Analysis of Thin-Walled Curved Beams with Variable Cross Section Taking into Account Discontinuity of Shear Center Line

An analytical study is presented of the bending and torsion problem of a thin-walled curved beam with verying cross section, concerning distortion out of its curvature plane. After derivation of the transfer matrix of the thin-walled circular beam owing to the Laplace transform, the reduction method is employed for solving the problem with due regard to the effect of discontinuity of the shear center axis of the beam. As an illustration of the procedure, numerical treatment is examined basing upon the solution developed here for a simply supported S-shaped girder having variable cross section and involving some deviation of the shear center line in horizontal plane at midspan. The results are shown in a warping moment diagram, compared with those of two other cases.