Studies On Nonlinear Bending Response And Instability Of The Cold-formed Thin-walled Members

With the increasing use of the steel structures in construction,cold-formed thin-walled members are widely used as structural components in building and many other civil engineering fields.The cold-formed thin-walled members are often used as purlin,roofing beam,column etc.These members may be subjected to axial and bending loads.With the increase of applied loads,the section of these members would suffer the same flattening as the Brazier’s flattening deformation(Brazier effect),which can lead the members to have nonlinear snap-through instability.However,despite the large number of publications on cold-formed thin-walled members,there is little work found on the nonlinear analysis with considering the effect of cross-sectional deformation on the bending response of the member.In this thesis,the Brazier approach is used to investigate the nonlinear bending response of thin-walled open cross-section(channel-section)and closed cross-section(box-section)beams when subjected to a uniformly distributed load.The bending response of simply supported channel-section beam about minor axis and box-section beam about principal axis of finite length are investigated by using energy methods.The basic assumptions used in the present study are that the total strain energy of a thin-walled beam subjected to uniformly distributed loading can be simplified into a two-stage analysis process.One is the local bending response of the web and the flange behaving as a plate;the other is the overall bending response of the beam with a deformed cross-section.Analytical solutions of nonlinear instability of the channel section and box section beams are derived by using the minimum potential energy principle.To validate the analytical solutions developed,geometric nonlinear finite element analyses are also conducted.Good agreement between the present solutions and the FEA results is demonstrated.Moreover,the effect of longitudinal stiffener(a stiffener added in the midline of the web)on the nonlinear bending response of channel-section beams is investigated.The dynamic instability of channel-section beam subjected to sudden step uniformly distributed load has been determined by using the Simitses’ s method.The effect of beam length on the nonlinear bending response and critical moment of channel-section and box-section beams is also discussed.It is found that the critical moment decreases slightly with the increase of the beam length.However,the maximum deflection increases rather quickly with the increase of the beam length.