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International Journal of Concrete Structures and Materials

Table 1 Empirical bond strength models.

From: Development of Mapping Function to Estimate Bond–Slip and Bond Strength of RC Beams Using Genetic Programming

Researcher

Equation*

Orangun et al. (1977)

\(\tau_{{{\text{max}}}} = \left( {1.2 + \frac{3c}{{d_{{\text{b}}} }} + \frac{{50d_{{\text{b}}} }}{{L_{{\text{e}}} }} + \frac{{A_{{{\text{st1}}}} f_{{{\text{yt}}}} }}{{72,500S_{{{\text{st}}}} d_{{\text{b}}} }}} \right)0.083\sqrt {f^{\prime}_{{\text{c}}} }\)

Xu (1990)

\(\tau_{{{\text{max}}}} = \left( {1.6 + \frac{0.7c}{{d_{{\text{b}}} }} + 20\rho_{{{\text{sv}}}} } \right)f_{{\text{t}}} = \left( {1.6 + \frac{0.7c}{{d_{{\text{b}}} }} + \frac{{20A_{{{\text{st1}}}} }}{{cS_{{{\text{st}}}} }}} \right)f_{{\text{t}}}\)

Harajli et al. (1995)

\(\tau_{{{\text{max}}}} = 0.78\left( {\frac{{c + K_{{\text{t}}} }}{{d_{{\text{b}}} }}} \right)^{2/3} \sqrt {f^{\prime}_{{\text{c}}} } = 0.78\left[ {\frac{{c + \frac{{7A_{{{\text{st}}}} }}{{S_{E} n}}}}{{d_{{\text{b}}} }}} \right]^{2/3} \sqrt {f^{\prime}_{{\text{c}}} }\)

Esfahani and Kianoush (2005)

\(\tau_{{{\text{max}}}} = \tau_{{\text{c}}} \frac{{1 + \frac{1}{M}}}{1.85 + 0.024\sqrt M }\left( {0.88 + \frac{{0.12c_{{{\text{med}}}} }}{c}} \right)\left( {1 + \frac{{0.015A_{{{\text{st1}}}} A_{{\text{s}}} }}{{cS_{{{\text{st}}}} }}} \right),\)

\({\text{where}} \;M = \cos \,h\left( {0.0022L_{{\text{e}}} \sqrt {3\frac{{f^{\prime}_{{\text{c}}} }}{{d_{{\text{b}}} }}} } \right)\) and \(\tau_{{\text{c}}} = 2.7\frac{{\frac{c}{{d_{{\text{b}}} }} + 0.5}}{{\frac{c}{{d_{{\text{b}}} }} + 3.6}}\sqrt {f^{\prime}_{{\text{c}}} }\)

Wu and Zhao (2013)

\(\tau_{{{\text{max}}}} = \frac{{2.5\sqrt {f^{\prime}_{{\text{c}}} } }}{{1 + 3.1e^{{ - 0.47(K_{{{\text{co}}}} + 33K_{{\text{t}}} )}} }}\), where \(K_{{{\text{co}}}} = \frac{c}{{d_{{\text{b}}} }}\) and \(K_{{\text{t}}} = \frac{{A_{{{\text{st}}}} }}{{nS_{{{\text{st}}}} d_{{\text{b}}} }}\)

  1. *\(A_{{\text{s}}}\): cross-sectional area of one longitudinal reinforcement (mm2), \(A_{{{\text{st}}}}\): cross-sectional area of all legs of transverse reinforcement (mm2), \(A_{{{\text{st1}}}}\): cross-sectional area of one leg of transverse reinforcement (mm2), \(L_{{\text{e}}}\): embedded length (mm), \(S_{{{\text{st}}}}\): spacing of transverse reinforcement (mm), \(c\): minimum of spacing and cover thickness (mm), \(c_{{{\text{med}}}}\): median of side cover, bottom cover, and rebar spacing, \(d_{{\text{b}}}\): diameter of rebar (mm), \(f_{{\text{t}}}\): tensile strength of concrete (MPa), \(f^{\prime}_{{\text{c}}}\): compressive strength of concrete (MPa), \(f_{{{\text{yt}}}}\): yield strength of transverse reinforcement (MPa), \(n\): number of tension bars enclosed by stirrups, \(s\): slip of rebar (mm), \(\tau_{{{\text{max}}}}\): maximum bond stress (MPa).
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