# Evaluation of the Ultimate Strength of the Ultra-High-Performance Fiber-Reinforced Concrete Beams
## 3 Test Results
### Strain Distribution and Failure Mode of Test Specimens  
Figure 6 shows the tensile flexural reinforcement strain at the center of the beam with a shear span to depth ratio of 3.4. All of the above-mentioned flexural failure type specimens experienced yielding of the flexural reinforcement, and shear failure type specimens showed the elimination of stress in the flexural reinforcement after experiencing maximum strength. The test specimens with a shear span to depth ratio of 2.0 were a shear failure due to the diagonal shear crack width expansion, as shown in Figure 5. However, as a result of examining the flexural reinforcement strain, the flexural reinforcement of the specimen H-0-F-2.0 was yielded, as shown in Figure 6.  
The measurement results for the deformation state of the diagonal cracks shown in Figure 7. When the cracks occurred by the naked eye, the diagonal cracks' occurrence time was tracked. These results are summarized in Table 6.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Specimens**} & \(\theta_{y}\) & \(M_{y}\) & \(\theta_{max}\) & \(M_{max}\) \\  & (mm/mm) & (kNm) & (mm/mm) & (kNm) \\ \hline U-S-F-6.6 & 0.01272 & 319.3 & 0.01488 & 331.7 \\ U-0-  
CS stands for concrete strain, and the number on the back is used as a symbol to distinguish the measurement location. LS means measurement through LVDTs, and the number at the end is also used as a symbol to distinguish the measurement location. In the case of LVDT, the deformation amount (mm) was expressed to confirm the crack width's expansion tendency after cracking, and the amount of deformation was determined through the right vertical axis of each graph. Figure 7 shows the strain in the diagonal direction of each specimen. According to Figure 7a, which is the strain distribution of the specimen U-0-0-3.4, it was found that all strain gauges had a smaller amount of strain than other specimens and the tendency to return to the state before the loading after the maximum load experience appeared. This phenomenon occurred because the strain gauge did not pass through the crack surface. The diagonal section's deformation amount was continuously increased even after the maximum load manifestation could be classified as a shear failure. It was also confirmed that the location where the deformation amount of LSS rapidly increased was similar to the time of the crack in the diagonal direction. Figure 7c also showed this phenomenon as it is. However, in U-S-0-3.4, as reinforcement by shear reinforcement was performed, the crack angle appeared close to 45 degrees, and it could be confirmed that the strain of the corresponding gauge increased rapidly by passing through the CS6 \begin{table}
\begin{tabular}{c c c c c} \hline \hline Specimens & \(\theta_{fer}\) & \(M_{fer}\) & \(\theta_{der}\) & \(M_{der}\) \\  & (mm/mm) & (kNm) & (mm/mm) & (kNm) \\ \hline U-S-F-6.6 & 0.00116 & 41.6 & 0.00341 & 102.7 \\ U-0-0-3.4 & 0.00029 & 15.1 & 0.00172 & 42.3 \\ U-S-0-3.4 & 0.00061 & 19.0 & 0.00131 & 45.7 \\ U-0-F-3.4 & 0.00121 & 42.5 & 0.00151 & 82.4 \\ U-S-F-3.4 & 0.00103 & 49.1 & 0.00306 & 88.1 \\ H-0-F-3.4 & 0.00082 & 23.2 & 0.00225 & 57.5 \\ H-S-F-3.4 & 0.00082 & 24.1 & 0.00221 & 64.2 \\ U-0-0-2.0 & 0.00054 & 18.7 & 0.00214 & 54.6 \\ U-0-F-2.0 & 0.00125 & 44.2 & 0.00418 & 129.2 \\ H-0-F-2.0 & 0.00071 & 27.7 & 0.00286 & 102.2 \\ \hline \hline \end{tabular} \(\theta_{fer}\): member rotation at the flexural cracking load, \(M_{fer}\): applied moment at the flexural cracking load, \(\theta_{der}\): member rotation at the diagonal cracking load. \(M_{der}\): applied moment at the diagonal cracking load.  
\end{table} 
Table 6: Cracking strength of test specimens. Figure 6: Tensile strain of longitudinal reinforcement (at center). strain gauge. The two specimens reinforced with steel fibers showed that, unlike the two specimens that were not reinforced with steel fibers, there was no sharp increase in the diagonal strain or the amount of deformation, but gradually increased.