Simplified stiffness models: Numerical optimization of story-dependent calibration for RC moment frames

Classical analytical formulations for lateral story stiffness in reinforced concrete (RC) moment-resisting frames (MRFs) are widely used in simplified seismic analysis but are known to overestimate elastic stiffness, particularly in multi-span configurations. This study proposes a numerical calibration framework to improve analytical story stiffness estimation while preserving the closed-form structure of classical formulations. Forty-nine RC MRF portal frame configurations with span numbers ranging from one to seven were analyzed using linear elastic numerical models to obtain reference story stiffness values. The analytical formulation is enhanced through a beam–column interaction factor and a span-dependent correction factor calibrated using nonlinear least-squares optimization with story-dependent parameters for base, middle, and top stories. The calibrated model shows excellent agreement with numerical results, achieving a coefficient of determination of R2 = 0.9998 with negligible systematic bias. The proposed approach provides a practical and computationally efficient tool for estimating lateral story stiffness in RC MRF structures for preliminary design and simplified seismic analysis.