Pultruded, fibre reinforced, polymeric composites are now being used in a wide range of structural engineering applications, due to their high strength to weight ratios and resistance to environmental conditions. However, such materials posses a relatively low shear modulus in relation to their axial and flexural moduli. This can result in shear deformation constituting a significant proportion of the total deformation and a reduction in buckling loads for various modes of instability. An experimental and theoretical study of the influence of shear deformation on the flexural and torsional stiffnesses and various modes of instability of pultruded polymeric bars of open cross-section is therefore presented. Theories for the bending and warping torsional response of pultruded, fibre reinforced polymeric bars of open cross-section, excluding and including the influence of shear deformation, are presented. Full section bending mechanical properties of several pultruded beams are determined using a static testing apparatus and a wide variety of span configurations. Full section warping torsional mechanical properties of several pultruded bars are determined using a new testing apparatus, capable of applying a torque to any cross-section along a bar, whilst maintaining the bars lateral position. Theories for the flexural, torsional and lateral instability of pultruded, fibre reinforced polymeric bars of open cross-section, excluding and including the influence of shear deformation, are developed and presented. Parametric studies of the influence of shear deformation in the flexural, torsional and lateral instability of various pultruded bars of open cross-section are also presented. The experimental and theoretical studies indicate that shear deformation reduces significantly the non-uniform bending stiffness of pultruded polymeric bars, but that its influence on the non-uniform and restrained warping torsional stiffness is practically negligible. Shear deformation has also been found to result in a significant reduction in flexural, torsional and coupled flexural-torsional or lateral buckling loads.

The present dissertation contributes to advancing methods of determining the elastic and inelastic buckling resistance of compressive members with single angle and back-to-back double angle cross-sections with end conditions representative of those commonly used in steel construction. The first contribution develops an elastic buckling solution for members with asymmetric sections, such as unequal-leg angle members, connected to gusset plates at both ends and subjected to pure compression. In this case, the gusset plate connections at the member ends provide a fixity restraint to the member within the plane of the gusset and nearly a pin restraint in a plane normal to the gusset. Since both directions do not coincide with the principal directions of the member, the classical flexural-torsional buckling solutions provided in standards become inapplicable. In this context, a variational principle is formulated based on non-principal directions and then used to derive the governing differential equations and associated boundary conditions for the problem. The coupled equations are then solved analytically subject to the boundary conditions, and the characteristic equations are recovered and solved for the flexural-torsional buckling load of the member. The validity of the solutions derived is assessed against 3D shell elastic eigen-value buckling models based on ABAQUS for benchmark cases and the solution is shown to accurately predict the elastic buckling load and mode shapes. The effect of non-principal end restraints on the buckling load of compression members is then investigated for members with angle and zed cross-sections in a parametric study. It is observed that when a member end is fixed about a non-principal direction and pinned about the orthogonal direction, the flexural-torsional buckling load of the member is significantly influenced by the angle of inclination between the fixity axis and the minor principal axis. The second contribution aims to obtain the inelastic buckling resistance for single angle compression members with end gusset plate connections by taking into consideration the effects of material and geometric nonlinearity, initial out-of-straightness, residual stresses, and load eccentricity induced by the offset of the member centroidal axis from the end gusset plate connection. Towards this goal, a series of 3D shell models based on ABAQUS are developed and validated through comparisons against experimental results by others and then used to generate a database of compressive capacities for over 900 eccentrically loaded angle members with various geometrical dimensions and load eccentricities. The database is then used to investigate the effect of slenderness ratio, leg width ratio, connected leg width-to-thickness ratio and gusset plate-to-angle thickness ratio on the compressive resistance of the members, assess the accuracy of solutions available in present design standards, and develop improved design expressions for the compressive resistance for the members. The third contribution develops solutions for predicting the elastic buckling resistance of back-to-back double angle assemblies with end gusset plates and intermediate interconnectors subjected to compressive loads. Towards this goal, two novel models are developed. (1) A thin-walled finite element buckling solution is formulated and implemented into a MATLAB code. The formulation treats each angle member as a line of 1D thin-walled beam elements where then both angle members are connected at intermediate points along the span at the locations of interconnectors. The formulation is equipped with a multi-point constraint feature to enforce the kinematic constraints at the interconnector locations and at both extremities of the member. The model captures the tendency of both angles to open relative to one another in between interconnectors while undergoing flexural-torsional buckling. (2) An analytical buckling solution is developed for the limiting case where enough interconnectors are provided between members to force the two angles to essentially behave as a monolithic entity. The resistance predicted by the former model was then shown to asymptotically approach that predicted by the later model as the number of interconnectors is increased. The validity of the finite element model is assessed against 3D shell models based on ABAQUS and published experimental results, and then used to assess the validity of present design rules based on the effective slenderness concept. The present models are then used to carry out a parametric study of 1250 runs while varying the member slenderness ratio, leg width ratio, connected leg width-to-thickness ratio, and angle spacing-to-thickness ratio. The database of results generated is used to develop a simple expression to characterize the elastic buckling load/stress of the assembly. The possible integration of the new expression with present design provisions in standards to predict the inelastic buckling resistance of the member is illustrated through a design example.

