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Este artigo tem como objetivo abordar os resultados parciais de uma pesquisa de Mestrado, que teve como objetivo investigar a influência do curso de formação continuada em Astronomia e seu ensino, ofertado ao NRE-Maringá, em 2018, para a constituição da identidade profissional dos professores de Ciências participantes. Dessa forma, seis professoras participantes do referido curso, através de reuniões online (gravadas) e Google Forms, responderam ao questionário – TALP (Técnica de Associação Livre de Palavras), a fim de identificarmos as representações sociais compartilhadas por elas quanto à Astronomia. Os dados foram analisados à luz da abordagem estruturalista de Abric (2000), identificando o núcleo central (nosso objeto de estudo) e os elementos periféricos e intermediários da RS (Representação Social). Assim, pudemos inferir que, no tocante ao Ensino da Astronomia, as professoras pesquisadas apresentam muito do universo consensual, não alcançando, muitas vezes, o universo reificado, o que nos permite compreender que muitos professores que ensinam conteúdos de Astronomia apresentam um nível de entendimento/conhecimento muito semelhante ao dos alunos, permanecendo por vezes, no universo consensual ao abordarem tais conteúdos.

This paper reports an in-depth and extensive numerical investigation aimed at assessing the accuracy of the current Direct Strength Method (DSM) design curve in predicting the failure load of cold-formed steel columns collapsing in global modes, namely flexural or flexural-torsional modes. This study concerns fixed-ended columns with a wide variety of cross-section shapes: plain channels, lipped channels, double-fold (return) lipped channels, web-stiffened lipped channels, web/flange-stiffened lipped channels, lipped zed-sections, hat-sections, rack-sections and I-sections (formed by back-to-back plain channels). The first part of the work is devoted to plain channel columns and starts with a parametric study aimed at gathering failure loads of columns with continuously varying geometries and yield stresses, so that they (i) buckle in either major-axis flexural-torsional or minor-axis flexural modes and (ii) cover a wide slenderness range. These failure loads are then used to assess the quality of their predictions yielded by the codified global DSM design and to propose modifications to improve this quality. The second part of the work employs the modified DSM-based global design curves, as well as the current one, to predict a fairly large number of numerical failure loads of columns exhibiting the remaining eight cross-section shapes. This extensive parametric study shows that the failure load predictions provided by the proposed/modified DSM global strength curves (i) have very high quality and, for the columns considered, (ii) clearly outperform those yielded by the current design curve. In addition, the advantages and disadvantages of the proposed DSM global design curves are also discussed.

This work presents and discusses numerical results of an ongoing investigation concerning the elastic post-buckling behaviour and imperfection sensitivity of regular convex polygonal cross-section (RCPS) tubular columns affected by local-distortional (L-D) interaction. This investigation is conducted by means of geometrically non-linear Generalized Beam Theory (GBT) analyses, extending the knowledge on the “pure” local and distortional post-buckling behaviours of RCPS tubes recently reported by Martins et al. [1] . Due to their inherent modal nature, the GBT analyses make it possible to acquire in-depth knowledge on the structural behaviour of RCPS tubes and also to include, in a straightforward fashion, arbitrary member initial geometrical imperfections. Columns with distortional-to-local critical buckling load ratios (i) close to 1 (“true L-D interaction” – the most trivial L-D interaction type) and (ii) significantly above 1 (“secondary-distortional bifurcation L-D interaction” – the most relevant L-D interaction type) are investigated. Local/distortional critical-mode initial geometrical imperfections and (linear) combinations of both are considered in the former columns, while only local initial imperfections are dealt with in the latter ones – several amplitudes are dealt with to assess the imperfection sensitivity. For comparison and validation purposes, ABAQUS shell finite element analysis results are also reported.

This paper presents and discusses numerical results concerning the (i) elastic local and distortional post-buckling behaviours and (ii) imperfection sensitivity of regular convex polygonal cross-section (RCPS) simply supported tubes under uniform compression (columns). Although it was shown recently that the local and distortional buckling behaviours may be often characterised by duplicate bifurcation modes, knowledge concerning the corresponding post-buckling behaviour is still lacking. The results presented are obtained through a geometrically non-linear Generalised Beam Theory (GBT) formulation previously reported by the authors. This GBT formulation is first employed to characterise the column bifurcation behaviour, namely by helping to pinpoint the occurrence of the above two distinct buckling behaviours. Then, post-buckling results are presented and discussed for (i) different combinations of the local-to-distortional buckling load ratio and the (ii) amplitude of the critical-mode initial geometrical imperfections, in order to characterise the RCPS column imperfection sensitivity. Such results provide the evolution, along given equilibrium paths, of the column deformed configurations (expressed in GBT modal form), relevant displacement profiles and participation diagrams based on either stress resultant strain energies or amplitude functions. For comparison and validation purposes, ABAQUS shell finite element values are reported.

