## 3 Calibration Tensile Test at Ambient Temperature
### Uniaxial Tensile Tests on Steel Cable  
The dimension of a steel cable specimen with ultimate strength of 1860 MPa is shown in Figure 8. The nominal diameter is 15.2 mm and cross section area is 139 mm\({}^{2}\). The process of marker painted is the same as mentioned in Section 3.1. Shown in Figure 9, the CCD camera was settled right ahead of the specimen in the distance of 1.5 m to form a measure plan and supplement brightness using a white lamp. Shown in Figure 10, an extensometer with the gauge length of 50 mm was settled in the mid-length of the same specimen. A couple of strain gauge was pasted on the surface of the mid-length. Thus, the stress-strain relationship of the steel cable was measured by three methods, i.e., strain gauge, extensometer and CCDC system, at ambient temperature. The standard tensile test was carried out by a servo-hydraulic test machine with a maximum stroke displacement of 75 mm and a capacity of 500 kN. There were four specimens repeatedly tested in a tensile test to get the average stress-strain curve as shown in Figure 10. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mechanical Properties**} & \multicolumn{2}{c}{**Measurement**} & \multirow{2}{*}{**Deviation**} \\ \cline{2-3}  & **Strain Gage** & & **CCDC** \\ \hline Elastic Modulus (\(E\)/GPa) & 201.5 & 204.2 & 1.34\% \\ Yield Strength (\(f_{y}\)/MPa) & 400.6 & 406.8 & 1.55\% \\ Ultimate Strength (\(f_{y}\)/MPa) & 472.6 & 472.6 & 0\% \\ Fracture Strain (\(\epsilon_{\text{u}}\)) & 0.095 & 0.308 & 225\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of S355 steel at ambient temperature. Figure 8: Dimension of a pre-stressed steel cable (Unit = mm). Figure 9: Tensile test set-up for pre-stressed steel cables at ambient temperature. Shown in Figure 11, the stress-strain curves were obtained by different measuring methods. The effective yield strength, elastic modulus, ultimate strength and rupture strength were derived from each stress-strain curve with the same method as mentioned in Section 3.1. The values of the mechanical properties of steel cables obtained by different measuring methods are listed in Tables 2-4. There is a blank in Table 2 as a strain gauge is difficult to paste on the surface of a wire with 5 mm diameter, one of strain gauges split away off the surface of a wire and induced a blank in Table 2. As the arm of an extensometer cannot grab the steel cable tightly enough, there was the slipping displacement between the surface of the arm and steel cable. Thus, there are a few of blanks in Table 3. Comparison of the values of elastic modulus and effective yield strength, which were obtained by an extensometer and CCDC system, showed that they matched well with only 1.13% and 0.6% deviation, respectively. However, the values of elastic modulus and effective yield strength measured by a strain gauge were larger than those obtained by the extensometer and CCDC system. For an elastic modulus obtained by strain, the deviation was 2.83% and 3.99% compared to that by an extensometer and CCDC system. For the effective yield strength, the deviation was 16.6% and 17.1%, respectively. Figure 11: Comparison of stress-strain curves of pre-stressed steel cables measuring by different measurement methods. Figure 10: Strain gauge and extensometer installation. As the strain gauge was pasted along twist wires, the strain measured by a strain gauge is off the longitudinal axis, which is smaller than the axis strain in the longitudinal direction. Thus, the smaller strain would induce the larger elastic modulus and yield strength. It also indicated that strain gauge cannot be suitable to measure the stress-strain curve of steel cables, which were twisted by a group of wires. As listed in Table 3, the extensometer cannot captured the ultimate strength and rupture strain as its arm must be removed before the ultimate strength due to limited travel distance. Thus, an extensometer cannot capture the full range of stress-strain curves in a material properties test, especially for steel cables.