## 4 Numerical Modelling for Structural Analysis of TEL-Gridshells
### Experimental Results and Comparison with Numerical Analysis
Undeformed geometry in lines and deformed geometry in coloured sections for point loads of 1.04 kN (amplification factor = 10). Figure 12: Experimental and numerical (model C5) deformation results of the three transverse laths of the TEL-gridshell (amplification factor = 10). transverse laths. The latter solution was used in a first permanent TEL-gridshell structure designed by the authors, in which double transverse laths were arranged (Figures 2 and 13). Analysing each of the different aspects involved in stiffness separately, it is observed that the addition of the LVL supports in the model is the most important to properly simulate the stiffness of the structure. The S5 model, without LVL supports but with slip at all joints, showed an average displacement much lower than that of any other model including LVL supports, even lower than that of the C1 model with all rigid joints. In particular, when comparing the S5 model with its counterpart C5 with supports, the mean displacement of the latter was more than three times higher than that of the former. Likewise, the assumption of semi-rigidity at the nodal joints and supports in the model is of relevant importance to adjust the stiffness of the structure. As can be seen in Table 6, the gridshell with LVL supports and semirigid _Type 1_ and _Type 2_ joints (C4 model) had a 40% higher \(\,\mathrm{I}\,\mathrm{U}\,\mathrm{l}\,\mathrm{mean}\) than the same structure with all rigid joints (C1 model). In short, similar to what happens in arches where their behaviour is strongly dependent on the stiffness of their supports, the gridshell under study requires the most accurate modelling possible of both the supporting structural elements and the connections of the laths resting on them. From a design point of view, it is a priority to provide the lateral supports and their connections with the maximum possible stiffness in order to minimise the deformations of the structure. The relative influence of considering the stiffness of the mechanical laminate joints in the transverse laths (joint _Type 3_) can be analysed by comparing models C1, C2 and C3. As can be observed, the semi-rigidity of the nodal joints (C2) increases the displacement values more significantly than the consideration of semi-rigidity in the transverse laths (C3). The latter is the least influential variable on the overall stiffness of the prototype. Similar conclusions from a qualitative point of view are obtained by analysing models without the LVL supports, which are ultimately equivalent to structures with rigid supports. A parameterised study of all geometric and stiffness variables would be necessary to generalise these statements for TEL-gridshells. In order to have an approximation of the stress level reached in the prototype members due to the external load alone, the stresses obtained numerically are also analysed. The stresses have not been verified with any experimental procedure, but since the deformation obtained with model C5 provides a reasonable agreement with the experimental deformation, it is reasonable to think that the stresses obtained with this model also offer an adequate approximation. Table 7 summarises the maximum values of axial forces (N), weak/strong axis bending moment (M\({}_{y}\) and M\({}_{z}\), respectively), torsion moment (M\({}_{t}\)), and weak/strong axis shear  
Figure 13: Detail of the double transverse laths of the first permanent TEL-gridshell. force (V\({}_{\rm y}\) and V\({}_{\rm z}\)) obtained with model C5. The results using model C1 (with all rigid connections) are also shown to better understand the influence of the joint stiffness on the stresses of the members. As can be seen, in the model without slip at the joints (C1), the bending stresses due to M\({}_{\rm y}\) and M\({}_{\rm z}\) are 90% and 65% of the model with slip (C5), respectively. In contrast, the axial stresses are approximately 13% higher.