Presently, the industry accepted method for the determination of the governing buckling strength for cold-formed purlins supporting a standing seam metal roof system is the 1996 AISI Specification for the Design of Cold-Formed Steel Structural Members, which contains provisions for local and lateral buckling. Previous research has determined that the AISI provisions for local buckling strength predictions of cold-formed purlins are highly unconservative and that the AISI provisions for lateral buckling strength predictions of cold-formed purlins are overly conservative. Therefore, a more accurate "hand" method is needed to predict the buckling strengths of cold-formed purlins supporting standing seam roof systems. The primary objective of this study is to investigate the accuracy of the Hancock Method, which predicts distortional buckling strengths, as compared to the 1996 AISI Specification provisions for local and lateral buckling. This study used the experimental results of 62 third point laterally braced tests and 12 laterally unbraced tests. All tests were simple span, cold-formed Z-section supported standing seam roof systems. The local, lateral, and distortional buckling strengths were predicted for each test using the aforementioned methods. These results were compared to the experimentally obtained data and then to each other to determine the most accurate strength prediction method. Based on the results of this study, the Hancock Method for the prediction of distortional buckling strength was the most accurate method for third point braced purlins supporting standing seam roof systems. In addition, a resistance factor was developed to account for the variation between the experimental and the Hancock Method's predicted strengths. / Master of Science

Presented are approximate finite strip methods for use in predicting elastic buckling strength of cold-formed steel columns. These methods were developed by examining elemental behavior of cross-sections in eigen-buckling analyses and validated using a large database of finite element rack-type columns with perforation patterns. The influence of perforations is accounted by reduced thicknesses related to the plate buckling coefficient and transverse web rotational stiffness in the prediction of local and distortional buckling respectively. Global buckling prediction including the influence of perforations uses critical elastic loads of an unperforated section multiplied by the ratio of weighted to gross cross-sectional moment of inertia for flexural buckling and the ratios of weighted to gross cross-sectional warping torsion constant and weighted to gross St. Venant torsional constant for flexural-torsional buckling. Concern for end-user was given and methods are presented in a way for incorporation into governing design standards. Data to support these findings are available at http://hdl.handle.net/10919/23797 / Master of Science

Os perfis de aço formados a frio apresentam, em geral, elevada relação largura/espessura, tornando-os suscetíveis à flambagem local, caracterizada por uma flambagem de chapa, mas que também pode ocasionar um outro modo de flambagem, denominado flambagem por distorção, desconsiderado no dimensionamento de perfis laminados, mas que pode resultar crítico principalmente nos perfis com enrijecedores de borda e constituídos por aço de elevada resistência mecânica. Tal fenômeno é caracterizado pela perda de estabilidade do conjunto formado pelo elemento comprimido e seu enrijecedor de borda, alterando a forma inicial da seção transversal. Portanto, as normas mais atuais têm apresentado procedimentos para avaliar a resistência de barras com base na flambagem por distorção, como o procedimento simplificado da norma australiana AS/NZS 4600:1996, proposto por HANCOCK e que foi também adotado pela recente norma brasileira NBR 14762:2001, o método direto de resistência, recentemente proposto para incorporação à especificação do AISI (American Iron and Steel Institute) e a GBT (Generalized Beam Theory).Nesse trabalho é feita uma abordagem dos procedimentos propostos para a avaliação da flambagem por distorção em barras submetidas à compressão centrada e à flexão, comparando-se os resultados obtidos pelo procedimento da norma brasileira, pela análise elástica via método das faixas finitas - MFF e pela análise via método dos elementos finitos - MEF, admitindo barras sem e com imperfeições iniciais. É feita também uma abordagem com relação aos outros procedimentos internacionais para a avaliação do fenômeno. / Cold-formed steel members present, in many cases, an elevated width/thickness ratio (thin-walled members), which probably lead up to the local buckling, which is characterized by a plate buckling, and also may lead up to another buckling mode, called distortional buckling, not considered on the design of hot-rolled members, but which may result critical in cold-formed members, specially in the ones with edge stiffeners and made with high strength steel. Such phenomena is characterized by the instability of the group formed by the compression flange and its stiffener, changing the initial shape of the cross section. Nowadays, codes present procedures to evaluate member’s resistance also due to distortional buckling, as the simplified method in the Australian code, AS/NZS 4600:1996, proposed by HANCOCK, which was adopted by the new Brazilian code, NBR 14762:2001, the Direct Strenght Method, recently proposed as an AISI (American Iron and Steel Institute) Draft, and the GBT (Generalilzed Beam Theory).This work talks about procedures proposed to evaluate distortional buckling in members under compression and bending, comparing results obtained by the method showed in the brazilian code, by numerical Finite Strip Method elastic analisys - FSM, and by Finite Element Method analisys – FEM, on members with and without initial imperfections. It is also done an explanation related to other international procedures to evaluate the phenomena.

