Table 6 Bar development length under static load.

ACI 318-19

\(l_{d} = \frac{{f_{y} d_{b} }}{{1.1\lambda \sqrt {f_{c}^{'} } }}\frac{{\psi_{t} \psi_{e} \psi_{s} }}{{\left( {c_{f} + K_{tr} } \right)/d_{b} }} \ge 300{\text{ mm}}\)

\((c_{f} + K_{tr} )/d_{b} \le 2.5\)

\(c_{f} = \hbox{min} (c_{b} ,c_{so} ,c_{si} ) + 0.5d_{b}\)

\(K_{tr} = 40A_{tr} /\left( {s_{t} n} \right)\)

1.0–1.3l_d

ACI 408R-03

\(l_{d} = \frac{{(f_{y} /\sqrt[4]{{f_{c}^{'} }} - \phi 57.4w)(\psi_{t} \psi_{e} \psi_{s} )d_{b} }}{{\phi 1.83(cw + K_{atr} )/d_{b} }}\)

\((cw + K_{atr} )/d_{b} \le 4.0\)

\(w = 0.1(c_{\hbox{max} } /c_{\hbox{min} } ) + 0.9 \le 1.25\)

\(K_{atr} = 6\sqrt {f_{c}^{'} } t_{d} A_{tr} /(s_{t} n)\)

\(t_{d} = 0.03d_{b} + 0.22\)

\(c = c_{\hbox{min} } + d_{b} /2\)

\(c_{\hbox{max} } = \hbox{max} (c_{b} ,c_{s} )\)

\(c_{\hbox{min} } = \hbox{min} (c_{b} ,c_{s} )\)

\(c_{s} = \hbox{min} (c_{so} ,c_{si} + 6.4)\)

l_d

Eurocode 2-04

\(l_{d} = \alpha_{2} \alpha_{3} \frac{{f_{y} d_{b} }}{{4f_{bd} }} \ge \frac{{l_{0} }}{1.5}\)

\(\alpha_{2} = 0.7 \le 1 - 0.15\left( {c_{d} - d_{b} } \right)/d_{b} \le 1.0\)

\(\alpha_{3} = 0.7 \le 1 - K\left( {\sum {A_{tr} - A_{s} } } \right)/A_{s} \le 1.0\)

\(f_{bd} = 2.25\eta_{2} \left[ {0.75(0.3)(f_{c}^{'} )^{2/3} } \right]\)

\(\alpha_{2} \alpha_{3} \ge 0.7\)

\(c_{d} = \hbox{min} (c_{b} ,c_{so} ,c_{si} )\)

\(l_{0} = \hbox{max} (0.45d_{b} f_{y} /(4f_{bd} ),15d_{b} ,200mm)\)

\(\eta_{2} = (132 - d_{b} )/100 \le 1.0\)

1.0–1.5l_d

Hwang et al. (2017)

\(f_{s} = \frac{{l_{d} }}{{d_{b} }}[3\tau_{1} + \tau_{2} ] \le f_{y}\)

\(\tau_{1} = \frac{{\tau_{u} }}{1.4}\left[ {\frac{{1 - (\Delta_{f} /s_{1} )^{1.4} }}{{1 - (\Delta_{f} /s_{1} )}}} \right] \le \tau_{u}\)

\(\frac{{\Delta_{f} }}{{s_{1} }} = 1 - \frac{{14.7l^{2} }}{{E_{s} d_{b} }}\frac{{\tau_{u} }}{{\sqrt {f_{c}^{'} } }} + 0.007\frac{{l_{d} }}{{\sqrt {f_{c}^{'} } }}\)

\(\tau_{u} = 0.91\alpha_{d} \sqrt {f_{c}^{'} } \left[ {\frac{{(cw + K_{atr} )/d_{b} }}{2.5}} \right]\)

\(\tau_{2} = \left[ {\frac{{16{ - }6C_{1} \tau_{1} }}{{16 + C_{1} \tau_{u} }}} \right]\tau_{u} \ge \frac{{\tau_{u} }}{2}\)

\(C_{1} = l_{d}^{2} /[1 - (\sqrt {0.003f_{c}^{'} } )E_{s} d_{b} ]\)

l_d