Esse trabalho tem como objetivo investigar como a formação de professores de Ciências dos anos finais do Ensino Fundamental, referente à como o ensino da Astronomia tem sido abordada nas produções acadêmicas no período de 2010 a 2020. A pesquisa possui uma abordagem qualitativa do tipo descritiva, os dados foram constituídos por meio de uma busca na Biblioteca Digital de Teses e Dissertações (BDTD) a partir das palavras-chave “ensino da astronomia”; “formação de professores de Ciências” e “ensino fundamental”. Foram analisadas, ao final, 10 dissertações que atenderam aos critérios de inclusão e exclusão definidos à priori. A análise dos dados foi realizada a partir dos pressupostos teóricos da Análise de Conteúdo Categorial de Bardin. A partir da pesquisa realizada, foi possível evidenciar que a abordagem proposta ainda tem sido pouco interpelada nas produções acadêmicas. Nesse sentido, entendemos que devemos (re)pensar a Formação dos Professores de Ciências, tanto inicial quanto continuada, de forma a contribuir para a superação dos obstáculos ao ensino da Astronomia, bem como servindo de aporte para que, teórica, metodológica ou reflexivamente, o professor tenha subsídios para conduzir adequadamente o processo ensino e aprendizagem.

Mumps is an infectious disease caused by a paramyxovirus. It can involve several organs in the acute stage of the infection, including central nervous system. (Rubin et al., 2015) [1] Neurological complications in the post-infectious period are also described, one of which is acute disseminated encephalomyelitis (ADEM). (Jonhson et al., 2004) [2] We present the case of an healthy young man previously vaccinated, who contracted ADEM after mumps.

This paper presents a proposal to improve the failure load prediction quality provided by the current Direct Strength Method (DSM) design curve for cold-formed steel fixed-ended columns failing in global modes, namely flexural and flexural-torsional ones. After (i) collecting the available numerical failure load data, comprising columns with several geometries (cross-section dimensions and length) and covering a wide slenderness range, and (ii) showing that the currently codified DSM column global design curve is unable to predict them adequately, the development of new strength curves, aimed at estimating more efficiently the column global failure loads, is addressed. Their merits are assessed through (i) the quality of the estimates of the available failure load data and (ii) the determination of the corresponding Load and Resistance Factor Design (LRFD) resistance factors. It is shown that the failure load predictions provided by either of the two proposed/modified DSM global design curves (i) exhibit a very high quality and (ii) clearly outperform those yielded by the currently codified strength curve for the whole set of columns considered in this work.

This work aims at presenting and discussing numerical results concerning the post-buckling behaviour, strength and design of cold-formed steel simply supported lipped channel and zed-section beams under uniform bending and undergoing distortional-global (D-G) interaction – two different support conditions are considered in the lipped channel beams. The relevance of the interaction effects is assessed by identifying the beams whose ultimate strength and/or failure mode are visibly affected by them. Distinct (i) global-to-distortional critical buckling moment ratios (RGD) and (ii) yield-to-non-critical buckling (distortional or global) moment ratios (Ry) are considered, which are expected to lead to different failure mode natures (global, distortional or interactive). For each beam type, combinations of 41 geometries and 11 yield stresses are considered, in order (i) to characterise the beams experiencing “true D-G interaction” (RGD ≈ 1.0) and “secondary global-bifurcation D-G interaction” (RGD > 1.0 and high Ry) and (ii) to investigate the possible occurrence of “secondary distortional-bifurcation D-G interaction” (RGD

This paper investigates the elastic post-buckling behaviour of simply supported thin-walled lipped channel beams undergoing local-distortional (L-D) interaction. The beams are uniformly bent about the major-axis and experience flange-triggered local buckling (most common situation in practice). Three beam geometries are considered, each exhibiting a different type of L-D interaction, namely (i) “true L-D interaction” (close local and distortional critical buckling moments – two critical-mode initial geometrical imperfections are used, akin to the competing critical buckling modes), (ii) “secondary local-bifurcation L-D interaction” or (iii) “secondary distortional-bifurcation L-D interaction” (critical distortional-to-local buckling moment ratio well below or above 1.0, respectively, with “high enough” yield stresses). The results presented and discussed are obtained through elastic geometrically non-linear Generalised Beam Theory (GBT) analyses and provide the evolution, along given equilibrium paths, of the beam deformed configuration (expressed in GBT modal form), relevant displacement profiles and modal participation diagrams, making it possible to acquire in-depth knowledge on the beam L-D interaction mechanics. Particular attention is devoted to interpreting the quantitative and qualitative differences exhibited by the beam post-buckling behaviours associated with the three aforementioned L-D interaction types.

The aim of this work is to provide an overview of the current status of an extensive ongoing investigation on cold-formed steel columns and beams affected by mode coupling phenomena involving distortional buckling, namely local-distortional (L-D), local-distortional-global (L-D-G) and distortional-global (D-G) interaction. The investigation comprises experimental tests, numerical simulations and design proposals, intended to (i) acquire in-depth knowledge on the post-buckling behaviour (elastic and elastic-plastic), ultimate strength and failure mode nature of the members under consideration, and (ii) take advantage of the above knowledge to develop, calibrate and validate efficient Direct Strength Method (DSM)-based design approaches to predict their ultimate strength. Initially, column results are used to illustrate and help grasp some fundamental concepts, namely the characterisation of the (i) three above mode coupling phenomena, (ii) different sources of mode interaction that may cause ultimate strength erosion, (iii) global post-buckling behaviour and (iv) the most detrimental initial geometrical imperfections. Then, the paper addresses separately each mode coupling phenomenon, for columns, and only L-D interaction for beams. For columns undergoing L-D and L-D-G interaction, the research activity reported concerns experimental investigations, numerical (shell finite element) simulations and the development and/or assessment of DSM-based design approaches and/or guidelines. The picture is different for columns experiencing D-G interaction and beams affected by L-D interaction, due to the lack of available experimental results − nevertheless, even if only numerical results are reported, they enable unveiling rather interesting (and unexpected) behavioural features concerning the real nature of these mode coupling phenomena.

