Fiber-reinforced polymers (FRPs) retrofit reinforced concrete (RC) structures. ABAQUS finite element software was used to perform numerical parametric analysis on a group of RC beams in this research. All specimens were retrofitted by FRP strips as an external retrofitting and experimentally tested up to previous researchers’ failure points. The range of subjects examined in these RC beams included cracking torque, ultimate torque, angle of twist, and the effect of using FRP on these subjects. We applied artificial neural networks (ANNs) to predict the structural behavior of RC beams under combined torsion and bending to develop the research accuracy. After testing, the ANN results were compared with the ABAQUS results. Consequently, a reasonable examination of the determined mathematical and trial results confirmed this study’s logical accuracy in predicting retrofitted RC beams’ structural behavior under combined loading.

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.

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.

Flexible passive protection structures are a sustainable and environmentally friendly solution for rockfall protection in mountainous regions, owing to their lightweight components and low environmental impact. Their energy dissipators absorb the impact kinetic energy of falling rocks through plastic deformation, accounting for 60~80% of the total energy dissipation. To clarify the influence of energy dissipator configuration and impact location on the energy dissipation distribution, an abstract two-stage model of ring nets and a three-stage equivalent model of braking ring groups were established, and an overall numerical model validated against a 1500 kJ full-scale impact test was constructed. Results show that, under the ETAG central impact mode, energy dissipators exhibit delayed activation and a high dissipation ratio, with the upper-to-lower ratio approaching unity. At a fixed impact energy level, the structural energy-dissipation ratio decreases with increasing working cable force (0.6~0.8 at 1000 kJ) and increases with impact energy level at a decreasing rate. When the impact location deviates from the center, the energy dissipation distribution changes markedly, reaching up to 1.8, 1.2 and 1.15 times the central values for the upper anchor rope, upper support rope and lower support rope. These findings support the sustainable design of flexible protection structures.