# Effects of Diagonal Friction Dampers on Behavior of a Building
## 2 Experimental Studies
### Design of Friction Dampers  
Attention was paid to the fact that the stiffnesses of the friction dampers used in this study constitutes more than half of the total stiffness of the relevant floor. From the numerical model results, it can be seen that the relative interstory drifts and the shear forces coming to the floors were determined to be greater on the lower floors. An appropriate shear force will have a positive effect on the behavior of the structure. Five friction dampers with different features were designed and manufactured to be used on each floor of the building. In the design of the friction dampers, a shear force of 0.6 g was taken into account for the friction dampers, since the peak ground acceleration of the design earthquake in the region where the building was designed was 0.684 g. According to this effect, the optimum shear force values calculated separately for each floor were found to be 174 N on the first floor, 166 N on the second floor, 153 N on the third floor, 121 N on the fourth floor, and 66 N on the fifth floor. The required pre-tension force in the bolts of friction dampers with helical compression springs was applied. The reason for this is that the minimum pre-tensioning amount that could be given to the bolts with classical pre-tension was greater than the required pre-tensioning force. The main functions of helical springs are to store the force applied on \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Geometric Scaling Factor** & **X Direction** & **Y Direction** & **Total Building Height** & **Weight** & **Frequency** \\
**n** & \(\lambda\) **= 1/n** & **(mm)** & **(mm)** & **(mm)** & **(kg)** & **(Cycles/Second)** \\ \hline
1 & 1 & 4000 & 2000 & 12,000 & 33,593.92 & 1.41 \\
2 & 0.5 & 2000 & 1000 & 6000 & 4199.24 & 1.99 \\
4 & 0.25 & 1000 & 500 & 3000 & 524.91 & 2.82 \\
6 & 0.167 & 666.67 & 333.33 & 2000 & 155.53 & 3.45 \\
8 & 0.125 & 500 & 250 & 1500 & 65.61 & 3.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Scaling of the structure using the geometric scaling factor. Figure 1: Model building: **(a)** numerical model; **(b)** experimental model. them as energy via compression, to apply force to the desired location, and to dampen the incoming impacts [32]. Helical compression springs perform displacement that is inversely proportional to their stiffness when impacted by an \"F\" force. In the equation of F = k.u, if a spring with a stiffness of \"k\" can be displaced by \"u\" and the spring can be fixed in its last position by preventing it from returning to its original state, the desired F front tensile force can be obtained in the helical compression spring. Thus, it can be seen that the amount of displacement to be applied to the springs is directly proportional to the desired pre-tensioning force in the damper on the relevant floor. The stiffness of the compression spring was calculated using Equation (1) [33]. Springs with the desired rigidity were specially manufactured using a spring drawing machine. \[\mathrm{k_{bask}}=\frac{\mathrm{d^{4}\cdot G}}{8\cdot\mathrm{N_{e}\cdot D^{3} }}\left(\mathrm{N/mm}\right) \tag{1}\]  
Here, d: diameter of spring wire (mm), D: ring (average) diameter of spring (mm), D\({}_{\mathrm{i}}\): inner diameter of spring ring (mm), G: shear modulus (G = 80,000 (N/mm\({}^{2}\)) for steel springs), N: number of spring turns, N\({}_{\mathrm{e}}\): number of effective spring turns, D\({}_{\mathrm{d}}\): outer diameter of spring ring (mm). The pre-tensile force value that must be applied to the bolts in order to obtain the optimum sliding force required in the friction dampers was calculated using Equation (2) [34]. \[\mathrm{R_{n}}=\mu\cdot\mathrm{D_{u}}\cdot\mathrm{h_{f}}\cdot\mathrm{T_{b}} \cdot\mathrm{n_{s}} \tag{2}\]  
Here, R\({}_{\mathrm{n}}\) is the friction-acting design shear force for a bolt, D\({}_{\mathrm{u}}\) is defined as a coefficient showing the ratio of the average pre-tension force applied during bolt assembly to the characteristic minimum pre-tension force, and is taken equal to 1.0.