Abstract
AbstractAn improved formulation for spatial stability and free vibration analysis of thin‐walled elastic beams is presented by applying Hellinger–Reissner principle and introducing Vlasov's assumption. It includes shear deformation effects due to flexural shear and restrained warping stress, rotary inertia effects and bendirsg–torsional coupling effects due to unsymmetric cross sections. Closed‐form solutions for determining flexural–torsional buckling loads and natural frequencies of unsymmetric simply supported beam‐columns subjected to eccentric axial force are newiy derived and also, the tangent stiffness matrix and stability functions for symmetric thin‐walled beam elements subjected to axial force are presented. In a companion paper,26 these analytic solutions are compared with the finite element solutions according to the increase of shear deformation effects.
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