Static Stability of Curved Thin‐Walled Beams

Abstract

Starting from a continuum mechanics basis, the principle of virtual displacements is used for deriving the differential equations of equilibrium for a horizontally curved I‐beam. In the present formulation, the effect of curvature is considered, while the condition of inextensibility, usually adopted in conventional analyses, is not required. The cross‐sectional displacements for the curved I‐beam are derived through employment of Vlasov's thin‐walled beam assumptions. Due to the inclusion of nonlinear strains in the virtual work equation, the instability effects caused by various loads, including the axial force, transverse shears, torque, bending moments, and bimoment are generally taken into account. The solutions are presented and compared with existing ones for two special cases.