# Investigations on Interface Shear Fatigue of Semi-Precast Slabs with Lattice Girders
## 2 Lattice Girders for Use in Cyclically Loaded Structures
### Fatigue Design of Semi-Precast Slabs with Lattice Girders in Germany  
In Germany, the design of semi-precast slabs with lattice girders follows the general technical approvals of lattice girders, which are based on the regulations of [28; 29]. The current design concept for monotonic loading, its differences compared to Eurocode 2, and the models that are the basis of the design concept are summarized in [53]. For fatigue, the stress range in the diagonals of the lattice girders needs to comply with a certain limit value. Due to absence of \(S\)-\(N\) curves, for many years, the verification was limited to a simplified verification with an approved characteristic stress range of \(\Delta\sigma_{\text{Rsk}}=92\) N/mm\({}^{2}\) for \(N=2.0\) million load cycles. Based on the research in Section 3, more detailed verifications using an \(S\)-\(N\) curve have recently been proposed. The \(S\)-\(N\) curve and its derivation can be found in Section 3.5. For interface shear design, the fatigue resistance of the lattice girders is derived by using an interface shear equation of [29] (Equation (1)). \[v_{\text{Rdi}}=cf_{\text{ctd}}+\upmu\cdot\sigma_{\text{n}}+\rho\cdot f_{\text {yd}}\cdot(1.2\cdot\upmu\cdot\sin\alpha+\cos\alpha)\leq 0.5\cdot\
u\cdot f_{\text {cd}} \tag{1}\]  
With  
\(v_{\text{Rdi}}\) design (d) shear resistance (R) of interface (i)  
\(c\) coefficient of adhesion  
\(f_{\text{ctd}}\) design value of concrete (c) tensile (t) strength of the weaker concrete layer  
\(\upmu\) coefficient of friction  
\(\sigma_{\text{n}}\) external normal (n) stress perpendicular to the interface acting simultaneously with the shear stress  
\(\rho\) interface reinforcement ratio \(\rho=A_{\text{si}}/A_{\text{i}}\)  
With  
\(A_{\text{si}}\) the area (A) of steel (s) reinforcement cross]sing the interface including shear reinforcement from shear design with sufficient anchorage at both sides of the interface  
\(A_{\text{i}}\) the area of the interface  
\(f_{\text{yd}}\) design yield (y) strength of the interface reinforcement  
\(\upalpha\) inclination of interface reinforcement \(45^{\circ}\leq\alpha\leq 90^{\circ}\)  
\(\upnu\) strength reduction factor for concrete cracked in shear  
\(f_{\text{cd}}\) design concrete cylinder compressive strength. For semi-precast slabs with lattice girders under cyclic loading, the interface shall have at least a rough surface [41; 42]. The roughness can be determined using the sand-patch-test or equivalent methods [29]. Thus, the formulation is modified by considering the coefficients for rough interfaces (\(\upmu=0.7\)[28]), neglecting the term of adhesion for fatigue (\(c=0\)) [29] and the term for friction (\(\upmu\cdot\sigma_{\text{n}}=0\)). Furthermore, the stress range is increased by the term \(1/0.6\). The factor \(0.6\) is based on regulations in DIN 1045 [54], which includes the conservative estimation of a flat angle of compression strut by a reduction factor of \(0.85\) and a correction factor \(0.7\) for the increased fatigue failure potential of the bent bars [55]. Substituting the yield strength of the reinforcement by the approved stress range and the partial fatigue safety factor for steel, as well as considering the inclination of every second angle of the diagonals with \(\alpha_{1}=90^{\circ}\), the verification of the stress range at an interface with lattice girders KTS or EQ follows Equation (2) [41; 42].