# Experimental Investigation on Shear Behavior of Dune Sand Reinforced Concrete Deep Beams
## 5 Prediction of the Shear Strength of the DSRC Beam  
The effects of the key parameters on DSRC beams were similar to those of normal beams. Therefore, DSRC beams use the same shear resistance mechanism as standard beams. There is no domestic or international code for shear design of DSRC deep beams. To compute the shear strength of DSRC deep beams, the shear strength prediction method for normal RC beams can be improved. The experimental data were compared to the predicted values provided by four national codes in this section. The details of the selected codes are shown below.  
The code GB50010-2010 [39], based on the strut and tie model, considers the shear span-to-depth ratio, the tensile strength of the stirrup and horizontal reinforcement, the concrete strength, and the span-to-height ratio. The shear strength for the NRC beam is calculated using the following equation:  
\[V_{\text{u}}=\frac{1.75}{\lambda+1}f_{\text{t}}bh_{0}+\frac{(l_{0}/h-2)}{3}f_{ \text{yv}}\frac{A_{\text{sv}}}{s_{\text{v}}}h_{0}+\frac{(5-l_{0}/h)}{6}f_{ \text{yh}}\frac{A_{\text{sh}}}{s_{\text{h}}}h_{0} \tag{1}\]  
where \(\lambda\) refers to the shear span-to-depth ratio, \(f_{\text{t}}\) represents the concrete tensile strength, \(b\) represents the beam section width, \(h_{0}\) represents the effective depth, \(l_{0}/h\) represents the effective span-to-height ratio, \(f_{\text{yv}}\) represents the yield strength of vertical reinforcement, \(A_{\text{sv}}\) represents the area of vertical reinforcement, \(s_{\text{v}}\) represents the spacing of vertical reinforcement, \(f_{\text{yh}}\) represents the yield strength of horizontal reinforcement, \(A_{\text{sh}}\) represents the area of horizontal reinforcement, and \(s_{\text{h}}\) represents the spacing of horizontal reinforcement.  
The code AC1318-11 [56], based on the strut-and-tie model, considers the effects of shear-to-span ratio, concrete strength, reinforcement ratio, and other factors. The shear strength for the normal RC deep beam was computed using the following equation:  
\[V_{\text{u}}=f_{\text{ce}}b_{\text{w}}w_{\text{s}}\sin\theta_{\text{s}} \tag{2}\]  
where the effective compressive strength of concrete is \(f_{\text{ce}}\)= 0.85\(\beta_{\text{s}}f_{\text{c}}^{\prime}\), \(\beta_{\text{s}}\) represents the concrete strut strength factor, \(f_{\text{c}}^{\prime}\) represents the concrete compressive strength, \(b\) represents the beam section width, \(w_{\text{s}}\) refers to the width of the concrete strut, and \(\theta_{\text{s}}\) refers to the angle between concrete struts and the longitudinal axis.  
The code EN 1992-1-1 (EC2) [57] modified the effective compressive strength of concrete based on ACI 318-11, as shown below:  
\[f_{\text{ce}}=0.60(1-\frac{f_{\text{c}}^{\prime}}{250})\frac{\alpha_{\text{ce }}f_{\text{c}}^{\prime}}{\gamma_{\text{c}}} \tag{3}\]The code CSA A23.3-04 [58] also modifies the effective compressive strength of concrete in ACI 318-11, as shown below:  
\[\begin{split} f_{\rm ce}&=\frac{f_{\rm c}^{\prime}}{0.8+ 170\epsilon_{1}}\\ \epsilon_{1}&=\epsilon_{\rm s}+(\epsilon_{\rm s}+0.002 )\cot^{2}\theta_{\rm s}\end{split} \tag{4}\]  
where \(\epsilon_{1}\) represents the principal tensile strain, \(\beta_{\rm s}\) represents the concrete strut strength factor, \(f_{\rm c}^{\prime}\) represents the concrete compressive strength, \(b\) represents the beam section width, \(w_{\rm s}\) represents the width of the concrete strut, and \(\theta_{\rm s}\) represents the angle between concrete struts and the longitudinal axis.