## 2 Proposal and Overview of LLFD V-Bracing System  
### Problems with Conventional Friction Damper Seismic Retrofitting Methods  
Friction dampers, i.e., one of the dampers used for vibration control, have been widely used because they are easy to produce and design, can secure both economic feasibility and structural safety, and efficiently absorb seismic input energy. However, existing friction dampers have low seismic energy dissipation capacities because they are produced as vertical dampers, thus making them prone to out-of-plane bending deformation and bucking in the axial direction under seismic loads. Thus, this study examined the seismic performance of an LLFD under out-of-plane loads by testing the existing typical vertical layer friction damper (VLFD) and the proposed LLFD. The LLFD was produced as a galvanized steel plate by applying zinc plating to SS275 steel. Based on the research results of [PERSON] et al. [35], the designed friction coefficient (\(\mu\)) was equal to 0.18. As shown in Figure 2, a displacement of up to 10 mm by an out-of-plane load was applied before applying the in-plane load in the test. The in-plane load was applied 10 times for 11 mm, 5 times for 22 mm, and 3 times for 33 mm to examine the seismic performances of the VLFD and LLFD. Figure 2: Set-up of VLFD and LLFD specimens for preliminary device test: (**a**) VLFD; (**b**) LLFD. VLFD and LLFD specimens were designed using Equations (1) and (2), i.e., the design formulas for friction joints in the slip limit state from the steel structure design standards of KDS 41 [23], as listed in Table 2. Their design strength (yield strength) was 126.0 kN. \[\mathcal{O}R_{n}=\mathcal{O}\cdot\mu\cdot h_{f}\cdot N_{s}\cdot N\cdot T_{volt} \tag{1}\]  
\[T_{volt}=\frac{T_{0}}{kd_{1}} \tag{2}\]  
Here, \(\mathcal{O}R_{n}\) is the design strength of the friction joints, \(\mathcal{O}\) is the shape reduction factor, \(\mu\) is the friction coefficient, \(h_{f}\) is the filler coefficient, \(T_{volt}\) is the clamp force of the bolted joint, \(N_{s}\) is the number of shear surfaces, \(N\) is the number of bolts, \(T_{0}\) is the torque, \(k\) is the torque coefficient, and \(d_{1}\) is the diameter of the bolt. Figure 3 shows the damage to the friction dampers after applying a target displacement of up to 10 mm to the out-of-plane load. The VLFD was damaged, but the proposed LLFD was not damaged despite the deformation of the H-frame. After applying the out-of-plane load, in-plane cyclic loading was applied. Figure 4 shows the load-displacement curves of the VLFD and LLFD for 11 mm (10 times), 22 mm (5 times), and 33 mm (3 times). A comparison of the curves showed that the VLFD had a value of 46.4 kN, i.e., approximately one-third of the design yield strength. In contrast, LLFD exhibited a value of 103.8 kN, slightly lower than the design strength, but exhibited a higher energy dissipation capacity than the existing horizontal friction damper because of its high strength. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimens**} & \multicolumn{2}{c}{**Number of Shear Surface (\(N_{s}\))**} & \multirow{2}{*}{**Number of Bolt (\(N\))**} & \multirow{2}{*}{**Diameter of Bolt (\(\mathbf{l_{0}}\)) [N\(\cdot\)m]**} & \multirow{2}{*}{**Torque (\(\mathbf{l_{0}}\)) [N\(\cdot\)m]**} & \multirow{2}{*}{**Clamp Force of Bolted Joint (\(\mathbf{l_{bol}}\)) [kN]**} & \multirow{2}{*}{**Design Strength of Friction Joints (\(\mathbf{\mathcal{O}R_{n}}\)) [kN]**} \\ \hline VLFD & 2 & 8 & 16 & 150 & 62.5 & 126.0 \\ \hline LLFD & 2 & 8 & 16 & 150 & 62.53 & 126.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Design strength of VLFD and LLFD specimens used in the device test for preliminary investigation of their structural properties. Figure 3: Damage of VLFD and LLFD specimens after out-of-plane load: (**a**) VLFD; (**b**) LLFD.