepsilon_{s}\leq\varepsilon_{uy}\\ f_{y,r}+k(\varepsilon_{s}-\varepsilon_{uy}),\varepsilon_{uy}<\varepsilon_{s} \leq\varepsilon_{u}\\ 0,\varepsilon_{s}>\varepsilon_{u}\end{array} \right. \tag{1}\]  
where \(E_{s}\) = the elastic modulus of the steel bar; \(\sigma_{s}\) = stress of the steel bar; \(f_{y,r}\) = the representative yield strength of the steel bar; \(\varepsilon_{y}\) = the yield strain corresponding to \(f_{y,r}\); \(\varepsilon_{uy}\) = the strain at the starting point of hardening; \(\varepsilon_{u}\) = the peak strain; and \(k\) = the slop of the hardening section. Constitutive equations of concrete: \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(\mathbf{P_{y}}\) & \(\mathbf{P_{max}}\) & \(\mathbf{\Delta_{y}}\) & \(\mathbf{\Delta_{max}}\) & \(\mathbf{M}\) & \(\mathbf{R_{u}}\) \\ \cline{2-7}  & **(kN)** & **(kN)** & **(mm)** & **(mm)** & **\(\mathbf{\mu}\)** = \(\mathbf{\Delta_{max}}\)/\(\mathbf{\Delta_{y}}\)** & **Ru** = \(\mathbf{\Delta_{max}}\)/H** \\ \hline test & 69.90 & 84.25 & 30 & 80 & 2.67 & 1/36 \\ FEM & 65.63 & 77.88 & 33.26 & 93.5 & 2.81 & 1/31 \\ \hline \end{tabular}
\end{table} 
Table 1: Characteristic displacement and load. Figure 3: Comparison of the skeleton. The stress-strain curve under axial compression:  
\[\sigma=(1-d_{c})E_{c}\varepsilon \tag{2}\]  
\[d_{c}=\left\{ \begin{array}{l}1-\frac{\rho_{t}n}{n-1-\frac{\rho_{c}}{n}},x\leq 1 \\ 1-\frac{\rho_{c}}{\alpha_{c}(x-1)^{2}+x},x>1\end{array} \right.