No abstract is provided for this article.
This paper reports the results of an experimental investigation aimed at assessing the post-buckling behaviour and ultimate strength of fixed-ended cold-formed steel lipped channel columns experiencing local/distortional mode interaction. A total of 26 columns were tested and the specimens were carefully selected to ensure various levels of local/distortional interaction effects (more or less close local and distortional critical stresses). The experimental results presented consist of the specimen geometries, material properties, initial imperfections, non-linear equilibrium paths and ultimate strength values. Since the collapse of most columns combines local and distortional deformations, these experimental results may be used to (i) assess the relevance of local/distortional interaction, (ii) calibrate and validate numerical simulations and (iii) provide experimental data aimed at developing a Direct Strength Method (DSM) approach to design cold-formed steel lipped channel columns against local/distortional interaction such a DSM approach is addressed in Part II of this paper.
Thin-walled metal member slenderness usually leads to structural behaviours governed by plasticity/ instability effects. Their assessment can be based on Generalised Beam Theory (GBT), an elegant/efficient well known approach with a unique modal nature – displacement field is a linear combination of crosssection deformation modes. The first inelastic postbuckling GBT formulation is due to Gonçalves & Camotim (2012), based on the J2-flow theory. Abambres et al. (2013b,c) developed/validated an alternative GBT code, (i) based on a distinct mode set and (ii) first applied to strain-hardened materials. This paper (i) presents an overview of the developed formulation, and (ii) shows its potential for tubular member analyses, validated against Abaqus SFEA.
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By emphasising on the axial compressive resistance of circular concrete-filled double-skin carbon steel short (CFDST) columns, this paper proposes a direct design that takes into account the confinement effect of both outer and inner tubes. First, available test results of axially-loaded CFDST short columns were collected from the literature. Then, the results obtained from available resistance models, including design specifications, were compared with the test results. The comparisons revealed that most design models are conservative, some being too conservative, and all of them do not own the same accuracy along the entire slenderness range of the circular tubes, a fact attributed to the absence of confinement effect provided by the inner tube. Accordingly, the test resistances were used to obtain the lateral pressure ( f r p ) due to the confinement effect provided not only by the outer tube (as in the previous studies) but rather by both outer and inner tubes of CFDST short columns with circular–circular and circular–square configurations. The calibrated formulae for f r p were used to propose a design resistance formula for axially-loaded CFDST short columns. The results showed that these formulae provide much better resistances than the available predictors for any tube slenderness and for columns manufactured from different grades of steel and concrete materials.
This paper presents the formulation of a Generalised Beam Theory (GBT) developed to analyse the vibration behaviour of composite thin-walled members made of laminated plates and displaying arbitrary orthotropy. Initially, the equilibrium equations and corresponding boundary conditions are derived and their terms are physically interpreted, i.e., related to the member mechanical properties. Then, the derived equations are used to study the local and global vibration behaviour of lipped channel members displaying cross-ply orthotropy. The GBT results are validated through a comparison with numerical values obtained from finite element analyses, which employ thin-shell elements to discretise the member. Finally, a brief investigation is carried out in order to assess the variation of the fundamental frequency value and vibration mode nature with the member length.
