On Transmission Of Beam-column Joints Warping Displacement And Bimoments

In frames composed of thin-walled members, for the issue of the transmission of warping deformation and bimoment through beam-to-column joints, the general finite element software are not correct in this aspect for long time, which different with solutions of finite element analysis using ANSYS SHELL elements. In order to solve torsion problem of thin-walled beam-to-column structure,we should have another condition:the relationship of generalized force bimoments or the relationship between the generalized force bimoments and generalized displacement warping deformation of the joint. For extended-flange stiffened joints which have specific simple ruleθ'b=-θ'c,this paper, with mathematical induction, verified that the general finite element software consider the couple of generalized force and generalized displacement as:θ'B=θ'c,BωB=BωC·However, the right way should be:θ'B=-θ'c, BωB=-BωC,having great agreements with solutions of finite element analysis using ANSYS SHELL elements.Research indicates that the transmission of bimoments and the twist rates at the joints influencing deformation of frames depends on the config.uration of the joints. This paper form a bidirectional parallel beam system for the frames. The flanges of beams and columns are seen as beams with narrow rectangular cross-sections. Bending and twisting of these beams are considered in establishing equilibrium equations at the four corners. Relating the corner displacements with the member end displacement and expressing the member end forces in terms of the flange plate forces make up a stiffness equation. Reasonable solution of warping transmission have the high accuracy theortically.Based on the suggested model, for the beam-to-column joints stiffened with extended flanges in rectangular frames, numerical examples using Shell63 of ANSYS have excellent agreements with the proposed method and the relation between the warping deformations of columns and beams at the joint,θ'b=-θ'c, is approximately valid; For three-stiffened joint, the diagonal stiffener make the difficulty arise, the same analysis method was used. 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. Comparison with FE Shell analysis verified the accuracy of the proposed model. The existence of diagonal stiffener prevent the transmission of warping, which related with the thickness of diagonal stiffener.The relation of bioments has not been fully touched. Using relations between the flange forces/corner point deformations of the panel zone and the member forces/member deformations, explicit formulas are found to relate the bimoments on the 4 interfaces between the panel zone and the beams/columns to the 4 warping deformations on the interfaces. Based on these relations, the common beam-to-column joints may be seen as "warping semi-rigid".