The main objective of this research was to study the buckling and post-buckling response of axially restrained beam-columns under thermal loading. Also the effects of slenderness ratios on pre-buckling and post-buckling behavior which is neglected in AISC specification was examined. The results of this study indicate that: a) Both the deflection and end moment amplification factors are significantly smaller for the restrained beam-columns subjected to temperature increase than the corresponding unrestrained beam-columns subjected to (mechanical) axial loads. b) The deflection amplification factors tend to decrease with decreasing ratio of end moments. However, reverse seems to occur for the moment amplification factors and as the moment amplification factors tend to increase with decreasing moment ratio particularly in the pre-buckling and the initial post-buckling range (0.1 < T/Tcr < 1.5). c) The thermal amplification factors tend to be smaller than the AISC values even in the pre-buckling range with those for the slender beam-columns significantly smaller than those for the shorter beam-columns.

Existing design provisions in design standards and conventional analysis methods for structural steel members are based on the simplifying kinematic Vlasov assumption that neglects cross-sectional distortional effects. While the non-distortional assumption can lead to reasonable predictions of beam static response and buckling strength in common situations, past work has shown the inadequacy of such assumption in a number of situations where it may lead to over-predicting the strength of the members. The present study thus develops a series of generalized theories/solutions for the static analysis and buckling analysis of steel members with wide flange cross-sections that capture distortional effects of the web. Rather than adopting the classical Vlasov assumption that postulates the cross-section to move and rotate in its own plane as a rigid disk, the present theories assume the web to be flexible in the plane of the cross-section and thus able to bend laterally, while both flanges to move as rigid plates within the plane of the cross-section to be treated as Euler-Bernouilli beams. The theories capture shear deformation effects in the web, as well as local and global warping effects. Based on the principle of minimum potential energy, a distortional theory is developed for the static analysis of wide flange steel beams with mono-symmetric cross-sections. The theory leads to two systems of differential equations of equilibrium. The first system consists of three coupled equilibrium differential equations that characterize the longitudinal-transverse response of the beam and the second system involves four coupled equilibrium differential equations of equilibrium and characterizes the lateral-torsional response of the beam. Closed form solutions are developed for both systems for general loading. Based on the kinematics of the new theory, two distortional finite elements are then developed. In the first element, linear and cubic Hermitian polynomials are employed to interpolate displacement fields while in the second element, the closed-form solutions developed are adopted to formulate special shape functions. For longitudinal-transverse response the elements consist of two nodes with four degree of freedom per node for longitudinal-transverse response and for lateral-torsional response, the elements consist of two nodes with eight degrees of freedom per node. The solution is able to predict the distortional deformation and stresses in a manner similar to shell solutions while keeping the modeling and computational effort to a minimum. Applications of the new beam theory include (1) providing new insights on the response of steel beams under torsion whereby the top and bottom flanges may exhibit different angles of twist, (2) capturing the response of steel beams with a single restrained flange as may be the case when a concrete slab provides lateral and/or torsional restraint to the top flange of a steel beam, and (3) modelling the beneficial effect of transverse stiffeners in reducing distortional effects in the web. The second part of the study develops a unified lateral torsional buckling finite element formulation for the analysis of beams with wide flange doubly symmetric cross-sections. The solution captures several non-conventional features. These include the softening effect due to web distortion, the stiffening effect induced by pre-buckling deformations, the pre-buckling nonlinear interaction between strong axis moments and axial forces, the contribution of pre-buckling shear deformation effects within the plane of the web, the destabilizing effects due to transverse loads being offset from the shear centre, and the presence of transverse stiffeners on web distortion. Within the framework of the present theory, it is possible to evoke or suppress any combination of the features and thus isolate the individual contribution of each effect or quantify the combined contributions of multiple effects on the member lateral torsional capacity. The new solution is then applied to investigate the influence of the ratios of beam span-to-depth, flange width-to-thickness, web height-to-thickness, and flange width-to-web height on the lateral torsional buckling strength of simply supported beams and cantilevers. Comparisons with conventional lateral torsional buckling solutions that omit distortional and pre-buckling effects quantify the influence of distortional and/or pre-buckling deformation effects. The theory is also used to investigate the influence of P-delta effects of beam-columns subjected to transverse and axial forces on their lateral torsional buckling resistance. The theory is used to investigate the load height effect relative to the shear centre. Comparisons are made with load height effects as predicted by non-distortional buckling theories. The solution is adopted to quantify the beneficial effect of transverse stiffeners in controlling/suppressing web distortion in beams and increasing their buckling resistance.