Resistencia al fuego de perfiles pultruídos de polímero reforzado con fibras de vidrio (GFRP) para aplicaciones en rehabilitación: Estudio experimental, numérico y analíticoRESUMENEl presente artículo presenta un estudio sobre la resistencia al fuego de vigas fabricadas con perfiles pultrusionados de polímero reforzado con fibra de vidrio (GFRP). Se realizaron ensayos de resistencia al fuego en vigas con un vano de 1.3 m, expuestas a la acción del fuego según la norma ISO 834. En estos ensayos, se evaluó el efecto de diferentes tipos de exposición al fuego y los niveles de carga aplicados, así como la eficacia de diferentes sistemas de protección. Se desarrolló un modelo numérico en el software ANSYS FLUENT para simular la evolución del campo de temperaturas en la sección transversal y un modelo analítico para determinar la evolución de la deformación de las vigas.Palabras clave: materiales compuestos, resistencia al fuego, campaña experimental, simulación numérica, modelo analítico. Fire Resistance of pultruded profiles of glass fiber reinforced polymer (GFRP) for rehabilitation applications: Experimental, numeric, and analytical studyABSTRACTThis article presents a study on the fire resistance of beams manufactured with pultruded profiles of glass fiber reinforced polymer (GFRP). Fire resistance tests were done on beams with a span of 1.3 m, exposed to the action of fire and according to the standard ISO 834. In these tests, the effect of different types of exposure to fire and the degrees of loads applied, as well as the efficiency of different protection systems were evaluated. A numeric model in the ANSYS FLUENT software was developed to simulate the evolution of the ranges of temperatures in the cross-section, as well as an analytical model to determine the evolution of deformation on the beams.Keywords: composite materials; resistance to fire; experimental campaign; numeric simulation; analytical model. Resistência ao fogo de perfis pultrudidos de polímero reforçado com fibras de vidro (GFRP) para aplicações em reabilitação: Estudo experimental, numérico e analíticoRESUMONeste artigo é apresentado um estudo sobre a resistência ao fogo de vigas em perfis pultrudidos de polímero reforçado com fibras de vidro (GFRP). Foram realizados ensaios de resistência ao fogo em vigas com um vão de 1.3 m, expostas ao fogo de acordo com a curva temperatura-tempo da norma ISO 834. Nestes ensaios, avaliou-se o efeito de diferentes tipos de exposição ao fogo (em uma e três faces) e níveis de carga aplicados, bem como a eficácia de diferentes sistemas de proteção. Foi desenvolvido um modelo numérico térmico bidimensional no software ANSYS FLUENT para simular a evolução das distribuições de temperatura na secção transversal. Foi ainda desenvolvido um modelo analítico para determinar a evolução das deformações das vigas. Palavras-chave: Materiais compósitos, resistência ao fogo, campanha experimental, simulação numérica, modelo analítico.
This paper reports the results of an investigation aimed at providing fresh insight on the mechanics underlying the local and global buckling behaviour of angle, T-section and cruciform thin-walled steel members (columns, beams and beam-columns). Due to the lack of primary warping resistance, members displaying these cross-section shapes possess a minute torsional stiffness and, therefore, are highly susceptible to buckling phenomena involving torsion – moreover, it is often hard to distinguish between torsion and local deformations. Almost all the numerical results presented are obtained by means of Generalised Beam Theory (GBT) analyses and, taking advantage of its unique modal features, it is possible to shed some new light on how to characterise and/or distinguish the local and global buckling modes of the above thin-walled members. Finally, some comments are made concerning the development of a rational and efficient (safe and economic) approach for their design.
A new approach to estimate the web crippling failure load of cold-formed steel beams under Internal Two Flange (ITF) loading using the Direct Strength Method (DSM) is proposed in this paper. After the description of the existing test data to calibrate the DSM-based formula, the accuracy of the analytical expressions given in Eurocode 3 [1] and the North-American Specification [2] is briefly assessed. In order to obtain additional information on the web crippling behaviour of each test specimen, several types of analyses are performed: (i) quasi-static non-linear analyses (using finite elements), (ii) elastic buckling analyses (using finite elements and the GBTWEB software), and (ii) rigid-plastic analyses (using yield-line theory). The coefficients of a DSM-based formula are determined on the basis of the set of 85 experimental results available in the literature and the corresponding buckling and plastic load values. In spite of the different cross-sections, fastening conditions and test set-ups considered in the calibration procedure, it is possible to establish a clear relationship between the web crippling slenderness and the nominal-to-plastic load ratio. Finally, it is shown that the proposed DSM-based formula for ITF loading yields reasonable predictions of web crippling loads and provides safe estimates of flange crushing loads.
