# Making a Case for Hybrid GFRP-Steel Reinforcement System in Concrete Beams: An Overview
## 3 Analytical Models for Hybrid GFRP-Steel Reinforced Beams
### Models Considering Mechanical Effects
#### 3.1.4 Shear Design  
Generally, the shear resistance of the concrete member can be computed by using V\({}_{\mathit{cf}}\) + V\({}_{\mathit{gf}}\) approach. It is also the most used and preferred approach. V\({}_{\mathit{cf}}\) and V\({}_{\mathit{gf}}\) refer to the shear strengths of the concrete and GFRP stirrups, respectively [116; 117; 118; 119]. This method was developed on the basis of the strut-and-tie model [120; 121], where the assumption was based on the modern truss model with parallel chords, vertical stirrup and constant inclination of 45\({}^{0}\) of the shear cracks [122; 123].  
The shear strength of RC beams is informed by the aggregate interlock, friction force along the shear crack, residual tensile strength, shear strength of the longitudinal reinforcement (dowel action) and the shear strength from the transverse reinforcement (stirrups) [124; 125]. It was identified that the dowel capability of GFRP is about 70% lower than that of steel. Previous research has shown that V\({}_{\mathit{cf}}\) is also influenced by the stiffness  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Reinforcement**} & \multicolumn{2}{c}{**Reinforcement Type**} & \multicolumn{2}{c}{**Ultimate**} & \multicolumn{2}{c}{**Ultimate Load**} & & & \\  & & **Content** & & & & **Moment (kNm)** & & (kN) & & \\ \cline{3-10}
**Source** & **Beam** & & & & & & & & & **Analytical** & \\
**ID** & **\%** & & & & & & & & & **Model** & **Failure** \\
**CR** & **Peff** & **Peff,b** & & & & & & & & **Referenced** & **Mode** \\ \hline \multirow{5}{*}{[85]} & CH1 & & & & & & & 92.00 & 88.00 & & & SY, CC \\  & CH2 & & & & & & 112.0 & 105.0 & & & SY, CC \\  & CH3 & & n/a & & & & 125.0 & 128.0 & & & & SY, CC \\  & CH4 & & & & & & 128.0 & 143.0 & & & SY, CC \\  & CH5 & & & & & & 160.0 & 169.0 & & & SY, CC \\ \hline \multirow{5}{*}{[86]} & GG1S & 0.95 & 0.25 & & & & 88.6 & 72.6 & & & SY, CC \\  & G2G2S & 1.18 & 0.25 & & & & 88.0 & 74.8 & & & SY, CC \\  & G3G2S & 1.57 & 0.25 & & & & 96.3 & 82.8 & & & SY, CC \\  & S3G & 1.18 & 0.25 & & & & 98.7 & 78.9 & & & CC \\  & G3S & 0.50 & 2.37 & & & & 67.2 & 65.18 & & & SY \\ \hline \multirow{5}{*}{[87]} & G2-S2 & 2.27 & 0.70 & & & & 57.5 & 46.98 & & & SY, CC \\  & G6-S2 & 2.27 & 0.72 & & & & 63.3 & 56.56 & & & SY, CC \\  & G2-S6 & 2.13 & 0.67 & & & & 56.37 & 45.8 & & & SY, CC \\  & G6-S6 & 2.13 & 0.69 & & & & 66.7 & 55.78 & & & \\  & G2S2D & 2.27 & 0.70 & & & 53.79 & 41.61 & & & SY, CC \\  & G6S2D & 2.27 & 0.72 & & & 50.56 & 50.69 & & & SY, CC \\ \hline \hline \end{tabular} SY—Steel Yielding, CC—Concrete Crushing, RUP—GFRP Rupture.  
\end{table}
Table 2: _Cont._  
Figure 7: Distribution of failure modes in hybrid GFRP–steel beams reported in Table 2.  
of the tensile reinforcement [108; 126; 127]. As such, an overall reduction in V\({}_{\mathit{df}}\) could be expected when GFRPs are used for longitudinal reinforcement, as those bars produce a larger tensile strain [128].  
Experimental studies observed a significant reduction in the ultimate capacity of GFRP bars when used as stirrups, with studies pointing out that the occurrence of failure initiated at the bends of the stirrups. It has been reported that the current design guidelines result in prescribing excessive shear reinforcement, making those procedures arguably very conservative [129; 130; 131].  
Attempts have been made to fit GFRP characteristics in conventional design equations, and new rules have been introduced to derive modified versions of existing equations [132]. Table 3 shows the modification to design equations as published in various standards.