# Seismic Vulnerability Assessment of Historical Masonry Buildings in Croatian Coastal Area
## 3 Development and Calibration of Vulnerability Model
### Static-Nonlinear Pushover Analysis of Representative Buildings
The roof above the attic was made as a wooden structure with double-sided water lines and a tile cover. The building is irregular in plan and elevation. The floors were modeled as flexible. The material properties of the walls were estimated according to [41], considering the results of in situ tests of the heritage building walls [42]. The mechanical material properties of the Public Library were assumed as an average of the reference values for building walls made of cut stone masonry with good bonding [41] as follows: compressive strength 2.60 MPa, tensile strength 0.10 MPa, modulus of elasticity 1700 MPa, shear modulus 580 MPa, and specific weights 21 kN/m\({}^{3}\). A limited knowledge level (KL1) of the building and a confidence factor of CF = 1.35 according to EC8-3 [48] were assumed. Figure 12: Public library: (**a**) photo of the building; (**b**) ground floor plan; (**c**) section view; (**d**) structural model used for non-linear seismic analysis. The pushover curves which give the lowest capacity accelerations \(\rm PGA_{c}\) in the x and y directions are shown in Figure 14, together with their bilinear idealizations, which are essential for capacity identification. The lowest capacity in both directions was obtained for the linear distribution. The peak ground accelerations associated with the collapse limit state were computed according to EC8 [46]. The capacity acceleration in terms of the collapse for the case study is equal to 0.123 g (0.561 \(\rm a_{g}\)) in the x direction and 0.079 g (0.363 \(\rm a_{g}\)) in the y direction, where \(\rm a_{g}\) represents the design ground acceleration, defined by the seismic hazard map for the return period of 475 years, and it is equal to \(\rm a_{g}=0.22\) g.  
The same procedure was applied to obtain the peak ground accelerations \(\rm PGA_{y}\), corresponding to the yield point. It is worth mentioning that the lowest values of \(\rm PGA_{y}\) and \(\rm PGA_{c}\) do not necessarily correspond to the same distribution of lateral forces. In this case, the capacity acceleration in terms of the yield is equal to 0.048 g (0.218 \(\rm a_{g}\)) in the x-direction and 0.028 g (0.130 \(\rm a_{g}\)) in the y-direction. \begin{table}
\begin{tabular}{c c c c c} \hline
**Direction** & **Load** & **Eccentricity** & **PGA\({}_{\rm y}\)/g** & **PGA\({}_{\rm c}\)/g** \\ \hline \(-\)x & linear & \(+5\%\) & 0.098 & 0.131 \\ \(-\)x & linear & \(-5\%\) & 0.136 & 0.557 \\ \(-\)x & modal  
Local mechanism failure was also analyzed to check local mechanisms such as those induced by a lack of connection among perpendicular walls, and poor connections among floors/roofs and walls. In the case of the Public Library building, the analysis showed that the lowest value of the failure acceleration for the local mechanism is 0.130 g. Hence, critical acceleration was obtained through global failure analysis. With this procedure, 11 typical buildings (Figure 15) at the historical core were analyzed. The results of the pushover analysis and vulnerability indexes for the analyzed buildings are shown in Table 3.  
Figure 16 shows the relationship between the vulnerability index and collapse/yield accelerations for 11 buildings at the test site. The cloud of points represents the sample of buildings analyzed with the pushover analysis. The trend lines I\({}_{\
u}\)-PGA\({}_{\gamma}\) and I\({}_{\
u}\)-PGA\({}_{c}\) for the yield and collapse states were obtained. The most representative functions were chosen. They can be used to approximately evaluate the yield and collapse peak ground accelerations for the historic center of Kastel Kambelovac. The vulnerability indexes for the buildings at the test site and the trend lines shown in Figure 16 were used to obtain the peak ground accelerations for early damage and collapse state. Figure 17 shows the collapse accelerations for the buildings in the test site. The next step is the definition of the vulnerability curves for the historical center.