## 4 Numerical Validation
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{Rectangular Section} \\ \hline
**Reference** & **Specimen** & **b** & **h** & **s** & **a/d** & \(\rho_{1}\) & \(\rho_{w}\) & \(f_{c}\) & \(f_{yl}\) & \(f_{ww}\) & **v** & **Test** \\  & **(mm)** & **(mm)** & **(mm)** & **(mm)** & **(\(\longrightarrow\))** & **(\(\longrightarrow\))** & **(\(\longrightarrow\))** & **(MPa)** & **(MPa)** & **(MPa)** & **(\(\longrightarrow\))** & **Type** \\ \hline \multirow{4}{*}{Lynn A.C. [31]} & 2 CLH18 & 457.2 & 457.2 & 457.2 & 3.74 & 0.02 & 0.0007 & 26.8 & 330.7 & 399.6 & 0.09 & DC \\  & 3 CLH18 & 457.2 & 457.2 & 457.2 & 3.74 & 0.03 & 0.0007 & 26.8 & 330.7 & 399.6 & 0.09 & DC \\  & 3 XLH18 & 457.2 & 457.2 & 457.2 & 3.74 & 0.03 & 0.0007 & 26.8 & 330.7 & 399.6 & 0.09 & DC \\  & 2 XLH8 & 457.2 & 457.2 & 457.2 & 3.74 & 0.02 & 0.0007 & 27.5 & 330.7 & 399.6 & 0.07 & DC \\  & 3 CMH18 & 457.2 & 457.2 & 457.2 & 3.74 & 0.03 & 0.0007 & 25.4 & 330.7 & 399.6 & 0.28 & DC \\  & 3 CMD12 & 457.2 & 457.2 & 457.2 & 3.74 & 0.03 & 0.0017 & 25.4 & 330.7 & 399.6 & 0.28 & DC \\ \hline \multirow{4}{*}{Saactioglu} & U1 & 350.0 & 350.0 & 150.0 & 3.28 & 0.03 & 0.0085 & 43.6 & 430.0 & 470.0 & 0.00 & SC \\  & U2 & 350.0 & 350.0 & 150.0 & 3.28 & 0.03 & 0.0085 & 30.2 & 453.0 & 470.0 & 0.16 & SC \\  & U3 & 350.0 & 350.0 & 750.0 & 3.28 & 0.03 & 0.0169 & 34.8 & 430.0 & 470.0 & 0.16 & SC \\ \hline \multicolumn{8}{c}{**Hollow Rectangular Section**} \\ \hline
**Reference** & **Specimen** & **b** & **h** & **s** & **a/d** & \(\rho_{1}\) & \(\rho_{w}\) & \(f_{c}\) & \(f_{yl}\) & \(f_{ww}\) & **v** & **Test** \\  & **(mm)** & **(mm)** & **(mm)** & **(\(\longrightarrow\))** & **(\(\longrightarrow\))** & **(\(\longrightarrow\))** & **(MPa)** & **(MPa)** & **(MPa)** & **(\(\longrightarrow\))** & **Type** \\ \hline \multirow{4}{*}{[PERSON] et al.} & T250 & 450.0 & 450.0 & 75.0 & 3.00 & 0.0177 & 0.0025 & 30.3 & 550.0 & 550.0 & 0.07 & SC \\  & 7500.0 & 450.0 & 450.0 & 75.0 & 3.00 & 0.0177 & 0.0025 & 29.7 & 550.0 & 550.0 & 0.15 & SC \\  & 7500 & 450.0 & 450.0 & 75.0 & 3.00 & 0.0177 & 0.0025 & 32.7 & 550.0 & 550.0 & 0.15 & SC \\  & 750 & 450.0 & 450.0 & 75.0 & 3.00 & 0.0177 & 0.0025 & 30.8 & 550.0 & 550.0 & 0.21 & SC \\ \hline \hline \end{tabular} b: column section width; h: column section height; s: stirrup spacing; a/d: aspect ratio (shear span/section depth); \(\rho_{l}\): longitudinal reinforcement ratio; \(\rho_{w}\): transverse reinforcement ratio; f\({}_{c}\): compressive strength of concrete; f\({}_{yl}\): yield strength of longitudinal steel; f\({}_{pw}\): yield strength of transverse steel; v: axial load ratio; Test type: SC (single cantilever), DC (double cantilever).  
\end{table} 
Table 1: Database of examined reinforced concrete elements. Figure 12: Specimen 2 CLH18: (**a**) Experimental behaviour. (**b**) Comparison of numerical cyclic response with experimental results. Figure 13: Specimen 3 CLH18: (**a**) Experimental behaviour. The square and circle marks represent respectively the experimental (Table 2) and calculated (Equation (17)) initiation of shear degradation. (**b**) Comparison of numerical cyclic response with experimental results. In Figures 12b and 13b the numerical analysis has been compared with the experimental one. In the numerical model the cracked stiffness of the shear spring, K\({}_{5,\text{cracked}}\) has been set equal to the one of the uncracked one, K\({}_{5,\text{uncracked}}\), following. Therefore, the black dash line of Figure 4, as given by Equation (3). It is clear from the experimental curve that the shear degradation starts at a drift value of about \((\Delta\text{s/L})_{\text{exp}}=0.01\) and displacement of about \(\Delta_{\text{s,expt}}=30.4\) mm (square mark in Figure 13a). Using Equation (17) is possible to calculate the drift ratio and displacement at shear degradation that are \((\Delta\text{s/L})_{\text{calc}}=0.024\) and \(\Delta_{\text{s,calc}}=71.4\) mm, respectively (circle mark in Figure 13a).