# Seismic Design Procedure for Low-Rise Cold-Formed Steel-Special Bolded Moment Frames
## 5 Nonlinear Analysis
### Evaluation of the Proposed Structural System  
FEMA P695 defines the adjusted collapse margin ratio (\(\mathit{ACMR}\)) for evaluation. This is due to the shape of the acceleration spectrum; the spectral shape factor (\(\mathit{SSF}\)) is considered. The \(\mathit{SSF}\) is determined from the system ductility and the fundamental period (\(T_{1}\)) of the structure. When the structure is ductile, the \(\mathit{SSF}\) will be greater than 1.0. As shown in Figure 20, the mechanism formed after a storey drift ratio of 4.0% was reached; therefore, it can be stated that this system was ductile. The \(\mathit{SSF}\) values computed using the FEMA P695 methodology are also shown in Table 9. The value of the \(\mathit{SSF}\) ranged from 1.14 to 1.22. The \(\mathit{ACMR}\) was computed as follows:  
\[\mathit{ACMR}=\mathit{SSF}\cdot\mathit{CMR} \tag{11}\]  
FEMA P695 provided the methodology used to evaluate the seismic design factors (SDFs), and the evaluation procedure was based on a probabilistic approach. The total collapse uncertainty \(\beta_{\mathrm{TOT}}\) was used to decide on the criteria; it corresponded to (1) the quality of the test data, (2) the preciseness of the structural design, and (3) the modelling of  
Figure 22: Collapse ratios of up to 50%: (**a**) S0202; (**b**) S0203; (**c**) S0302T; (**d**) S0302.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Frame Name** & **S0202** & **S0203** & **S0302T** & **S0302** & **Avg.** \\ \hline \(T_{1}\) (sec.) & 0.56 & 0.50 & 0.78 & 0.78 & \\ \(\mathit{CMR}\) & 1.69 & 1.85 & 1.56 & 1.45 & \\ \(\mathit{SSF}\) & 1.14 & 1.22 & 1.22 & 1.21 & \\ \(\mathit{ACMR}\) & 1.93 & 2.26 & 1.90 & 1.75 & 1.96 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Collapse margin ratio, spectral shape factor, and adjusted collapse margin ratio.  
the analysis model. The \(\beta_{\text{TOT}}\) ranged from 0.275 to 0.950. A larger value of \(\beta_{\text{TOT}}\) meant that there was much uncertainty. The structural system studied here was based on full-scale testing and precise inelastic modelling of the bolted connections [3; 4; 5]. The beams and columns were designed to be essentially elastic; therefore, this system can be classified as \"good\" according to FEMA P695. Consequently, in this study, \(\beta_{\text{TOT}}\) = 0.525 could be used as a reasonable value.  
If the randomness was assumed to be lognormally distributed, the acceptable _CMR_ could be determined from the total collapse uncertainty \(\beta_{\text{TOT}}\) and collapse probability [13]. Collapse probabilities of 10% and 20% were used in the FEMA P695 evaluation. The acceptable values that were used in this evaluation are summarised in Table 10.  
FEMA P695 provides two criteria for checking the safety margin. The following two inequalities needed to be satisfied for the proposed system. If not, the assumed \(R\) value (response modification coefficient) needed to be modified. Equation (12) is the average from the system group; Equation (13) is for the individuals. The values in Tables 9 and 10 were used for these checks.  
\[\overline{ACMR}_{i}\geq ACMR_{10\%} \tag{12}\]  
\[ACMR_{i}\geq ACMR_{20\%} \tag{13}\]  
where \(\overline{ACMR}_{i}\) is the average of the adjusted collapse margin ratio of the archetype frame group.  
As seen in Tables 9 and 10, the two inequalities shown above were fulfilled. In the member design, \(R\) was assumed to be equal to 8.0. From these results, it can be concluded that this assumed response modification coefficient can be used for middle-storey low-rise buildings with CFS-SBMF systems.