Fixed‐End Moments and Thrusts of Planar Curved Beams

Formulas of fixed-end moments and thrusts for a curved member of constant section subjected to a uniformly distributed in-plane load are presented. Expressions are 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 works of Parcel and Moorman, and Leontovich. Given a curved beam with the known beam-height-to-span ratio and loading, the fixed-end moments and thrusts can be obtained from the derived expressions. Finally, with some modifications, the present investigation can be applied to curved beams of variable moment of inertia.