# FRP Bridges in the Flanders Region: Experiences from the C-Bridge Project
## 6 Structural Analysis
### Comparison with Representative Calculation Notes
#### 6.1.2 Double-Sided Clamped Footbridge Mortsel  
The most important results of the calculation are given in Table 3. In the first column, the relevant parameter is addressed; in the second column is its value as given in the calculation note; in the third column is its value as derived using the calculation tool (based on [41]); and in the last column is its value derived using the calculation tool after modification, explained hereafter.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Calculation Note** & **Calculation Tool** & **Calculation Tool (Modified)** \\ \hline \multicolumn{4}{c}{_General features_} \\ \hline Total mass, Mbridge, tot [kg] & 8210 & 8221 & 8221 \\ Bending stiffness, FIX [M\(\mathrm{N}\mathrm{m}^{2}\)] & 135 & 137 & 137 \\ Shear stiffness, GAAX [MN] & 250 & 249 & 249 \\ \hline \multicolumn{4}{c}{_Checks SLS_} \\ \hline Natural frequency, unloaded, f0, unload, lt [Hz] & 3.4 & 2.83 & 3.3 \\ Natural frequency, loaded, f0, load, lt [Hz] & 2.9 & 2.44 & 2.9 \\ Deflection distributed load, wLC3, lt [mm] & 158 & 159 & 159 \\ Deflection service vehicle, wLC4, lt [mm] & 38 & 39 & 39 \\ \hline \multicolumn{4}{c}{Checks ULS} \\ \hline Compression upper flange, ox, uf, M [MPa] & 122 & 81 & 119 \\ Tension lower flange, ox, lf, M [MPa] & 122 & 80 & 117 \\ Shear stress web, rxy, w, V [MPa] & 34 & 33 & 37 \\ Compression web, \(\sigma\)y, w, LC5 [MPa] & 33 & 40 & 34 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison between the calculation note and the (modified) calculation tool for the simply supported FRP footbridge in Puurs.  
* The values of bending stiffness and shear stiffness are not identical. In the calculation note, the structure of each of the laminates is specified in detail, from which the laminate properties are determined in the calculation tool based on the CLT. Since all checks are significantly influenced by the laminate structure, its effects should be analysed. The calculation tool initially provides a reasonable approximation of the reported values. However, the laminate structures reported in the calculation note are highly detailed, with different fibre volume fractions in different plies of the same laminate, while only one fibre volume fraction for the entire bridge can be entered into the calculation tool. When the underlying calculation of the tool is adjusted to provide stiffness values based on the specified detailed laminates, better matching values are obtained. The small differences that are still present are likely due to slightly different starting values for the properties of the E-glass fibres and the polyester resin.
* In the calculation note, the natural frequency in unloaded condition is determined from finite element software and deviates considerably from the calculated values from the calculation tool. This is most likely due to the simplified clamped boundary conditions, based on the beam theory, that are used in the calculation tool.
* The values for the deflection as a result of the self-weight are fairly close.
* The deflection due to the uniformly distributed load deviates significantly due to a difference in the applied load. In the calculation tool, a combination value of one is used on the live load, whereas in the calculation note, this is 0.35.  
After correction for the causes mentioned above, which are essentially not related to the design method, a modified calculation is performed with the calculation tool. The results indicate that in all cases, the differences can mostly be eliminated by this modification, although the results remain influenced by the laminate stiffness values. As such, the method from [41] is in accordance with the calculation note except for the first natural frequency as a result of the simplification of the boundary conditions.