## 4 Numerical Modelling for Structural Analysis of TEL-Gridshells
### Experimental Results and Comparison with Numerical Analysis  
The experimental displacements of the gridshell prototype points where the targets were placed were easily calculated from the coordinates of these points before and after loading. The average displacement of all nodes was 10.22 mm. The displacement vectors of the target points in the different numerical models were also obtained. Comparison of the experimental and numerical displacement values for the 145 measured points is shown in Table 6. The first row shows the sum of the displacements in absolute value for all nodes, \(\Sigma\,\mathrm{|\,U\,|}\). It provides an overview of the deformability of the structure. The second row presents the ratio of the above parameter for each numerical model in relation to the experimental one, \(\Sigma\,\mathrm{|\,U\,|}_{\mathrm{num}}/\Sigma\,\mathrm{|\,U\,|}_{\mathrm{exp}}\). The third row gives the value of the mean displacement at each point, \(\mathrm{|\,U\,|}_{\mathrm{mean}}\). The following five rows show the displacements corresponding to the control points A-E presented in Table 2. The last rows show the deviation of the numerical results with respect to the experimental ones, providing the absolute difference between the experimental and numerical displacement vectors, \(\mathrm{|\,U_{\mathrm{exp}}-U_{\mathrm{num}}\,|}\), and the angle (in absolute value) formed by their directions. As can be observed from Table 6, the C5 model, which incorporates the LVL supports and semi-rigidity in all joints, gives the best results. For this model, the calculated gridshell deformation shows reasonable agreement with the experimental values. The mean displacements are in the same range as the actual ones with a mean error of 1.85 mm and a standard deviation of 1.6 mm. This numerical error is very close to the mean error of the experimental measurement (1.63 mm, see Section 3.6), so better fittings of the numerical model are difficult to quantify. Figure 11 shows the final global deformations of the C5 model. For easier comparison with the experimental results, the three transverse lat  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Without LVL Supports (S-Models)**} & \multicolumn{6}{c}{**With LVL Supports (C-Models)**} \\ \cline{2-11}  & **Exp. ** & **S1** & **S2** & **S3** & **S4** & **S5** & **C1** & **C2** & **C3** & **C4** & **C5** \\ \hline \(\Sigma\,\mathrm{|\,U\,|}\) (mm) & 1481.90 & 189.9 & 292.7 & 296.9 & 401.2 &  
As can be seen, the deformations at the load application points resulted greater in the experimental test than in the numerical model. Although the maximum experimental displacement in this area was 13.8 mm (14.6 mm from LVDT measurement), which is below the maximum value corresponding to SLS (L/300 = 21.7 mm), the stress in the joints may exceed their service range due to the application of heavy concentred loads. This could lead to local effects not considered in the model, such as non-linearity phenomena in the slip of the joints. To improve the model fitting in this respect, experimental studies of the joints would be necessary to determine their stiffness over the entire load range and to implement non-linear laws for the behaviour of the springs. It should be noted that the greatest displacements of the structure do not occur in the load application points, but in the lower part of the transverse laths, which close inwards when the vertical loads are applied. This behaviour highlights the lack of stiffness of the structure in this area, and points to the need for design modifications. Numerical simulations carried out by the authors have shown that an increase in the cross-sections of the longitudinal laths had practically no influence in this respect [11]. To increase the gridshell stiffness in that area, it is necessary to have an edge beam of large cross-section or to increase the moment of inertia of the  
Figure 11: Model C5.