Nonlinear Buckling Analysis of Steel Arch Structures

Nonlinear buckling analysis of steel arch structures examines their stability under loads that induce large deformations, geometric imperfections and material nonlinearities. Unlike classical linearised treatments, nonlinear approaches capture both bifurcation and limit point phenomena, including sudden snap-through behaviour. Analyses typically employ the principle of virtual work or energy methods to derive equilibrium equations that account for the coupling between axial force and curvature change. Analytical beam models based on Euler–Bernoulli or Timoshenko kinematics afford closed-form estimates of critical loads, while numerical schemes such as the Rayleigh–Ritz procedure and finite element simulations validate pre- and post-buckling paths. Key parameters influencing stability include arch slenderness, rise-to-span ratio, boundary conditions and any variations in temperature or multilayer bonding. Advances in composite and layered steel systems have further highlighted the role of interlayer slip and temperature-induced axial forces, emphasising the need for comprehensive nonlinear formulations to guide safe and efficient design of arch roofs, bridges and architectural shells.

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Technical terms

Bifurcation buckling: The emergence of multiple equilibrium paths from an initial configuration when a critical load is reached.

Limit point buckling: A turning point on the load–displacement curve beyond which snap-through instability occurs.

Interlayer slip: Relative movement between bonded layers in a multilayer arch, affecting overall stiffness and stability.

Slenderness ratio: The ratio of arch span to cross-sectional dimension, governing susceptibility to buckling.

Temperature gradient: Variation of temperature across an arch’s depth that induces non-uniform axial stresses and influences buckling behaviour.

References

1. In-plane instability of shallow layered arches with interlayer slip. Acta Mechanica (2022).
2. In-plane buckling of flexibly bonded three-layer pinned-fixed half-sine shallow arches. International Journal of Non-Linear Mechanics (2023).
3. In‐Plane Instability of Parabolic Arches under Uniformly Distributed Vertical Load Coupled with Temperature Gradient Field. Advances in Civil Engineering (2022).