Analysis Of Warping Transfer At Joints Between Box-columns And I-beams

Torsional loads produce significant warping displacements in thin-walled members. Its influence on strength, stability and vibration of thin-walled members must be considered in many cases. Most of the early studies on warping torsion were concentrated on isolated members. Warping displacements transfer through beam-to-column joints is unknown, and warping in structures composed of thin-walled members has not been well solved. At present, the elements of stiffness matrices for beams and columns corresponding to warping displacements are simply added directly, which is also used in some popular finite element programs. This treatment implies that the warping degrees of freedom for beams and columns are identical, which may produce unexpected result.A column and two perpendicular beams meet together at a rigid joint of a 3-D frame, considering the three warping displacements different each other, and there will be nine displacements at the joint instead of seven variables currently used, i.e. 3 translational, 3 rotational and 3 warping degrees of freedom. In fact, some relations exist between the three warping degrees of freedom, which may be used to eliminate one or two warping degrees of freedom.Box section has many advantages in mechanical performance, such as almost the same stability and rigidity of the two principal axes, high torsional rigidity, high bearing capability, less steel consumption and simple assemblage of joints. This paper analyzes the warping transfer at joints between box-columns and I-beams. Box section belongs to close section, the torsional rigidity of which is great but the warping rigidity is small, sometimes equaling zero. When the warping rigidity equals zero, no warp happens and the torsion of thin-walled members is always free torsion, warping degree of freedom not needed. Therefore, two cases, the warping rigidity of box section equaling zero and the warping rigidity of box section not equaling zero, are discussed. The former case is analyzed in chapter 2, a virtual warping degree of freedom for the column at the joint is introduced, very simple relations between which and the two warping displacements of the beams are then obtained. The end warping restraints for beams at the joint are studied. The latter case is analyzed in chapter 3, very simple relations between the three warping displacements are obtained, thus only one warping degree of freedom is needed at the joint. Relations of bimoments and warping displacements for beams at the joint are also deduced. Elastic flexural-torsional buckling of some simple frames composed of thin-walled members is analyzed in chapter 4, and warping transfer at joints mentioned in this paper is employed.The method of this paper is programmed by modifying the traditional thin-walled beam element matrix. The solutions using obtained relations are compared with solutions of finite element analysis using ANSYS SHELL elements, and very good agreements are achieved, while the results with traditional continuous warping assumption has great differences with the finite element results.