Analysis Of Warping Displacements Transmission Through Beam-to-Column Joints

Torsional loads produce 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. At the beam-to-column joints, the influence of warping on twisting of contiguous members has not been well solved. In finite element analysis, a difficulty also arises in transforming the warping displacements from local member coordinate system to the global coordinate system. At present, the elements of stiffness matrices for beams and columns corresponding to warping displacements are simply added directly. This treatment implies that the warping degrees of freedom for beams and columns are identical, which is certainly not correct.A column and two perpendicular beams meet together at a joint of a 3-D frame, 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. If some relations exist between the three warping degrees of freedom, these relations may be used to eliminate one or two warping degrees of freedom. This paper analyzed the transmission of warping displacements through commonly used beam-to-column joints.For the most frequently used extended-flange stiffened joints, very simple relations between the three warping displacements are obtained, these relations are then used to eliminate the warping displacements of beams to reduce the number of joint variables to seven. For diagonally stiffened beam-to-column joints, two simple relations between two joint bimoments and two joint warping degrees of freedom are found through a complicated derivation, in which the bending and torsional deformations of beam and column flanges in their own planes within the panel zone, the bending deformation and twisting of the diagonal stiffener were also considered in the proposed model and the restraining of web in the panel zone to the twist of the diagonal stiffener was taken into account. These two equations are then used to modify the stiffness matrices of beam and column connected to the joint. For three-stiffened joint, the same analysis method was used, and eight equations are provided which are then used to get the relations of bimoments and warping displacements of the joint.The suggested model can be implemented simply through modifying the traditional thin-walled beam element matrix. The solutions of different types of joint 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. The suggested model is applicable for flexural and torsional linear and nonlinear analysis of frames composed of thin-walled members.