M. Tech. (Department of Mechanical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / Though aluminium (Al) is justifiably described as a green metal with an increasing rate of application in structures, designers still restrain themselves from its applications as a load-bearing skeleton in structure due to insufficient design guidelines. This insufficient information is more with channel sections that might experience lateral-torsional buckling (LTB) when used as a load-bearing skeleton in structures. This study investigates the effects on imperfections on LTB load-carrying stability for 6061-T6 Al alloy channel section arches and proposed design guidelines. The case study focused on freestanding circular fixed end arches subjected to a transverse point load at the shear centre. The software package Abaqus was used to study a total of 110 arch models from three separate channel sections with an additional 16 arch models for validation. Sixty-six channel arches were developed at a constant length, while the remaining 44 arches were formed at constant slender ratios using 11 discrete included angles. The FE analyses methods used for the investigation were validated with existing analytical methods and showed good agreement, despite the assumptions of the bilinear curve used for material nonlinearity, initial geometric imperfections and residual stresses that presented the imperfections of the models. The different investigated factors include slender ratios, change in cross-section area, imperfections, and angles. These factors were found to have substantial impacts on the prebuckling state, which turns to impact LTB behaviour and load-carrying capacity. From arches developed at constant span length, the arches with moderately included angles (50°≤2𝛼≤90°) were found suitable for the designs against LTB, followed by the shallow (2𝛼<50°) and deep arches (90°<2𝛼≤180°) respectively. For arches developed at constant slender ratios, the deep arches were found to be more suitable in the design against LTB, followed by the moderate and shallow arches, respectively. In addition, it was realised that the change in web-flange thickness, section depth and slender ratios, had significant effects on the LTB loads magnitudes and very insignificant effects on the general behaviour across the included angles. The same occurrence was also observed on the prebuckling analyses. All the investigated channel section arches showed the imperfections to have significant impacts on the LTB loads. Arches developed at constant span length showed the maximum elastic LTB loads to have overestimated the expected real LTB loads by approximately 48 percent. While the maximum elastic LTB loads of arches developed at 𝑆𝑟𝑥⁄= 60 and 90 showed that the real LTB loads were overestimated by about 39 and 14 percent, respectively. That said, the elastic LTB loads on average overestimated the real LTB loads by over 50 percent for the arches developed at the constant span length and by only 18 percent for arches developed at the constant slender ratios.

Slender structures are elegant aesthetically. The insufficiency in knowledge of the real resistance to buckling of very slender reinforced concrete columns leads to an exaggeration of the sizes of the columns. _The examples of concrete compression members cited and constructed in Industry on a global basis suggest that very slender columns have inherent safety both from the point of view of the ultimate strength and stability. The strengths of columns given. by the British codes would seem to be exceeded by many of the long slender reinforced concrete columns and struts which have been used Internationally. Both the theoretical and the experimental short term investigations have been carried out to establish the behaviour of hinged, very slender reinforced concrete columns at various stages'of axial loading. Forty three very slender reinforced concrete columns of two different square cross sections with two sizes of longitudinal reinforcements with lateral ties were cast. Slenderness rates, L A, were varied from 30 to 79. Special factors were obtained to relate the actual modulus of elasticity of concrete in columns at buckling failure to a knowledge of the initial modulus of elasticity of concrete in control cylinder specimens. Both theoretical and experimental graphs of load against moment, made dimensionless for critical sections of columns have been obtained. Dimensionless load-moment interaction diagrams using material failure as the criterion have been superimposed on these graphs to show considerable inherent material strength of the tested columns near buckling collapse failures. A theory using the fundamental approach has, been developed to predict the deflected shape and moments along the, heights of the columns at various stages of loading. The proposed theory predicts with good correlations the experimental deflections and moments of any loading stages of the columns. The theory has been used to obtain the required variables, to arrive at the initial predicted design loads of the investigated columns. Good correlations of the moments derived from observed strains have also been obtained. The developed theory predicts satisfactorily the buckling collapse loads of the columns. Although the theory has been derived for axially I loaded very slender reinforced concrete-columns, it seems to accept satisfactorily eccentricities of up to about 10 mm. This was confirmed after extensive comparisons of the theoretical buckling collapse loads with the applicable tests of other authors. Creep In the columns investigated was discovered to be one of the major factors for serious consideration. This was conclusively revealed from the observations on the last two very long term creep tests on columns. The actual safe sustained loads for these very slender columns of slenderness ratios, L/H, between 40 and 79 seem to be between 33% and 19% of the short term buckling collapse loads. The reduced modulus approach to predict the safe long term sustained loads seems to give reasonable values for L/H ratios of 40 and 50. The recommendations given for the proposed design of very slender reinforced concrete columns seem to be adequate and simple to use in practice. They are further simplified by the derivation of two equations for the reduction factors, R, for the slenderness ratios between 36 and 40 and between 40 and 79 respectively. The investigation has proved that very slender reinforced concrete columns are very dangerous structural members, as they tend to have violent buckling failures. Nevertheless, It must be prudent not to design against disaster at any cost. This Investigation seemed to have enhanced considerably knowledge of the design of very slender reinforced concrete columns. / Scientific Research Council

