# Multi-Step Prestressing with Hybrid SMA Wires
## 4 Multi-Step Prestressing Test  
### Test Variables and Specimens  
In this section, we describe a multi-step prestressing test that was conducted with a prestrained hybrid SMA wire to confirm the applicability of the multi-step recovery behavior obtained in the previous section. The multi-step prestressing test was performed by measuring the amount of prestress \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{5}{c}{**Temperature (\({}^{\circ}\)C)**} & \multicolumn{5}{c}{**Displacement (mm)**} \\ \cline{2-9}  & \(T_{S1}\) & \(T_{E1}\) & \(T_{S2}\) & \(T_{E2}\) & \(D_{S1}\) & \(D_{E1}\) & \(D_{S2}\) & \(D_{E2}\) \\ \hline \multirow{4}{*}{NiTi50} & 1 & 46.8 & 68.8 & - & - & 1.71 & 86.07 & - & - \\  & 2 & 45.1 & 69.5 & - & - & 1.62 & 85.95 & - & - \\  & 3 & 45.6 & 65.4 & - & - & 1.82 & 87.35 & - & - \\  & Avg. & 45.8 & 67.9 & - & - & 1.72 & 86.46 & - & - \\ \hline \multirow{4}{*}{NiTi90} & 1 & 77.4 & 103.5 & - & - & 4.17 & 88.20 & - & - \\  & 2 & 77.8 & 102.5 & - & - & 4.20 & 86.50 & - & - \\  & 3 & 77.2 & 101.3 & - & - & 3.41 & 85.60 & - & - \\  & Avg. & 77.5 & 102.4 & - & - & 3.93 & 86.77 & - & - \\ \hline \multirow{4}{*}{50-90-50} & 1 & 45.3 & 72.0 & 80.5 & 105.5 & 2.13 & 77.64 & 78.32 & 87.47 \\  & 2 & 42.5 & 65.5 & 78.6 & 101.3 & 2.25 & 78.50 & 78.73 & 85.46 \\  & 3 & 42.5 & 66.3 & 80.1 & 98.7 & 2.65 & 80.47 & 80.49 & 88.59 \\  & Avg. & 43.4 & 67.9 & 79.7 & 101.8 & 2.34 & 78.87 & 79.18 & 87.17 \\ \hline \multirow{4}{*}{90-50-90} & 1 & 46.2 & 67.7 & 77.2 & 103.7 & 3.01 & 40.52 & 40.66 & 88.82 \\  & 2 & 45.7 & 68.9 & 76.8 & 103.7 & 3.38 & 42.01 & 42.04 & 90.36 \\ \cline{1-1}  & 3 & 44.3 & 69.1 & 78.6 & 103.0 & 2.98 & 39.26 & 40.35 & 86.09 \\ \cline{1-1}  & Avg. & 45.4 & 68.6 & 77.5 & 103.5 & 3.10 & 40.60 & 41.00 & 88.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparisons of results of shape recovery tests. introduced according to the SME triggered by heating in the chamber. Heating the specimen causes the concrete to thermally expand before SME starts to appear. Then, when the SMA wire reaches the shape recovery temperature, prestress is introduced into the test specimen. If the thermal expansion of concrete is not distinguished from the measurement result, our analysis of the experimental data will be compromised. Therefore, in this experiment, the main specimen including the SMA wire and a dummy specimen excluding the SMA wire were fabricated to help us distinguish the strain generated by the thermal expansion of concrete from the measured data. The hybrid SMA wire used in the experiment consisted of two types of SMA wires (NiTi50 and NiTi90), as described in the previous section. The specifications of the test specimens used in this experiment are listed in Table 4 and Figure 11. Three specimens were fabricated to check the repeatability of the results. Before fabrication of the SMA wire specimens, the individual SMA wires were tensioned with a universal testing machine to induce residual strain in the SMA wires. This residual strain was used to introduce prestress. The diameter of the SMA wire used in this study was 1 mm. Because the wire was too thin, it was difficult to measure the strain induced in the wire with an extensometer. Therefore, we measured strain by using the image processing method. A tension force of 250 N was applied to the wire was 250 N. Figure 12a,b show the experimental set-up and the load-strain curves measured at the time of introducing residual strain. Residual strains of 0.059 and 0.049 were induced in NiTi50 and NiTi90 wires, respectively. If an SMA wire embedded in a concrete girder has anchorage parts, it will be possible to effectively introduce prestress. Therefore, in this study, both ends of the SMA wire were bent in J-shape, as shown in Figure 13, to act as anchorages. [PERSON] et al. [28] evaluated the pull-out resistance of SMA wire anchorages with J-shaped ends. They derived Equation (1) to calculate the anchorage pull-out resistance. Equation (1) consists of three parts.