Static Analysis of Thin - Walled Curved Beam Element Including Watping Effects


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