# Nonlinear Seismic Response of Multistory Steel Frames with Self-Centering Tension-Only Braces
## 2 Analytical Model of SC-TOBFs
### Prototype Building Design  
As illustrated in Figure 3, the prototype building is a steel-framed office building with nine stories and five bays, which can be considered as typical of intermediate structures. It has a constant story height of 3.9 m totaling 35.1 m and a constant bay width of 9 m totaling 45 m. Column types 1 to 6 are identified in Figure 3. Nonmoment-resisting beam-column connections are assumed in the design,  
Figure 2: Simulation of the SC-TOB frame (SC-TOBF): (**a**) SC-TOB arrangement; (**b**) multilinear elastic element (MEE) hysteresis; (**c**) multilinear plastic element (MPE) hysteresis; and (**d**) SC-TOB hysteresis.  
because such connections have sufficient rotation capacity to accommodate a large drift demand without damaging the connection region [32]. The building uses four perimeter-braced frames for resisting seismic load in either earthquake direction.  
It is assumed that all the seismic energy is dissipated by the SC-TOBs, and the load-resisting elements always remain elastic during an earthquake. The braced bays are designed to resist both gravity loading and lateral seismic loading, whereas the unbraced bays only need to resist gravity loading. The beams and columns are made of Q345 steel having a yield stress of 345 MPa, and the cables are made of HSS strands, with an ultimate strength of 1670 MPa. Geometric nonlinearity is incorporated to consider the P-Delta effects through large displacement analysis. Rayleigh damping is used with inherent 4% critical damping at the first two modes of vibration. The geometric properties of structural elements are selected according to design codes [33; 34; 35] as listed in Table 1. All the SC-TOBs used in the prototype building are designed to activate at a story drift angle \(\theta_{a}\) of 0.4%, which is consistent with the code-prescribed elastic limit for steel structures [34]. The hysteresis of each type of SC-TOB is depicted in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Unbraced Bays**} & \multicolumn{3}{c}{**Braced Bays**} \\ \cline{2-7} \multirow{2}{*}{**Story**} & \multirow{2}{*}{\begin{tabular}{c} **Beam** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Column** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Beam** \\ **(mm)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Column** \\ **(mm)** \\ \end{tabular} } & \multicolumn{3}{c}{**SC-TOB**} \\ \cline{5-8}  & & & **(mm)** & & **(mm)** & **(mm)** \\ \hline \multirow{2}{*}{7-9} & \multirow{4}{*}{\(\begin{array}{c}  
Since pinned beam-to-column connections are assumed in the design, and each column is continuous and pinned at its base, lateral seismic resistance is provided and equally distributed by the two braced frames, along the direction of the earthquake. In view of the symmetrical plan dimensions of the prototype building, the torsion effect can be neglected, thereby allowing for a 2D analysis in lieu of a 3D analysis for efficiency and simplicity (see Figure 5). In the 2D model, the link beams between columns 4 and 1 are assumed to act as rigid diaphragms that transfer lateral deformations from braced to unbraced frames. The 2D analytical model is validated to be feasible by the modal analysis comparison as shown in Table 2, and it is therefore used in the following investigations.