# Investigations on Interface Shear Fatigue of Semi-Precast Slabs with Lattice Girders
## 4 Fatigue Tests on Semi-Precast Slabs with Lattice Girders
### Test Evaluation and Comparison to Design Regulations  
To assess the interface shear concepts of the general technical approval of the lattice girders for fatigue, the conducted fatigue tests and the fatigue tests from literature (see Section 2.2) were evaluated by the calculated stress ranges in the lattice girders. For the 47 fatigue tests, the calculated characteristic stress ranges \(\Delta\sigma_{\text{test,Rki}}\) were related to the approved stress range according to the technical approvals \(\Delta\sigma_{\text{Rsk}}=92\) N/mm\({}^{2}\) and plotted over the achieved number of load cycles (Figure 20a-c). Even though the design is limited to \(N=2.0\) million load cycles, all tests were related to the approved stress range of \(\Delta\sigma_{\text{Rsk}}=92\) N/mm\({}^{2}\). Specimens with divergent failure modes, e.g., anchorage failure of lattice girders or longitudinal reinforcement, were excluded. To determine the calculated stress range, the applied shear stress ranges \(\Delta\
u=\beta\cdot\Delta\
u/(b_{1}\cdot z)\) were calculated in accordance with [28] (Equation (6.24), Chapter 6.2.5) with \(\beta=1.0\) and the applied shear ranges \(\Delta V\). The applied shear stress range was then implemented in the interface shear design expression according to [28] (Equation (6.25), Chapter 6.2.5), Equation (1) taken from [29] (Equation (6.25), Chapter 6.2.5) and Equation (2) taken from the technical approvals (TA) of the lattice girders ([41,42], Equation (1), Chapter 3.2.3.5), without partial safety factors.  
Relating to the simplified verification with \(\Delta\sigma_{\text{Rsk}}=92\) N/mm\({}^{2}\), the expression of the TA (Figure 20c) gives the best accordance to the test data. The expression according to [28] (Figure 20a), which allows a 50% consideration of the adhesive term for fatigue, and the expression according to [29] (Figure 20b), which neglects the term of adhesion for fatigue and increases the resistance of the interface reinforcement by the factor 1.2, show a similar trend level. The [28] approach, however, gives a larger range of scatter, especially for large numbers of load cycles, whereas [29] shows a small decrease of scatter for large numbers of load cycles.  
Figure 20: Evaluation of calculated stress ranges for the design of lattice girders as interface reinforcement [53]: simplified verification according to EC2:2011 (**a**), EC2+NA(D) (**b**) and technical approvals (**c**) and verification using the \(S\)-\(N\) curve (**d**).  
The verification of the \(S\)-\(N\) curve for lattice girders, which has been included in the latest revision of the technical approvals (see Section 3.5), is illustrated in Figure 20d. Therefore, the approved characteristic stress ranges were calculated depending on the reached number of load cycles for each test. Figure 20d shows the calculated stress ranges in the lattice girders according to the regulations in the TA related to the approved stress ranges. Compared to the evaluation with an approved stress range of \(\Delta\sigma_{\text{Rk}}=92\) N/mm\({}^{2}\) (Figure 20c), the evaluation with the \(S\)-\(N\) curve gives a better agreement, especially for \(N\leq 2.0\) million load cycles. For \(N>2.0\) million load cycles, the \(S\)-\(N\) curve gives smaller allowable stress ranges, which lead to slightly higher related stress ranges in the lattice girders. However, with the \(S\)-\(N\) curve, the range of application for fatigue design of lattice girders can be extended to a reliable verification allowing \(N>2.0\) million load cycles.