Theoretical And Experimental Study On Distortional Buckling Of Thin-Walled Members Under Compression

As structural steels with greater and greater strength were developed, the cross-section of cold-formed steel became more open and slim by the requirement on lightweighting structures and the benefits driven on saving steel. This lead to the distortional buckling or distortional interaction buckling may govern the design of compression members.C-section and hat section cold-formed steel compression members experiencing distortional buckling or distortional interaction buckling are studied by combining experimental investigations, theoretical analysis and numerical simulation. The work presented in this thesis is concerned with the following three aspects.1. An analytical theory on distortional buckling of thin-walled members under compressionA total of 36 C-section compression members were tested in order to reveal the influnces of the ratio of web width to flange width, h/b, and the length of memer,lon buckling mode and ultimate load. The deformation of cross-section and the post-buckling were analyzed. Based on the tests, buckling mode identification was proposed.The physical meaning of the effective length factor was revealed, the effective length factors of distortional buckling and local buckling were proposed to unify the characterization of buckling problem. Decomposition analysis method was developed, and the coefficient of boundary conditions of the effective length factor was derived based on the classic plate buckling theory. The total energy equation and the equilibrium equations of flexural-torsional buckling were derived by employing energy method. The equilibrium equations of members with continuous elastic supports were also derived.The results showed that the presented analytical theory was coherent and clear physical meaning. Based on the presented analytical theory, a unified object was proposed, and a chronic problem that the object of buckling problem was different due to different section shape, load conditions or boundary conditions, was solved. The key factor was underlined by the presented analytical theory, and the groundwork was laid for estabilishing theory and design approach on distortional buckling.2. Theory and design approach on distortional buckling of thin-walled members under compressionOn the distortional buckling load, the finite strip method software CUFSM was employed to analysis the effect of Young’s modulus, boundary conditions and scale parameter on the distortional buckling load. Based on the proposed analytical theory of distortion buckling and Lau and Hancock model, unified formulae of the distortional buckling load were derived by employing Galerkin method. A unified theory of the distortional buckling load, Pcr,D , was derived and the general formulae of Pcr,D was proposed. The accuracy and the scope application of the Pcr,D general formulas was checked and determined by the software CUFSM. The Pcr,D general formulae were also compared with other available software and other theoretical formulae. The results shown that the Pcr,D general formulae had higher accuracy and wider scope of application than Lau and Hancock formulae and Schafer formulae.On the distortional buckling ultimate load, the philosophy of structural design, Exhaustive enumeration and Minimization were used to rewrite Schafer formulae of ultimate load, Pu,d for compression members with fixed-end boundary condition. After proposing Pu,D formulae for simply supported members, a unified theory of Pu;D was established and Pu,D general formulae were proposed. ANSYS results of 17 C-section and 17 hat section were employed to validate the accuracy of Pcr,D general formulae again. ANSYS results of 42 C-section and 42 hat section fixed-ended members were employed to verify the accuracy and reliability of Pu,D general formulae.On the condition of distortional buckling and the nature of design theory of distortional buckling, the relations between distortional buckling and λD andλL was developed, a criteria on the condition of distortional buckling was proposed. The ultimate load formulae of different forms were compared and the nature of those formulae was revealed. The nature of the ultimate load theory for distortional buckling is to solve the instability problem instead of strength problem. All those formulae are essentially the same as Direct Strength Method but different from Effective Width Method.Due to the proposed theory and design approach herein, the lack of Pcr,D analytical formulae of fixed-end members was solved. The scope application of the Pcr,D general formulas was expanded. Interface between critical load Pcv,D and ultimate load Pu,D for certain boundary conditions was also sovled.3. Theory and design approach of ultimate load of thin-walled members under compressionOn the basis of the proposed theory and design approach on distortional buckling, the Pu,G practical formulae and the Pcr,L practical formulae, a unified theory of ultimate load was developed. Three different Ultimate Limit State, ULSⅣ, ULSⅥ and ULSⅦ, including different buckling mode, were proposed. The ultimate load, Pu,Ⅳ, Pu, Ⅵ and Pu,Ⅶ corresponding to ULSⅣ, ULSⅥ and ULSⅧ were obtained through the unified theory of ultimate load for a total of 196 C-section and 32 hat section compression members with fixed-ended boundary condition, and also 45 C-section compression members with simple supported condition. The theoretical results were compared with the experimental datas. To improve calculation accuracy and to raise overall material utilization factor, the relations between buckling mode, load-carrying efficiency and λD,λL was developed. A criterion of local-distortional buckling and a criterion of ultimate state were established, respectively. The ultimate loads of those specimens were determined based on those criteria. Finally, recommendations on scale parameter and material were proposed.The results showed that the accuracy of the ultimate load and the load-carrying efficiency are strongly affected by λDandλL.If λD≤ 1.290 and/or λL≤1.130 are satisfied, high load-carrying efficiency and more accurate ultimate load will be obtained. The load-carrying efficiency of local-distortional buckling is low, therefore the buckling mode should be limited. To save the structural steel and improve the accuracy of the ultimate load, the scale parameter of cross-section and the materials of the thin-walled members under compression should be coordinated.The highlights of this thesis are:1. The physical meaning of the effective length factor was revealed for the first time, the objective of buckling problem was unified, that is a member or partial member of length of half-wavelength and with simply supported boundary conditions.2. The unified theories of distortional buckling critical load, Pcr,D and the ultimate load, Pu,D were established and the general formulae of Pcr,D and Pu,D were proposed for the first time.3. The relations between distortional buckling and local-dostortional buckling and λD and λL were founded, and the completely criterion of local-dostortional buckling was proposed for the first time.