•The predictive expressions of moment and curvature limit states for high-strength reinforced high-strength concrete (HSC-HSSB) rectangular columns were proposed.•The predictive expressions of drift displacement and shear force limit states for HSC-HSSB rectangular columns were proposed.•Considering the uncertainty of structures, the standard deviation of limit states corresponding to drift displacement and shear force were proposed, which can be applied in fragility analysis. This study presents the derivation of closed-form component limit state expressions for high-strength concrete columns reinforced with high-strength steel bars (HSC-HSSB) from an extensive database through the moment–curvature analysis approach. Initially, sensitivity analysis was conducted to investigate the regularity of the parameters (section size, axial-load ratio, longitudinal reinforcement ratio, stirrup reinforcement ratio, concrete compressive strength, and yield strength of longitudinal reinforcement) on the curvature limit state. The approach being convenient, massive samples were obtained in a short time, therefore, 6^7(279936) levels were generated to derive the predictive expressions of curvature and moment limit states by using the logarithm linearity model. Subsequently, based on the cross-section expressions, the drift displacement and shear force limit states predictive expressions were derived and verified by experimental studies, and these limit states were predicted with high precision. Moreover, after considering the uncertainty of material and section size, the curvature and drift displacement of the HSC-HSSB column exhibited a lognormal distribution, and the useful suggested standard deviations (βc) in different limit states were proposed for practical application of fragility curves to assess the vulnerability of bridge columns to earthquakes.