# 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
#### 3.1.3 Flexure Modelling  
Flexural strength is the intensity of force acting perpendicular to its longitudinal axis a beam can resist without ultimate failure. RC beams experience flexure and encounters different stress stages with the assumption of tensile-governed failure [114]. Implementation of GFRP reinforcement exclusively may result in beams exhibiting reduced flexural strength and brittle failure mode [23]. Hybrid GFRP-steel reinforcement systems are proposed to overcome these downsides [33]. In such hybrid systems, the characteristic plasticity of the steel contributes to the ductility of the RC beam, and the high tensile strength of the GFRP defines its ultimate load-bearing capacity [115]. Figure 6 depicts the moment-curvature (\(M-\varphi\)) curves of various flexural members with equivalent reinforcement areas [101].  
Experimental studies on the flexure modelling of hybrid GFRP-steel RC beams are summarised in Table 2. It is seen that nearly all the beams tested failed due to steel yielding and concrete crushing. The investigations presented in Table 2, however, show the progress in developing the hybrid RC beams concept with under-reinforced beam characteristics. These studies have demonstrated the use of hybrid GFRP-steel reinforcement systems are effective in maintaining the required flexural responses. Furthermore, these studies are mostly based on the analytical models recommended in ACI standards that have been adjusted for hybrid beam designs. The altered design models are then calibrated and correlated with experimental results.  
In general, the studies investigating the flexural behaviour of hybrid GFRP-steel RC beams summarised in Table 2 indicate distinct behaviour compared to conventional steel RC beams. The hybrid beam is characterised by a flexure-shear failure mode with narrower crack propagation. On the other hand, steel RC beams are normally characterised by wider crack widths when subjected to similar displacement and loading conditions. Additionally, for hybrid GFRP-steel RCs many of the rupture failure identified [43, 85] are attributed to the shear failure between longitudinal reinforcement and concrete. This debonding lead to the formation of horizontal cracks in flexure beams.  
Further analysis of the failure modes in studies is summarised in Table 2 and is visually represented in Figure 7. It is clear that a significant proportion (78%) of failure modes observed are from \"steel yielding and concrete crushing\" as shown in Figure 7. Only 3.1% is from \"GFRP rupture\". Data collection is from experiments conducted that have the beam specimen designed with additional shear reinforcements that restrict shear. This limited the gathering of information about the flexure-shear failure characteristics of the hybrid GFRP-steel RC beams.  
Figure 6: Moment–curvature for beams with different reinforcement systems [101]. Reproduced with permission from ASCE 2023.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Reinforcement**} & \multicolumn{3}{c}{**Reinforcement Type**} & \multicolumn{3}{c}{**Ultimate**} & \multicolumn{3}{c}{**Ultimate Load**} & & & \\  & \multicolumn{3}{c}{**Content**} & \multicolumn{3}{c}{**Reinforcement Type**} & \multicolumn{3}{c}{**Moment (kNm)**} & \multicolumn{3}{c}{**Ultimate (kN)**} & & & \\ \cline{3-10}
**Source** & **Beam** & & & & & & & & & & **Analytical** & & \\
**ID** & **\