Promoting prefabricated steel structures is considered one of the crucial approaches to meeting the objectives of “carbon peak” and “carbon neutrality” in the construction industry. Due to insufficient practical experience and incomplete fine engineering techniques in civil construction, the sustainable development of prefabricated building systems in China faces many challenges. Taking steel components as an example, the design process of tubular columns does not pay enough attention to the influence of the cold-working effect on material mechanical properties, and the constitutive relationship of cold-formed steels is not clear, which will cause an engineering economic burden and may affect the judgment of catastrophic problems. To serve the refined design and meet the intelligent construction technology using the computer platform, a modified Menegotto-Pinto model using a continuously derivable function is proposed in the paper. The proposed model can successfully describe the complete stress-strain curve of cold-formed circular mild steels as long as the basic mechanical parameters of the parent material are determined. Taking into account the influence of the strength and thickness of the parent steel sheets, as well as the internal bending radius r, on the cold-rolling effect, the model can also flexibly track the elastic-plastic nonlinearity of the cold-formed materials. In addition, the research shows that the cold-rolling effect will weaken with the increase of the yield strength f_sy,0 of the parent steels and r/t ratio, and may disappear when f_sy,0 reaches 1748 MPa or the r/t ratio is approximately 60, which can be used as economic indicators during the design process.

Limit state analysis provides building designers with a better understanding of fundamental structural resistance and deformation requirements, resulting in an overall material economy and offering clear safety boundary conditions for intelligent structural design. Cold-formed high-strength steel has extensive application prospects in structural engineering due to its excellent mechanical properties and flexible cross-sectional options. However, most existing research focuses on its ultimate strength-related behavior, lacking sufficient investigation into deformation properties. This study aims to comprehensively reveal the continuous variation laws of structural resistance and ductility of cold-formed high-strength CHSs (circular hollow sections) with different cross-sectional selections under axial load. Through reliable finite element analysis, the effects of yield strength (f_sy) of cold-formed CHSs, diameter-to-thickness ratio (D/t), and cross-sectional slenderness (λ) on compressive performance in the limit state, including failure mode, axial load-end shortening curve, ultimate-to-yield strength ratio (N_u/N_y), and ductility indicators (displacement ductility coefficient (μ) corresponding to the ascending stage and post-buckling ductility degradation coefficient (R_0.85)), were systematically investigated. The results indicate that the dominant failure mode of high-strength CHSs exhibits outward deformation. With an increase of f_sy and D/t, the value of N_u/N_y decreases, and the development of multiple compression performance exhibits significant nonlinearity, which indicates that blindly improving material strength may not necessarily be conducive to developing structural compressive performance or achieving efficient and economical design solutions. To better serve the ductile limit design of high-strength CHSs, combined with available experimental data and simulation results, the upper limit of λ is proposed to be 0.22, and the predictive models of μ and R_0.85 are established, respectively.

Multi-criteria group decision making (MCGDM) under linguistic uncertainty remains a fundamental challenge in applied mathematics, where decision makers seldom assign crisp numerical evaluations and frequently exhibit heterogeneous risk attitudes shaped by behavioural factors. An integrated mathematical framework, hereafter PLR-3WBC (Probabilistic Linguistic Regret-driven Three-Way Bayesian Consensus), is developed to systematically integrate four methodological components that have each been individually validated in the MCGDM literature: representation of decision information with explicit probability mass on linguistic terms; quantification of decision-maker regret and rejoice psychology under linguistic uncertainty; classification of alternatives into three actionable decision regions rather than a single-valued ranking; and group consensus reaching with credal weight aggregation. Each component has demonstrated its effectiveness in its respective domain; the present framework capitalises on their complementary strengths by embedding them within a single pipeline equipped with formal guarantees, an integration that has not been previously reported. The framework integrates five methodological components: probabilistic linguistic term sets (PLTS) for information representation; the Bayesian best–worst method (BBWM) for credal criterion weighting; a regret–rejoice value function adapted to the linguistic domain for behavioural evaluation; three-way decision (3WD) thresholds derived from a loss-function model for actionable classification; and a distance-based consensus reaching process with feedback mechanism for group convergence. A case study on age-friendliness evaluation of twelve aging urban residential communities under an indicator system of five dimensions and eighteen criteria, with four expert decision makers, demonstrates that PLR-3WBC delivers an actionable three-way classification, recovers a transparent group consensus, and produces rankings broadly consistent with classical TOPSIS, VIKOR, PROMETHEE-II, and BWM-TOPSIS (Spearman rank correlation exceeding 0.97), thereby confirming that the integrated framework preserves the ordinal reliability of these established methods, while additionally delivering three outputs that arise from the methodological integration: an actionable three-way classification enabling discrete budget-aligned decisions, credal weight intervals quantifying the depth of expert agreement on criterion importance, and a behavioural reordering of borderline non-dominated alternatives that reflects the loss-averse psychology of the decision panel and would remain hidden under single-method deployment. Sensitivity analyses with respect to the regret aversion coefficient, the loss function parameters, and the consensus threshold confirm that the qualitative classification is stable across a wide parameter envelope, supporting the practical deployment of PLR-3WBC in age-friendly community renewal programmes.

