# 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 Physical Effects: Fire Modelling  
The fire resistance of an RC structural element is obtained by measuring the strength of an element as a function of the time required to attain its structural failure [139]. To ensure the appropriate fire performance of hybrid GFRP-steel RC structures, adequate information on concrete elements at elevated temperatures is indispensable [140]. Such information on concrete's thermo-mechanical properties are derived from data obtainable from the thermal analysis of cementitious binders. The effect of temperature on the cementitious binder in concrete is well documented and generally visually represented with thermo-gravimetery (TG) and differential thermo-gravimetery (DTG). It is generally agreed that changes in Portland cement binder concrete observed at temperatures exceedingly ambient can be described in two stages [141] before the complete breakdown of the binding effect in mortar matrix in concrete. In the first stage (temperature range 22-120 \({}^{\circ}\)C) an increase in partial pressure caused by evaporative loss of absorbed water can cause some swelling but rarely is related to a significant loss of strength of the concrete matrix [142]. The second stage is typically at about 350 \({}^{\circ}\)C and is accompanied by a structural breakdown of the hydration reaction for the cement bond. This stage is typically represented by a sharp mass loss in a TG and a well-defined DTG peak [141]. Figure 8 shows the typical TG signal for some cementitious concrete binder phases. The gradual TG mass loss below 200 \({}^{\circ}\)C is consistent with evaporative water loss, and the sharp TG mass loss of about 20-30% between 300-400 \({}^{\circ}\)C represents the structural breakdown of the concrete binder. This sets the limits of maximum tolerable temperature for an RC load bearing system. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Source** & \(\mathbf{V_{df}}\) & \(\mathbf{V_{gf}}\) \\ \hline
[119] & \(0.2\cdot\sqrt[]{\frac{1}{d}}\cdot\sqrt[]{100.\frac{A_{f}}{b_{w}d}\frac{E_{f}}{ E_{s}}}\cdot\sqrt[]{f_{c}}\cdot b_{w}\cdot d\) & \(\frac{A_{f}\sim E_{f}\sim E_{f}}{5}\cdot Z\) \\ \hline
[133] & \(0.79\cdot\left(\frac{100}{b_{w}\cdot d}\cdot A_{f}\cdot\frac{E_{f}}{200}\right) ^{1/3}\cdot\left(\frac{400}{d}\right)^{1/4}\cdot\left(\frac{f_{w}}{25}\right) ^{1/3}\) & \(\frac{0.0025E_{f}\cdot A_{f}}{b_{w}\cdot 5}\) \\ \hline
[116] & \(0.4\ \sqrt{f_{c}^{\prime}}\,b_{w}c\) & \(\frac{A_{f}\sim E_{f}}{5}\) \\ \hline
[134] & \(0.035\ \lambda\left(f_{c}^{\prime}\rho_{f}E_{f}\frac{V_{f}}{M_{d}}\right)^{1/5}b_{ w}d\) & \(\frac{0.4\ A_{f}\sim E_{f}}{5}\) \\ \hline
[117] & \(1.3\left(\frac{E_{f}}{E_{s}}\right)^{1/2}\tau_{R}k\left(1.2+40\rho_{f}\right)b _{w}d\) & \(\frac{A_{f}\sim E_{f}}{5}\) \\ \hline
[135; 136] & \(0.12\left(1+\sqrt{\frac{200}{d}}\right)\left(100\cdot\frac{A_{f}}{b_{w}d}\frac{ E_{s}}{E_{s}}\cdot\rho_{z}\cdot f_{ck}\right)^{1/3}b_{w}d\) & \(\frac{0.0025E_{f}\cdot Z\cdot A_{f}}{S}\) \\ \hline
[135; 137] & \(0.79\left(\frac{100}{b_{w}\cdot d}\cdot A_{f}\cdot\frac{E_{f}}{200}\cdot \rho_{z}\right)^{1/3}\cdot\left(\frac{400}{d}\right)^{1/4}\cdot\left(\frac{f_{w }}{25}\right)^{1/3}b_{w}d\) & \(\frac{0.0025E_{f}\cdot A_{f}}{b_{w}\cdot 5}\) \\ \hline
[135; 138] & \(V_{c}\cdot\left(\frac{E_{f}}{E_{s}}\cdot\rho_{z}\right)^{1/3}\) & \(\frac{0.0025E_{f}\cdot A_{f}}{S}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Modifications to code design equations. It generally takes up to 3 h for a fire's heat to go through a concrete member's cover and reach the reinforcement [143; 144; 145]. A recent study by [PERSON] et al. [146] have detailed fire effects on temperature gradients and demonstrated that a temperature of around 400 \({}^{\circ}\)C is obtainable at the 40 mm depth in a concrete zone within 3 h of exposure to a standard fire [147].