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

Distortional lateral-torsional buckling theories assume that the flanges remain undistorted, while the web is free to distort as a thin plate. Most theories adopt a cubic polynomial distribution along the web height to relate the lateral displacement of the web to the displacements and angles of twist both flanges. The present study develops a family of finite element solutions for the distortional buckling of wide flange beams in which the flanges are assumed to remain undistorted. In contrast to past theories, the lateral displacement distribution along the web height is characterized by superposing (a) two linear modes intended to capture the classical non-distortional lateral-torsional behavior and (b) any number of user-specified Fourier terms intended to capture additional web distortion. In the longitudinal direction, all displacement fields characterizing the lateral displacements are taken to follow a cubic distribution. The first contribution of the thesis develops a finite element formulation that is able to replicate the classical non-distortional lateral torsional buckling solutions when the distortional modes are suppressed while enabling more accurate predictions for distortional lateral torsional buckling compared to those solutions based on the conventional cubic interpolation of the lateral displacement. The formulation is used to conduct an extensive parametric study to quantify the reduction in critical moments due to web distortion relative to the classical non-distortional predictions in the case of simply-supported beams, cantilevers, and beams with an overhang. The solution is then used to generate interaction curves for beams with an overhang subjected to various proportions of uniformly distributed and point loads. The second contribution of the thesis adds two additional features to the formulation (a) to capture the destabilizing effect due to the load height relative to the shear center and (b) a module that incorporates any number of user-defined multi-point kinematic constraints. The additional features are employed to investigate the effect of load height, bracing height, and combined effects thereof in practical design problems. A distortional indicator is then introduced to characterize the distribution of web distortion along the beam span as the beam undergoes distortional lateral buckling. A systematic design optimization technique is then devised to identify the location(s) along the span at which the addition of transverse stiffeners would maximize the critical moment capacity.

No description available.

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.

The mechanical behaviour of the three advanced high strength steel grades, Docol 600DP, Docol 1200M and HyTens 1000, has been experimentally investigated under various types of deformation, and material models have been developed, which account for the experimentally observed behaviour. Two extensive experimental programmes have been conducted in this work. In the first, the dual phase Docol 600DP steel and martensitic Docol 1200M steel were subjected to deformations both under linear and non-linear strain paths. Regular test specimens were made both from virgin materials, i.e. as received, and from materials pre-strained in various directions. The plastic strain hardening, as well as plastic anisotropy and its evolution during deformation of the two materials, were evaluated and modelled with a phenomenological model. In the second experimental program, the austenitic stainless HyTens 1000 steel was subjected to deformations under various proportional strain paths and strain rates. It was shown experimentally that the material is sensitive both to dynamic and static strain ageing. A phenomenological model accounting for these effects was developed, calibrated, implemented in a Finite Element software and, finally,validated. Both direct methods and inverse analyses were used in order to calibrate the parameters in the material models. The agreement between the  numerical and experimental results are in general very good. This thesis is divided into two main parts. The background, theoretical framework and mechanical experiments are presented in the rst part. In the second part, two papers are appended.