## 4 Analysis of Relevant Influencing Parameters
### Effect of Delaminations
#### 4.3.3 Final Remarks on Practical Analytical Calculations for Design  
In conclusion, some final analytical calculations were carried out, in order to assess--even in the lack of more detailed experimental methods--the actual bonding effect of the PVB foils in use for the tested LG specimens, with respect to practical literature recommendations. Given that the fundamental frequency of the selected LG beams is strictly related to several parameters, the degradation of shear stiffness for the PVB foils in use--as a direct effect of long-term performances--represents another relevant parameter, as also discussed in the previous sections.  
Literature contributions addressing the actual dynamic shear modulus of PVB foils (including both the storage and loss moduli), however, are available for dynamic estimates at different vibration frequencies (i.e., Figure 3), or different temperature scenarios, which can be hardly adapted to specific case-studies. Long-term effects of design loads (up to 50 years) are mostly referred to the relaxation of the storage modulus of PVB (and other common interlayers) under permanent loads only (see for example [23] and others).  
In this regard, Figure 21 collects some analytical estimates for the tested LG beams. Following the research outcomes that are partly summarized in Figure 20, and the real experimental scenarios of Figure 9, three levels of delamination were taken into account, i.e., corresponding to (i) un-delaminated LG beams, or to a MoE degradation up to (ii) 5% and (iii) 15% the nominal value (based also on Equation (13)). In addition, two tentative storage moduli were considered for the PVB foils in use, namely represented by:  
- \(G_{2}\) = 0.50 MPa, as derived from technical data sheets, for PVB foils at 25 \({}^{\circ}\)C and 15 years of time loading (see [52]), and  
- \(G_{2}\) = 0.07 MPa, corresponding to the recommended value for the design of LG elements under permanent, dead loads [23].  
As shown in Figure 21 and Table 3, the best correlation between analytical frequencies and most of the experimental results was obtained in the presence of a relatively weak PVB layer (\(G_{2}\) = 0.07 MPa).  
Besides that, the collected comparisons allow for further emphasizing the key role of multiple input parameters on the reliable assessment of in-service glass structures, and, in particular, the role of restraints (compared to C-C or S-S conditions) and the presence of possible delaminations, which should be properly taken into account.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**Delamination Severity (Equation (13))—E\({}_{d}\)/E**} \\ \cline{2-10}  & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**0.95**} & \multicolumn{2}{c}{**0.85**} \\ \hline
**Restraint** & **C-C** & **K\({}_{r}\)** & **S-S** & **C-C** & **K\({}_{r}\)** & **S-S** & **C-C** & **K\({}_{r}\)** & **S-S** \\ \(G_{2}\) = 0.5 MPa & +40.8 & +35.6 & \(-37.4\) & +32.2 & +30.1 & \(-38.7\) & +38.1 & +27.8 & \(-41.2\) \\ \(G_{2}\) = 0.07 MPa & +20.6 & +17.7 & \(-46.2\) & +17.9 & +15.3 & \(-47.5\) & +15.5 & +10.1 & \(-49.9\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Percentage scatter \(\Delta\) (mean value) of analytical frequency estimates, compared to experimental data.