Study On The Lateral Torsional Buckling And The Distortional Buckling Of The T Shaped Steel Columns Under Axial Compression Based On Plate-beam Theory

Due to the advantages of high strength,light weight,good overall stiffness and strong antideformation ability,steel structures have widely applied in construction engineering.And with the development of economic construction,the structural form is becoming more and more complex and changeable.Flexural-torsional buckling and distortional buckling are common buckling modes in steel structures.Therefore,research on buckling of steel structures has been paid much attention by scholars.However,at present,the research on buckling of steel structures,especially on the problem of distortional buckling,is mainly on experiments and empirical formulas,and the theoretical analysis is less.In reality,only when the problems of flexural-torsional buckling and distortional buckling are solved in theory can the further development of steel structures be go on.Thus,the research on the flexural-torsional buckling and distortional buckling of steel column in this paper has high scientific value and academic significance,and it is also a complex engineering problem to be solved.Therefore,based on the “plate-beam” theory proposed by Professor Zhang Wenfu and the traditional energy method,the flexural-torsional buckling and distortional buckling of T-shaped section columns are studied theoretically.The main contents of this paper are as following:(1)For the flexural-torsional buckling of T shaped slender columns,it is subdivided into 4situation for discussion: the T shaped section cantilever column under constant axial compression,the T shaped section cantilever column under non-constant axial compression,the T shaped section simply supported column under constant axial compression,the T shaped section simply supported column under non-constant axial compression.Then,based on the “plate-beam” theory and the traditional energy method,by giving the cross-section lateral displacement u and the cross-section rotating angle θ,the strain energy and the initial stress potential energy of the member are expressed,and then the total potential energy equation of the member is obtained.After,according to the principle of minimum potential energy,the partial derivative of the total potential energy function is obtained,and the energy matrix of flexural-torsional buckling is obtained.So the required flexuraltorsional buckling critical load by the method of minimum eigenvalue could be given.(2)Using ANSYS finite element program,the finite element models of the T shaped section cantilever column under constant axial compression,the T shaped section cantilever column under non-constant axial compression,the T shaped section simply supported column under constant axial compression,the T shaped section simply supported column under non-constant axial compression are established.Then the element analysis of the flexural-torsional buckling behavior is carried out,and finite element solution is compared with the theoretical analytical solution to verify the precision of the theoretical analytical solution.(3)For the distortional buckling of the T shaped section stub column under 3 conditions,based on the “plate-beam” theory and the traditional energy method,by giving the cross-section lateral displacement u,the cross-section rotating angle θ and the longitude displacement of w with undetermined coefficients,the strain energy and the initial stress potential energy of the member are expressed,and then the total potential energy equation of the member is obtained.After,according to the principle of minimum potential energy,the partial derivative of the total potential energy function is obtained,and the energy matrix of flexural-torsional buckling is obtained.So the required flexuraltorsional buckling critical load by the method of minimum eigenvalue could be given.(4)Using ANSYS finite element program,the finite element models of the T shaped section hinged stub column under constant axial compression,T shaped section cantilever stub column under constant axial compression,T shaped section cantilever stub column under non-constant axial compression are established.Then the element analysis of the distortional buckling behavior is carried out,and finite element solution is compared with the theoretical analytical solution to verify the precision of the theoretical analytical solution.(5)Bleich theory is introduced and used to calculate the critical distortional buckling load of T shaped section hinged supported column.The results are compared with the results of “plate-beam”theory and the finite element respectively.So the accuracy of the “plate-beam” theory in solving the problems of distortional buckling are proved.