No description available.

This study focuses on the improvement of the axial buckling capacity of elliptical composite cylinders through the use of a circumferentially-varying lamination sequence. The concept of varying the lamination sequence around the circumference is considered as a viable approach for off-setting the disadvantages of having the cylinder radius of curvature vary with circumferential position, the source of the reduced buckling capacity when compared to a circular cylinder with the same circumference. Post-buckling collapse behavior and material failure characteristics are also of interest. Two approaches to implementing a circumferential variation of lamination are examined. For the first approach the lamination sequence is varied in a stepwise fashion around the circumference. Specifically, each quadrant of the cylinder circumference is divided into three equal-length regions denoted as the crown, middle, and side regions. Eight different cylinders designs, whereby each region is constructed of either a quasi-isotropic or an axially-stiff laminate of equal thickness, are studied. Results are compared to the baseline case of an elliptical cylinder constructed entirely of a quasi-isotropic laminate. Since the thickness of the quasi-isotropic and axially-stiff laminates are the same, all cylinders weight the same and thus comparisons are meaningful. Improvements upwards of 18% in axial buckling capacity can be achieved with one particular stepwise design. The second approach considers laminations that vary circumferentially in a continuous fashion to mitigate the effects of the continuously-varying radius of curvature. The methodology for determining how to tailor the lamination sequence circumferentially is based on the analytical predictions of a simple buckling analysis for simply-supported circular cylinders. With this approach, axial buckling load improvements upwards of 30% are realized. Of all the cylinders considered, very few do not exhibit material failure upon collapse in the post-buckled state. Of those that do not, there is little, if any, improvement in bucking capacity. Results for the pre-buckling, buckling, post-buckling, and material failure are obtained from the finite-element code ABAQUS using both static and dynamic analyses. Studies with the code demonstrate that the results obtained are converged. / Ph. D.

Stiffeners attached to composite panels and shells may significantly increase the overall buckling load of the resultant stiffened structure. Initially, an extensive literature review was conducted over the past ten years of published work wherein research was conducted on grid stiffened composite structures and stiffened panels, due to their applications in weight sensitive structures. Failure modes identified in the literature had been addressed and divided into a few categories including: buckling of the skin between stiffeners, stiffener crippling and overall buckling. Different methods have been used to predict those failures. These different methods can be divided into two main categories, the smeared stiffener method and the discrete stiffener method. Both of these methods were used and compared in this thesis. First, a buckling analysis was conducted for the case of a grid stiffened composite pressure vessel. Second, a buckling analysis was conducted under the compressive load on the composite stiffened panels for the case of one, two and three longitudinal stiffeners and then, using different parameters, stiffened panels under combined compressive and shear load for the case of one longitudinal centric stiffener and one longitudinal eccentric stiffener, two stiffeners and three stiffeners. / Master of Science

