## 4 Analysis of Relevant Influencing Parameters  
### Stiffness Contribution of Point-Fixings  
The actual stiffness contribution of the joints in use was first assessed, with the support of FE numerical models (ABAQUS). In Figure 12, the reference numerical model is shown, being representative of the nominal geometry for a connection detail. A small portion of glass (\(0.14\times 0.14\) m) was also taken into account to reproduce the actual joint region and interactions. In doing so, a set of three-dimensional (3D) solid brick elements was used to describe the steel restraint (C3D8R type from ABAQUS element library). The mesh size and pattern was chosen to ensure a refined description of the examined system, with 3300 solid elements for the steel joint and the portion of LG plate. The mechanical interaction between the steel connector and the LG portion was accounted in the form of a _penalty & normal behaviour_ surface-to-surface contact algorithm (ABAQUS library), so as to allow for possible relative sliding between the steel and glass components in the region of glass hole, but also the possible separation under tensile loads. Rigid nodal restraints were applied at the bottom face of the steel connector. At the same time, the LG plate was restrained in its thickness and width (end section), so as to avoid possible rotations, being a part of a full beam in bending about the minor axis. A preliminary static nonlinear analysis was carried out to estimate the expected stiffness contributions under the assumption that the so assembled FE model can be representative of the actual end region for one of the tested specimens. Based on Figure 12, the bending performance of the small scale FE model was, in fact, explored by imposing a linearly increasing bending moment \(M_{z}\) at the top face of the steel point-fixing (via a reference RP node, and hence distributed on the full surface of steel with a \"_coupling_\" constraint). Hence, the longitudinal (i.e., \(x\) direction) and vertical (i.e., \(y\) direction) displacements of four selected control points were monitored, so that the corresponding elastic stiffnesses (both rotational and  
Figure 11: Experimental and analytical frequency estimates for the examined LG specimens, grouped by \(L_{0}\), with (S-S) or (b) clamped (C-C) configurations. translational/axial) could be properly calculated. Two of these control points, see Figure 12, were set at the edges of the hole, to monitor the bending rotation of the portion of LG plate, with respect to the steel connector. Globally, the translational stiffness \(K_{s}\) was found to be relatively high, hence justifying the assumption of an ideal rigid joint for comparative purposes (i.e., \(K_{s}=\infty\)). Given the reference system of Figure 12, otherwise the rotational stiffness was estimated in \(K_{r}\approx 150\) kN m/rad. The so-calculated stiffness was first used form some preliminary FE calculations, carried out in ABAQUS with the support of Equation (3), to explore the sensitivity to \(K_{r}\) of the experimentally predicted frequencies. In Figure 13a, comparative estimates are shown for selected LG specimens. Frequency estimates are also proposed for the limit configurations of C-C and S-S beams. In general, it is possible to notice that \"ideal\" analytical calculations tend to result in marked percentage scatter, with respect to on-site experiments (Figure 13b). For the S-S calculations, the FE predictions resulted in a mean \(\Delta=-29\%\), as compared to the test data (with \(\Delta_{\text{min}}=-14\%\), \(\Delta_{\text{max}}=-40\%\), Dev.St = \(\pm 7\)). Given that the S-S boundary fully disregards the rotational role of the point-fixings in use, such an assumption is generally expected to severely underestimate the actual bending stiffness of a given composite system, thus the corresponding frequency.