## 4 Parameter Study and Design Buckling Curves  
Design buckling curves are a widely used and user-friendly method for considering the stability behavior of components. For other construction materials, such curves are already integrated into the different parts of the Eurocode (e.g., EN 1993-1-1 for LTB of steel girders). Using design buckling curves also for structural glass components was already proposed by other authors in earlier investigations. A summary can be found among others in [8]. Following this approach, design buckling curves have been calibrated for the here investigated case of cantilever beams, which can be seen as an extension of the previously performed work on this topic. Therefore, the definitions used in the literature and Eurocode 3 were used as well:  
\[ \begin{split}\overline{\lambda}_{\text{LT}}=\sqrt{\frac{\text{W} _{\text{y}}\cdot\overline{\lambda}_{\text{cr}}}{\text{M}_{\text{cr}}}}; \Phi=\frac{1}{2}\left[1+\alpha\left(\overline{\lambda}_{\text{LT}}-\overline {\lambda}_{0}\right)+\overline{\lambda}_{\text{LT}}^{2}\right];\chi_{\text{LT }}=\frac{1}{\Phi+\sqrt{\Phi^{2}-\overline{\lambda}_{\text{LT}}^{2}}}\leq 1.0\\ \text{M}_{\text{b,Rd}}=\chi_{\text{LT}}\text{-W}_{\text{y}} \text{-f}_{\text{d}};\frac{\text{M}_{\text{cr},\text{Fd}}}{\overline{ \text{M}}_{\text{b,Rd}}}\leq 1.0\end{split}  \tag{3}\]  
For laminated safety glass, the critical moment \(\text{M}_{\text{cr}}\) depends strongly on the shear modulus but can be calculated easily by using a FE-software and by performing a linear-buckling analysis (LBA). For practical use, the formulas based on a sandwich-theory appear to be more comfortable and faster. Such equations can be found among others in [19]. In doing so, the time-dependent behavior of the PVB-foil can be taken into account by using the corresponding shear-modulus \(\text{G}>0\), which results in a higher stiffness of the cross-section (and therefore lower slenderness) and a higher load-carrying capacity than in the case of a long-term behavior with \(\text{G}\to 0\). The here presented design buckling curves have been determined based on a parameter study by calibrating the imperfection factor \(\alpha\) and the threshold value \(\overline{\lambda}_{0}\). The parameters used for the parameter study are defined in Table 7. All parameters were combined, and a total number of 512 calculations were carried out. The parameters used cover a broad range of systems (relative slenderness \(\overline{\lambda}_{\text{LT}}\) from 0.4 to 2.8). Values not included in the used parameter range seemed to be unrealistic for practical usage. The following criteria were defined to determine the ultimate load:  
* The maximum principal stress reaches the characteristic strength \(\text{f}_{\text{k}}\),
* the lateral deflection or the vertical deflection reaches a value of \(\text{L}/50\),
* the rotation reaches a value of 0.3 rad. The defined values were used to guarantee the serviceability for beams with large deformations. The used values are similar to those used in steel constructions for lateral-torsional buckling problems, see [25; 26]. In most cases, the maximum principal stress was reached first. The geometric criteria were achieved in some cases only (especially for FT-glass with higher slenderness). In general, the influence of the geometric criteria was low; therefore, the results derived from excluding the geometric criteria will not be further disclosed. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Parameter Range** \\ \hline Thickness of a single glass pane t in mm & 8/12 \\ \hline Height of the glass beam h in mm & 150/300 \\ \hline Length of the glass beam L in m & 0.5/0.75/1.0/1.25/1.5/2.0/2.5/3.0 \\ \hline Shear modulus G in MPa & 0.05/0.20/0.40/0.80 \\ \hline Load distribution & Single load F at the free end of the beam/Distributed load q over the whole beam length \\ \hline Number of glass panels & 2/3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Used parameters and parameter range.