Static Closed-Form Solutions for In-Plane Thick Curved Beams with Variable Curvatures

Abstract

An analytical method is derived for obtaining the in-plane static closed-form general solutions of thick curved beams with variable curvatures. The strain considering thickness-curvature effect is adopted to develop static governing equations. The governing equations are formulated as functions of the angle of tangent slope by introducing the coordinate system defined by the radius of centroidal axis and the angle of tangent slope. To solve the governing equations, one can define the fundamental geometric properties, such as the first and second moments of the arc length with respect to horizontal and vertical axes. As the radius is given, the fundamental geometric quantities can be calculated to obtain the static closed-form solutions of the axial force, shear force, bending moment, rotation angle, and displacement fields at any cross-section of curved beams. The closed-form solutions of the ellipse, parabola, and exponential spiral beams under various loading cases are presented. The results show the consistency in comparison with existed results.