Thin-walled steel sections made from high strength thin cold-reduced G550 steel to Australian Standard AS 1397-1993 under compression are investigated experimentally and theoretically in this thesis. This thesis describes three series of compression tests performed on box-section stub columns, box-section long columns and lipped channel section columns cold-formed from high strength steel plates in 0.42 mm or 0.60 mm thickness with nominal yield stress of 550 MPa. The tests presented in this thesis formed part of an Australian Research Council research project entitled: Compression Stability of High Strength Steel Sections with Low Strain-Hardening. For the fix-ended stub column tests, a total of 94 lipped-square and hexagonal section stub columns were tested to study the influence of low strain hardening of G550 steel on the compressive section capacities of the column members. For the pin-ended long column tests, a total of 28 box-section columns were tested to study the stability of members with sections which undergo local instability at loads significantly less than the ultimate loads. For the fix-ended lipped channel section columns, a total of 21 stub and long columns were tested to study the failure resulting from local and distortional buckling with interaction between the modes. A numerical simulation on the three series of tests using the commercial finite element computer program ABAQUS is also presented as part of this thesis. The post-buckling behaviour of thin-walled compression members is investigated. The effect of changing variables, such as geometric imperfections and end boundary conditions is also investigated. The ABAQUS analysis gives accurate simulations of the tests and is in good agreement to the experimental results. Theoretical studies using finite strip methods are presented in this thesis to investigate the buckling behaviour of cold-formed members in compression. The theoretical studies provide valuable information on the local and distortional buckling stresses for use in the interaction buckling studies. The finite strip models used are the semi-analytical and spline models. As expected for the stub columns tests, the greatest effect of low strain hardening was for the stockier sections where material properties play an important role. For the more slender sections where elastic local buckling and post-local buckling are more important, the effect of low strain hardening does not appear to be as significant. The pin-ended and fix-ended long column tests show that interaction, which is between local and overall buckling in the box sections, and between local and distortional buckling in the open channel sections, has a significant effect on their member capacities. The results of the successful column tests and ABAQUS simulation have been compared with the design procedures in the Australian & New Zealand Standard for Cold-Formed Steel Structures AS&NZS 4600 and the North American Specification for Cold-Formed Steel Structural Members prepared by the American Iron and Steel Institute. The stub column tests show that the current design rules give too conservative predictions on the compressive section capacities of the column members; whereas the long column tests show that the current column design rules are unconservative if used in their current form for G550 steel. Three design proposals are presented in this thesis to account for the effects of high strength thin steels on the section and member capacities.

