# Prediction of Deflection of Shear-Critical RC Beams Using Compatibility-Aided Truss Model
## 5 Conclusions  
A method to predict the deflection of shear-critical RC beams was developed. Existing methods for calculating the deflection of RC beams may considerably underestimate the deflection values, as the prediction of shear deformation of shear-critical RC beams is essential for reasonably calculating the deflection. In this study, a compatibility-aided truss model was used to predict shear deformation. The calculated results were compared with the experimental results and verified. The following conclusions can be drawn:  
1. The flexural deflection analytically obtained using the effective moment of inertia substantially underestimated the experimental results for the deflection at peak load with an average of 0.44. This is because shear deflection increases as the shear deterioration of shear-critical RC beams occurs. However, the bending theory does not consider this phenomenon. On the other hand, the proposed analytical method predicted an average of 1.02 for the peak load and an average of 1.23 for the deflection at peak load. Although the deflection prediction using the proposed method gave somewhat conservative results, it was shown to be reliable and reasonable in terms of applicability. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimens**} & \multicolumn{2}{c}{**Experimental**} & \multicolumn{2}{c}{**Analytical**} & \multicolumn{2}{c}{**Ana./Exp.**} \\ \cline{2-7}  & **Load** & \(\Delta_{\text{exp.}}\) & \(\Delta_{f}\) & \(\Delta_{\text{pro.}}\) & \(\Delta_{\text{cor.}}\) & \(\Delta_{\text{exp.}}\) \\  & **(kN)** & **(mm)** & **(mm)** & **(mm)** & **(mm)** & \(\Delta_{\text{cor.}}\) & \(\Delta_{\text{exp.}}\) \\ \hline \multirow{8}{*}{S1-3.0} & 148.6 & 1.34 & 0.94 & 1.16 & 0.70 & 0.87 \\  & 193.3 & 1.81 & 1.24 & 2.01 & 0.69 & 1.11 \\  & 240.4 & 2.54 & 1.55 & 3.04 & 0.61 & 1.20 \\  & 284.5 & 3.51 & 1.84 & 4.26 & 0.53 & 1.21 \\  & 323.4 & 4.26 & 2.10 & 5.67 & 0.49 & 1.33 \\ \hline \multirow{8}{*}{S1-3.5} & 147.8 & 2.13 & 1.50 & 1.77 & 0.71 & 0.83 \\  & 192.2 & 2.88 & 1.97 & 2.93 & 0.68 & 1.02 \\  & 238.8 & 4.05 & 2.46 & 4.39 & 0.61 & 1.08 \\  & 268.1 & 4.93 & 2.76 & 5.54 & 0.56 & 1.12 \\  & 295.2 & 5.83 & 3.05 & 6.85 & 0.52 & 1.18 \\ \hline \multirow{8}{*}{S1-4.0} & 147.4 & 2.68 & 2.25 & 2.57 & 0.84 & 0.96 \\  & 176.2 & 3.28 & 2.70 & 3.53 & 0.82 & 1.08 \\  & 207.2 & 4.23 & 3.18 & 4.68 & 0.75 & 1.11 \\  & 237.8 & 5.23 & 3.66 & 6.01 & 0.70 & 1.15 \\  & 266.8 & 6.58 & 4.11 & 7.54 & 0.62 & 1.15 \\ \hline \multirow{8}{*}{S2-2.5} & 139.4 & 0.88 & 0.61 & 0.75 & 0.69 & 0.85 \\  & 185.2 & 1.36 & 0.82 & 1.48 & 0.60 & 1.09 \\  & 233.2 & 2.02 & 1.04 & 2.40 & 0.51 & 1.19 \\  & 276.4 & 2.62 & 1.24 & 3.47 & 0.47 & 1.33 \\  & 304.2 & 3.06 & 1.36 & 4.36 & 0.45 & 1.43 \\ \hline \multirow{8}{*}{S2-3.0} & 139.0 & 1.42 & 1.06 & 1.23 & 0.75 & 0.87 \\  & 172.1 & 1.92 & 1.32 & 1.98 & 0.69 & 1.03 \\ \cline{1-1}  & 208.2 & 2.8 & 1.61 & 2.92 & 0.57 & 1.04 \\ \cline{1-1}  & 242.5 & 3.52 & 1.88 & 4.03 & 0.53 & 1.14 \\ \cline{1-1}  & 273.4 & 4.39 & 2.12 & 5.30 & 0.48 & 1.21 \\ \hline \multirow{8}{*}{S2-3.5} & 138.4 & 1.85 & 1.68 & 1.90 & 0.91 & 1.03 \\ \cline{1-1}  & 171.1 & 2.48 & 2.09 & 2.94 & 0.84 & 1.19 \\ \cline{1-1}  & 206.6 & 3.48 & 2.54 & 4.27 & 0.73 & 1.23 \\ \cline{1-1}  & 229.3 & 4.16 & 2.82 & 5.33 & 0.68 & 1.28 \\ \cline{1-1}  & 250.5 & 5.02 & 3.09 & 6.54 & 0.61 & 1.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction results of deflection of specimens for each load step. 2. The experimental results showed that the strain of the tension reinforcing bars behaved almost linearly until the peak load, even if the shear-critical RC beams experienced shear deterioration. The superposition of flexural and shear deflections is a reasonable for the analysis of this result. In contrast, while the shear deformation increased rapidly after the peak load, the strain of the tension reinforcing bars no longer increased.