This work aims at presenting and discussing Generalised Beam Theory (GBT) numerical results concerning the elastic geometrically non-linear behaviour of simply supported lipped channel (LC) beams under uniform major-axis bending and experiencing distortional-global (D-G) interaction, making it possible to shed fresh light on the mechanics underlying this coupling phenomenon. Two LC beam geometries are considered, each exhibiting a different type of D-G interaction, namely (i) “true D-G interaction”, associated with close distortional ( M crD ) and global ( M crG ) critical buckling moments, and (ii) “secondary global-bifurcation interaction – SGI”, corresponding to M crD M crG . While the latter beam geometry contains a critical-mode distortional initial imperfection, the former one is analysed with initial geometrical imperfections exhibiting three critical-mode shapes (one distortional and two global, due to the lack of symmetry). Moreover, an investigation conducted to assess the possible occurrence of “secondary distortional-bifurcation D-G interaction – SDI” ( M crG M crD ) is also presented and discussed. In order to clarify the surprising behaviour of the beam undergoing a SGI, an additional beam is analysed, exhibiting a “pure” distortional post-buckling behaviour (i.e., involving no coupling phenomenon). The GBT-based results provide the evolution, along given equilibrium paths, of the beam deformed configuration (expressed in modal terms), relevant displacement profiles and modal participation diagrams. The knowledge acquired has visible impact on the development of rational design rules for CFS beams affected by D-G interaction.

This work reports the results of a numerical investigation concerning the elastic post-buckling behaviour of fixed-ended thin-walled lipped channel and zed-section columns affected by distortional-global (D-G) interaction – “unexpected” features associated with the global buckling nature are unveiled in both cases. The columns analysed (i) exhibit cross-section dimensions and lengths ensuring the simultaneous occurrence of distortional and global critical buckling, and (ii) contain critical-mode initial geometrical imperfections (linear combinations of the critical distortional and global buckling mode shapes). For comparison and clarification purposes, the post-buckling behaviour of lipped channel columns buckling in an “isolated” distortional mode and containing “pure” distortional and global (flexural-torsional) initial geometrical imperfections are also analysed. The results presented and discussed are obtained through geometrically non-linear Generalised Beam Theory (GBT) analyses and provide the evolution, along given equilibrium paths, of the column deformed configuration (expressed in GBT modal form), relevant displacement profiles and modal participation diagrams, making it possible to acquire in-depth insight on the mechanics underlying D-G interaction in columns. Finally, particular attention is paid to interpreting the differences exhibited by the various column post-buckling behaviours investigated.

This work presents and discusses numerical results concerning cold-formed steel simply supported beams subjected to uniform bending and exhibiting (i) three cross-section shapes (lipped channels, zed-sections and hat-sections), and (ii) two end support conditions (differing in the warping and local displacement/rotation restraints, which are either free or fully prevented). A systematic numerical investigation is carried out, in order to characterise the post-buckling behaviour and ultimate strength of beams experiencing more or less severe L-D interaction effects. 43 geometries and 11 yield stresses are considered for each combination of cross-section shape and support conditions, thus ensuring distinct (i) ratios between the local ( M crL ) and distortional ( M crD ) critical buckling moments (0.50 ≤ M crD / M crL ≤ 2.00), and (ii) local or distortional slenderness values, ranging from 0.50 to 3.50. The numerical results are obtained through Abaqus shell finite element analyses and concern the (i) post-buckling behaviour (elastic and elastic-plastic), ultimate strength and failure mechanisms of beams previously selected to undergo considerable L-D interaction. Based on the acquired information, a first contribution towards the Direct Strength Method (DSM) design of cold-formed steel beams undergoing different “levels” of L-D interaction is presented and discussed.

O presente trabalho objetiva-se em analisar todo processo de mudanças no discurso de um grupo de professores de física participantes de um curso de formação continuada, vinculados ao Núcleo Regional de Educação (NRE) do município de Maringá. Após a análise dos dados, evidenciou-se três importantes fases oriundas do comportamento desse grupo de professores: a primeira, marcada por situações de queixas pelo fato do descrédito em relação a educação e aos muitos desafios enfrentados no cotidiano escolar, a segunda diretamente ligada às práticas metodológicas equivocadas assumidas em sala de aula, e a terceira por uma mudança de postura mais reflexivo. Para análise dos dados utilizou-se das metodologias oriundas dos pressupostos teóricos e metodológicos de Bardin, baseado na Análise de Conteúdo, cujo pesquisadores delimitam alguns parâmetros e categorias, demonstrando todo conhecimento por parte do aprendiz. Diante de tais práticas, conclui-se que somente será possível uma mudança no discurso da queixa ao discurso reflexivo quando o professor efetivamente convencer-se da necessidade de constantes aperfeiçoamentos, bem como o resgate por sua autoridade muitas vezes perdida em sala de aula.