Thin-walled steel sections made from high strength thin cold-reduced G550 steel to Australian Standard AS 1397-1993 under compression are investigated experimentally and theoretically in this thesis. This thesis describes three series of compression tests performed on box-section stub columns, box-section long columns and lipped channel section columns cold-formed from high strength steel plates in 0.42 mm or 0.60 mm thickness with nominal yield stress of 550 MPa. The tests presented in this thesis formed part of an Australian Research Council research project entitled: Compression Stability of High Strength Steel Sections with Low Strain-Hardening. For the fix-ended stub column tests, a total of 94 lipped-square and hexagonal section stub columns were tested to study the influence of low strain hardening of G550 steel on the compressive section capacities of the column members. For the pin-ended long column tests, a total of 28 box-section columns were tested to study the stability of members with sections which undergo local instability at loads significantly less than the ultimate loads. For the fix-ended lipped channel section columns, a total of 21 stub and long columns were tested to study the failure resulting from local and distortional buckling with interaction between the modes. A numerical simulation on the three series of tests using the commercial finite element computer program ABAQUS is also presented as part of this thesis. The post-buckling behaviour of thin-walled compression members is investigated. The effect of changing variables, such as geometric imperfections and end boundary conditions is also investigated. The ABAQUS analysis gives accurate simulations of the tests and is in good agreement to the experimental results. Theoretical studies using finite strip methods are presented in this thesis to investigate the buckling behaviour of cold-formed members in compression. The theoretical studies provide valuable information on the local and distortional buckling stresses for use in the interaction buckling studies. The finite strip models used are the semi-analytical and spline models. As expected for the stub columns tests, the greatest effect of low strain hardening was for the stockier sections where material properties play an important role. For the more slender sections where elastic local buckling and post-local buckling are more important, the effect of low strain hardening does not appear to be as significant. The pin-ended and fix-ended long column tests show that interaction, which is between local and overall buckling in the box sections, and between local and distortional buckling in the open channel sections, has a significant effect on their member capacities. The results of the successful column tests and ABAQUS simulation have been compared with the design procedures in the Australian & New Zealand Standard for Cold-Formed Steel Structures AS&NZS 4600 and the North American Specification for Cold-Formed Steel Structural Members prepared by the American Iron and Steel Institute. The stub column tests show that the current design rules give too conservative predictions on the compressive section capacities of the column members; whereas the long column tests show that the current column design rules are unconservative if used in their current form for G550 steel. Three design proposals are presented in this thesis to account for the effects of high strength thin steels on the section and member capacities.

Os perfis de aço formados a frio apresentam, em geral, elevada relação largura/espessura, tornando-os suscetíveis à flambagem local, caracterizada por uma flambagem de chapa, mas que também pode ocasionar um outro modo de flambagem, denominado flambagem por distorção, desconsiderado no dimensionamento de perfis laminados, mas que pode resultar crítico principalmente nos perfis com enrijecedores de borda e constituídos por aço de elevada resistência mecânica. Tal fenômeno é caracterizado pela perda de estabilidade do conjunto formado pelo elemento comprimido e seu enrijecedor de borda, alterando a forma inicial da seção transversal. Portanto, as normas mais atuais têm apresentado procedimentos para avaliar a resistência de barras com base na flambagem por distorção, como o procedimento simplificado da norma australiana AS/NZS 4600:1996, proposto por HANCOCK e que foi também adotado pela recente norma brasileira NBR 14762:2001, o método direto de resistência, recentemente proposto para incorporação à especificação do AISI (American Iron and Steel Institute) e a GBT (Generalized Beam Theory).Nesse trabalho é feita uma abordagem dos procedimentos propostos para a avaliação da flambagem por distorção em barras submetidas à compressão centrada e à flexão, comparando-se os resultados obtidos pelo procedimento da norma brasileira, pela análise elástica via método das faixas finitas - MFF e pela análise via método dos elementos finitos - MEF, admitindo barras sem e com imperfeições iniciais. É feita também uma abordagem com relação aos outros procedimentos internacionais para a avaliação do fenômeno. / Cold-formed steel members present, in many cases, an elevated width/thickness ratio (thin-walled members), which probably lead up to the local buckling, which is characterized by a plate buckling, and also may lead up to another buckling mode, called distortional buckling, not considered on the design of hot-rolled members, but which may result critical in cold-formed members, specially in the ones with edge stiffeners and made with high strength steel. Such phenomena is characterized by the instability of the group formed by the compression flange and its stiffener, changing the initial shape of the cross section. Nowadays, codes present procedures to evaluate member’s resistance also due to distortional buckling, as the simplified method in the Australian code, AS/NZS 4600:1996, proposed by HANCOCK, which was adopted by the new Brazilian code, NBR 14762:2001, the Direct Strenght Method, recently proposed as an AISI (American Iron and Steel Institute) Draft, and the GBT (Generalilzed Beam Theory).This work talks about procedures proposed to evaluate distortional buckling in members under compression and bending, comparing results obtained by the method showed in the brazilian code, by numerical Finite Strip Method elastic analisys - FSM, and by Finite Element Method analisys – FEM, on members with and without initial imperfections. It is also done an explanation related to other international procedures to evaluate the phenomena.

