STATIC ANALYSIS OF THIN-WALLED CURVED BEAM ELEMENT INCLUDING WARPING EFFECTS

Abstract

A new mathematical model for three-dimensional thin-walled curved beam element of closedsection with seven degree-of-freedom per node is derived using the finite element procedure. Theseventh degree-of-freedom is to account for warning restraint effects in thin-walled closed sections.These effects may become significant and should be fully considered in such sections for whichwarping deformations are relatively large. This model considers the coupled action due to thecurved geometry of the element using its exact static behavior in the derivation of the displacementfield. Also, the modei considers the non-uniform torsional behavior of closed thin-walled sectionsin cases where additional axial direct stresses and complementary shear stresses are formed. Thedeveloped warping function of this model considers the interaction between the normal warpingstresses and the accompanying warping shear stresses as well as the coupled action between thetorsion and bending.In addition to the ordinary axial and flexural deformations, the strain energy, which is used toobtain the stiffness matrix of the developed curved beam element fully, considers the additionalaxial, primary and secondary shear deformations due to warping restraint. The validity of thiselement is investigated by comparing the developed program analysis results with some availableanalytical solutions.