This work presents and discusses numerical results concerning the elastic post-buckling behaviour and imperfection sensitivity of regular convex polygonal cross-section (RCPS) tubular beams buckling in local, distortional and mixed local–distortional modes, a topic currently lacking research. This study is carried out in the framework of Generalised Beam Theory (GBT) geometrically non-linear analyses, enriched with a branch switching technique, and takes advantage of the GBT intrinsic modal nature to shed new light on the mechanics underlying the post-buckling behaviour of these members. Due to the small half-wavelength of all the buckling phenomena addressed, only simply supported members under uniform bending are investigated. In particular, this work investigates the post-buckling behaviour and imperfection sensitivity of RCPS beams (i) exhibiting several wall numbers (6, 8, 10, 14, 20, 30) with distinct combinations of circumradius-to-thickness ratios (ii) having distinct lengths, and (iii) containing critical-mode initial geometrical imperfections with several amplitudes. Relevant displacement profiles and modal participation diagrams are provided along trivial and non-trivial equilibrium paths, in order to draw meaningful conclusions concerning the post-buckling behaviour of RCPS tubes under bending. For comparison and validation purposes, ABAQUS shell finite element results are also presented.

This paper reports an experimental investigation, carried out at The University of Hong Kong, on the behaviour of cold-formed steel lipped channel beams affected by local-distortional (L-D) interaction under non-uniform bending – to the authors’ best knowledge, these are the first tests specifically devoted to this topic. This investigation consists of 16 non-conventional four-point simply supported bending tests involving twin lipped channel beams arranged in a “back-to-back” configuration and laterally restrained at the loading points. The 32 lipped channel specimens were brake-pressed from high-strength zinc-coated G450 grade structural steel sheets. Tensile coupon tests were performed to obtain the specimen material properties and initial geometrical imperfections were measured prior to testing. The beam geometries were carefully selected to enable testing beams that are prone to “true L-D interaction” (close critical distortional-to-local buckling moments) when acted by trapezoidal bending moment diagrams with four distinct gradients – all the tested specimens exhibited the sought L-D interactive nature. The output of the experimental investigation consists of (i) applied moment vs. displacement equilibrium paths, (ii) photos showing beam deformed configurations along those paths (including the failure modes) and (iii) the failure moment data. Lastly, the experimental failure moments obtained are compared with their predictions provided by the (i) current local and distortional Direct Strength Method (DSM) strength curves and (ii) available DSM-based approaches against L-D interactive failures, which were developed and calibrated exclusively in the context of beams subjected to uniform bending.

The paper reports the results of a numerical (A baqus shell finite element analysis) investigation on the influence of local-distortional (L-D) interaction on the ultimate strength and design of fixed-ended cold-formed steel lipped channel columns with web and flange intermediate stiffeners. The columns analysed exhibit various geometries and yield stresses, ensuring several combinations of ratios between the (i) local and distortional critical buckling stresses, and (ii) yield stress and the highest of the above two critical buckling stresses (local or distortional). The objectives of this work are (i) to acquire in-depth understanding on the mechanics underlying the L-D interaction in the columns under consideration, and also (ii) to provide a contribution towards the development of an efficient Direct Strength Method (DSM) approach to design these structural elements. The results presented and discussed concern the post-buckling behaviour, ultimate strength and failure mode of fixed-ended web-flange-stiffened lipped channel columns previously selected to undergo more or less severe L-D interaction. Special attention is paid to the comparison between the ultimate strength erosion, due to L-D interaction, occurring in the columns analysed in this work and the (i) “plain” cross-section (i.e., without intermediate stiffeners) and (ii) web-stiffened lipped columns investigated earlier by the authors. Then, available experimental ultimate strengths of web-flange-stiffened lipped channel columns failing in L-D interactive modes are employed, together with the numerical failure loads obtained in this work, to assess the quality of the estimates provided by the existing DSM design approaches. The paper closes with (i) the reliability assessment of the DSM-based L-D approaches to predict the numerical and experimental failure loads, and (ii) some considerations about the impact of the findings reported on the design of cold-formed steel columns undergoing L-D interaction.

This work reports the results of a numerical (A baqus shell finite element analysis) investigation on the influence of local–distortional (L–D) interaction in the ultimate strength and design of fixed-ended cold-formed steel web-stiffened lipped channel columns, hereafter termed “WSLC columns”. These results concern columns with various geometries and yield stresses, ensuring a wide variety of combined ratios between (i) the distortional and local critical buckling stresses, and (ii) the yield stress and the higher of the above two buckling stresses. The objectives of the work are two-fold: (i) acquire in-depth knowledge on the mechanics underlying the L–D interaction in the WSLC columns analysed, all selected to ensure that local buckling is triggered by the flanges, and also (ii) provide a first contribution towards the efficient Direct Strength Method (DSM) design of these columns. The results presented and discussed concern the (i) post-buckling behaviour (elastic and elastic–plastic), (ii) ultimate strength and (iii) failure mechanisms of WSLC columns undergoing L–D interaction. Special attention is paid to the comparison between the ultimate strength erosion, stemming from L–D interaction, exhibited by web-stiffened and plain lipped channel columns (the latter were studied earlier by the authors). The paper closes with some considerations about the impact of the findings reported in this work on the design of cold-formed steel columns experiencing different levels of L–D interaction.

