## Results
### Sub-Structures' Stiffness Parameters  
The following sub-structure's stiffness parameters are obtained using the approach proposed in Section 2.2:  
-Internal frame in the \(x\) direction  
\[D_{l}^{ifx} =\sum_{i=0}^{7}EI_{s}^{HD}=3.019\cdot 10^{9}\,\mathrm{N\ m^{2}} \tag{56}\] \[D_{0}^{ifx} =\sum_{i=0}^{7}EA_{c,i}^{HD}\ c_{i}^{2}=9.589\cdot 10^{12}\, \mathrm{N\ m^{2}} \tag{57}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Section** & \(\mathbf{A}\) & \(\mathbf{I_{5}}\) (**Strong Axis**) & \(\mathbf{I_{av}}\) (**Weak Axis**) \\  & \([m^{2}]\) & \([m^{4}]\) & \([m^{4}]\) \\ \hline HD400 \(\times\) 463 & \(5.88\times 10^{-2}\) & \(1.797\times 10^{-3}\) & \(6.703\times 10^{-4}\) \\ IPE360 & - & \(1.552\times 10^{-4}\) & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometrical properties of the frame sections.  
Figure 1: The case study: 3d view (**a**), an external frame (**b**) and an internal frame (**c**).  
\[S_{b}^{ifx} =\sum_{i=0}^{7}\frac{12\,EI_{s}^{IPE360}}{l_{i}\,h}=1.632\cdot 10^{8} \,\mathrm{N} \tag{58}\] \[S_{c}^{ifx} =\sum_{i=0}^{7}\frac{12\,EI_{s}^{HD}}{h^{2}}=2.382\cdot 10^{9}\, \mathrm{N}\] (59) \[S^{ifx} =\left(\left(S_{b}^{ifx}\right)^{-1}+\left(S_{c}^{ifx}\right)^{- 1}\right)^{-1}=1.63\cdot 10^{8}\,\mathrm{N}. \tag{60}\]  
-Internal frame in the \(y\) direction  
\[D_{l}^{ify} =\sum_{i=0}^{7}EI_{w}^{HD}=1.126\cdot 10^{9}\,\mathrm{N}\, \mathrm{m}^{2} \tag{61}\] \[D_{0}^{ify} =\sum_{i=0}^{7}EA_{c,i}^{HD}\,c_{i}^{2}=9.589\cdot 10^{12}\, \mathrm{N}\,\mathrm{m}^{2}\] (62) \[S_{b}^{ify} =\sum_{i=0}^{7}\frac{12\,EI_{s}^{IPE360}}{l_{i}\,h}=1.632\cdot 10^{8 }\,\mathrm{N}\] (63) \[S_{c}^{ify} =\sum_{i=0}^{7}\frac{12\,EI_{w}^{HD}}{h^{2}}=8.884\cdot 10^{9}\, \mathrm{N}\] (64) \[S^{ify} =\left(\left(S_{b}^{ify}\right)^{-1}+\left(S_{c}^{ify}\right)^{- 1}\right)^{-1}=1.379\cdot 10^{8}\,\mathrm{N}. \tag{65}\]  
-External frame in the \(x\) direction  
The external frames in the \(x\) direction have a bracing system (Figure 1). In this case, the bending stiffness \(D_{0}\) is the same of Equation (57), while the shear stiffness is computed using Equation (26). Furthermore, since the topmost part of the bracing has smaller dimensions (Figure 2), the weighted mean for the length \(d_{m}\) and the vertical height \(h_{m}\) are used in place of \(d\) and \(h\) in (26).  
\[h_{m}=\frac{7\cdot 23.4+15.6}{8}=22.425\,\mathrm{m},\qquad d_{m}=\frac{7\cdot 38. 13+33.9}{8}=37.598\,\mathrm{m}. \tag{66}\]  
Therefore, the values assumed for the external frame in the \(x\) direction are the following:  
\[D_{l}^{efx} =\sum_{i=0}^{7}EI_{s}^{HD}=3.019\cdot 10^{9}\,\mathrm{N}\, \mathrm{m}^{2} \tag{67}\] \[D_{0}^{efx} =\sum_{i=0}^{7}EA_{c,i}^{HD}\,c_{i}^{2}=9.589\cdot 10^{12}\, \mathrm{N}\,\mathrm{m}^{2}\] (68) \[S_{b}^{ifx} =\sum_{i=0}^{7}\frac{12\,EI_{s}^{IPE360}}{l_{i}\,h}=1.632\cdot 10^{ 8}\,\mathrm{N}.\] (69) \[S_{c}^{ifx} =\sum_{i=0}^{7}\frac{12\,EI_{s}^{HD}}{h^{2}}=2.382\cdot 10^{9}\, \mathrm{N}\] (70) \[S^{ifx} =\left(\left(S_{b}^{ifx}\right)^{-1}+\left(S_{c}^{ifx}\right)^{- 1}\right)^{-1}=1.632\cdot 10^{8}\,\mathrm{N}\] (71) \[S^{t} =\frac{Et_{m}L^{2}A_{d}}{d_{m}^{3}}=1.124\cdot 10^{10}\,\mathrm{N}\] (72) \[S^{efx} =S^{ifx}+S^{t}=1.139\cdot 10^{10}\,\mathrm{N}. \tag{73}\]- External frame in \(y\) direction  
\[D_{l}^{efy} =\sum_{i=0}^{7}EI_{w}^{HD}=1.126\cdot 10^{9}\,\mathrm{N}\, \mathrm{m}^{2} \tag{74}\] \[D_{0}^{efy} =\sum_{i=0}^{7}EA_{c,l}^{HD}\,c_{i}^{2}=9.589\cdot 10^{12}\, \mathrm{N}\,\mathrm{m}^{2}\] (75) \[S_{b}^{ify} =\sum_{i=0}^{7}\frac{12\,EI_{s}^{IPE360}}{l_{i}\,h}=1.632\cdot 10^{8 }\,\mathrm{N}\] (76) \[S_{c}^{ify} =\sum_{i=0}^{7}\frac{12\,EI_{HD}^{HD}}{h^{2}}=8.884\cdot 10^{9}\, \mathrm{N}\] (77) \[S^{ify} =\left(\left(S_{b}^{ify}\right)^{-1}+\left(S_{c}^{ify}\right)^{- 1}\right)^{-1}=1.379\cdot 10^{8}\,\mathrm{N}\] (78) \[S^{t} =\frac{Et_{m}L^{2}A_{d}}{d_{m}^{3}}=1.124\cdot 10^{10}\, \mathrm{N}\] (79) \[S^{efy} =S^{ify}+S^{t}=1.138\cdot 10^{10}\,\mathrm{N}. \tag{80}\]