ANALYSIS OF STATIC CHARACTERISTICS OF THIN-WALLED CURVED U-SHAPED BEAMS CONSIDERING SELF-EQUILIBRIUM

In the consideration of shear lag effects, shear deformation and warping torsion, a new warping displacement model of curved U-shaped beams is chosen to meet the axial self-equilibrium condition for shear lag warping stress, and a more accurate approach is proposed to analyze the mechanical characteristics of curved U-shaped beams used in engineering commonly. The minimum potential principle is applied to establish the governing differential equations and corresponding natural boundary conditions, and thus closed-form solutions of generalized displacements are obtained. The variations of stress of curved U-shaped beams are discussed, caused by the change of factors such as a span-width ratio, the radius of curved beams, the type of loading, and the contribution of self-equilibrium conditions, shear lag effects, shear deformations to stress and the deflection of the U-shaped beam is analyzed in detail, and the importance about the introduction of self-equilibrium conditions is proved.