Stiffness Coefficients of Noncircular Curved Beams

Abstract

The stiffness coefficient matrix for a curved member of constant cross section considering the effect of flexural deformation is presented. This matrix relates the member-end rotations, vertical deflections, and horizontal translations to the internal bending moments, vertical shears, and horizontal thrusts. Expressions of the stiffness coefficients have been derived for noncircular curved beams of cycloidal, catenary, elliptic, and sine shapes. For curved beams of circular and parabolic shapes, expressions can be found from the writers' previous work. For a given curbed beam with the beam-height-to-span ratio known, the stiffness coefficients can be obtained from the derived expressions. Finally, with some modifications, this matrix can be applied to curved beams of variable moment of inertia.