This paper presents and discusses results of an ongoing numerical investigation on stainless steel columns under elevated temperatures and prone to local or global buckling, performed in the context of the project “StaSteFi – Fire Design of Stainless Steel Members”. Geometrically and materially non-linear shell finite element models are employed to obtain the structural response and the failure loads of columns (i) with several cross-section shapes (SHS, RHS, CHS, EHS and I-section), (ii) prone to local or global (major- and/or minor flexural) buckling, (iii) made from three common stainless steel grades (ferritic 1.4003, austenitic 1.4301 and duplex 1.4462), (iv) subjected to various elevated temperatures (θ = 100, 200, 300, 400, 500, 600, 700 and 800 °C), (v) containing both initial geometrical imperfections and residual stresses, and (vi) covering a wide local or global slenderness range. The variation of the influence of the residual stresses as the temperature increases is also assessed. Lastly, the failure loads gathered are used to assess the quality of their prediction provided by (i) the currently codified Eurocode 3 stainless steel fire design rules, and (ii) recently proposed design rules for local and global (flexural) failures of I-section stainless steel columns, as well as to explore their extension/accuracy in the context of SHS and RHS columns.

This paper describes a test campaign concerning the behaviour and strength of cold-formed steel (CFS) lipped channel (LC) beams experiencing local-distortional (L-D) interaction made of G450-G500 high-strength steel grades. This investigation involves the performance of 20 tests on simply supported beams arranged in a “back-to-back” configuration, subjected to four-point major-axis bending and laterally restrained at the loading points. All tested specimens failed in the expected L-D interactive modes and exhibited critical distortional-to-local buckling moment ratios ranging between 1.09 and 1.46 (i.e., prone to “true L-D interaction”). The experimental results obtained and reported consist of beam (i) moment-displacement equilibrium paths, (ii) photos evidencing the evolution of the beam deformed configurations along those equilibrium paths (including the failure modes) and (iii) failure moments - it is found that these results are in good agreement with recently performed numerical simulations. Finally, the experimental failure moments obtained are compared with their estimates provided by the (i) currently codified Direct Strength Method (DSM) strength curves associated with local and distortional failures, and (ii) other available DSM-based design approaches developed to handle L-D interactive failures. This comparison provides solid evidence that the CFS specifications must include a DSM-based design approach able to handle beam L-D interactive failures - the current L and D design curves clearly overestimate all the experimental failure moments.

This paper presents a new modal theory for the wrinkling analysis of membranes and discusses the stretch-induced wrinkling behaviour of fixed-ended thin sheets. This modal theory corresponds to an extension of Generalised Beam Theory (GBT) to analyse the wrinkling behaviour of highly stretched sheets. The inherent GBT modal nature adopted in this investigation enables the acquisition of an in-depth knowledge (when compared with the traditional shell finite element analysis) of the behaviour underlying this peculiar buckling phenomena. In order to conduct this study, the work begins by presenting the formulation, describing its main steps and concepts involved in the determination of the “deformation modes” (cross-section analysis), followed by the description of the procedures involved in the development and implementation of the aforementioned formulation that accounts for pre-wrinkling and wrinkling analysis (member analysis). Then, an illustrative example is presented and discussed in detail, which involves the characterisation of the sheet “signature curve” (tensile critical stress vs. length), respective critical wrinkling modes, modal participation diagrams and pre-wrinkling stress distribution patterns. For comparison and validation purposes, refined ABAQUS shell finite element wrinkling results are also reported. Finally, several conclusions are drawn regarding the wrinkling behaviour of stretched sheets, mostly based on the modal nature of this formulation.

The objective of this work is to report a careful experimental investigation, planned at the University of Lisbon and carried out at The University of Hong Kong, concerning the behaviour and ultimate strength of cold-formed steel web-flange-stiffened (WFSLC) and web-stiffened (WSLC) lipped channel columns undergoing local-distortional (L-D) interaction. It involves 31 specimens (16 WFSLC+ 15 WSLC), brake-pressed from high-strength zinc-coated grades G450, G500 and G550 structural steel sheets, exhibiting critical distortional-to-local buckling load ratios ranging between 0.75 and 1.88. The column geometries were carefully selected to enable testing fixed-ended columns undergoing true L-D interaction and secondary distortional-bifurcation L-D interaction (ensuring evidence of the latter required selecting rather slender columns) − all tested specimens exhibited the expected L-D interactive failures. The specimen material properties were obtained from tensile coupon tests and their initial geometrical imperfections were measured prior to testing. The experimental results presented and discussed consist of column (i) load-displacement equilibrium paths, (ii) photos evidencing the evolution of the column deformed configurations along those paths (including the failure mode) and (iii) failure loads. Finally, the experimental failure load data obtained are compared with their estimates provided by the currently codified DSM design approaches for columns failing in L and D modes, showing their inadequacy to handle L-D interactive failures − the fresh light shed by this comparison will contribute to the timely codification, in the near future, of a DSM design procedure for columns affected by L-D interaction.

This paper enhances the available generalized beam theory (GBT) geometrically nonlinear (elastic) formulations by including (1) the whole set of nonlinear membrane strain terms, and (2) the...