This paper shows that chiral carbon nanotubes (CNTs) under twisting show highly dependent strength and fracture toughness on (i) the level of axial tension and (ii) the direction of twisting. To achieve this conclusion, numerous computational intensive molecular dynamics simulations of chiral (6,3) CNTs were performed using the LAMMPS code and the AIREBO potential for C–C bonds. First, we have studied the influence of the tension level and the direction of twisting on the buckling and failure of the chiral CNTs. We show that the applied torques and angles of twist at the buckling and failure stages strongly depend on the level of tensile loading and on the twist direction. In order to explain such noticeable anisotropic behaviour, we have studied the evolution of two kinematic variables (C–C bond length and hexagonal cell angle) as a function of the twist–tension rate. We conclude that the anisotropic failure of chiral CNTs strongly depends on the type of rupture mechanism, which varies with (i) the level of axial tension and (ii) the direction of twisting. Finally, we summarize the information by means of tension–twisting interaction diagrams, which are very dissimilar for direct and inverse twisting. We conclude that inverse twisting influences very negatively the collapse behaviour of chiral CNTs under tension. On the other hand, for low-to-moderate twist–tension rates, the coupling between tension and direct twisting is highly beneficial for the behaviour of chiral CNTs against collapse. This scenario changes dramatically for moderate-to-high twist–tension rates, as the coupling between tension and direct twisting becomes highly detrimental for the chiral CNT collapse process. These original findings might be relevant for the design of nano-devices made of chiral CNTs, as we show that the fracture toughness of chiral CNTs under tension can be highly increased if low-to-moderate direct twisting is added.
This paper presents an investigation on the use of quasi-static analyses with explicit integration to evaluate the web crippling behaviour of cold-formed steel beams. Web crippling failure occurs due to the application of transverse concentrated loads, which can be applied statically or dynamically. In the majority of the examples found in the literature, the web crippling phenomenon has been investigated by means of purely static shell finite element (SFE) models with implicit integration. In this work, the ABAQUS code was employed to implement SFE models aimed at replicating an experimental test and quasi-static analyses with an explicit integration scheme were adopted. First, a brief literature review on the topic of the numerical investigation of web crippling of cold-formed steel members is presented. Then, the paper addresses the characterisation of the quasi-static analysis concept with particular emphasis on the control of dynamic effects and the SFE model of a lipped channel beam under External Two Flange (ETF) loading is described. Several conventional parameters of standard SFE analysis, such as the SFE type, mesh selection, steel model, hardening effects due to cold-forming, residual stresses, initial imperfections and support conditions are explained, as well as additional specifications pertaining to the adoption of quasi-static analyses, such as the load rate, mass scaling, contact and friction, smoothed amplitude curves and inhibition of inertia (noise) effects. Finally, the results obtained are presented in the context of the ETF case, including load–displacement curves, curves of kinetic-to-internal energy ratio vs. displacement and beam deformed shapes (failure modes). It is concluded that explicit analysis leads to rigorous simulations of experimental test results, in terms of ultimate load, post-collapse load–deflection curve and failure mechanism. The failure mode obtained with the quasi-static analysis provides a better approximation of the one observed experimentally than its non-linear static analysis counterpart. Indeed, the failure mechanism emerges considerably more clearly when the quasi-static analysis is adopted.
This chapter addresses the derivation of Generalized Beam Theory (GBT)-based analytical distortional buckling formulae for cold-formed steel rack-section columns and beams. Such formulae provide bifurcation stress estimates for members with arbitrarily inclined intermediate stiffeners and pinned/free-to-warp or fixed/warping-free end sections. The accuracy and validity of the GBT-based analytical estimates are assessed by means of a comparison with exact FEM results concerning several rack-section member geometries and, for some pinned/free-to warp columns only, also with the values yielded by the formulae developed by Lau & Hancock. The various concepts and steps involved in deriving GBT-based (approximate) analytical formulae to estimate distortional buckling stresses in thin-walled rack-section columns and beams are presented in the chapter. Such formulae automatically incorporate folded-plate theory concepts—an important feature which is responsible for the fact that they directly account for cross-section distortion and (partially) flexural deformation effects. The derived formulae, which require the preliminary (numerical) solution of an auxiliary standard matrix eigen value problem and can be readily programmed even in a hand calculator, provide distortional critical lengths and bifurcation stress resultant estimates for rack-section columns and beams with arbitrarily inclined intermediate stiffeners and pinned/free-to-warp or fixed/warping-free end sections. The chapter presents a detailed analysis of a set of four identical columns/beams with pinned/free-to-warp or fixed/warping-free end sections, in order to illustrate the application of the proposed formulae.