Thin-walled cold-formed steel (CFS) has exhibited inherent structural and architectural advantages over other constructional materials, for example, high strength-to-weight ratio, ease of fabrication, economy in transportation and the flexibility of sectional profiles, which make CFS ideal for modern residential and industrial buildings. They have been increasingly used as purlins as the intermediate members in a roof system, or load-bearing components in low- and mid-rise buildings. However, using CFS members in building structures has been facing challenges due to the lack of knowledge to the fire performance of CFS at elevated temperatures and the lack of fire design guidelines. Among all available design specifications of CFS, EN1993-1-2 is the only one which provided design guidelines for CFS at elevated temperatures, which, however, is based on the same theory and material properties of hot-rolled steel. Since the material properties of CFS are found to be considerably different from those of hot-rolled steel, the applicability of hot-rolled steel design guidelines into CFS needs to be verified. Besides, the effect of non-uniform temperature distribution on the failure of CFS members is not properly addressed in literature and has not been specified in the existing design guidelines. Therefore, a better understanding of fire performance of CFS members is of great significance to further explore the potential application of CFS. Since CFS members are always with thin thickness (normally from 0.9 to 8 mm), open cross-section, and great flexural rigidity about one axis at the expense of low flexural rigidity about a perpendicular axis, the members are usually susceptible to various buckling modes which often govern the ultimate failure of CFS members. When CFS members are exposed to a fire, not only the reduced mechanical properties will influence the buckling capacity of CFS members, but also the thermal strains which can lead additional stresses in loaded members. The buckling behaviour of the member can be analysed based on uniformly reduced material properties when the member is unprotected or uniformly protected surrounded by a fire that the temperature distribution within the member is uniform. However if the temperature distribution in a member is not uniform, which usually happens in walls and/or roof panels when CFS members are protected by plaster boards and exposed to fire on one side, the analysis of the member becomes very complicated since the mechanical properties such as Young’s modulus and yield strength and thermal strains vary within the member. This project has the aim of providing better understanding of the buckling performance of CFS channel members under non-uniform temperatures. The primary objective is to investigate the fire performance of plasterboard protected CFS members exposed to fire on one side, in the aspects of pre-buckling stress distribution, elastic buckling behaviour and nonlinear failure models. Heat transfer analyses of one-side protected CFS members have been conducted firstly to investigate the temperature distributions within the cross-section, which have been applied to the analytical study for the prediction of flexural buckling loads of CFS columns at elevated temperatures. A simplified numerical method based on the second order elastic – plastic analysis has also been proposed for the calculation of the flexural buckling load of CFS columns under non-uniform temperature distributions. The effects of temperature distributions and stress-strain relationships on the flexure buckling of CFS columns are discussed. Afterwards a modified finite strip method combined with the classical Fourier series solutions have been presented to investigate the elastic buckling behaviour of CFS members at elevated temperatures, in which the effects of temperatures on both strain and mechanical properties have been considered. The variations of the elastic buckling loads/moments, buckling modes and slenderness of CFS columns/beams with increasing temperatures have been examined. The finite element method is also used to carry out the failure analysis of one-side protected beams at elevated temperatures. The effects of geometric imperfection, stress-strain relationships and temperature distributions on the ultimate moment capacities of CFS beams under uniform and non-uniform temperature distributions are examined. At the end the direct strength method based design methods have been discussed and corresponding recommendations for the designing of CFS beams at elevated temperatures are presented. This thesis has contributed to improve the knowledge of the buckling and failure behaviour of CFS members at elevated temperatures, and the essential data provided in the numerical studies has laid the foundation for further design-oriented studies.