Cold-formed steel roof truss systems that use complex stiffener patterns in existing hat shape members for both top and bottom chord elements are a growing trend in the North American steel framing industry. When designing cold-formed steel sections, a structural engineer typically tries to improve the local buckling behavior of the cold-formed steel elements. The complex hat shape has proved to limit the negative influence of local buckling, however, distortional buckling can be the controlling mode of failure in the design of chord members with intermediate unbraced lengths. The chord member may be subjected to both bending and compression because of the continuity of the top and bottom chords. These members are not typically braced between panel points in a truss. Current 2001 North American Specifications (NAS 2001) do not provide an explicit check for distortional buckling. This dissertation focuses on the behavior of complex hat shape members commonly used for both the top and bottom chord elements of a cold-formed steel truss. The results of flexural tests of complex hat shape members are described. In addition, stub column tests of nested C-sections used as web members and full scale cold-formed steel roof truss tests are reported. Numerical analyses using finite strip and finite element procedures were developed for the complex hat shape chord member in bending to compare with experimental results. Both elastic buckling and inelastic postbuckling finite element analyses were performed. A parametric study was also conducted to investigate the factors that affect the ultimate strength behavior of a particular complex hat shape. The experimental results and numerical analyses confirmed that modifications to the 2001 North American Specification are necessary to better predict the flexural strength of complex hat shape members, especially those members subjected to distortional buckling. Either finite strip or finite element analysis can be used to better predict the flexural strength of complex hat shape members. Better understanding of the flexural behavior of these complex hat shapes is necessary to obtain efficient, safe design of a truss system. The results of these analyses will be presented in the dissertation. / Ph. D.

Apresenta-se neste trabalho um estudo teórico-experimental sobre a instabilidade de perfis formados a frio submetidos à flexão. A instabilidade distorcional se faz comum na presença de tensões de compressão atuando sobre perfis enrijecidos e fabricados com aços de elevada resistência mecânica. A parte teórica abrange os métodos de cálculo analíticos e numéricos para a análise de instabilidade distorcional de perfis de seção aberta formados a frio. Na parte experimental inclui-se o estudo de perfis formados a frio com seções do tipo U enrijecidos submetidos aos ensaios à flexão. Nestes ensaios variou-se a altura de alma e espessura de chapa procurando-se abranger maior número de condições geométricas para análise da estabilidade distorcional. Inclui-se também a análise de instabilidade numérica dos perfis do programa experimental através do método de resistência direta via método das faixas finitas. Com base nos resultados experimentais, numéricos e na análise teórica do problema, verificou-se o procedimento adotado pela NBR14762/2001 e efetuou-se comparação entre curvas de resistência propostas para o dimensionamento de perfis formados a frio à flexão. Foi verificado que o fenômeno de instabilidade distorcional pode ser o estado limite último crítico para o dimensionamento dos perfis formados a frio. / This work present a study theoretical-experimental about the distortional buckling of cold-formed steel members under bending. The distortional buckling is common for members with edge-stiffened sections and manufactured with steel of high strength. The theorical part present the analitic and numerical methods for stability analysis by distortional buckling. The experimental part included the study of cold-formed with sections channel altering flange width and thickness by proof in flexural members. Included too the numerical analysis by Direct Strength Method in Finite Strip Method on members with the same configurations of experimental investigation. Based on the experimental measurements, numerical analysis and in the theorical analysis of work, verified the procedures adopted in brazilian code NBR14762/2001 and compared with others distortional curve proposed for to design of cold-formed members under bending. Verified that the distortional buckling may control the design being the critical mode for the ultimate limit state.