[pt] Este trabalho tem como objetivo investigar o desempenho e a resistência de cantoneiras curtas de abas iguais pultrudadas em polímero reforçado com fibra de vidro (PRFV) submetidas à compressão centrada de curta duração. Os fundamentos teóricos associados ao comportamento de cantoneiras perfeitas e reais são apresentados e os resultados de um programa experimental que envolveu caracterização dos materiais e ensaios à compressão são reportados e discutidos. Ao todo, vinte e uma colunas bi-engastadas com diferentes razões largura/espessura das abas, comprimentos e propriedades mecânicas foram testadas. As forças críticas experimentais para o modo de flambagem à flexo-torção foram determinadas e comparadas com as previsões teóricas, apresentando boa concordância. A resistência à compressão de cada coluna foi obtida experimentalmente, discutindo-se a influência do comportamento pós-flambagem e das imperfeições na capacidade de carga final com relação à esperada para coluna perfeita e, finalmente, uma equação para resistência de coluna é proposta para resolver o problema. / [en] This paper aims to investigate performance and strength of glass-fiber reinforced polymer (GFRP) pultruded short equal leg angle columns subject to short-term concentric compression. Background theories associated with the behavior of perfect and real angle struts are presented and the results of an experimental program that involved material characterization and compression tests are reported and discussed. In all, twenty-one fixed-ended columns having different leg width-to-thickness ratio and lengths and mechanical properties were tested. Experimental critical loads for flexural-torsional buckling mode were determined and compared with theoretical predictions, showing a good agreement with each other. Compressive strength for each column was obtained, the influence of post-buckling behavior and imperfections in the final load-carrying capacity with respect to that expected for perfect column condition is discussed and, finally, a column strength equation is proposed to address the problem.

As vigas de rolamento são estruturas destinadas ao suporte de pontes rolantes, estas amplamente utilizadas para movimentação de cargas em galpões industriais. O presente trabalho apresenta um estudo sobre as vigas de rolamento de aço sem contenção lateral entre apoios, em geral projetadas com vão inferior a 7 metros, portanto destinadas ao suporte de pontes rolantes leves (capacidade nominal até 250 kN). A ausência de contenções laterais intermediárias aliada ao desalinhamento e à imprecisão na locação dos trilhos, bem como à presença de forças horizontais transversais ao eixo da viga (aceleração/frenagem do trole), impõem flexão lateral e torção, esforços que são equilibrados apenas pelas contenções nos apoios. A análise foi realizada utilizando o Método dos Elementos Finitos (MEF), considerando a análise não linear física e geométrica do problema, ou seja, um modelo mais próximo da viga real. Os resultados numéricos, quando comparados aos obtidos por meio da teoria de flexo-torção, mostraram uma inversão na distribuição esperada de tensões na mesa superior do perfil, ou seja, nos pontos onde deveria ocorrer aumento da tensão longitudinal de compressão, ocorreu redução. Esta inversão pode ou não ocorrer, dependendo da espessura da mesa superior, intensidade e posição da força vertical da roda da ponte. Além disso, os resultados determinados via MEF foram comparados com os obtidos via modelo tradicional de barra (momento de torção substituído por um binário de forças horizontais nas mesas). A comparação indicou divergência entre os resultados, podendo o dimensionamento pelo modelo de barra levar tanto a situações a favor da segurança como contra a segurança. / The runway girders are structures intended for support cranes, these broadly used to movement of loads in industrial buildings. This research presents a study about the runway girders without lateral bracing between support points, generally designed with span lower than 7 meters, therefore intended for support of light cranes (rated capacity until 250 kN). The absence of intermediate lateral bracing allied to misalignment and imprecision location of the rail, also the presence of the side thrust on the girder (acceleration/ braking of the trolley), causes lateral flexural and torsion, which are balanced only by the lateral containment on support points. The analysis was made using the Finite Element Method (FEM), which includes a nonlinear physical and geometric analysis of the structural problem, in other words, a model closest to the real girder. The numerical results, when compared to the results of the flexural-torsional theory, showed an inversion in the expected distribution of stress on the top flange of the shape, in other words, at the points where must occur increase of the longitudinal stress, reduction occurred. This inversion may or may not occur, depending on the thickness of the top flange, modulus and position of the load of the crane wheel. Besides, the numerical results were compared with the results of classical bar model for beams (torque is replaced by a couple of horizontal forces applied on the flanges). The comparison showed a divergence between the results, where the design by bar classical model can lead to situations of high safety or against safety.

