## 4 Numerical Simulation of a Vehicle Collision with Column  
### Finite Element Models of Vehicles and Reinforced Concrete Columns  
Two SUV types of car models were used in this study. Two Ford van vehicles, namely Economic and Explorer, were incorporated into the model to simulate an accident of a vehicle crashing into a reinforced concrete column. The models were developed by the National Crash Analysis Center (NCAC) at George Washington University and have been used in support of several NHTSA programs [31]. The geometry of the vehicle's models is brought into finite element form by digitizing all the vehicles' parts. The vehicles' parts are represented using shell, solid, and beam elements. The connectivity between the parts is properly selected to allow the vehicle to move and act in a realistic manner [40]. The overall weight of the Economic and Explorer vehicles in the finite element models is 2131 and 2254 kg, respectively. Table 2 shows the main features of the finite element model of the vehicles. The selection of the vehicle model was not random since it is based on the size and weight of the vehicle, taking into account that the proposed protection system for columns is dedicated for car parking where only passenger vehicles are permitted. Therefore, a Ford van (Econoline-2007) and the Ford Explorer were selected because their weight is higher than most normal passenger vehicles. The altitude of the frontal part of the selected cars is also considerably high, which means that most of the other brands and categories of passenger vehicles can crash the protection barrier at points lower than the point reached by the Ford SUV vehicles. Figure 6 shows the finite element models of the vehicles and columns that are adopted in this study. Furthermore, the model was tested for stability in crash testing up to a speed of 65 km/h by the developer, indicating that the developed car model can be used for crashworthiness simulations at speeds equal to or lower than the tested speed of 65 km/h. \begin{table}
\begin{tabular}{c c c} \hline  & **Econoline** & **Explorer** \\ \hline Number of parts & 438 & 923 \\ \hline Number of nodes & 295,555 & 724,628 \\ \hline Number of solids & 15,952 & 33,690 \\ \hline Number of beams & 2 & 185 \\ \hline Number of springs & 6 & 42 \\ \hline Number of mass elements & 90 & 456 \\ \hline Number of shells & 278,535 & 680,288 \\ \hline Number of elements & 300,066 & 714,661 \\ \hline \end{tabular}
\end{table} 
Table 2: Main features of the vehicle model. Figure 6: Finite element model of the Ford Econoline and Explorer vehicles with a column at a parking garage. The validated reinforced concrete column with axial load was used as a reference column to simulate the vehicle-column collision. The column was attached to a typical footing with a fixed boundary at the bottom, and the upper end of the column was only allowed to move vertically. The axial load carrying capacity of the RC column was calculated using Equation (3), following the guideline of ACI318-14 [41]. \[P_{n}=0.85\;A_{c}f_{c}+A_{s}f_{y} \tag{3}\]  
where \(P_{n}\) is the design load, \(A_{c}\) is the concrete area, \(A_{s}\) is the main reinforcement area, \(f_{c}\) is the compressive strength of concrete, and \(f_{y}\) is the steel yield strength. In this study, approximately 75% of the design axial load was applied to the column. The axial load was applied individually to the concrete nodes and reinforcing bars. A portion of the total axial load was applied on the concrete nodes uniformly at the top surface of the column. The rest of the axial force was applied through the longitudinal reinforcement. The load distribution between the concrete and steel rods was performed with the assumption of uniform strain distribution, i.e., \(\varepsilon_{c}=\varepsilon_{s}\), where \(\varepsilon_{c}\) is the concrete strain and \(\varepsilon_{s}\) is the steel strain.