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Structural Engineering and Mechanics
  Volume 21, Number 1, September10 2005, pages 19-33

Free vibration and elastic analysis of shear-deformable non-symmetric thin-walled curved beams:
A centroid-shear center formulation
Nam-Il Kim and Moon-Young Kim

    An improved shear deformable thin-walled curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled free vibration and elastic analysis. For this, the displacement field considering the shear deformation effects is presented by introducing displacement parameters defined at the centroid and shear center axes. Next the elastic strain and kinetic energies considering the shear effects due to the shear forces and the restrained warping torsion are rigorously derived. Then the equilibrium equations are consistently derived for curved beams with non-symmetric thin-walled sections. It should be noticed that this formulation can be easily reduced to the warping-free beam theory by simply putting the sectional properties associated with warping to zero for curved beams with L- or T-shaped sections. Finally in order to illustrate the validity and the accuracy of this study, finite element solutions using the isoparametric curved beam elements are presented and compared with those in available references and ABAQUS? shell elements.
Key Words
    free vibration; elastic analysis; curved beam; thin-walled; shear deformation; warping.
Nam-Il Kim; Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742, USA
Moon-Young Kim; Department of Civil and Environmental Engineering, Sungkyunkwan University,Cheoncheon-Dong, Jangan-Ku, Suwon 440-746, Korea

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