Table 3 Bond strength models.

Hiroyuki and Wu (1997)

\( \tau_{u} = 0.27L^{ - 0.669} \quad P_{u} = \tau_{u} Lb_{p} \)

Tanaka (1996) and Sato et al. (1996)

\( \tau_{u} = 6.13 - \ln (L)\quad P_{u} = \tau_{u} Lb_{p} \)

Maeda et al. (1997)

\( \tau_{u} = (110.2 \times 10^{ - 6} )E_{f} t \)

\( P_{u} = \tau_{u} L_{e} b_{p} \quad L_{e} = e^{{6.134 - 0.58\ln (E_{f} t_{f} )}} \)

Khalifa et al. (1998)

\( \tau_{u} = (110.2 \times 10^{ - 6} )(f_{c}^{\prime } /42)E_{f} t \)

\( P_{u} = \tau_{u} L_{e} b_{p} \quad L_{e} = e^{{6.134 - 0.58\ln (E_{f} t_{f} )}} \)

Sato et al. (1997) and JCI (2003)

\( \tau_{u} = 2.68 \times 10^{ - 5} (f_{c}^{\prime } )^{0.2} E_{f} t_{f} \)

\( P_{u} = \tau_{u} L_{e} (b_{p} + 7.4) \)

\( L_{e} = 1.89(E_{f} t_{f} )^{0.4} \quad {\text{if }}L > L_{e} :L = L_{e} \)

Iso’s Model; JCI (2003)

\( \tau_{u} = 0.93(f_{c}^{\prime } )^{0.44} E_{f} t_{f} \quad P_{u} = \tau_{u} L_{e} b_{p} s \)

\( L_{e} = 1.25(E_{f} t_{f} )0.57\quad {\text{if }}L > L_{e} :L = L_{e} \)

Yang et al. (2007)

\( P_{u} = \left( {0.5 + 0.08\sqrt {0.01E_{f} t_{f} /f_{t} } } \right)^{{}} b_{p} L_{e} \tau_{u} \)

\( L_{e} = 100{\text{ mm}}\quad \tau_{u} = 0.5f_{t} \)

Chen and Teng (2001)

\( P_{u} = 0.427\beta_{p} \beta_{L} \sqrt {f_{c}^{\prime } } L_{e} \quad L_{e} = \sqrt {\frac{{E_{p} t_{p} }}{{\sqrt {f_{c}^{\prime } } }}} \)

\( \beta_{p} = \left[ {\frac{{2 - (b_{p} /b_{c} )}}{{1 + (b_{p} /b_{c} )}}} \right]^{0.5} \quad \beta_{L} = \left\{ {\begin{array}{*{20}c} 1 & {L \ge L_{e} } \\ {\sin \left( {\frac{\pi L}{{2L_{e} }}} \right)} & {L < L_{e} } \\ \end{array} } \right\} \)

Täljsten (1994)

\( P_{u} = b_{p} \sqrt {\frac{{2G_{f} E_{f} t_{f} }}{{1 + (E_{f} t_{f} /E_{c} t_{c} )}}} \)

Yuan and Wu (1999)

\( P_{u} = b_{p} \sqrt {\frac{{2G_{f} E_{f} t_{f} }}{{1 + (E_{f} t_{f} b_{f} /E_{c} t_{c} b_{c} )}}} \)

Kanakubo (2003)

\( P_{u} = 1.1f_{c}^{\prime 0.2} b_{f} L_{e} \quad (L_{b} > L_{e} ) \)

\( L_{e} = 0.7\sqrt {\frac{{E_{f} t_{f} }}{{f_{c}^{\prime 0.2} }}} \)