A yield curvature model considering axial compression ratio

Advances in Bridge Engineering

Table 1 Summary of some prediction models

Index	Source	Prediction model
Effective yield curvature	Chinese (2020)	\({\varphi }_{y}^{*}=1.957{\varepsilon }_{y}/L\)
	Olivia (Olivia and Mandal 2005)	\({\varphi }_{y}^{*}==\frac{{f}_{y}}{{E}_{s}\left(1-k\right)L}\)
	European (En 2005)	\({\varphi }_{y}^{*}={2.1\varepsilon }_{y}/L\)
	California (ATC-40. 1996)	\({\varphi }_{y}^{*}={2.2\varepsilon }_{y}/L\)
Yield curvature	Hernández (Hernández-Montes and Aschleim 2003)	\({\varphi }_{y}=\frac{{\varepsilon }_{y}}{L}\left[2.3-{\left(0.6-2.5{R}_{ac}\right)}^{2}\right]\)
Yield curvature	Zhong (Zhong et al. 2022a)	\({\varphi }_{y}\)=\({0.0054}_{{\rho }_{s}^{-0.0065}{\rho }_{l}^{0.0341}{R}_{ac}^{0.2097}{L}^{-1.0160}}\)

\({\varphi }_{y}^{*}\) = effective yield curvature; \({\varphi }_{y}\) = yield curvature;\({\varepsilon }_{y}={f}_{y}/{E}_{s}; {f}_{y}\) = the yield strength of longitudinal steel bar;\({E}_{s}\) = the elastic modulus; L = section size; R_ac = axial compression ratio; ρ_s = stirrup reinforcement ratio; ρ_l = longitudinal reinforcement ratio