Relevance of web-triggered L-D interaction in cold-formed steel columns investigated.Numerical results concerning lipped channel, hat, zed and rack-section columns presented.Two quite different types of L-D mode interaction are identified and characterised.Development/calibration of DSM-based design approaches against L-D interactive failures.Use of numerical/experimental ultimate strengths to assess the DSM design approach merits. The paper reports the results of a numerical investigation on the relevance of web-triggered local-distortional interaction on the ultimate strength of a large number of cold-formed steel fixed-ended (plain) lipped channel, zed, hat and rack-section columns. These results concern columns with various geometries (cross-section dimensions and unrestrained length) and yield stresses, ensuring a wide variety of combined ratios between the (i) distortional and local critical buckling stresses (RDL) and (ii) yield and non-critical buckling stresses (Ry). To avoid interaction with global buckling, all columns have global critical buckling stresses much higher than their local, distortional and yield counterparts. The aim of this study is to identify combinations of these ratios for which L-D interaction is relevant, in the sense that it affects visibly the column elastic and elastic-plastic post-buckling behaviours, ultimate strength and failure mechanism - special attention is devoted to the ultimate strength erosion. The numerical ultimate strength data obtained are then compared with the predictions of (i) the currently codified DSM (Direct Strength Method) strength curves for the design of columns failing in local and distortional modes and (ii) available DSM-based design approaches specifically developed to handle local-distortional interactive failures. Then, experimental results available in the literature concerning lipped channel and rack-section columns failing in local-distortional interactive modes are used to assess the quality of the estimates provided by the DSM-based design approaches. Finally, the paper closes with some considerations on the design of cold-formed steel columns undergoing L-D interaction.

This paper provides an overview of the latest developments of the research activity carried out by the authors concerning the non-linear behaviour, ultimate strength and Direct Strength Method (DSM) design of cold-formed steel (plain and stiffened) columns experiencing local–distortional (L–D) interaction. Initially, numerical results obtained by means of Generalized Beam Theory (GBT) elastic post-buckling analyses are presented and their unique modal nature is used to illustrate and provide the main behavioural/mechanics features of this mode coupling phenomenon. Then, both experimental and numerical (obtained from Abaqus shell finite element analyses – SFEA) are presented and discussed, making it possible to provide clear evidence and characterize the column L-D interactive behaviour and failure. Besides reporting on two experimental test series performed by the authors, the paper also presents a critical review of other experimental results available in the literature concerning columns undergoing L–D interaction. The numerical results deal with columns exhibiting different cross-section shapes and fairly extensive parametric studies are carried out, in order to (i) assess the relevance of L–D interaction, as far as the ultimate strength erosion is concerned, and (ii) gather substantial ultimate strength data. Next, after showing the inadequacy of the currently codified DSM column design curves to predict L–D interactive failures, the paper presents and assesses the merits of DSM-based design approaches recently developed specifically to handle such failures.

In this paper a statistical analysis was done, to assess the most adequate statistical distributions and corresponding parameters for the timber-concrete connection properties, aiming linear and non linear analysis. The properties considered for the linear analysis were the load-slip modulus and load carrying capacity. For the non-linear analysis five mathematical models were selected to describe the connection load-slip behavior. The models were fitted to the load-slip curves available in the references. The obtained parameters were subjected to a statistical analysis in order to assess the most adequate statistical distributions. On this analysis the whole set of suitable results available included more than 1000 single test results to have a sample as broad as possible. A chi-square goodness-of-fit with a 5% of significance level were performed to selected distributions, in most of the situations the normal distribution was found to be adequate. Furthermore, for most of the connection types good load-slip descriptions could be obtained with the 3 parameter models.

The financial support of the European Commission, through the Research Fund for Coal and Steel project RFCS-2015–709892, “Overall-Slenderness Based Direct Design for Strength and Stability of Innovative Hollow Sections—HOLLOSSTAB”, is gratefully acknowledged. This paper presents and discusses numerical results concerning the elastic post-buckling behaviour and imperfection sensitivity of Regular Convex Polygonal cross-Section (RCPS) tubes under uniform compression (columns) and affected by interaction between local and distortional buckling. As the authors showed previously, these tubes are characterised by duplicate bifurcation modes (local or distortional) and, for some geometries, local and distortional buckling may occur simultaneously (local-distortional interaction). A particularly efficient Generalised Beam Theory (GBT) non-linear formulation, specialised for RCPS tubes and employed earlier to characterise their bifurcation behaviour, is used to help pinpoint the occurrence of possible coupling phenomena. The post-buckling results presented and discussed concern columns with different ratios between the critical local and distortional buckling loads, and containing critical-mode initial geometrical imperfections. They are obtained through Abaqus shell finite element analyses and make it possible to draw a few conclusions on the post-buckling behaviour of RCPS columns affected by local-distortional interaction. authorsversion published

