# Fatigue Assessment of Prestressed Concrete Slab-Between-Girder Bridges
## 3 Results
### Assessment of the Case Study Bridge for Punching
In the introduction, we stated that there was discussion about the punching capacity of the decks in the existing slab-between-girder bridges. The reason why this assessment showed that the deck met the code requirements was the higher punching capacity established based on the results of the drilled cores. In a next step of the assessment, the maximum loads obtained in the static tests were applied to the assessment of the Van Brienenoord Bridge. When assessing the bridge based on the results of the experiments, we could replace the design capacity according to the Eurocode \(V_{R,c}\), using the capacity obtained in the tests. To translate the capacity obtained in the test to a representative design capacity of the case study bridge, we had to consider the following (see Annex D of NEN-EN 1990:2002 [43]):  
* The laboratory setup was a 1:2 scale of the case study bridge, resulting in a factor \(2^{2}\);
* Considering scaling laws, a scale factor of 1.2 [13] had to be included in the capacity;
* The partial factor derived from the experiments \(\gamma_{T}\) had to be included. First, we derived the partial factor from the experiments \(\gamma_{T}\). To calculate this factor, we compared the punching capacity obtained in the static experiments with the average punching stress capacity \(v_{R,c}\) according to NEN-EN 1992-1-1:2005 [3]. The expression for \(v_{R,c}\) was given in the background report of Eurocode 2 [44] as follows:  
\[k=1+\sqrt{\frac{200\text{ mm}}{d}}\leq 2 \tag{7}\]2  
To find the punching shear capacity \(V_{R,c}\), the stress \(v_{R,c}\) was then multiplied with \(u\times d\), where \(u\) was determined as shown in Figure 8, for the considered wheel print. Table 5 combines the experimental results \(V_{exp}\) and the predicted capacities \(V_{R,c}\), as well as the ratio of the tested to predicted capacity \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wheel Print** & \(V_{Ed}\) **(kN)** & \(V_{R,c}\) **(kN)** & **Unity Check** \\ \hline
400 mm \(\times\) 400 mm & 236 & 337 & 0.70 \\
230 mm \(\times\) 300 mm & 232 & 287 & 0.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Overview of the resulting Unity Checks according to the Eurocode. \(V_{exp}/V_{R,c}\). The average value of \(V_{exp}/V_{R,c}\) was 2.61, with a standard deviation of 0.296 and a coefficient of variation of 11%. This information led to the derivation of \(\gamma_{T}\) as determined in Annex C of NEN-EN 1990:2002 [43]:  
\[\gamma_{T}=\frac{\mu}{B_{Rd}} \tag{17}\]  
With  
\[B_{Rd}=\mu(1-\alpha\times\beta\times COV)=2.61(1-0.8\times 4.3\times 0.11)=1.622 \tag{18}\]  
where \(\alpha=0.8\) is the factor for considering the experimental results, and \(\beta\) is the target reliability index. The value for \(\gamma_{T}\) then becomes:  
\[\gamma_{T}=\frac{\mu}{B_{Rd}}=\frac{2.61}{1.622}=1.61 \tag{19}\]  
As for the influence of the difference in scale between the test setup in the laboratory and the case study bridge, the experimental result \(V_{exp}\) could be scaled to the capacity of the bridge \(V_{BB}\) as follows:  
\[V_{BB}=V_{exp}\times\frac{2^{2}}{1.2} \tag{20}\]  
where the factor \(2^{2}\) corrects for the 1:2 scale, and 1.2 is the scaling factor. The design capacity based on the test results is then:  
\[V_{BB,d}=\frac{V_{BB}}{\gamma_{T}} \tag{21}\]  
Table 6 shows the results for the \(V_{BB}\) according to Equation (20) and \(V_{BB,d}\) according to Equation (21), as well as the demand \(V_{Ed}\) that corresponds to the wheel print in the experiment under consideration (see Table 4). The average value of \(V_{BB,d}/V_{Ed}=3.06\), which meant that the margin of safety was 3.23, or that the Unity Check was the inverse, \(UC=0.33\). When comparing this value based on the experiments to the values in Table 4, we observed the beneficial effect of compressive membrane action on the capacity of the thin, transversely prestressed concrete slabs.