# Fatigue Assessment of Prestressed Concrete Slab-Between-Girder Bridges
## 3 Results
### Assessment of Case Study Bridge for Fatigue  
The results of the experiments and the developed Wohler curve could be interpreted for the assessment of fatigue. Given the geometry of the deck (see Figure 1), only two wheels (one of each axle) out of the four wheels of the tandem could act together on the deck. The clear span was 2.1 m whilst the width of the design tandem was 2.4 m in total, and 2.0 m center-to-center. For the interpretation of the test results, this meant that the outcome of the tests with a double wheel print (Wohler curve in Figure 7b) should be evaluated for the case study bridge over 250 million cycles, and that the outcome of the tests with a single wheel print (Wohler curve in Figure 7b) should be evaluated for the case study bridge over \(2\times 250\) million cycles = 500 million cycles. To use the Wohler curves derived in the experiments for the assessment of the Van Brienenoord Bridge for fatigue, we scaled the fatigue load model to the 1:2 size of the test setup. Note that this approach differed from the assessment for punching, where we scaled up the capacity from the laboratory setup to the capacity of the case study bridge. Here, we used the opposite approach to avoid having to change the Wohler curve. The concentrated load of the fatigue load model was 105 kN. Scaling this load down to the 1:2 scale model, we used a factor \(2^{2}=4\), so that the concentrated load became 26.25 kN. The distributed lane load of the fatigue load model was 3.105 kN/m\({}^{2}\). For the 1:2 scale model, the distributed lane load became 0.776 kN/m\({}^{2}\). In the 1:2 scale model, only the concentrated loads were used, so the load that represented the concentrated load, as well as the distributed lane load, should be determined. To determine the region over which the distributed lane load should be considered, the cracking patterns in the experiments were studied. The cracking pattern extended over 1.2 m for the experiments with a single wheel load, and over 2 m for the experiments with a double wheel load. To find the equivalent point load, we first determined the bending moment caused by the distributed load, considering that the slab spanned over 1.8 m:  
\[M_{dist,1 whel}=\frac{1}{8}\big{(}0.776\ \frac{\mathrm{kN}}{\mathrm{m}^{2}} \times 1.2\ \mathrm{m}\big{)}\big{(}1.8\ \mathrm{m}\big{)}^{2}=0.38\ \mathrm{kNm} \tag{22}\]  
\[M_{dist,2 zehel}=\frac{1}{8}\big{(}0.776\ \frac{\mathrm{kN}}{\mathrm{m}^{2}} \times 2\ \mathrm{m}\big{)}\big{(}1.8\ \mathrm{m}\big{)}^{2}=0.63\ \mathrm{kNm} \tag{23}\]  
The equivalent concentrated load was then:  
\[F_{\alpha}=\frac{4M_{dist}}{l_{span}} \tag{24}\]  
which resulted in \(F_{\alpha}=0.83\) kN for a single wheel load, and \(F_{\alpha}=1.40\) kN for a double wheel load. Then, the total load was \(F=27.08\) kN for a single wheel load and \(F=27.65\) kN for a double wheel load. The punching shear capacity of setup 2 is given in Table 5 for FAT1S1 or cast 1 of the concrete as 124.4 kN, and for FAT7S1 or cast 2 as 127.4 kN based on the Eurocode punching provisions. Recall that the design value of the enhancement factor was \(B_{Rd}=1.622\). As such, the design capacity of the punching resistance with the punching perimeter around one wheel load, including the enhancing effect of compressive membrane action became \(1.622\times 124.4\) kN = 201.8 kN, for the most critical case (lowest capacity \(V_{Rd,c}\) as a result of the lowest concrete compressive strength). To determine the capacity for punching with the case of a double wheel print, one could expect a double capacity. However, the results in Table 2 show that the capacity in the FAT8S2 was 1.64 times the capacity in FAT7S1. This ratio was used to determine the punching shear capacity. The capacity was now \(1.64\times 201.8\) kN = 331.0 kN. The load ratio could now be determined. For a single wheel load, the load ratio was 27.08 kN/201.8 kN = 0.134, and for a double wheel load, the load ratio was \(2\times 27.65\) kN/331.0 kN = 0.167.