# Estimation of the Ultimate Strength of FRP Strips-to-Masonry Substrates Bond
## 2 Research Objectives
### Overview of Existing Formulas
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model’s Name** & **References** & **Existing Equations** \\ \hline [PERSON] & [55] & \(P_{\max}=b_{p}\times\sqrt{2\times E_{p}\times l_{p}\times G_{c}}\) \\  & [55] & \(G_{c}=1.43\ (\frac{N,\text{mm}}{\text{mm}^{2}})\) \\ \hline [PERSON] & [5] & \(P_{\max}=l_{b}p_{p}(6.13-\ln l_{b})\) \\ \hline [PERSON] et al. & [6] & \(P_{\max}=110.2\times 10^{-6}\times E_{p}\times l_{p}\times l_{e}\times b_{p}\) \\  & \(l_{e}=e^{6.134-0.58\times\ln(E_{p}\times l_{p})}\)unit of \(E_{p}\) is GPa \\ \hline [PERSON] & [56] & \(P_{\max}=(b_{p}+7.4)\times\sqrt{2\times E_{p}\times l_{p}\times G_{c}}\) \\  & \(G_{c}=0.514\times f^{0.236}_{cm}\) \\ \hline [PERSON] & [28] & \(P_{\max}=b_{p}\times\sqrt{12\times E_{p}\times l_{p}\times\sqrt{f^{\prime}_{ cm}}}\) \\ \hline [PERSON] et al. & [57; 58] & \(P_{\max}=2.68\times 10^{-5}\times(f^{\prime}_{cm})^{0.23}\times E_{p}\times t_{p} \times l_{e}\times(b_{p}+7.4)\) \\  & \(l_{e}=1.89\times\left(E_{p}\times t_{p}\right)^{0.4}\text{ if }l_{b}\geq l_{e}\) \\ \hline [PERSON] & [57] & \(P_{\max}=0.93\times\left(f^{\prime}_{cm}\right)^{0.44}\times b_{p}\times l_{e}\) \\  & \(l_{e}=0.125\times\left(E_{p}\times t_{p}\right)^{0.57}\text{ if }l_{b}\geq l_{e}\) \\ \hline [PERSON] et al. & [57; 59] & \(P_{\max}=(0.5+0.08\times\sqrt{\frac{0.01\times E_{p}\times l_{p}}{f_{at}}}) \times\frac{l_{e}\times b_{p}\times f_{at}}{2}\) \\  & \(l_{e}=100\ (\text{mm})\) \\ \hline [PERSON] et al. & [52] & \(P_{\max}=1.45\times\phi_{f}^{0.263}\times f^{0.6}_{at}\times\sqrt{l_{per} \times E_{p}\times l_{p}\times l_{b}}\) \\  & \(\phi_{f}=\frac{1}{2+b_{p}}\) for EB case \\  & & \(l_{per}=2+b_{p}\) \\ \hline [PERSON] et al. & [5] & \(P_{\max}=13.69\times\phi_{f}^{0.84}\times f^{0.9}_{at}\times\sqrt{l_{per} \times E_{p}\times l_{p}\times l_{b}}\) \\  & & \(\phi_{f}=\frac{1}{2+b_{p}}\) for EB case \\  & & \(l_{per}=2+b_{p}\) \\ \hline [PERSON] and [PERSON] & [60; 61] & \(l_{e}=\sqrt{\frac{E_{p}\times l_{p}}{2\times f_{at}}}\ \ \alpha=(\frac{l_{b}}{l})(2- \frac{l_{b}}{l})\) \\  & & \(k_{p}=\sqrt{1.125\times\frac{2-\frac{b_{p}}{l_{p}}}{1+\frac{b_{p}}{200}}}\) \\ \hline [PERSON] & [60; 62] & \(P_{\max}=0.5\times l_{b}\times b_{p}\times f_{ut}\) \\ \hline [PERSON] et al. & [19] & \(P_{\max}=\left[f^{1.5}_{ut}\times L_{b}-L_{b}\times t_{p}\times c_{1}\right]+ \left[f^{3}_{ut}\times b_{m}-b^{2}_{p}\times t_{p}\right]\) \\  & & \(+[L^{1.5}_{1}+c_{2}+\frac{l_{e}}{c_{0}}\times(L_{b}+E_{p})]\) \\  & & \(c_{1}=9.941346\ \ c_{2}=9.58728\ \ c_{0}=9.351684\) \\ \hline Camli and Binici & [3] & \(\omega\) is a coefficient that depends on the substrate material type (see Ref. [3]) \\  & & \(\delta_{u}=f^{\prime}_{cm}\alpha^{\left(\frac{l_{p}}{l_{e}}\right)^{\beta}} \left(\frac{b_{p}}{b_{u}}\right)^{\gamma}\) \\  & & \(\alpha\), \(\beta\) and \(\gamma\) are exponents that can be determined by nonlinear regression analysis based on Ref. [3] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._In Table 1, \(f^{\prime}_{cm}\) and \(f_{ut}\) are the compressive and tensile strength of masonry in the MPa unit and defined as follows:  
\[f_{ut}=0.53\times\sqrt{f^{\prime}_{cm}} \tag{1}\]  
It should be noted that in Table 1, [PERSON] and [PERSON] models were reported from [4]. Moreover, [PERSON], [PERSON], and Yang models were extracted from [57]. Finally, [PERSON] and Van-Gemert models were presented here from [60]. It should be noted that equations available in the literature (see Table 1) referred to specific geometry and materials in most cases.