## 3 Results
### Experimental and Numerical Obtained Loads  
The experimentally and numerically obtained load-deflection curves for \(\mathrm{h}=150\) mm and \(\mathrm{h}=300\) mm are shown in Figures 6 and 7, respectively. In most cases, a good match can be observed. Some tests behave stiffer than the simulation, something probably due to the stiffer foil.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Specim** & **F\({}_{\mathrm{exp}}\) [kN]** & **f\({}_{\mathrm{exp}}\) [MPa]** \\ \hline FT\_150\_6 & 12.15 & 169 \\ FT\_150\_7 & 12.12 & 169 \\ \hline HS\_150\_4 & 7.33 & 95 \\ HS\_150\_5 & 7.29 & 95 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Estimation of the actual glass strength.  
Figure 5: Exemplarily some results from the numerical simulations: (**a**) Lateral displacements v (mm, in \(y\)-direction), (**b**) maximum principal stress (MPa).  
Figure 6: Experimental and numerical load-deflection curves (values obtained at the free end of the cantilever beam) from test specimens with a glass-height of 150 mm.  
The differences between test and simulation for specimen HS_300_3 result from a relatively large offset of one of the glass panes. Due to the offset, the load acted eccentric and the load-deflection curve, as well as the whole system, behaved less stiff. Test specimen HS_300_3 was the only one with a larger offset of the glass panes. To avoid such problems, a bearing arrangement with mortar-interlayer represents a good alternative.  
Irregularities are present in some of the load-displacement curves, which are due to the unavoidable friction, for example between the trolley and the rail. Nevertheless, all curves show a clear tendency. After the breakage of all glass panes, none of the glass beams showed any residual capacity (see Figure 2b).  
For comparison, the experimental and numerical obtained ultimate loads are summarized in Table 5 (for FT) and Table 6 (for HS). In addition, Figure 8 shows a comparison of these values. It can be seen that with a conservative assumption of the imperfections and the shear-modulus, the ultimate load can be well approximated. The range of the ultimate loads from conservative to non-conservative assumptions is small; hence, the conservative obtained values are still economical.  
Figure 7: Experimental and numerical load-deflection curves (values obtained at the free end of the cantilever beam) from test specimens with a glass-height of 300 mm.  
Based on the obtained results, a lateral imperfection \(\
u(x)\) according to Equation (2) with an amplitude of \(\
u_{0}=L/400\) and an unfavorable rotational imperfection of \(\phi_{0}=0.01\) rad has been used in the following parameter study. The value of \(\
u_{0}=L/400\) was also obtained by other authors (see [8]) and could be confirmed here (see Table 2).  
\[\
u(x)=\pi\cdot\
u_{0}\cdot\left[1-\cos\left(\frac{\pi\cdot x}{2\cdot L}\right)\right] \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Specim** & \begin{tabular}{c} **Load Duration** \\ **[s]** \\ \end{tabular} & **Experiment [kN]** & \
\begin{tabular}{c} **FEM in [kN] for** \\ \(\sigma_{\text{max}}\)\(\
eq\)70 MPa 1,2 \\ \end{tabular} &
\begin{tabular}{c} **FEM in [kN] for** \\ \(\sigma_{\text{max}}\)\(=\)95 MPa 1,2 \\ \end{tabular} \\ \hline HS\_150\_1 & 737 & 6.25 & 4.69/4.69 & 6.39/6.40 \\ HS\_150\_2 & 870 & 8.09 & 4.70/4.68 & 6.36/6.41 \\ HS\_150\_3 & 1170 & 6.14 & 4.79/4.78 & 6.53/6.53 \\ \hline HS\_300\_1 & 913 & 18.39 & 17.31/18.03 & 18.63/20.76 \\ HS\_300\_2 & 925 & 17.88 & 17.76/18.40 & 19.06/21.26 \\ HS\_300\_3 & 1214 & 17.63 & 17.45/18.04 & 18.78/20.93 \\ \hline \hline \end{tabular} \({}^{1}\) Calculated loads when the maximum principal stress reached \(\sigma_{\text{max}}\). \({}^{2}\) First value calculated with \(G_{\text{min}}\) and second value with \(G_{\text{mean}}\).  
\end{table}
Table 6: Comparison of ultimate loads from experiments and numerical simulations for HS-glass.  
Figure 8: Comparison of the ultimate loads.