## 4 Structural Vulnerability Analyses on Two-Story CFS Shear Wall Systems
### Effects of End Stud Type on the Collapse Modes of RCFS Shear Wall Systems  
RCFS shear wall systems suffer not only vertical loads but also bending moments because both the beam-column joints and support joints in the walls are rigid. The end studs thereby become a critical factor in the collapse resistance of the structure. The specimen \(W_{2\text{-}1}\) is selected as a comparison with the specimen \(W_{2}\), and the construction is presented in Figure 4c in detail. In comparison with \(W_{2}\), the section and layout type of \(W_{2\text{-}1}\) are changing from \(\square 140\times 140\times 13\times 1.5\) to \(\square 89\times 89\times 13\times 0.9\) and changing from the type depicted in Figure 4b to the type illustrated in Figure 4c, respectively.  
The vulnerability results of specimen \(W_{2\text{-}1}\) are listed in Table 4, and the total collapse mode with the maximum vulnerability index is shown in Figure 11b. The specimen lost its axial loading-bearing capacity because compression buckling occurred in the lower parts of the end studs (see Figure 14a,b); moreover, joints \(R_{1}\) and \(R_{2}\) lost their restraints on the rotation of the end studs (see Figure 14c,d) due to buckling. The total collapse tendency of the specimen, which behaves as a result of failure occurring on an end stud, is in accordance with that shown in Figure 11a. Thus, the validity of the improved vulnerability analysis method is further verified.  
It can be concluded from Tables 3 and 4 that for specimen \(W_{2}\) with the end studs' stiffness being large enough, the maximum vulnerability index of the total collapse modes is about 24.3% to 29.2% lower than that of the traditional shear wall system \(W_{1}\), as such, the level of safety guarantee of the RCFS shear wall systems is higher. The reason for the safety is that the collapse resistance of the whole structure can be effectively enhanced due to the second defense line in addition to the sheathings, which is provided by the framework integrated by beams and end studs under rigid connection conditions. Moreover, the vulnerability index indicates that the RCFS shear wall system exhibits better structural robustness, which is because a structure with lower robustness has a higher vulnerability index [28; 29]. On the other hand, in the case of end studs with insufficient stiffness, RCFS shear wall  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Collapse Mode** & **Failure Mode** & **Sepateness \(\gamma\)** & **Relative Damage Demand \(D_{\mathbf{r}}\)** & **Vulnerability Index \(\Phi\)** \\ \hline Total collapse & Figure 11a & 1.0 & 0.3534 & 3.413 \\ mode & **Figure 11b** & **1.0** & **0.2233** & **4.478** \\ \hline \hline \end{tabular} Note: Bold indicates the same failure mode as in the test results.  
\end{table}
Table 4: Vulnerability results of specimen \(W_{2\text{-}1}\).  
systems may have a total collapse mode caused by end stud failure, which is disadvantageous to the collapse resistance of the structure.  
As in whole, the authors hold a point that the robust mid-rise RCFS shear wall system should be likely to fail in the mode shown in Figure 11f under severe earthquakes. Two reasons can support such a point: (1) the performance of structural members can be fully used, and two energy dissipating paths (wallboard is the first path and the beam-column joint is the second one) can be formed to delay the total collapse; (2) the vulnerability of such a failure mode is the lowest one, the disproportionate collapse degree of such a failure mode is the lowest one, thus the seismic robustness of the corresponding structure is the highest one, which is beneficial for the anti-seismic design for the RCFS shear wall system.  
Therefore, conceptional rules of \"strong frame, weak wallboard\" and \"strong column, weak beam\" were proposed to guide the seismic design for the RCFS shear wall systems.