## 5 Incremental Dynamic Analysis (IDA)
### Modelling in OpenSees  
The numerical dynamic analyses have been performed through OpenSees (Python version 3.5.1) [37] (Supplementary Materials File S1). Each tcl or Python file is characterised by a precise syntax, and the structural system model must follow the following order:  
* **Geometric Data**: Defines the basic model and problem size for analysis, specifying the degrees of freedom for each node. * **Nodal Coordinates:** Specifies the coordinates of all nodes in the x-y-z reference system, with the x-y plane as the working plane. * **Constraints:** Establishes boundary conditions using the fix command for free or constrained degrees of freedom. Internal constraints, such as real hinges, are inserted using the EqualDof command. * **Materials:** Defines the system's materials utilizing constitutive laws from the uniaxial-Material library [37]. * **Sections:** Defines model sections using a fibre modelling approach, creating rectangular models with discretised fibres, often with specific commands like patch rect and wide flange. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & **MDOF** & & **Equivalent SDOF** & \
\begin{tabular}{c} **ADRS** \\ **Spectrum** \\ \end{tabular} &
\begin{tabular}{c} **Nassar and** \\ **Krawinkler** \\ \end{tabular} \\ \hline \multirow{2}{*}{_Limit State_} & \(\alpha_{LS}\) & \(\delta_{LS}\) & \(F_{LS}\) & \(\delta^{*}\) & \(F^{*}\) & \(S_{a}(T^{*})\) & \(S_{a}(T^{*})\) \\  & [-] & **[m]** & **[kN]** & **[m]** & **[kN]** & **[g]** & **[g]** \\ \hline Fully operational & & & & & & & \\
[FOOTNOTE:]Footnote [ENDFOOTNOTE] & 2.27 & 0.086 & 742.99 & 0.063 & 544.86 & **0.307** & **0.307** \\ Operational & & & & & & & \\
[O] & & & & & & & \\ Life Safety & 4.81 & 0.554 & 1572.21 & 0.406 & 1152.96 & **1.983** & **2.040** \\
[LS] & & & & & & & \\ Near Collapse & 4.66 & 0.858 & 1523.57 & 0.629 & 1117.28 & **3.071** & **3.151** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Capacity in terms of spectral acceleration and displacements according to ADRS Spectrum and Nassar and Krawinkler approach for the case study \(1\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & **MDOF** & & **Equivalent SDOF** & \
\begin{tabular}{c} **ADRS** \\ **Spectrum** \\ \end{tabular} &
\begin{tabular}{c} **Nassar and** \\ **Krawinkler** \\ \end{tabular} \\ \hline \multirow{2}{*}{_Limit State_} & \(\alpha_{LS}\) & \(\delta_{LS}\) & \(F_{LS}\) & \(\delta^{*}\) & \(F^{*}\) & \(S_{a}(T^{*})\) & \(S_{a}(T^{*})\) \\  & [-] & **[m]** & **[kN]** & **[m]** & **[kN]** & **[g]** & **[g]** \\ \hline Fully operational & & & & & & & \\
[FOOTNOTE:]Footnote [ENDFOOTNOTE] & 0.42 & 0.096 & 115.48 & 0.072 & 86.77 & **0.087** & **0.087** \\ Operational & & & & & & & \\
[O] & 0.53 & 0.124 & 145.73 & 0.093 & 109.49 & **0.112** & **0.112** \\ Life Safety & & & & & & & \\
[LS] & 0.53 & 0.188 & 145.73 & 0.141 & 109.49 & **0.171** & **0.182** \\ Near Collapse & & & & & & & \\
[NC] & 0.40 & 0.245 & 109.98 & 0.184 & 82.63 & **0.224** & **0.236** \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Capacity in terms of spectral acceleration and displacements according to ADRS Spectrum and Nassar and Krawinkler approach for the case study \(2\). **Transformation:**: Defines the transformation of the reference system to account for stiffness and stresses, such as a P-delta transformation for second-order effects in certain structural types. **Elements:**: Defines individual elements of the system, associating end nodes, sections, and geometric transformations using default commands like _dispBeamColumn_, _nonLinearBeamColumn_, and _elasticBeam_. **Loads:**: Specifies loads at nodes or previously defined elements. Often includes detailed steps on applying loads incrementally for nonlinear analysis, like the proportional application of gravitational loads in multiple steps. **Recorders:**: Defines the outputs to be saved for analysis, commonly including element stresses and structural node displacements for data interpretation.