# Prediction of Deflection of Shear-Critical RC Beams Using Compatibility-Aided Truss Model
## 4 Verification of Proposed Method
### Verification of Proposed Method  
Figure 7 shows the experimental results of S1-3.0 failed in shear. The figure on the left shows the load-deflection curve, and the one on the right shows the strain measured by the strain gauge attached to the tension reinforcement at the mid-span of the specimen. Since all the specimens shared similar characteristics to those shown in Figure 7, this study describes only the experimental results of S1-3.0, treating it as the representative sample. During the early loading stage, the first flexural crack occurred at the mid-span of the specimen. As shown in Figure 7, this initial flexural crack had a significant effect on the behavior of the tension reinforcement. The load-deflection curve of the specimen displayed a linear behavior after flexural cracking until severe shear deterioration occurred; the behavior of the tension reinforcement was also linear. As shown in Figures 1 and 7, unlike flexure-critical RC beams, the stiffness of shear-critical RC beams decreased and deflection increased after shear deterioration occurs. On the other hand, the strain of the tension reinforcement of S1-3.0 continued linearly up to the peak load, regardless of the shear deterioration. This means that the flexural deformation up to the peak load of the shear-critical RC beams can be calculated without being affected by the shear deformation. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimens**} & \multicolumn{8}{c}{**Experimental Details and Results**} & \multicolumn{8}{c}{**Analytical Results**} \\ \cline{2-11}  & \(f^{\prime}_{c}\) & _all_ & \(\rho_{tt}\) & \(f_{ly}\) & \(\rho_{t}\) & \(\eta\) & \(P_{u,exp.}\) & \(\Delta_{u,exp.}\) & \(\Delta_{u,exp.}\) & \(\Delta_{u,exp.}\) & \(P_{exp.}\) \\  & **(MPa)** & **(\%)** & **(MPa)** & **(MPa)** & **(KN)** & **(mm)** & **(mm)** & **(\%)** & **(\%)** & **(\%)** & **(\%)** \\ \hline S1-3.0 & 42.2 & 3.0 & 3.60 & 402.0 & 0.215 & 0.05 & 372.5 & 5.86 & 0.39 & 1.23 & 0.96 \\ S1-3.5 & 42.2 & 3.5 & 3.60 & 402.0 & 0.215 & 0.05 & 327.5 & 8.08 & 0.41 & 1.03 & 0.98 \\ S1-4.0 & 42.2 & 4.0 & 3.60 & 436.3 & 0.215 & 0.05 & 284.3 & 8.15 & 0.60 & 1.39 & 1.11 \\ S2-2.5 & 37.0 & 2.5 & 3.29 & 402.0 & 0.324 & 0.09 & 325.4 & 3.55 & 0.42 & 1.58 & 1.03 \\ S2-3.0 & 37.0 & 3.0 & 3.29 & 402.0 & 0.324 & 0.09 & 280.3 & 5.56 & 0.42 & 1.21 & 1.07 \\ S3-3.5 & 37.0 & 3.5 & 3.29 & 402.0 & 0.324 & 0.09 & 271.5 & 8.72 & 0.40 & 0.95 & 0.99 \\ \hline \multicolumn{1}{c}{} & \multicolumn{3}{c}{Mean} & \multicolumn{8}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} \\  & & \multicolumn{2}{c}{COV} & & & & & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Details of specimens and experimental and analytical results. Figure 6: Details of typical specimens (unit: mm): (**a**) S1 series (S1-3.5); (**b**) S2 series (S2-3.5). That is, the calculation of flexural deflection using the effective moment of inertia assumed in Section 2 is valid. As shown in Figure 7, the deflection of the specimen increased after the peak load, but the strain of the tension reinforcement decreased. This means that the post-peak behavior of the specimen was dominated by shear rather than flexure. Therefore, the principle of superposition of flexural and shear deflections cannot be applied after the peak load of the shear-critical RC beams, as described in Section 2. In this study, the load-deflection relationship up to the peak load was predicted using the proposed shear analytical model. As shown in Table 3, the proposed method predicted the shear strength of the six specimens with an average of 1.02 and a coefficient of variation (COV) of 5.9%. The deflection at peak load was evaluated somewhat conservatively as approximately 1.2 times. On the other hand, the analytical results obtained using Equation (3), which represents the flexural deflection, greatly underestimated the experimental results with an average of 0.44.