This paper presents a study on the suitability of shell models to assess the buckling behaviour of single-walled carbon nanotubes (CNTs) under torsion. It is shown that the simultaneous use of both well known (i) Donnell shell model and (ii) uniform helix deflected shape (HDS) of CNTs, leads to incorrect values of the critical angle of twist per unit of length, as they do not match the results obtained from molecular dynamic simulations. Conversely, more sophisticated models, like the Sanders shell model (SSM) with non-uniform HDS is found to lead to correct results of critical angle of twist. It is established that there is a transitional aspect ratio (length-to-diameter ratio) that separates the group of short CNTs, mostly influenced by end conditions, from the group of long CNTs, mostly influenced by warping deformation. Based on the SSM with non-uniform HDS, straightforward analytical expressions to calculate the critical angle of twist are proposed for each of these groups. Despite its simplicity, the procedure presented is shown to give rather accurate results for a wide range of CNT lengths, diameter and chirality.
A non-linear finite element model for the simulation of the mechanical in-plane behaviour of γ-graphyne is presented in this paper. Different types of bonds (Single CC, Aromatic CC, Triple CC) are simulated by means of non-linear springs, which accurately take into account the different behaviour of interatomic forces in tension and compression at 0K temperature. Then, the finite element model is used to conduct six tests (two uniaxial tension–compression tests, one biaxial tension–compression test, two uniaxial shear tests, one biaxial shear test) to evaluate the non-linear mechanical behaviour of γ-graphyne. After that, a set of linear elastic properties (Young’s modulus, Poisson’s ratio, shear modulus, bulk modulus) and non-linear elastic properties (limit of proportionality stress and strain, ultimate stress and strain) is reported and compared with values reported in the literature (mostly linear elastic properties). This validation shows that the developed finite element model is able to predict accurately the linear and non-linear mechanical properties of γ-graphyne (i.e. stiffness and strength). Additionally, some remarks are drawn regarding the anisotropy of γ-graphyne and its distinct behaviour under tension and compression.
This paper presents a formulation of Generalised Beam Theory (GBT) developed to analyse the influence of non-classical effects on the structural behaviour of FRP composite circular hollow section members. Unlike other existing beam theories, the present GBT formulation incorporates non-classical effects comprising (i) elastic material couplings, (ii) deformation of cross-section contour, (iii) warping deformation and (iv) shear deformation. With the purpose of solving the GBT system of differential equilibrium equations, a finite element formulation is briefly presented. In order to clarify the concepts involved in the formulated GBT and illustrate its application and capabilities, the linear ( 1 st order) behaviour of two composite members exhibiting elastic couplings is analysed and the results obtained are thoroughly discussed and compared with estimates available in the literature. It is shown that accurate solutions can only be achieved if these non-classical effects are incorporated in the analysis.
This paper presents a computational study on the monotonic and hysteretic in-plane behaviour of graphene. With this purpose, atomistic finite element models of graphene were developed taking into account the degradation of stiffness and strength through an elastic-plastic model. The study extends the typical unidirectional tests (in armchair and zigzag directions) to the bidirectional test and the shear test, establishing a consistent and comprehensive set of both elastic and strength properties. The mechanical properties obtained from the monotonic analyses (elastic and strength properties) are validated from the comparison with those available in the literature (experimental, density functional theory, molecular dynamic simulations and finite element models). The strain-softening behaviour of graphene is assessed through these atomistic models. The failure modes of graphene sheets in different loading tests are detailed and its load carrying capacity is explained. Finally, the hysteretic behaviour of graphene is discussed. The stress-strain curves and the variation of dissipated energy with the strain are given for different number of cycles. Then, some concluding remarks are drawn.
