## 3 Numerical Analyses
### Fiber Model  
The fiber FE model of the tower was implemented in Midas GEN [48] using only beam elements (Figure 4b). Each level is characterized by an appropriate hollow squared cross-section, according to the drawings reported in Figure 2. The masses of the vaults, slab and roof were taken into account as nodal loads applied at different levels. Dead and live loads--evaluated according to the Italian Standard (NTC18) [19]--acting on the vaults, slab and roof were also considered as nodal loads. The openings were neglected. The fiber model was calibrated to be equivalent to the shell FE model in terms of total weight, fundamental natural periods, and vibration mode shapes. The site response spectrum was evaluated according to the NTC18 (Figure 8). The constitutive law proposed by [PERSON] and [PERSON] [51] was chosen to describe the masonry compressive behavior with the following parameters: compressive strength \(\ell^{*}_{\rm c}\) = 1.4 MPa, strain at maximum stress \(\varepsilon_{\rm c0}\) = 0.004, confinement coefficient K = 1 (no lateral confinement considered), ultimate strain \(\varepsilon_{\rm cu}\) = 0.014, and slope of the strain-softening branch \(Z\) = 533. The tensile strength of the material was ignored. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\boldsymbol{\Psi}\) & \(\varepsilon\) & \(\boldsymbol{f_{\rm b0}/f_{\rm e0}}\) & \(\boldsymbol{\mathrm{K}}\) & \(\boldsymbol{\mathrm{\mu}}\) \\ [\({}^{\circ}\)] & [-] & [-] & [-] & [-] \\ \hline
10 & 0.1 & 1.16 & 0.667 & 0.002 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of the parameters adopted to define the CDP model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\boldsymbol{h}\) & \(z_{i}\) & \(\boldsymbol{W_{i}}\) & \(\boldsymbol{W_{i}}\cdot z_{i}\) & \(\boldsymbol{F_{i}}\) \\
**[m]** & **[m]** & **[kN]** & **[kNm]** & **[kN]** \\ \hline \(-2.24\) & 0 & 0 & 0 & 0 \\
0 & 2.24 & 3729 & 8354 & 99 \\
3.62 & 5.86 & 3990 & 23,382 & 278 \\
8.92 & 11.16 & 5394 & 60,199 & 716 \\
13.89 & 16.06 & 4759 & 76,431 & 909 \\
19.72 & 21.96 & 5479 & 120,326 & 1431 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Equivalent static loads distribution used to represent the seismic action. Two kind of load profiles were defined for the pushover analyses: one profile was proportional to the first (or second) vibration mode shape, and the other one was a uniform acceleration distribution. Figure 9 shows the obtained capacity curves in terms of base shear and top displacement for both X and Y directions. The results show that the uniform acceleration profile leads to a greater value of collapse base shear with respect to the modal load case. In the X direction, the collapse base shear is 5247 kN for the modal distribution and 9532 kN for the uniform acceleration, with an increase of 82%, while in the Y direction, the collapse base shear is 5265 kN for the modal distribution and 9720 kN for the uniform acceleration with an increase of 85%. Therefore, as expected, the tower behavior is more similar to that of a cantilever than that of a frame structure, which usually collapses for soft story mechanisms associated to a uniform acceleration distribution. Figure 7: Stresses that exceed the tension strength for (**a**) +X, (**b**) -X, (**c**) +Y, and (**d**) -Y loading directions with the respective horizontal load multipliers. Starting from the obtained results, it was possible to evaluate the values of the behavior factor q, according to the N2 method proposed by [52], by transforming the multi degrees of freedom (MDOF) capacity curves into the equivalent single degree of freedom (SDOF) capacity curves. Nonlinear force-displacement relations were simplified into elastic-plastic relations, whose main parameters are reported in Table 4 in which T* is the period of the equivalent bilinear system, F*y is the plastic limit force with respective displacement d*y, and d*u is the ultimate displacement of the bilinear system.