Resumo Um recurso atual em destaque nas pesquisas sobre o ensino da Matemática é a Webquest, uma proposta didática envolvente, em razão das situações desafiadoras que propõe ao participante. No entanto, como em qualquer proposta, pode deixar o aluno diante de dificuldades gerando, em nível afetivo, ansiedades diversas e, sendo assim, a questão que se coloca é: Como os sentimentos convocados durante sua resolução articularam-se às interações dos alunos com o conhecimento matemático (sobre álgebra linear) e entre o grupo de colegas? Esta pesquisa caracteriza-se como qualitativa e, com base na teoria de Piaget – sobre a construção de conhecimento e sua relação com a afetividade –, analisou como 21 alunos interagiram na aplicação de três desafios da Webquest. Para coleta de dados foram aplicadas questões semiestruturadas: antes, durante e depois da realização de cada desafio. Os resultados indicaram que as interações foram pautadas, sobretudo, por cooperação. No início de cada desafio, prevaleceram sentimentos como interesse, medo e ansiedade. À medida que os alunos avançavam em outros desafios, ora acertando e ora errando, os sentimentos foram: alegria, desânimo, interesse, medo, entre outros. Concluiu-se que os sentimentos foram desencadeadores das ações cognitivas dos alunos e, mesmo aqueles que não conseguiram um resultado positivo, persistiram nas atividades até o final, ou seja, ninguém desistiu e isso ocorreu, em especial, pelo aspecto afetivo instigador e interessante que a Webquest promoveu naquele contexto de aprendizagem matemática. Abstract Webquest is a current research proposal for teaching Mathematics. It is a captivating technological resource, which offers challenging situations to its participants. However, as it usually happens to any proposal, students may run into difficulties leading to anxiety at the affective level, and in that case the issue raised here is: How are feelings aroused during its resolution linked to the students' interactions with mathematical knowledge (about linear algebra) and among the group mates? This is a qualitative research based on Piaget's theory - about the acquisition of knowledge and its relationship with affectivity - it analyzed how 21 students interacted in the application of three Webquest challenges. To collect the data, we used semi-structured questions: before, during and after the accomplishment of each challenge. The results showed that the interactions were mainly guided by cooperation. At the beginning of each challenge feelings such as interest, fear, and anxiety prevailed. As the students advanced in other challenges, sometimes being successful, sometimes making mistakes, the feelings aroused were joy, frustration, interest, fear, among others. We concluded that such feelings aroused the students' cognitive actions and even those who had not achieved a positive result persisted in the activities until the end, that is, nobody gave up and that happened due mainly to the instigating and interesting affective feature which Webquest encouraged within that context meant for learning mathematics.

This paper reports the latest results of an ongoing investigation on the accuracy of the codified Direct Strength Method (DSM) global strength curve in predicting the ultimate strength of cold-formed steel columns failing in flexural-torsional modes. The first part of the paper is devoted exclusively to fixed-ended columns and continues recent work by the authors [1, 2] on the improvement of the flexural-torsional failure load estimation, in the moderate or high slenderness ranges − it is shown that the use of a novel set of strength curves, dependent on a cross-section normalised geometric parameter (involving the area, major and minor moments of inertia, and warping constant), leads to excellent failure load predictions, eliminating the large scatter stemming from the codified design curve and improving the DSM-based design approach proposed in [2]. The second part of the paper aims at extending the investigation to columns with other support conditions, namely three types of pinned supports, all fixed with respect to torsion and having warping prevented: end cross-sections attached to rigid plates resting on spherical or cylindrical hinges (i.e., pinned with respect to major and/or minor-axis flexure). Initially, a parametric study is performed, aimed at gathering failure loads concerning columns (i) with the cross-section shapes considered earlier (plain channels, unstiffened and stiffened lipped channels, return lipped channels, hat-sections and rack-sections), (ii) with various geometries (cross-section dimensions and lengths) and (iii) covering a wide slenderness range. These failure load data are then used to assess the quality of their estimates provided by the codified global DSM strength curve and by the strength curve set developed for fixed-ended columns. It is found that neither of them yields consistently good failure load estimates, which prompts (i) an in-depth comparative study on the elastic post-buckling strength of fixed-ended and pin-ended columns, and (ii) the proposal of modifications that lead to an efficient failure load prediction for the pin-ended columns − although the failure load set obtained in this work is necessarily limited, the fact that their predictions by the proposed DSM global design curves (i) exhibit very high quality and (ii) clearly outperform those yielded by the current design curve provides strong encouragement to search for further experimental and numerical validation.

This paper presents and discusses elastic geometrically non-linear Generalised Beam Theory (GBT) results on simply supported cylindrical steel panels under in-plane bending stresses, extending the knowledge on curved panels under uniform compression recently reported by the authors. Due to its inherent modal nature, GBT enables the acquisition of in-depth knowledge on the behaviour of these complex structural elements, which cannot be obtained with standard shell finite element analysis. In particular, a modal analysis investigation is conducted to assess the imperfection sensitivity of curved panels characterised by distinct curvatures and by considering (i) four distinct loading conditions (including the pure bending case), (ii) two distinct critical-mode initial geometrical imperfection shapes (first two bifurcation modes), and (iii) three distinct amplitudes – whenever relevant, three “positive” and “negative” amplitudes are considered. The work begins by the GBT buckling analysis of the selected panels followed by an in-depth investigation on the corresponding post-buckling behaviour. These results provide the evolution, along the equilibrium paths, of relevant modal displacement profiles, modal participation diagrams and deformed configurations. For comparison and validation purposes, ABAQUS shell finite element results are also reported.

This paper presents and discusses numerical results on the (i) elastic post-buckling behaviour and (ii) imperfection sensitivity of simply supported cylindrical steel panels under uniform compression. The results presented are obtained by means of a geometrically non-linear Generalised Beam Theory (GBT) formulation previously reported by the authors, which can include arbitrary member initial geometrical imperfections. The modal decomposition features of GBT enables extending the knowledge on the mechanics underlying these structural elements, which cannot be obtained with standard shell finite element analysis. The work begins by describing the GBT buckling analysis of four curved panels with distinct curvatures. Then, post-buckling results are presented and discussed for each of the four panels geometries, by considering (i) two distinct critical-mode initial geometrical imperfections shapes and (ii) five distinct amplitudes to assess the imperfection sensitivity – if the “sign” of the initial geometrical imperfection is relevant, ten amplitudes are considered. These results provide the evolution, along the equilibrium paths, of relevant modal displacement profiles, modal participation diagrams and deformed configurations. For comparison and validation purposes, shell finite element results are also reported.