As the core interception component of flexible rockfall barriers, the accurate characterization of the mechanical behavior of metal ring nets is essential for the safety assessment of the whole system. To overcome the limitations of existing computational models in reflecting the large-deformation states of the nets and the activation of energy dissipators, systematic uniaxial tension tests and puncture tests were first carried out on five specifications of ring nets (R8 to R19, 30 specimens in total). The results reveal a two-stage deformation feature (an initial low-force tensioning stage followed by a stiffness-hardening rapid-rise stage) and a parallel-superposition load-carrying mechanism under both loading cases. The experimental data were then normalized by dividing the force by the number of steel wires and non-dimensionalizing the dis-placement, on the basis of which a unified piecewise two-stage constitutive model, consisting of a linear tensioning segment and a power-hardening segment, was estab-lished to describe the response up to the peak point; the tensile and puncture cases share the same model form and are distinguished only by different parameters (fitting coefficient of determination R2 not lower than 0.97, with mean values of 0.98 and 0.983, respectively). A full-scale numerical model of the overall structure was subsequently established using LS-DYNA, in which the two side spans adopt the tensile constitutive model and the middle impact span adopts the puncture constitutive model. The model was verified against a 1500 kJ full-scale impact test. The computed time histories of the support-rope forces, the activation states of the energy dissipators (pressure-relief rings), the maximum interception deformation (computed 8.23 m versus measured 8.8 m, with a relative error of about 6.5%) and the energy-dissipation distribution of the pressure-relief rings (average relative error of about 5.2%) all agreed well with the experimental results. The proposed two-stage computational model can therefore accurately reflect the force and deformation states of the ring nets in the actual structure and correctly describe the transmission of the impact force and the activation of the energy dissipators, providing a reliable theoretical basis for the refined design of flexible rockfall barriers.

Metal ring nets are the core interception components of flexible rockfall barriers, and the accurate characterization of their mechanical behavior is essential for the safety assessment of the whole system. To overcome the limitations of existing computational models in reflecting the large-deformation states of the nets and the activation of energy dissipators, systematic uniaxial tension tests and puncture tests were first carried out on five specifications of ring nets (R8 to R19, 30 specimens in total). The results reveal a two-stage deformation feature (an initial low-force tensioning stage followed by a stiffness-hardening rapid-rise stage) and a parallel-superposition load-carrying mechanism under both loading cases. The experimental data were then normalized by dividing the force by the number of steel wires and non-dimensionalizing the displacement, on the basis of which a unified piecewise two-stage constitutive model, consisting of a linear tensioning segment and a power-hardening segment, was established to describe the response up to the peak point; the tensile and puncture cases share the same model form and are distinguished only by different parameters (fitting coefficient of determination R² not lower than 0.97, with mean values of 0.98 and 0.983, respectively). A full-scale numerical model of the overall structure was subsequently established using LS-DYNA, in which the two side spans adopt the tensile constitutive model and the middle impact span adopts the puncture constitutive model. The model was verified against a 1500 kJ full-scale impact test. The computed time histories of the support-rope forces, the activation states of the energy dissipators (pressure-relief rings), the maximum interception deformation (computed 8.23 m versus measured 8.8 m, with a relative error of about 6.5%) and the energy-dissipation distribution of the pressure-relief rings (average relative error of about 5.2%) all agreed well with the experimental results. The proposed two-stage computational model can therefore accurately reflect the force and deformation states of the ring nets in the actual structure and correctly describe the transmission of the impact force and the activation of the energy dissipators, providing a reliable theoretical basis for the refined design of flexible rockfall barriers.