# Experimental Investigation into Failure Modes of Low-Yield-Point Steel Plate Shear Walls
## 2 Horizontal Cyclic Loading Test
### Experimental Results
#### 2.2.4 First Principal Stress Inclination of Wall Panel  
The angle \(\alpha\) between the first principal stress of the wall panel and the horizontal direction can be calculated by utilizing the measured strain values derived from the three-dimensional strain rosettes at the four corners of shear panel, which is deduced by Equation (4) and Table 6.  
\[tg(2\alpha)=\frac{-\gamma_{\rm xy}}{\varepsilon_{\rm x}-\varepsilon_{y}} \tag{4}\]  
Figure 21: Variations of strains in the left column of specimen 1: (**a**) Strains at the middle of web; (**b**) Strains at the lower part of web; (**c**) Strains at the lower part of left flange; (**d**) Strains at the lower part of right flange; (**e**) Strains during forwarding loading; (**f**) Strains during reverse loading.  
The inclination angle of the first principal stress at each part in the shear wall panel during forward and reverse loading is shown in Figure 22. The angle variation with the number of loading levels is shown in Table 7. As can be seen from the figure, the inclination angle of the first principal stress at the same part under the forward loading was larger than that under the reverse loading. The development trend of the first principal stress inclinations was generally consistent under the forward and reverse loading, which is gradually increasing at the first 3 levels, remaining flat or decreasing from 4 to 12 levels, and finally progressively expanding. It can be seen from the table that, on the whole, the inclination angle of the first principal stress for the shear panel in the specimen varies from 8\({}^{\circ}\) to 45\({}^{\circ}\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Levels**} & \multirow{2}{*}{**Infill Panel**} & \multicolumn{2}{c}{**Upper Right**} & \multicolumn{2}{c}{**Lower Left**} & \multicolumn{2}{c}{**Lower Right**} \\ \cline{2-7}  & **Forward** & **Reverse** & **Forward** & **Reverse** & **Forward** & **Reverse** \\ \hline
1 & 31.33 & 30.78 & 37.20 & 23.34 & 31.29 & 7.97 \\
2 & 31.81 & 35.63 & 38.06 & 31.57 & 24.54 & 8.75 \\
3 & 36.01 & 26.04 & 44.65 & 25.00 & 18.41 & 11.09 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The inclination angle of the first principal stress at each part of wall panel under the forward and reverse loading test (units: \({}^{\circ}\)).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Direction of Strain Rosette**} & \multicolumn{2}{c}{**Calculating Equations of Axial Strain \(\varepsilon_{\mathbf{x}}\), \(\varepsilon_{\mathbf{y}}\) and Shear Strain \(\gamma_{\mathbf{xy}}\)**} \\ \hline \hline \multirow{2}{*}{**Direction of Strain Rosette**} & \multirow{2}{*}{\(\varepsilon_{\mathbf{x}}=\varepsilon_{0^{\prime}}\), \(\varepsilon_{y}=\varepsilon_{90^{\prime}}\), \(\gamma_{\mathbf{xy}}=\varepsilon_{0^{\prime}}+\varepsilon_{90^{\prime}}-2 \varepsilon_{45^{\prime}}\)} \\  & & & & & \\ \hline \hline \multirow{2}{*}{**Direction of Strain Rosette**} & \multirow{2}{*}{\(\varepsilon_{\mathbf{x}}=\varepsilon_{0^{\prime}}\), \(\varepsilon_{y}=\varepsilon_{90^{\prime}}\), \(\gamma_{\mathbf{xy}}=\varepsilon_{0^{\prime}}+\varepsilon_{90^{\prime}}-2 \varepsilon_{45^{\prime}}\)} \\  & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Calculation formula of strain in the direction of strain rosette.  
Figure 22: Variation of the inclination angle of the first principal stress in the wall panel.