[pt] Em virtude de sua eficiência, elementos estruturais de paredes finas com seções abertas são comuns em estruturas de aço, sendo secção em I, L, C e T usuais na prática de engenharia. A maior parte das vigas de parede fina tem uma boa resistência à flexão em relação ao eixo principal de inércia, mas uma baixa rigidez à flexão em relação ao eixo de menor inércia e uma baixa rigidez em torção. É por isso que estes elementos apresentam em geral uma instabilidade que leva a um acoplamento de flexo-torção. Muitas destas estruturas trabalham em um regime não linear e uma formulação não linear que leve em conta grandes deslocamentos e os acoplamentos inerentes é necessária. Neste trabalho um modelo não linear para vigas de seção aberta e paredes finas, considerando grandes deslocamentos, os efeitos de encurtamento e acoplamentos em flexão e torção é adotado. Inicialmente um estudo das frequências naturais, das cargas críticas e da relação frequência-carga axial é apresentado para diversos perfis. Com base nestes resultados, faz-se um estudo detalhado do comportamento dinâmico não linear destes perfis destacando o efeito do acoplamento não linear na região de ressonância e sua influência na estabilidade dinâmica da estrutura. Para isto são usadas diversas ferramentas de dinâmica não linear, tais como diagramas de bifurcação, respostas no tempo e plano de fase e bacias de atração. Os resultados mostram que a consideração dos acoplamentos não lineares é essencial para se avaliar o nível de segurança destas estruturas. / [en] Due to its efficiency, thin-walled structural elements with open sections, such as I, L, C and Z profiles, are common in steel structures, being usual in engineering applications. Most thin-walled beams have a good flexural strength around of the principal axis of inertia, but a low one around the axis of lower inertia as well as low torsional stiffness. That is why these elements, generally, show instabilities that lead to flexural torsional coupling. Many of these structures do not work in a linear range and a non-linear formulation that takes into account large displacements and associated couplings is required. This dissertation presents a nonlinear model for extensional beams with thin-walled open section, considering large displacements, and flexural-torsional couplings. Initially a study of the natural frequencies, critical load and axial load vs. frequency relation is presented for different profile kinds. Based on these results, a detailed study of the dynamic behavior of non-linear profiles is made, highlighting the effect of non-linear coupling in the resonance region and its influence on the dynamic stability of the structure. For this, various tools of nonlinear dynamics are used, such as bifurcation diagrams, time histories and phase-space portraits and basins of attraction. The results show that the consideration of non-linear couplings is essential to availed the safety level of these structures.

As vigas de rolamento são estruturas destinadas ao suporte de pontes rolantes, estas amplamente utilizadas para movimentação de cargas em galpões industriais. O presente trabalho apresenta um estudo sobre as vigas de rolamento de aço sem contenção lateral entre apoios, em geral projetadas com vão inferior a 7 metros, portanto destinadas ao suporte de pontes rolantes leves (capacidade nominal até 250 kN). A ausência de contenções laterais intermediárias aliada ao desalinhamento e à imprecisão na locação dos trilhos, bem como à presença de forças horizontais transversais ao eixo da viga (aceleração/frenagem do trole), impõem flexão lateral e torção, esforços que são equilibrados apenas pelas contenções nos apoios. A análise foi realizada utilizando o Método dos Elementos Finitos (MEF), considerando a análise não linear física e geométrica do problema, ou seja, um modelo mais próximo da viga real. Os resultados numéricos, quando comparados aos obtidos por meio da teoria de flexo-torção, mostraram uma inversão na distribuição esperada de tensões na mesa superior do perfil, ou seja, nos pontos onde deveria ocorrer aumento da tensão longitudinal de compressão, ocorreu redução. Esta inversão pode ou não ocorrer, dependendo da espessura da mesa superior, intensidade e posição da força vertical da roda da ponte. Além disso, os resultados determinados via MEF foram comparados com os obtidos via modelo tradicional de barra (momento de torção substituído por um binário de forças horizontais nas mesas). A comparação indicou divergência entre os resultados, podendo o dimensionamento pelo modelo de barra levar tanto a situações a favor da segurança como contra a segurança. / The runway girders are structures intended for support cranes, these broadly used to movement of loads in industrial buildings. This research presents a study about the runway girders without lateral bracing between support points, generally designed with span lower than 7 meters, therefore intended for support of light cranes (rated capacity until 250 kN). The absence of intermediate lateral bracing allied to misalignment and imprecision location of the rail, also the presence of the side thrust on the girder (acceleration/ braking of the trolley), causes lateral flexural and torsion, which are balanced only by the lateral containment on support points. The analysis was made using the Finite Element Method (FEM), which includes a nonlinear physical and geometric analysis of the structural problem, in other words, a model closest to the real girder. The numerical results, when compared to the results of the flexural-torsional theory, showed an inversion in the expected distribution of stress on the top flange of the shape, in other words, at the points where must occur increase of the longitudinal stress, reduction occurred. This inversion may or may not occur, depending on the thickness of the top flange, modulus and position of the load of the crane wheel. Besides, the numerical results were compared with the results of classical bar model for beams (torque is replaced by a couple of horizontal forces applied on the flanges). The comparison showed a divergence between the results, where the design by bar classical model can lead to situations of high safety or against safety.

