The Analysis Of Restrained Torsion Of Thin-walled Beams Based On First-order Theory

Thin-walled(TW)members are widely used in the fields of civil,mechanical,and naval construction.Since the wall thickness is much smaller than other dimensions of the member,the mechanical properties of TW member are different from those of solid members.Eider-Bernoulli beam theory does not consider the effect of shear deformation on the behavior of beams.Timoshenko beam theory includes the effect of shear deformation,but is limited to flexural analysis of solid beam as well as Euler-Bernoulli beam theory and cannot be used to flexural and torsional analysis of thin-walled beam.Vlasov developed an integrated theory which can analyze the flexural and torsional behavior of thin-walled beam.Benscoter theory is presented for the restrained torsion of closed thin-walled beam.With the growth of national economy,the steel members are widely used.When span-to-height-ratio becomes small,the effect of shear deformation cannot be ignored.The research group proposed a first-order theory for the restrained torsion of TW member.This theory both considers the influence of warping,and effects of shear deformation.Based on the first-order theory and finite element theory,this paper studies the restrained torsion of open and closed TW beams,and the torsional element stiffness matrix are deduced analytical solutions.and the effects of torsion warping and shear deformation is included.The main contents of this paper are given as follows:(1)Derivation of stiffness matrix of restrained torsion element for open TW members.The element has two nodes,each of which has two degrees of freedom,i.e.the total rotation and the twist rate of free warping rotation.Based on the analytical solution of the differential equations of the first-order torsion theory,an accurate interpolation function of the restrained torsion element of an open TW member is obtained.In this interpolation function,the torsional shear coefficient is introduced,which can include the influence of shear deformation,and avoid the phenomenon of shear looking of restrain torsion,and open TW beam.According to the principle of virtual work,the element stiffness matrix of element is obtained.(2)Derivation of stiffness matrix restrained torsion element for closed thin-walled members.The derivation process is similar to the open thin-walled members.According to the particularity of the closed thin-walled section,the influence of Bredt’s torque and secondary restrained torque needs to be considered.According to the principle of virtual work,the element stiffness matrix of closed TW beam element is obtained.(3)Compilation of the torsion element program and analysis.According to the torsion element stiffness matrix of opening and closed TW beam,secondary development is performed though ABAQUS’s UEL.Based on the UEL program.Numerical examples are given to verify the reliability of the current element and the influence of shear deformation.