Elementos estruturais como as placas finas fazem parte de um grande número de aplicações nas mais diversas áreas da engenharia e são de grande importância para a engenharia naval e aeronáutica, na construção de cascos de embarcações e estruturas offshore, e na construção de fuselagens de aviões. Por constituírem-se em um elemento estrutural esbelto, estão sujeitas a um comportamento mecânico diferenciado denominado de flambagem, proveniente de um carregamento de compressão uniaxial. O fenômeno da flambagem pode ser dividido em flambagem elástica e elasto-plástica, sendo dependente de aspectos dimensionais, construtivos e/ou operacionais. A inclusão de perfurações em placas provoca uma redistribuição de suas tensões internas, afetando não apenas a sua resistência, mas também as suas características de flambagem. Neste trabalho, desenvolveu-se a análise do comportamento mecânico de placas finas perfuradas de aço, simplesmente apoiadas em suas bordas, e submetidas à compressão. Serão analisados dois graus de liberdade: H/L e H0/L0. Para H/L, serão analisadas placas com H/L = 1,00 e H/L = 0,50, sendo que H e L representam, respectivamente, a largura e o comprimento da placa. Para H0/L0, serão analisadas infinitas possibilidades, sendo que H0 e L0 representam, respectivamente, a largura e o comprimento da perfuração. As placas utilizadas possuem espessura (h) de 10,00 mm e perfuração centralizada. Quanto às perfurações, estas serão dos tipos: oblonga longitudinal, oblonga transversal, elíptica, retangular, losangular, hexagonal longitudinal e hexagonal transversal. Ainda em relação às perfurações, serão consideradas as seguintes frações ϕ = 0,08; 0,10; 0,15; 0,20 e 0,25, sendo que (ϕ) corresponde ao volume da perfuração. Para a determinação das cargas crítica e última de flambagem, foi utilizada a simulação numérica com o auxílio do software Ansys®, que é baseado no método dos elementos finitos. A aplicação do método Design Construtal, possibilitou a determinação das geometrias ótimas para todos os tipos de perfurações, todos os valores de (ϕ) e para todas as relações de H/L. Os resultados obtidos mostram que há influência do tipo, da forma e do tamanho da perfuração na definição das curvas limites à flambagem e das curvas à flambagem elasto-plástica. Foi possível definir, para cada tipo de perfuração e para todos os valores de (ϕ), os pontos de transição entre a flambagem elástica e à elasto-plástica, assim como os pontos que definem os valores máximos para o fator TLNMáx (tensão limite normalizadora). / Structural elements such as thin plates are part of a large number of applications in various areas of engineering and are of great importance for marine and aerospace engineering, construction and offshore structures hulls, and the construction of airplane fuselages. Being a slender structural element, they are subject to a different mechanical behavior known as buckling, caused by a compressive loading. The phenomenon of buckling can be divided in elastic and elasto-plastic buckling, being dependent dimensional, construction and / or operational aspects. The inclusion of perforations in plates causes a redistribution of its internal stress, affecting not only their resistance but also their buckling characteristics. In this work it was performed the analysis of the mechanical behavior of thin perforated steel plates, simply supported on its edges, and subjected to compression. In the analysis it was considered two degrees of freedom: H/L and H0/L0. For H/L will be analyzed plates with H/L = 1.00 and H/L = 0.50, wherein H and L represent respectively the width and length of the plate. There are endless possibilities for the relation H0/L0. The studied plates have a thickness (h) of 10.00 mm and centralized perforation. The following types of perforation will be used: longitudinal oblong, transverse oblong, elliptical, rectangular, diamond, longitudinal hexagonal and transverse hexagonal. Also in relation to perforations, it will be considered the following fractions (ϕ = 0.08; 0.10; 0.15; 0.20 and 0.25), wherein (ϕ) corresponds to the volume ratio of the perforation. For determining the critical and ultimate buckling loads it was utilized numerical simulation with the assistance of Ansys® software, which is based on the finite element method. The application of the Constructal Design method of this study made it possible to determine the optimal geometries for all types of perforations, for all values of (ϕ) and all the relations H/L. The results show that there is an influence of the perforation type, shape and size, in defining the limit curves of the buckling and the curves of the elasto-plastic buckling. It was also possible to define, for each type of perforation and for all (ϕ) values, the transition points between elastic and elasto-plastic buckling; as well as the points that define the maximum values for the TLNMáx factor (normalized limit stress).

The recent substantial increase in world demand for energy and raw material resources has accelerated oil and gas exploration and production. At the same time, the depletion of onshore and shallow water oil resources presents a challenge to engineers to develop new means of harvesting and transporting oil and gas from harsh and remote areas. Sandwich Pipe (SP) is a relatively new design concept developed to address the transportation of oil in deep and ultra-deep waters as well as in cold environments. The main focus of this thesis is on the characterization of the structural performance of these novel systems. Deep and ultra-deep water offshore pipelines are subjected to excessive hydrostatic external pressure during installation and operation. In this research, an innovative analytical solution was developed to evaluate the external pressure capacity of SPs by calculating the linear eigenvalues of the characteristic equations of the system. In the proposed solution, the interface condition between the layers of the system is accounted for in the governing equations. As well, a set of comprehensive parametric studies using the Finite Element (FE) method was developed to investigate both the elastic and plastic buckling response of SPs. The influence of various structural parameters such as the material, geometrical and intra-layer interaction properties on the characteristic behavior and the buckling pressure of SPs was examined. In addition to the proposed analytical solution, two sets of semi-empirical equations based on the FE analysis results were recommended in calculating the elastic and plastic buckling pressure of SPs. As bending represents an important loading state in the installation and service life of SPs, it should be considered a governing loading scenario. In this thesis, the behavior of SPs under bending was investigated using a comprehensive set of parametric studies. SP systems with a wide practical range of physical parameters were analyzed using the FE method, and the influence of various structural parameters on the characteristic response and bending capacity of the system was explored, including pipe geometry, core layer properties, material yield anisotropy of high-grade steel pipes, and various intra-layer adhesion configurations.