Local stability analysis of single-arch ribbed steel box tied arches using a multi-scale model

Studying the local stability of steel arches is a key issue in design, particularly considering non-linear effects. However, existing research still has shortcomings, and the analysis cost when considering non-linear factors has significantly increased. Multi-scale models can provide ideas to address these issues. First, a beam element model and a beam–shell element multi-scale model were established for a single-arch ribbed steel box tied arch; based on elastic stability analysis, non-linear factors were considered in order to study its overall and local stability, as well as the sensitivity of structural parameters to local stability. The results show that the multi-scale model’s live load ratio coefficients were 13.43% and 13.09% lower than those of the beam element model in two different loading scenarios. This indicates that ignoring local instability can overestimate stability. Sensitivity analysis shows that the number of diaphragms seriously affects stability. For 1–3 diaphragms, the coefficient increases with number. Longitudinal stiffener thickness from 12 mm to 18 mm raised the coefficient and reduced the top plate’s transverse wave buckling tendency. When the number of longitudinal stiffeners (per side) on the top plate is 2–5, the coefficient increased with number. Changing stiffener type from rigid to flexible shifted the plastic zone location from the top plate and its stiffeners to the web plate and its stiffeners.