A prediction model for the calculation of effective stiffness of circular hollow reinforced concrete piers

To develop a more rational and practical model for estimating the effective stiffness (ES) of circular hollow reinforced concrete piers (CHRCPs), this study compiled a database of 50 quasi-static tests on CHRCPs exhibiting flexural failure, covering axial load ratios of 0.05–0.3, longitudinal reinforcement ratios of 1.0%–5.4%, shear-span ratios of 2.5–6.1, and hollowness ratios of 0.25–0.77. The applicability of existing reinforced concrete piers ES models to CHRCPs was systematically evaluated. Key influencing parameters the ES of CHRCPs were identified and quantified using a simplified three-component yield displacement model. Meanwhile, a new regression-based model was proposed and calibrated through parametric analysis. The model’s accuracy was validated by simulating the lateral force–displacement responses of one full-scale and one scaled CHRCPs. The results demonstrate that, most existing ES models significantly overestimate the ES of CHRCPs, with mean calculated-to-experimental stiffness ratios ranging from 1.41 to 3.68 and coefficients of variation (CVs) of 0.25–0.41. The ES of CHRCPs increases with the axial load ratio, longitudinal reinforcement ratio, and shear-span ratio but decreases with the hollowness ratio. The interaction between shear-span and hollowness ratios was effectively captured via an equivalent shear-span ratio. The proposed model achieves a mean calculated-to-measured stiffness ratio of 1.04 with a CV of 0.21, indicating significantly improved accuracy and reduced dispersion. The proposed model showed good applicability to 11 round-ended hollow piers, achieving a mean stiffness ratio of 0.976 and a mean relative error of 14%, outperforming existing models.