Cold-formed steel members have been widely used in residential, industrial and commercial buildings as primary load bearing structural elements and non-load bearing structural elements (partitions) due to their advantages such as higher strength to weight ratio over the other structural materials such as hot-rolled steel, timber and concrete. Cold-formed steel members are often made from thin steel sheets and hence they are more susceptible to various buckling modes. Generally short columns are susceptible to local or distortional buckling while long columns to flexural or flexural-torsional buckling. Fire safety design of building structures is an essential requirement as fire events can cause loss of property and lives. Therefore it is essential to understand the fire performance of light gauge cold-formed steel structures under fire conditions. The buckling behaviour of cold-formed steel compression members under fire conditions is not well investigated yet and hence there is a lack of knowledge on the fire performance of cold-formed steel compression members. Current cold-formed steel design standards do not provide adequate design guidelines for the fire design of cold-formed steel compression members. Therefore a research project based on extensive experimental and numerical studies was undertaken at the Queensland University of Technology to investigate the buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. As the first phase of this research, a detailed review was undertaken on the mechanical properties of light gauge cold-formed steels at elevated temperatures and the most reliable predictive models for mechanical properties and stress-strain models based on detailed experimental investigations were identified. Their accuracy was verified experimentally by carrying out a series of tensile coupon tests at ambient and elevated temperatures. As the second phase of this research, local buckling behaviour was investigated based on the experimental and numerical investigations at ambient and elevated temperatures. First a series of 91 local buckling tests was carried out at ambient and elevated temperatures on lipped and unlipped channels made of G250-0.95, G550-0.95, G250-1.95 and G450-1.90 cold-formed steels. Suitable finite element models were then developed to simulate the experimental conditions. These models were converted to ideal finite element models to undertake detailed parametric study. Finally all the ultimate load capacity results for local buckling were compared with the available design methods based on AS/NZS 4600, BS 5950 Part 5, Eurocode 3 Part 1.2 and the direct strength method (DSM), and suitable recommendations were made for the fire design of cold-formed steel compression members subject to local buckling. As the third phase of this research, flexural-torsional buckling behaviour was investigated experimentally and numerically. Two series of 39 flexural-torsional buckling tests were undertaken at ambient and elevated temperatures. The first series consisted 2800 mm long columns of G550-0.95, G250-1.95 and G450-1.90 cold-formed steel lipped channel columns while the second series contained 1800 mm long lipped channel columns of the same steel thickness and strength grades. All the experimental tests were simulated using a suitable finite element model, and the same model was used in a detailed parametric study following validation. Based on the comparison of results from the experimental and parametric studies with the available design methods, suitable design recommendations were made. This thesis presents a detailed description of the experimental and numerical studies undertaken on the mechanical properties and the local and flexural-torsional bucking behaviour of cold-formed steel compression member at ambient and elevated temperatures. It also describes the currently available ambient temperature design methods and their accuracy when used for fire design with appropriately reduced mechanical properties at elevated temperatures. Available fire design methods are also included and their accuracy in predicting the ultimate load capacity at elevated temperatures was investigated. This research has shown that the current ambient temperature design methods are capable of predicting the local and flexural-torsional buckling capacities of cold-formed steel compression members at elevated temperatures with the use of reduced mechanical properties. However, the elevated temperature design method in Eurocode 3 Part 1.2 is overly conservative and hence unsuitable, particularly in the case of flexural-torsional buckling at elevated temperatures.