# Structural Behavior of Large-Scale I-Beams with Combined Textile and CFRP Reinforcement
## 5 Discussion
### Failure of Compression Strut  
The design of beam FT02 indicated that compression failure of the web might be governing at \(\cot(\theta)=1\) with a compressive stress resistance of \(v_{\text{Rm,max}}=0.6\cdot(1-100/250)\cdot 100=36\) MPa. At failure, crack angles between 39.1\({}^{\circ}\) (\(\cot(\theta)=1.23\)) and 43.7\({}^{\circ}\) (\(\cot(\theta)=1.05\)) were observed (Figure 9, right). The results of FE calculations in Figure 14 (bottom) show that in the last compressive field near the support the principal compressive stress trajectories are inclined with 44\({}^{\circ}\) to 45.4\({}^{\circ}\) (\(\cot(\theta)\approx 1\)) at the level of experimental peak load. Compressive stresses in this region range from 19 to 37 MPa. This corresponds well with the assumptions in design. At lower load levels and towards mid-span, the angle of the compressive field is smaller, with 30.3\({}^{\circ}\) (\(\cot(\theta)=1.71\)) (Figure 14 (center)). The model shows a redistribution of different compressive struts and the change of crack inclination throughout the test, which was also observed in the experiments (Figure 12). With experimentally determined maximum shear force and the angle of compressive field from FE-results, reverse calculation of compressive stresses in the concrete struts at failure (\(\sigma_{\text{c,strut}}=\
u_{1}\cdot f_{\text{cm}}\)) is possible (shown in (1)). As marked in Figure 11, the load from one of the five hydraulic cylinders acted within distance \(d\) from the support and was transferred directly to the support. Thus, it was not considered for ultimate shear load in the section of compressive failure of the web. \[V_{Rm,max}=\frac{b_{w}\cdot z\cdot\sigma_{c,strut}}{(\cot\theta+\tan\theta)} \Rightarrow\frac{4}{10}\cdot 1.469\;MN=\frac{0.05\cdot 0.9\cdot 0.832\cdot v_{1} \cdot 100}{(1+1/1)}\iff v_{1}=0.31 \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Experiment**} & \multicolumn{3}{c}{**Spreadsheet**} & \multicolumn{2}{c}{**ABAQUS**} \\ \cline{2-9}  & \(M_{\text{us,exp}}\) & \(F_{\text{exp}}\) & **Strain** & \(F_{\text{calc}}\) & **Strain** & \(F_{\text{calc}}\) & **Strain** \\ \hline
**No.** & **[kNm]** & **[kN]** & **[\%]** & **[kN]** & **[\%]** & **[kN]** & **[\%]** \\ \hline FT01 & 600.23 & 686.0 & \(\frac{\epsilon_{\text{FFP}}=8.96\;^{\star}}{\epsilon_{\text{c}}=1.73\;^{ \dagger}}\) & 696.9 & \(\frac{\epsilon_{\text{FFP}}=11.04}{\epsilon_{\text{c}}=1.71}\) & 631.3 & \(\frac{\epsilon_{\text{FFP}}=1.81}{\epsilon_{\text{c}}=1.81}\) \\ \hline FT02 & 1284.93 & 1468.5 & \(\frac{\epsilon_{\text{FFP}}=6.74\;^{\star}}{\epsilon_{\text{c}}=2.66\;^{ \dagger}}\) & 1534.2 & \(\frac{\epsilon_{\text{FFP}}=7.89}{\epsilon_{\text{c}}=2.67}\) & 1533.0 & \(\frac{\epsilon_{\text{FFP}}=9.06}{\epsilon_{\text{c}}=2.67}\) & 1533.0 & \(\frac{\epsilon_{\text{FFP}}=9.06}{\epsilon_{\text{c}}=2.67}\) & 14150 kN: \(\epsilon_{\text{c}}=3.18\) \\ \hline FT03 & 316.6 & 361.8 & \(\frac{\epsilon_{\text{FFP}}=5.81\;^{\star}}{\epsilon_{\text{c}}=0.92\;^{ \dagger}}\) & - & - & - & - \\ \hline \hline \end{tabular} \({}^{\star}\) only strain gauges considered which were functional at ultimate load. \({}^{\dagger}\) strain gauge D9C.  
\end{table} 
Table 5: Comparison of ultimate loads and strains in compression chord and main reinforcement. with: \(z=0.9\cdot d=0.9\cdot 0.832\) m measured at the centroid of all 20 carbon bars in the shear crack after failure. The strength reduction factor \(\
u_{1}=0.6\cdot(1-f_{c}/250)=0.36\) chosen in design is larger than the experimentally determined \(\
u_{1}=0.31\). This additional reduction of concrete strength might be attributed to the dense reinforcement in the web. The artificial discontinuities of the yarns with lower transverse modulus of elasticity compared to concrete lead to out-of-plane stresses due to internal deviation of stress trajectories.