2007 Volume 1 Issue 11 Pages 1362-1373
An analytical method is derived for obtaining the in-plane static closed-form general solutions of shear deformable curved beams with variable curvatures. The shear deformation effect based on the Timoshenko beam theory is included to develop the general theories of thin and thick curved beams. In these theories, the governing equations are formulated as functions of the tangent angle by introducing the coordinate system defined by the radius of centroidal axis and the angle of tangent. 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 of centroidal axis 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-sections 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.
