## 4 Experimental Test Results
### Life Estimation of Fatigue of GFRP-Reinforced Precast FDDP  
A realistic representation of the service loads is usually variable amplitude, which should consider the accurate measure of the applied load on the existing structure and predict loads on the structure that do not exist yet. Loads can be obtained from real-life histories or through simplified segmental loading. The fatigue cycle counting method compares the effect of the variable amplitude fatigue load histories to the fatigue data and curves obtained with the simple constant amplitude fatigue loading cycles. Applying the linear damage rule where cumulative linear damage, \(D=1.0\) requires the knowledge of the mean and amplitude of the load to which the damaging event is compared. One approach to the variable load histories is the concept of the damage, known as fraction life or cycle ratio. These fractions are added together with the sum of 1.0 as defined in Equation (1) by the linear damage rule as proposed by [PERSON] (2009) and later again by [PERSON] (2010). \[D=\sum\frac{n_{i}}{N_{fi}}=1 \tag{1}\]  
where \(n\) is the number of cycles and \(N_{f}\) is the number of repetitions of the same cycle that equals life to failure. The damaging effect of \(n_{1}\) cycles at \(P_{1}\) load amplitude is assumed to be \(n_{1}D_{1}=n_{1}/N_{f1}\), while the damaging effect of \(n_{2}\) cycles at \(P_{2}\) load amplitude is assumed \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Joint Type**} & \multicolumn{4}{c}{**Slab S1 with CAF Loading \({}^{*}\)**} & \multicolumn{4}{c}{**Slab S2 with VAF Loading \({}^{*}\)**} \\ \cline{2-10}  & **Cumulative** & **Load** & **Deflection** & **k = F/d \({}^{**}\) & **Cumulative** & **Load** & **Deflection** & **k = F/d \({}^{**}\) \\  & **Cycles (N)** & **(kN)** & **(mm)** & **k = F/d \({}^{**}\)** & **Cycles, N** & **(kN)** & **(mm)** & **k = F/d \({}^{**}\)** \\ \hline \hline \multicolumn{10}{c}{Slab S5 with CAF loading \({}^{*}\)} \\ \hline
0 & 184.55 & 1.78 & 103.68 & 100,000 & 183.74 & 3.12 & 58.89 \\ \hline
500,000 & 183.76 & 1.99 & 92.34 & 200,000 & 183.76 & 3.2 & 57.42 \\ \hline
1,000,000 & 183.75 & 2.07 & 88.77 & 300,000 & 183.76 & 3.5 & 52.5 \\ \hline
1,250,000 & 183.75 & 2.09 & 87.92 & 400,000 & 183.75 & 4.55 & 40.38 \\ \hline
1,500,000 & 183.76 & 2.06 & 89.2 & 500,000 & 183.76 & 6.19 & 29.68 \\ \hline
1,750,000 & 183.75 & 2.14 & 85.86 & 600,000 & 183.75 & 7.64 & 24.05 \\ \hline
2,000,000 & 183.77 & 2.14 & 85.87 & 700,000 & 183.75 & 8.77 & 20.95 \\ \hline
2,250,000 & 183.75 & 2.15 & 85.46 & 800,000 & 183.83 & 10.88 & 16.89 \\ \hline
2,500,000 & 183.75 & 2.17 & 84.68 & 895,000 & \({}^{**}\) & & & \\ \hline
2,750,000 & 183.75 & 2.18 & 84.29 & 916,736 & \({}^{**}\) & & & \\ \hline
3,000,000 & 183.75 & 2.71 & 67.80 & & & & \\ \hline
3,250,000 & 183.75 & 2.77 & 66.33 & & & & \\ \hline
3,500,000 & 183.76 & 2.77 & 66.34 & & & & \\ \hline
3,750,000 & 183.76 & 2.76 & 66.58 & & & & \\ \hline
4,000,000 & 183.76 & 2.74 & 67.06 & & & & \\ \hline \hline \end{tabular} \({}^{*}\) CAF = constant amplitude fatigue loading; VAF = variable amplitude fatigue load. \({}^{**}\) k is the spring constant in kN per mm, F is the ultimate load in kN, and d is the deflection in mm.  
\end{table} 
Table 6: _Cont._to be \(n_{2}D_{2}=n_{2}/N_{f2}\). Similarly, the cycle ratio or damage caused by \(n_{i}\) cycles at \(P_{i}\) load amplitude is \(n_{i}D_{i}=n_{i}/N_{fi}\). Failure is predicted when the sum of all ratios becomes 1 or 100%. The assumption of the linear damage depends on the rate of damage accumulation and load amplitude, which leads to \(n_{i}/N_{fi}\
eq 1\) for a low-to-high or a high-to-low loading sequence. Miner's Rule does not account for overload or high stress, which may occur in compressive residual stress that leads to retarding of the crack growth. High-to-low stresses may have less damage due to compressive residual stress. However, it is widely used for simplicity and hardly to achieve better agreement with the current experimental data.