Until recently, the hot-rolled steel members have been recognized as the most popular and widely used steel group, but in recent times, the use of cold-formed high strength steel members has rapidly increased. However, the structural behavior of light gauge high strength cold-formed steel members characterized by various buckling modes is not yet fully understood. The current cold-formed steel sections such as C- and Z-sections are commonly used because of their simple forming procedures and easy connections, but they suffer from certain buckling modes. It is therefore important that these buckling modes are either delayed or eliminated to increase the ultimate capacity of these members. This research is therefore aimed at developing a new cold-formed steel beam with two torsionally rigid rectangular hollow flanges and a slender web formed using intermittent screw fastening to enhance the flexural capacity while maintaining a minimum fabrication cost. This thesis describes a detailed investigation into the structural behavior of this new Rectangular Hollow Flange Beam (RHFB), subjected to flexural action The first phase of this research included experimental investigations using thirty full scale lateral buckling tests and twenty two section moment capacity tests using specially designed test rigs to simulate the required loading and support conditions. A detailed description of the experimental methods, RHFB failure modes including local, lateral distortional and lateral torsional buckling modes, and moment capacity results is presented. A comparison of experimental results with the predictions from the current design rules and other design methods is also given. The second phase of this research involved a methodical and comprehensive investigation aimed at widening the scope of finite element analysis to investigate the buckling and ultimate failure behaviours of RHFBs subjected to flexural actions. Accurate finite element models simulating the physical conditions of both lateral buckling and section moment capacity tests were developed. Comparison of experimental and finite element analysis results showed that the buckling and ultimate failure behaviour of RHFBs can be simulated well using appropriate finite element models. Finite element models simulating ideal simply supported boundary conditions and a uniform moment loading were also developed in order to use in a detailed parametric study. The parametric study results were used to review the current design rules and to develop new design formulae for RHFBs subjected to local, lateral distortional and lateral torsional buckling effects. Finite element analysis results indicate that the discontinuity due to screw fastening has a noticeable influence only for members in the intermediate slenderness region. Investigations into different combinations of thicknesses in the flange and web indicate that increasing the flange thickness is more effective than web thickness in enhancing the flexural capacity of RHFBs. The current steel design standards, AS 4100 (1998) and AS/NZS 4600 (1996) are found sufficient to predict the section moment capacity of RHFBs. However, the results indicate that the AS/NZS 4600 is more accurate for slender sections whereas AS 4100 is more accurate for compact sections. The finite element analysis results further indicate that the current design rules given in AS/NZS 4600 is adequate in predicting the member moment capacity of RHFBs subject to lateral torsional buckling effects. However, they were inadequate in predicting the capacities of RHFBs subject to lateral distortional buckling effects. This thesis has therefore developed a new design formula to predict the lateral distortional buckling strength of RHFBs. Overall, this thesis has demonstrated that the innovative RHFB sections can perform well as economically and structurally efficient flexural members. Structural engineers and designers should make use of the new design rules and the validated existing design rules to design the most optimum RHFB sections depending on the type of applications. Intermittent screw fastening method has also been shown to be structurally adequate that also minimises the fabrication cost. Product manufacturers and builders should be able to make use of this in their applications.

Apresenta-se neste trabalho um estudo teórico-experimental sobre a instabilidade de perfis formados a frio submetidos à flexão. A instabilidade distorcional se faz comum na presença de tensões de compressão atuando sobre perfis enrijecidos e fabricados com aços de elevada resistência mecânica. A parte teórica abrange os métodos de cálculo analíticos e numéricos para a análise de instabilidade distorcional de perfis de seção aberta formados a frio. Na parte experimental inclui-se o estudo de perfis formados a frio com seções do tipo U enrijecidos submetidos aos ensaios à flexão. Nestes ensaios variou-se a altura de alma e espessura de chapa procurando-se abranger maior número de condições geométricas para análise da estabilidade distorcional. Inclui-se também a análise de instabilidade numérica dos perfis do programa experimental através do método de resistência direta via método das faixas finitas. Com base nos resultados experimentais, numéricos e na análise teórica do problema, verificou-se o procedimento adotado pela NBR14762/2001 e efetuou-se comparação entre curvas de resistência propostas para o dimensionamento de perfis formados a frio à flexão. Foi verificado que o fenômeno de instabilidade distorcional pode ser o estado limite último crítico para o dimensionamento dos perfis formados a frio. / This work present a study theoretical-experimental about the distortional buckling of cold-formed steel members under bending. The distortional buckling is common for members with edge-stiffened sections and manufactured with steel of high strength. The theorical part present the analitic and numerical methods for stability analysis by distortional buckling. The experimental part included the study of cold-formed with sections channel altering flange width and thickness by proof in flexural members. Included too the numerical analysis by Direct Strength Method in Finite Strip Method on members with the same configurations of experimental investigation. Based on the experimental measurements, numerical analysis and in the theorical analysis of work, verified the procedures adopted in brazilian code NBR14762/2001 and compared with others distortional curve proposed for to design of cold-formed members under bending. Verified that the distortional buckling may control the design being the critical mode for the ultimate limit state.