This chapter presents a state-of-the-art report on the direct strength method (DSM), which may be viewed as the most modern and universally accepted approach for the development of methodologies to design a wide variety of thin-walled structural systems, namely cold-formed steel structures. The introductory section describes the basic concepts and procedures of the method, and provides a historical perspective of its development in the last two decades. Then the chapter addresses the development, validation, and application of the currently codified DSM design expressions (strength curves), making a distinction between “first generation” and “second generation”: the former are those originally codified 12 years ago, concerning members under compression (columns) or bending (beams), and the latter correspond to subsequent developments that have reached codification, concerning members under shear (including bending–shear interaction) and perforated columns and beams. The last section is devoted to recent advances and future developments of the DSM. It reports on ongoing research activity concerning structural problems/failures for which DSM-based design expressions are currently being sought, and includes topics that constitute possible/promising extensions of the DSM domain of application. The chapter has an extensive list of references covering the various aspects addressed and making it easy for the reader to acquire additional information on specific topics.

This work reports numerical results concerning cold-formed steel simply supported beams buckling and failing in distortional modes under uniform bending and exhibiting three cross-section shapes, namely (i) lipped channels bent about the major-axis, (ii) zed-sections under skew bending causing uniform flange compression (worst case), and (iii) hat-sections subjected to either major-axis or minor-axis bending (compressed lips in the latter case). Two end support conditions are considered, differing in the warping and local displacement/rotation restraints, which are either completely free or fully prevented. The beams analysed have several cross-section dimension ratios and lengths, in order to assess their influence on the distortional post-buckling behaviour and ultimate strength – particular attention is paid to the influence of (i) the flange-web and lip-flange width ratios, and (ii) the critical (distortional) half-wave number. In addition, the beams exhibit different yield stresses, making it possible to cover wide distortional slenderness ranges. After presenting and discussing the numerical elastic and elastic-plastic post-buckling results obtained, consisting of equilibrium paths, deformed configurations, plastic strain distributions, failure moments and collapse mechanisms, the paper shows that the currently codified Direct Strength Method (DSM) design curve fails to predict adequately the failure moments of some of the beams analysed and addresses the development/proposal of novel DSM strength curves, providing better quality predictions of all the numerical failure moments available.

This paper present and discusses proposals for the codification of efficient design approaches for cold-formed steel columns affected by local-distortional (L-D) interaction. These proposals, based on the Direct Strength Method (DSM), were developed, calibrated and validated on the basis of experimental and numerical (shell finite element) failure load data concerning columns with several cross-section shapes (plain, web-stiffened and web-flange-stiffened lipped channels, hat-sections, zed-sections and rack-sections) and obtained from investigations carried out by various researchers. Three types of L-D interaction are taken into account, namely “true L-D interaction”, “secondary-local bifurcation L-D interaction” and “secondary-distortional bifurcation L-D interaction”. Moreover, previously available DSM-based design approaches developed to handle column L-D interactive failures are reviewed and their merits are assessed and compared with those exhibited by the present proposals. The paper also presents reliability assessments of the failure load predictions provided by the available and proposed DSM-based design approaches, following the procedure prescribed by the current version of the North American Specification for the Design of Cold-Formed Steel Structural Members.

This work reports the available results of an ongoing numerical (shell finite element) investigation on the post-buckling behaviour, strength and design of fixed-ended cold-formed steel columns undergoing distortional-global (D-G) interaction. Columns with different cross-section shapes are analysed, namely plain lipped channel (LC), web-stiffened lipped channel (WSLC) and zed-section (Z) columns, in order to investigate distinct D-G interaction natures: involving either distortional and (global) flexural-torsional buckling (LC and WSLC columns) or distortional and (global) minor-axis flexural buckling (Z columns). In particular, the relevance of these D-G interaction types is discussed, by assessing when they affect visibly the column ultimate strength and/or failure mode. The results presented and discussed concern columns with various geometries and yield stresses, thus ensuring a wide variety of range combinations involving (i) global-to-distortional critical buckling load ratios (RGD) and (ii) squash-to-non critical buckling (distortional or global) load ratios (Ry) and leading to non-negligible failure load erosion. The possible occurrence and failure load impact of “secondary (distortional or global)-bifurcation D-G interaction” (RGD 1.0 and high Ry) are investigated - it is well known that such impact may be significant in columns experiencing “true D-G interaction” (RGD ≈ 1.0). The above results consist of (i) relevant non-linear (elastic and elastic-plastic) equilibrium paths, (ii) deformed configuration evolutions along those paths, evidencing D-G interactive effects, and (iii) figures providing the failure mode characterisation. Then, the numerical failure load data obtained are compared with their predictions by (i) the currently codified DSM (Direct Strength Method) column global and distortional strength curves, and (when necessary) (ii) proposed DSM-based design approaches, specifically developed to handle D-G interactive failures - a few design considerations are drawn from these comparisons.