## 2 Workflow
Next, the base shear \(F_{b}\) is computed according to:  
\[F_{b}=S_{d}(T_{1})\,m\,\lambda \tag{2}\]  
where \(m\) is the total mass of the building and \(\lambda\) a possible reduction factor, set to 1 in our analysis. Finally, the shear force is distributed to each \(i\)-th story, depending on the story height \(h_{i}\) and weight \(W_{i}\), by using:  
\[F_{i}=F_{b}\,\frac{h_{i}\,W_{i}}{\sum_{j=1}^{n}h_{j}\,W_{j}} \tag{3}\]  
For the sake of simplicity, in this research the orientation of the equivalent seismic action is assumed along an axis of symmetry at the bottom plan, as indicated in Figure 1b. An example of the tall building structures is shown in Figure 2.  
A tubular steel section is assigned to the diagonal diagrid elements, with a diameter of 80 cm and a thickness of 2 cm. For the horizontal members of the diagrid, a 60 cm diameter and a 1.5 cm thickness are specified. The floor slabs are modelled as a shell mesh in C45/55 concrete and it acts as a rigid diaphragm, redistributing the seismic load \(F_{i}\) from the centre of mass of each floor to the diagrid nodes on the same plane. Furthermore, diagrid nodes are connected by pinned joints. The boundary condition of the building is set at the ground level through pinned joints. Finally, the structural model of each building contains about 60 shell elements for each rigid floor slab and about 12,000 Euler-Bernoulli beam elements. The structural analysis is then carried out with the mentioned software Karamba(tm). As anticipated, in the analysis each structure is assumed to behave linearly, avoiding to consider possible damage states, see [31]. The results of the analysis are processed in terms of: input parameters related to the architectural design, such as the number of polygon edges at the top and bottom floors, the total gross area, the diagrid degree (namely the angle between the horizontal plane and a diagonal truss element), and the facade area; output parameters related to the structural response, such as the total weight, and relevant drift (measured by the horizontal displacement at the top of the building), the maximum utilization of the structural components, the total length of diagrid members, the expected design weight (the sum of the products of each member utilization times its weight) and the maximum normal force. A naive but sometimes useful method adopted to comparatively \begin{table}
\begin{tabular}{c c} \hline \hline \(S\) & 1.15 \\ \(T_{B}\) (s) & 0.2 \\ \(T_{C}\) (s) & 0.6 \\ \(T_{D}\) (s) & 2.0 \\ \(a_{g}\) (g) & 0.35 \\ \(q\) & 2 \\ \(\lambda\) & 1 \\ \(\beta\) & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the considered site in Tehran, Iran. Data adapted from the design spectrum in [34]. assess the effects of the shape of the building on its structural performance is shown in Figure 3, where the 12 \(\times\) 12 grid already depicted in Figure 1 is related to coded colours to report a feature of the structural response. For example, in Figure 3 the drift is considered as ranging between 41 cm and 177 cm; depending on the specific feature reported, the pattern in this and similar diagrams may change. This type of diagrams provides a first insight into the structural response: it can be seen that, by increasing the number of polygon edges, the response gets characterized by smaller drift values [30]. In Figure 4, the forms showing the best, the average, and the worst solutions are visible: model 132 (dark blue) turns out to be the best, with the minimum drift (41 cm) and the minimum expected design weight (about 800 tons), as linked to its 24-sided polygons at the top and bottom plans; model 51 (light blue), having a 5-sided polygon at top plan and a 7-sided polygon at the bottom plan, performs as a kind of average solution, with a drift equal to 125 cm and 1113 tons as expected design weight; model 103 (green), with 9-sided polygon at the top plan and a 11-sided polygon at the bottom plan, is instead the worst form with a maximum drift (177 cm) and the highest expected design weight (1250 tons).