Theoretical nonlinear force-displacement constitutive model of hollow tapered steel energy-dissipating restrainers for long-span bridges

Existing tapered steel energy-dissipating restrainers (TSERs) are characterized by solid sections, which limit the internal steel’s ability to dissipate energy fully during the energy dissipation process. The increasing demand for large-tonnage TSERs in long-span bridges has led to several challenges, including increased device weight and installation difficulties. Furthermore, there is a notable absence of theoretical nonlinear force-displacement constitutive models (TNFCMs) for TSERs in current research. To address these limitations, this study proposes a hollow tapered steel energy-dissipating restrainer (HTSER). A TNFCM for the HTSER under monotonic loading was derived, encompassing its elastic, elastic-plastic, and plastic hardening stages. The derivation is based on the uniform strength design principle and a sectional moment-curvature analysis. To systematically validate the TNFCMs for HTSERs, this study combines experimental and numerical approaches: full-scale HTSER specimens with inner-to-outer diameter ratios ( β ) of 0.7 and 0 were fabricated and subjected to quasi-static experiments; furthermore, six refined numerical models were established to provide multi-scenario verification of the theoretical curves. The results demonstrate that the HTSER exhibits stable, full hysteresis loops, indicating excellent energy dissipation capacity. Both experimental and numerical simulation results confirm that the theoretical force-displacement curves agree well with the measured and simulated skeleton curves, with key mechanical parameter errors remaining below 18 %. The proposed theoretical model, validated through multiple dimensions, provides a direct and reliable tool for the design and performance prediction of HTSERs in engineering practice.