## 3 Seismic Numerical Analysis
### Modeling Procedure in OpenSees  
#### 3.2.1 Types of Connections Used for Modeling  
In this study three types of connections, shown in Figures 5-8, which are commonly used in practice for achieving the desired ductility, were used for the connections of selected frames. Figures 5-8 show the models of implemented connections in Open Sees software. The Schematic view and the OpenSees model of first-type connection are shown in Figures 5 and 7, respectively. This type of connection, which is the center-to-center nonlinear model connection, has been used in modeling the dual bracing structure. This type of modeling is modeled without considering the loss of stiffness and strength, and considering the connection source. These models allow for submission in beams and columns. For this purpose, concentrated plasticity is usually used as a torsion spring at the end of the beam or column. In this model, the spring remains rigid until the member surrenders to the moment, but then the strain stiffening behavior, which is defined as a percentage of the initial stiffness (\(\alpha_{s}\)), controls the behavior of the member. It is shown that \(\alpha_{s}=0.03\) gives acceptable results in calculating the relative displacement of the floor. Then, after reaching the maximum moment, the assigned behavior curve can be in a straight line (zero slope). Considering this, for designing new structures or evaluating existing structures, two criteria for accepting member strength and structural stiffness (relative displacement of the floor) should be controlled, but linear modeling from center to center is acceptable for designing dual bracing frames. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Number of Story** & **Position of Buckling** & **Bays\({}^{\prime}\)** & **Height (m)** & **Type of Resistant System** \\ \cline{1-1}  & 3 & All floors have a bracing & & \(=\)3 \(\times\) 3.2 = 9.6 & \\ \cline{1-1}  & 2 & 10 & system and simple & & \(=\)12 \(\times\) 3.2 = 32 \\ \cline{1-1}  & 3 & 15 & connections & & \(=\)12 \(\times\) 3.2 = 48 \\ \cline{1-1}  & 4 & 3 & All floors have a & & \(=\)3 \(\times\) 3.2 = 9.6 & special convergent \\ \cline{1-1}  & 5 & 10 & semi-rigid bracing & & \(=\)12 \(\times\) 3.2 = 32 \\ \cline{1-1}  & 6 & 15 & system (RBS) & & \(=\)12 \(\times\) 3.2 = 48 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the structures considered in this research. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{3}{c}{**15 Story building, with bracing system in all stories**} \\ \hline \hline
**Story Level** & **Column** & **Beam** & **Brace** \\ \hline
1–5 & Box 700 \(\times\) 700 \(\times\) 40 & IPE 400 & Tube 160 \(\times\) 160 \(\times\) 10 \\ \hline
6–10 & Box 600 \(\times\) 600 \(\times\) 35 & IPE 360 & Tube 140 \(\times\) 140 \(\times\) 12.5 \\ \hline
11–15 & Box 450 \(\times\) 450 \(\times\) 25 & IPE 330 & Tube 120 \(\times\) 120 \(\times\) 12.5 \\ \hline \multicolumn{3}{c}{**10 Story building, with bracing system in all stories**} \\ \hline \hline Story Level & Column & Beam & Brace \\ \hline
1–5 & Box 600 \(\times\) 600 \(\times\) 35 & IPE 330 & Tube 160 \(\times\) 160 \(\times\) 10 \\ \hline
6–10 & Box 500 \(\times\) 500 \(\times\) 30 & IPE 300 & Tube 140 \(\times\) 140 \(\times\) 12.5 \\ \hline \multicolumn{3}{c}{**3 Story building, with bracing system in all stories**} \\ \hline \hline Story Level & Column & Beam & Brace \\ \hline
1–4 & Box 220 \(\times\) 220 \(\times\) 15 & IPE 270 & Tube 120 \(\times\) 120 \(\times\) 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Used sections in each selected buildings’ frame (for two types of connections in this research). The Schematic view and the OpenSees model of second-type connection are shown in Figures 6 and 8, respectively. This type of connection, which is used in the frame with low and high ductility, is the non-linear model type with the connection spring in mind.