Physics-Guided Prediction of Peak Secant Stiffness Degradation in Reinforced Concrete Columns for Frame-Level Numerical Assessment

Peak secant stiffness degradation in reinforced concrete (RC) columns governs how lateral stiffness is redistributed and where deformation concentrates during repeated earthquake loading. Fixed stiffness-reduction factors and prescribed degradation functions cannot simultaneously account for member properties and deformation demand. This study develops a hierarchical framework for predicting the deformation-dependent peak secant stiffness of rectangular RC columns. Separate specimen-level models estimate the first-reference peak secant stiffness, K0, and the drift capacity, θu, from mechanical descriptors. A physics-guided cumulative sequence model then predicts the normalized stiffness-degradation path, with deformation demand normalized by the predicted drift capacity, θu. Non-negative degradation increments ensure bounded, monotonic stiffness loss. On the test set, the selected K0 predictor achieved R2 = 0.935, MAE = 4.098 kN/mm, and RMSE = 7.666 kN/mm; the selected θu predictor achieved R2 = 0.927, MAE = 0.346 percentage points, and RMSE = 0.512 percentage points. With normalization based on predicted drift capacity, the degradation submodel achieved R2 = 0.9272, MAE = 0.0542, and RMSE = 0.0788, substantially outperforming constant, linear, exponential, and power-law global functions. At frame level, the predicted K^0, θ^u, and degradation ratio are incorporated into an equivalent secant-stiffness procedure. Column shear is obtained directly from the updated stiffness and interstory displacement, without a separate strength-degradation law. Comparisons with OpenSeesPy fiber-frame analyses of 12 two-, three-, and four-story frames yielded mean errors of 8.26–21.88% for base shear, 11.42–24.54% for story shear, and 10.19–23.51% for column shear; the mean absolute error in structural stiffness ratio ranged from 0.019 to 0.068. These comparisons establish a numerical consistency benchmark for the adopted frame configurations and modeling assumptions. The method is intended for stiffness-based peak-response assessment, not as a complete hysteretic constitutive model.