# 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  
#### 3.1.1 Ductility Analysis  
Ductility refers to the ability of a material to endure loads whilst experiencing significant strain before failure. Figure 5 compares the idealised ductile behaviour of GFRP and steel reinforcements [89]. Ductile responses are a significant aspect of the performance of GFRP-steel hybrid beams [90; 91], where the implementation of hybrid concepts aims to achieve enhanced ductility of flexural beams [92; 93]. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Tensile Strength** & **Compressive** & **Young’s Modulus** & **Advantages** & **Disadvantages** \\
**(MPa)** & **Strength (MPa)** & **(GPa)** & & & -High tensile strength compared & \\  & & & & & to steel reinforcement & \\  & & & & & - Corrosion resistance & \\ GFRP & 600–1100 & 100–400 & 45–80 & - Can be easily cut and shape & -Lower strength compared to CFRP & \\  & & & & & - Low cost & and BFRP \\  & & & & & - Can be used in wet and dry & \\  & & & & & conditions & - Non-conductive \\ \hline  & & & & & -Very high tensile strength & \\  & & & & & -High strength-to-weight ratio & \\ CFRP & 1500–4000 & 600–200 & 120–400 & -Corrosion resistant & -Higher cost & compared to GFRP \\  & & & & & -Son-conductive & \\ \hline  & & & & & -High tensile strength & -Lower availability \\  & & & & & -High strength-to-weight ratio & and higher cost \\  & & & & & -Corrosion resistant & compared to GFRP \\  & & & & & -Son-conductive & -Potential for \\ \hline \end{tabular}
\end{table} 
Table 1: Overview of FRP variants. Figure 5: Tensile behaviour of steel compared to FRP (A) Steel, (B) Basalt FRP, (C) Basalt FRP, (D) Glass FRP, (E) Basalt FRP [89]. Reproduced with permission from Springer Nature 2023. The objectives of the studies conducted in this area are framed to provide evidence that the hybrid application of steel and GFRP can significantly improve their ductility performance compared to the GFRP-only reinforcement [94; 95]. Such outcomes led to further investigations on the requirement for ductility models applicable to make the hybrid reinforcement design safer and more efficient. However, conventional ductility concepts cannot be suitably applied to hybrid systems without modifications [96]. Traditional ductility models are described on the foundational concepts of cracking, yielding, and ultimate points. The current ductility indices are derived from stress-strain information of steel between yielding and ultimate stress where there is significant plastic deformation. For GFRP RC, the ductility indices become complex since the stiffness of GFRPs is considerably lower than that of steel and also because it does not exhibit the characteristic yielding at ultimate stress that is accompanied by large plasticity as the case in steel. Conventional ductility indices and concepts are arguably not valid for beams with GFRP reinforcements [97; 98; 99; 91]. Though design codes now exist for designing GFRR, RCs, there is a need to develop a more reliable design approach that would consider the complexity of defining the ductility of hybrid GFRP-Steel RCs [100]. Different parameters related to deformation are generally used to express the ductility indices, include displacements, curvatures, and rotations. However, such approaches are unsuitable for GFRPs as they do not incorporate indices related to the primary characteristics and behaviour of GFRPs. New parameters are proposed to quantify the ductility of concrete beams reinforced with hybrid GFRP-steel bars [99]. Two major approaches are considered in developing updated equations [101; 102]:  
deformation-based, which relies on equivalent deformability factor \(\mu_{M}\), and energy-based where the factor \(\mu_{en}\) defines the ductility as energy absorbing capacity. Based on these concepts, these approaches were considered in the development of analytical models that express the ductility of hybrid GFRP-steel reinforced concrete beams. Taking the energy approach, [PERSON] et al.