## 5 The Step towards Full Dynamic Seismic Assessment Tools
### Comparison of Rocking Analysis Results with Code-Based Assessment Procedures
#### 5.2.2 Church Loaded Out-of-Plane  
In the case of the church, the collapse mechanism found through the upper bound limit analysis was that of out-of-plane (OOP) failure of the facade with the partial overturning of the side walls as well. The equivalent rocking parameters computed for this mechanism by the GhPython script are listed in Table 5. Note that the coefficient of restitution \(\eta_{COR}\) is again negative due to one-sided rocking being assumed for this mechanism as well. Figure 16: Masonry wall with openings. Comparison of the code-based (equivalent static) and rocking (non-linear dynamic) demand-capacity ratios for both (**a**) pulse and (**b**) non-pulse type recorded ground motions, scaled to \(a_{g}\) = 0.35 g.  
Figure 17: Masonry wall with openings. Variation of number of collapses predicted using rocking dynamics with PGA, for both pulse and non-pulse type recorded ground motions. In the first set of analyses, the rocking equation of motion was solved by scaling the suite of ground motions to \(a_{g}=0.48\) g for both the artificial and recorded accelerograms, which was the PGA predicted to cause collapse by the code's displacement-based approach. In the case of the artificial accelerograms, a comparison between the code-based predictions and those obtained from the rocking analyses again revealed the code to consistently be the more conservative of the two (Figure 18, positive polarity indicated in black, negative in white). Specifically, using the actual response spectra for each accelerogram, the code predicted collapse in 60% of the cases (points lying above the solid horizontal line), while the maximum response predicted by the rocking model never exceeded 21% of \(\theta_{ov,c}\) or 8.4% of \(\theta_{ov}\). In the case of the recorded accelerograms, the rocking model actually predicted larger demands than the code in 4% of the cases for pulse-type ground motions (Figure 19), which could be due, in part, to the higher level of scaling employed as well as the increased slenderness of the church mechanism, as compared to the wall with openings. More specifically, from these analyses, it was found that the code predicted collapse in 64% of the cases, while the rocking model predicted collapse (according to the code and not according to equilibrium) in 2% of the cases (i.e., points lying to the left of the vertical line in Figure 19). However, the maximum rocking response never exceeded 51% of \(\theta_{ov}\). In the case of non-pulse type motions, the code predicted larger demands than the rocking model in 100% of cases, but only predicted collapse in 44% of cases, while the maximum response predicted by the rocking model never exceeded 58% of \(\theta_{ov,c}\) or 23% of \(\theta_{ov}\). Nevertheless, for both types of ground motions (artificial and recorded, pulse and non-pulse type), it can be seen that the code is much more conservative than the rocking model, and that the PGA of 0.48 g is insufficient to cause rocking collapse. Again, in a second set of analyses using recorded ground motion, the scaling of the ground motion was again progressively increased until complete rocking collapse occurred (i.e., \(\theta=\pi/2\)). From these analyses, it was found that for the church, a minimum PGA of 0.63 g is required for at least one record to cause collapse, with the PGA having to be increased to 1.40 g for 50% of the recorded accelerograms (average of pulse and non-pulse type records) to cause the complete overturning of the structure (Figure 20), which is 2.9 times higher than the corresponding code-based prediction of 0.48 g. Again, the pulse-type ground motions were found to have more of a destructive effect on the rocking  
Figure 18: Comparison of the code-based (equivalent static) and rocking (non-linear dynamic) demand-capacity ratios for the different artificial accelerograms, for the church (scaled to \(a_{g}=0.48\) g).