## 4 Results
### Suggestion of Nonlinear Rotational Stiffness
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Classification**} & \multicolumn{3}{c}{**K Value (kNm/rad)**} & \multicolumn{3}{c}{\(\mathbf{\beta\) **Value (rad)**} \\ \cline{2-7}  & **K\({}_{1}\)** & **K\({}_{2}\)** & **K\({}_{3}\)** & \(\mathbf{\beta_{1}}\)** & \(\mathbf{\beta_{2}}\) & \(\mathbf{\beta_{3}}\) \\ \hline New-S-1 & 14.375 & 5.501 & 3.885 & 0.039 & 0.057 & 0.15 \\ New-S-2 & 25.955 & 5.523 & 1.302 & 0.02 & 0.108 & 0.178 \\ New-S-3 & & & & Not measured & & \\ New-S-4 & 32.092 & 6.845 & 2.114 & 0.013 & 0.064 & 0.154 \\ New-S-5 & 26.816 & 7.820 & 1.986 & 0.013 & 0.062 & 0.189 \\ New-S-6 & 31.817 & 7.026 & 1.653 & 0.018 & 0.079 & 0.178 \\ New-S-7 & 30.481 & 8.206 & 2.325 & 0.014 & 0.069 & 0.189 \\ New-S-8 & 35.725 & 4.730 & 1.594 & 0.021 & 0.081 & 0.177 \\ New-S-9 & 24.378 & 7.195 & 2.376 & 0.017 & 0.071 & 0.184 \\ New-S-10 & 15.666 & 6.805 & 1.901 & 0.022 & 0.052 & 0.185 \\ New-S-11 & 18.134 & 5.715 & 1.674 & 0.024 & 0.125 & 0.186 \\ New-S-12 & 35.236 & 6.261 & 2.491 & 0.011 & 0.103 & 0.177 \\ New-S-13 & 25.576 & 5.813 & 2.015 & 0.016 & 0.121 & 0.193 \\ \hline Reuesd-1-1 & 24.467 & 3.166 & 0.289 & 0.022 & 0.114 & 0.202 \\ Reuesd-1-2 & 22.501 & 6.340 & 2.472 & 0.018 & 0.053 & 0.124 \\ Reuesd-1-3 & 19.875 & 3.829 & 0.947 & 0.024 & 0.113 & 0.180 \\ Reuesd-1-4 & 25.468 & 3.398 & 1.148 & 0.02 & 0.127 & 0.190 \\ Reuesd-1-5 & 24.713 & 4.166 & 0.959 & 0.020 & 0.110 & 0.173 \\ Reuesd-1-6 & 18.443 & 3.860 & 1.353 & 0.027 & 0.118 & 0.175 \\ Reuesd-1-7 & 24.007 & 3.716 & 1.418 & 0.023 & 0.123 & 0.170 \\ Reuesd-1-8 & 24.759 & 5.953 & 2.570 & 0.020 & 0.080 & 0.123 \\ Reuesd-1-9 & 23.132 & 3.266 & 0.71 & 0.023 & 0.108 & 0.174 \\ Reuesd-1-10 & 27.071 & 6.481 & 2.426 & 0.020 & 0.058 & 0.101 \\ Reuesd-1-11 & 25.098 & 3.674 & 1.131 & 0.023 & 0.125 & 0.190 \\ \hline \end{tabular}
\end{table} 
Table 7: K and \(\beta\) values in trilinear model for all specimens. The average rotational stiffness values, standard deviations, coefficients of variation, and rotation angle limit values of the joints of the new and reused specimens are shown in Table 8, and the results are compared in Figure 15. When the average rotational stiffness values of the two models were analyzed by interval, it was observed that the stiffness changed significantly depending on the beta value, which is the basis of the stiffness change. Therefore, the rotational stiffness was calculated as the average for each specimen, whereas the rotation angle limit value was calculated as a weighted arithmetic mean, with the rotational stiffness used for weighting, as shown in Equation (2):  
\[\beta=\frac{\mathrm{k_{n}}\cdot\beta_{\mathrm{n}}}{\Sigma\mathrm{k_{n}}} \tag{2}\]  
where \(\beta\) is the rotation angle limit value evaluated as a weighted arithmetic mean, \(\mathrm{K_{n}}\) is the rotational stiffness of each specimen, and \(\beta_{\mathrm{n}}\) is the rotational stiffness limit value of each specimen. According to Table 8, which lists the rotational stiffnesses in the trilinear model for the wedge joint stiffnesses by interval and by reuse period, the initial rotational stiffness of the new specimens was approximately 26.354 kNm/rad (rotation angle limit value: 0.018), but the initial rotational stiffness decreased to 23.594 kNm/rad (rotation angle limit value: 0.022), 21.263 kNm/rad (rotation angle limit value: 0.022), and 17.922 kNm/rad (rotation angle limit value: 0.022) as the reuse period increased to one, four, and seven years, respectively. In the second interval, the average rotational stiffness was the highest for the new specimens (6.453 kNm/rad), followed by the average rotational stiffnesses for the specimens with a one-year reuse period (4.350 kNm/rad), a four-year reuse period (4.060 kNm/rad), and a seven-year reuse period (3.643 kNm/rad).