Table 1 GYC for angle steel in different design codes.

GB50017-2017²⁹

Single-sided connection: \(N \le \eta \varphi Af\);

Single-angle members: \(N \le \varphi A_{{\text{e}}} f\)

Including only normal force

DL/T5154-2012³⁰

\(N \le m_{N} \varphi Af\)

ASCE10-2015³¹

\(N \le AF_{{\text{a}}}\);

When \({{Kl} \mathord{\left/ {\vphantom {{Kl} r}} \right. \kern-0pt} r} \le C_{{\text{c}}}\), \(F_{{\text{a}}} = \left[ {1 - \frac{1}{2}\left( {\frac{{{{Kl} \mathord{\left/ {\vphantom {{Kl} r}} \right. \kern-0pt} r}}}{{C_{{\text{c}}} }}} \right)^{2} } \right]F_{y}\);

When \({{Kl} \mathord{\left/ {\vphantom {{Kl} r}} \right. \kern-0pt} r} > C_{{\text{c}}}\), \(F_{{\text{a}}} = \frac{{{\uppi }^{2} {\text{E}}}}{{\left( {{{Kl} \mathord{\left/ {\vphantom {{Kl} r}} \right. \kern-0pt} r}} \right)^{2} }}\)

ANSI/AISC360-16³³

\(P_{{\text{n}}} = F_{{{\text{cr}}}} A_{{\text{g}}}\);

\(F_{{{\text{cr}}}} = \left\{ {\begin{array}{*{20}l} {\left[ {0.658^{{{{f_{y} } \mathord{\left/ {\vphantom {{f_{y} } {F_{e} }}} \right. \kern-0pt} {F_{e} }}}} } \right]f_{y} ,} \hfill & {\quad {{Kl} \mathord{\left/ {\vphantom {{Kl} r}} \right. \kern-0pt} r} \le 4.71\sqrt {{E \mathord{\left/ {\vphantom {E {\left( {f_{y} } \right)}}} \right. \kern-0pt} {\left( {f_{y} } \right)}}} } \hfill \\ {0.877F_{e} ,} \hfill & {\quad {{Kl} \mathord{\left/ {\vphantom {{Kl} r}} \right. \kern-0pt} r} > 4.71\sqrt {{E \mathord{\left/ {\vphantom {E {\left( {f_{y} } \right)}}} \right. \kern-0pt} {\left( {f_{y} } \right)}}} } \hfill \\ \end{array} } \right.\)

EC3²⁵

\({\frac{N}{{{{\chi_{x} Af_{y} } \mathord{\left/ {\vphantom {{\chi_{x} Af_{y} } {\gamma_{{{\text{M1}}}} }}} \right. \kern-0pt} {\gamma_{{{\text{M1}}}} }}}} + K_{xx} \frac{{\beta_{mx} M_{x} }}{{{{\chi_{LT} W_{1x} f_{y} } \mathord{\left/ {\vphantom {{\chi_{LT} W_{1x} f_{y} } {\gamma_{{{\text{M1}}}} }}} \right. \kern-0pt} {\gamma_{{{\text{M1}}}} }}}} + K_{xy} \frac{{\beta_{my} M_{y} }}{{{{W_{1y} f_{y} } \mathord{\left/ {\vphantom {{W_{1y} f_{y} } {\gamma_{{{\text{M1}}}} }}} \right. \kern-0pt} {\gamma_{{{\text{M1}}}} }}}} \le 1}\);

\({\frac{N}{{{{\chi_{y} Af_{y} } \mathord{\left/ {\vphantom {{\chi_{y} Af_{y} } {\gamma_{{{\text{M1}}}} }}} \right. \kern-0pt} {\gamma_{{{\text{M1}}}} }}}} + K_{yy} \frac{{\beta_{my} M_{y} }}{{{{W_{1y} f_{y} } \mathord{\left/ {\vphantom {{W_{1y} f_{y} } {\gamma_{{{\text{M1}}}} }}} \right. \kern-0pt} {\gamma_{{{\text{M1}}}} }}}} + K_{yx} \frac{{\beta_{mx} M_{x} }}{{{{\chi_{LT} W_{1x} f_{y} } \mathord{\left/ {\vphantom {{\chi_{LT} W_{1x} f_{y} } {\gamma_{{{\text{M1}}}} }}} \right. \kern-0pt} {\gamma_{{{\text{M1}}}} }}}} \le 1}\);

\(\chi_{x} = \frac{1}{{\Phi_{x} + \sqrt {\Phi_{x}^{2} - \overline{\lambda }_{x}^{2} } }},\) \(\chi_{y} = \frac{1}{{\Phi_{y} + \sqrt {\Phi_{y}^{2} - \overline{\lambda }_{y}^{2} } }}\);

\(\overline{\lambda } = \sqrt {{{Af_{y} } \mathord{\left/ {\vphantom {{Af_{y} } {N_{{{\text{cr}}}} }}} \right. \kern-0pt} {N_{{{\text{cr}}}} }}}\);

\(\chi_{{{\text{LT}}}} = \frac{1}{{\Phi_{{{\text{LT}}}} + \sqrt {\Phi_{{{\text{LT}}}}^{2} - \overline{\lambda }_{{{\text{LT}}}}^{2} } }}\);

\(\Phi_{{{\text{LT}}}} = 0.5\left[ 1 + \alpha \left( {\overline{\lambda }}_{{{\text{LT}}}} - 0.2 \right) + {\overline{\lambda }}_{{{\text{LT}}}}^{2} \right]\)

Including both normal force and bi-axial bending, with excessive parameters and complex form

AS/NZS4600-2018²⁸

\(\frac{N}{{A_{e} f_{y}^{\prime} }} + \frac{{M_{y} }}{{\alpha_{y} M_{Py} }} + \frac{{M_{z} }}{{\alpha_{z} M_{Pz} }} = 1\);

\(f_{y}^{\prime} = \left\{ {\begin{array}{*{20}l} {0.658^{{\lambda_{c}^{2} }} f_{y0} ,} \hfill & {\quad \lambda_{c} \le 1.5} \hfill \\ {\frac{0.877}{{\lambda_{c}^{2} }}f_{y0} ,} \hfill & {\quad \lambda_{c} > 1.5} \hfill \\ \end{array} } \right.\);

\(\alpha_{y} = 1 - \frac{N}{{N_{Ey} }},\;\;\alpha_{z} = 1 - \frac{N}{{N_{Ez} }}\)

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