# Fatigue Assessment of Prestressed Concrete Slab-Between-Girder Bridges
## 3 Results
### Assessment of the Case Study Bridge for Punching  
First, the capacity of the thin slab for punching was evaluated based on the experimental results. The shear capacity according to NEN-EN 1992-1-1:2005 [3] was calculated:  
\[v_{Rd,c}=C_{Rd,c}k\left(100\rho_{avg}f_{ck}\right)^{1/3}+k_{1}\sigma_{cp}\geq v _{\min}+k_{1}\sigma_{cp} \tag{6}\]  
With  
\[k=1+\sqrt{\frac{200\text{ mm}}{d}}\leq 2 \tag{7}\]  
And  
\[\rho_{avg}=\sqrt{\rho_{l}\times\rho_{l}} \tag{8}\]  
\[\sigma_{cp}=\frac{\sigma_{cx}+\sigma_{cy}}{2} \tag{9}\]  
The recommended value for \(k_{1}=0.1\), for \(C_{Rd,c}=0.18/\gamma_{c}\) with \(\gamma_{c}=1.5\), and for \(v_{\text{min}}\):  
\[v_{\text{min}}=0.035k^{3/2}\sqrt{f_{ck}} \tag{10}\]  
Using the properties in Table 1, we found that \(k=2\) and the punching shear stress capacity of the case study bridge equals:  
\[v_{Rd,c}=\frac{0.18}{1.5}\times 2\times(100\times 0.001388\times 53.3\text{ MPa})^{1/3}+0.1\times 1.25\text{ MPa}=0.572\text{ MPa} \tag{11}\]  
To find the maximum punching force, we calculated the punching perimeter around the 400 mm wheel print as sketched in Figure 8:  
\[u=4\times 400\text{ mm}+2\pi\times 2\times 162\text{ mm}=3636\text{ mm} \tag{12}\]  
For the 230 mm \(\times\) 300 mm wheel print, the punching perimeter length became:  
\[u=2\times(230\text{ mm}+300\text{ mm})+2\pi\times 2\times 162\text{ mm}=3096\text{ mm} \tag{13}\]  
The maximum punching force for these two wheel prints then became:  
\[V_{Rd,c}=0.572\text{ MPa}\times 3636\text{ mm}\times 162\text{ mm}=336.8\text{ kN} \tag{14}\]  
\[k=1+\sqrt{\frac{200\text{ mm}}{d}}\leq 2 \tag{7}\]0  
The load that the deck has to resist is a combination of the concentrated live load and the distributed live load. The axle load of 300 kN results in a whe  
\[k=1+\sqrt{\frac{200\text{ mm}}{d}}\leq 2 \tag{7}\]1 Punching perimeter around the wheel print. distributed lane load was \(1.15\times 9\) kN/m\({}^{2}=10.35\) kN/m\({}^{2}\). The contributions of the self-weight and asphalt were \(25\) kN/m\({}^{3}\times 200\) mm \(=5\) kN/m\({}^{2}\) and \(23\) kN/m\({}^{3}\times 120\) mm \(=2.8\) kN/m\({}^{2}\), respectively. The area over which these loads were considered was the area within the punching perimeter, \(A_{u}=(400\) mm\()^{2}+4\times 162\) mm \(\times 400\) mm \(+\pi(162\) mm/\(2)^{2}=439,812\) mm\({}^{2}=0.4398\) m\({}^{2}\). The corresponding loads for the distributed lane load, self-weight, and asphalt then became 4.55 kN, 2.2 kN, and 1.23 kN, respectively, when the Eurocode wheel print was considered. For the smaller wheel print, the area within the punching perimeter became \(A_{u}=0.2613\) m\({}^{2}\), resulting in loads of 2.7 kN, 1.3 kN, and 0.7 kN, respectively, for the distributed lane load, the self-weight, and the asphalt. The load combination for the assessment of existing bridges in the Netherlands depends on the required safety level, as prescribed by NEN 8700:2011 [42] and the RBK (Richtlijnen Beoordeling Kunstwerken = Guidelines for the Assessment of Existing Bridges) [32]. The highest level was the \"design\" level (associated reliability index \(\beta=4.3\)), which gave the following load combination: \(U=1.25 DL+1.25 DW+1.50 LL\), with \(DL\) being the dead load, \(DW\) the superimposed dead load, and \(LL\) the live load. The resulting factored concentrated load for evaluation then became 236 kN, for the 400 mm \(\times\) 400 mm wheel print, and 232 kN, for the 230 mm \(\times\) 300 mm wheel print. The assessment was carried out based on the Unity Check, where the Unity Check is the ratio of design demand to design capacity. In this case, for punching, the Unity Check was the ratio of the factored concentrated load acting on the wheel print to the design punching shear force capacity. To fulfil the code requirements, the Unity Check has to be smaller than 1. Table 4 gives an overview of the resulting Unity Checks for the different wheel prints that were studied. We observed that assessment of the deck using the Eurocode shows that it already fulfils the code's requirements.