## 3 Validation of [PERSON]'s Resistance Integration Method (RIM) for Fire Design of Bonded Anchors
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Adhesive**} & **Anchor Geometry** & **Applied Load** & **Pull-Out Failure Time** & **Pull-Out Resistance acc.** & **Pull-Out Resistance acc.** \\  & **(Size \(\times\) Embedment [km])** & **Applied Load** & **under Fire Conditions** & **[PERSON]’s RIM Results** & **[PERSON]’s RIM Results** \\  & & **[km]** & **[km]** & **(Cut at \(T_{max}\))** & **(Extended to 450 \({}^{\circ}\)C)** \\ \hline \multirow{6}{*}{\
\begin{tabular}{} \end{tabular} } & \(\text{M10}\times 60\) & 0.50 & 185 (no failure) & 0 & 0 \\  & 1.00 & 66 & 0 & 0.38 \\  & 1.50 & 60 & 0.20 & 0.49 \\ \cline{2-5}  & \(\text{M10}\times 85\) & 0.50 & 180 (no failure) & 0 & 0 \\ \cline{2-5}  & & 0.50 & 185 (no failure) & 0 & 0 \\  & 0.75 & 93 & 0 & 0.30 \\  & 1.00 & 81 & 0 & 0.49 \\  & 1.50 & 81 & 0 & 0.49 \\  & 1.80 & 72 & 0.28 & 0.65 \\  & 2.00 & 56 & 0.81 & 1.08 \\ \cline{2-5}  & \(\text{M12}\times 90\) & 1.00 & 158 & 0 & 0.36 \\ \cline{2-5}  & \(\text{M16}\times 80\) & 1.00 & 101 & 0 & 0.32 \\  & 1.50 & 82 & 0 & 0.76 \\  & 3.00 & 73 & 0.49 & 1.04 \\ \cline{2-5}  & 1.00 & 180 (no failure) & 0 & 0.34 \\  & 2.50 & 118 & 0.64 & 1.27 \\ \cline{2-5}  & \(\text{M20}\times 90\) & 3.50 & 75 & 0.80 & 1.57 \\ \cline{2-5}  & \(\text{M20}\times 110\) & 2.50 & 137 & 0.20 & 1.32 \\ \cline{2-5}  & & 2.00 & 106 & 0 & 0.64 \\  & 5.50 & 72 & 1.17 & 2.18 \\  & 6.50 & 52 & 3.32 & 4.06 \\ \cline{2-5}  & \(\text{M24}\times 120\) & 2.50 & 142 & 0.13 & 1.70 \\ \hline \multirow{6}{*}{
\begin{tabular}{} \end{tabular} } & \(\text{M8}\times 70\) & 0.60 & 80 & 0 & 0.17 \\  & 0.70 & 69 & 0 & 0.23 \\  & 0.75 & 112 & 0 & 0.08 \\  & 0.75 & 75 & 0 & 0.20 \\  & 0.90 & 100 & 0 & 0.11 \\ \cline{2-5}  & & 1.50 & 146 & 0 & 0.46 \\  & 1.80 & 115 & 0.31 & 0.69 \\  & 1.80 & 60 & 1.80 & 1.80 \\  & 2.40 & 55 & 2.12 & 2.40 \\  & 2.90 & 68 & 1.42 & 1.69 \\  & 9.0 & 29 & 6.57 & 6.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 11: Fire resistance of M10 \(\times\) 50 bonded anchor using Adhesive-1. From the previous results it can be concluded that [PERSON]'s method (resistance integration) can be used for the design of bonded anchors under fire conditions. [PERSON]'s method yields conservative design values compared to fire tests. However, some calculated resistances are too conservative where the design method shows that the anchor possesses no resistance under fire conditions. This is due to the fact that resistance integration is based on the bond stress vs. temperature curve. So far, this curve was only assessed through the approach in EAD 330087 up to a maximum temperature \(T_{max}\) for a maximum test duration of less than 3 h, beyond which no extrapolation is allowed. Therefore, in the resistance integration process, when the temperature of the anchor (in a segment or over the whole embedment depth) exceeds the maximum temperature of the bond stress vs. temperature curve, the segment is attributed zero bond stress, hence no contribution to the fire resistance. It should be noted that for an anchor exposed directly to fire conditions, temperature profiles reach and exceed the maximum tested temperatures in Figures 8-10 (usually chosen for fire evaluation of Post-Installed Rebars) along the embedment depth very rapidly. This explains the difference between calculated resistances and fire test results, where in reality the anchor still shows a certain resistance at these high temperatures (mostly by friction). Figure 12: Fire resistance of M12 \(\times\) 70 bonded anchor using Adhesive-2. Figure 13: Fire resistance of M8 \(\times\) 70 bonded anchor using Adhesive-3. In order to minimize the difference between calculated resistances ([PERSON]'s RIM) and fire test results, a parametric study was conducted to assess the influence of considering the remaining bond stress beyond \(T_{max}\) in the resistance integration method. This study is only informative and is only based on test data points up to \(T_{max}\) around 300 \({}^{\circ}\)C. The curve is extrapolated beyond \(T_{max}\).