The buckling behaviour, ultimate strength and failure of columns with semi-elliptical hollow section are examined in this paper, using finite-strip analyses and shell finite-element analyses. Semi-elliptical hollow sections are a unique case of section shape, since they possess a flat part (plate behaviour) and a semi-elliptical part (shell behaviour). Assessing the contribution of each part to the buckling and ultimate behaviour of semi-elliptical hollow section columns is the main objective of this paper. The buckling behaviour is first analysed using finite-strip software and the ultimate behaviour is then studied using shell finite-element software. From the finite-strip results it is shown that local buckling of semi-elliptical hollow section columns is solely governed by the instability of the flat part. From shell finite-element results it is shown that the ultimate behaviour is mostly governed by the pre-buckling stiffness of the semi-elliptical part. Some columns have ultimate loads well above the critical load (associated with local plate buckling) due to the stiffness of the semi-elliptical part, for which the buckling stress is much higher than that of flat part. Finally, some preliminary design guidance is proposed. An expression to predict the ultimate strength is presented and shown to provide accurate results.
No abstract is provided for this article.
This paper reports the results of a numerical investigation aimed at providing fresh insight on the mechanics underlying the buckling and (mostly) post-buckling behaviour of short-to-intermediate equal-leg thin-walled angle steel columns exhibiting fixed and pinned (but with the secondary warping prevented) end supports. Although most of the numerical results presented and discussed were obtained through Abaqus shell finite element analyses, the paper also includes some GBT-based critical stresses and buckling mode shapes, whose interpretation help clarifying the distinction between local and global buckling. The shell finite element results displayed consist of (i) elastic post-buckling equilibrium paths and (ii) curves and diagrams providing the evolution, along a given path, of the column deformed configurations and normal stress distributions.
No abstract is provided for this article.
The chapter presents results of a study concerning the second-order behavior of unbraced single-bay pitched-roof steel frames and proposes, validates, and illustrates the application of an efficient methodology to design this kind of commonly used frames. After characterizing relevant frame buckling modes and second-order effects, and addressing the calculation of the associated bifurcation loads and secondary bending moments, the chapter discusses the incorporation of these concepts in an efficient design procedure. In particular, the second-order behaviors of orthogonal beam-and-column and pitched-roof frames are qualitatively different because of the rafter slope. The chapter illustrates the proposed concepts and methods through the presentation of numerical results involving fixed and pinned-base frames.
This paper presents procedures for the design of fixed- and pin-ended equal-leg angle columns with short-to-intermediate lengths. First, some remarks concerning the buckling and postbuckling behavior of the angle columns are presented that (1) illustrate the main differences between the fixed- and pin-ended column responses and (2) demonstrate the need for specific design procedures. Then, the paper reports an in-depth investigation aimed at gathering a large column ultimate strength data bank that includes (1) experimental values collected from the literature and (2) numerical values obtained from shell finite-element analyses carried out in the code ABAQUS. The set of experimental results is comprised of 41 fixed-ended columns and 37 pin-ended columns and the numerical results obtained include 89 fixed-ended columns and 28 pin-ended columns; various cross-section dimensions, lengths, and yield stresses are considered. Finally, the paper closes with the proposal of new design procedures for fixed- and pin-ended angle columns based on the direct strength method (DSM). The two procedures adopt modified global and local strength curves, and it is shown that the proposed DSM approach leads to accurate ultimate strength estimates for short-to-intermediate columns covering a wide slenderness range.
This paper presents a Molecular Dynamics (MD) study on the characterization of the compressive behavior of an aluminum (Al) material reinforced with carbon nanotubes (CNTs). Firstly, a detailed literature review of recent experimental and numerical works dedicated to the characterization and mechanical enhancement of CNT–Al composites is presented. Then, the paper describes a computational approach based on MD simulations used to analyze the mechanical behavior of the CNT–Al composite material under compression. Finally, the paper presents and discusses several results that comprise (i) curves relating the energies (total, Al, CNT, interface) with the imposed axial shortening displacement, (ii) plots of deformed shapes and failure modes of CNT–Al specimen and (iii) curves relating the acting stress with the imposed strain. In this study, we adopted two limit cases for bonding between the CNT and Al matrix, one in which the displacements are imposed to the Al atoms (case A) and another in which displacements are imposed to both Al and C atoms (case B). In comparison with pure Al, the Young’s modulus increases about 50% in case A and 100% in case B. These increases are not only due to the CNT intrinsic stiffness but also to the interface slip stresses, which are about 16MPa (case A) and 75MPa (case B). In opposition, it is seen that both yield stress and yield strain do not increase. This evidence is mostly due to premature failure of the CNT–Al composite due to CNT local buckling. This study not only confirms previous results obtained by other researchers (e.g. Laha et al. [1]) but also provides some understanding on the compressive behavior of CNT-based composites, which might be different to standard tensile behavior.
No abstract is provided for this article.
This paper presents the derivation, validates and illustrates the application of a Generalised Beam Theory (GBT) formulation developed to analyse the buckling behaviour of thin-walled members with arbitrarily ‘branched’ open cross-sections. Following a brief overview of the conventional GBT, one addresses in great detail the modifications that must be incorporated into its cross-section analysis procedure, in order to be able to handle the ‘branching’ points — they concern mostly issues related to (i) the choice of the appropriate ‘elementary warping functions’ and (ii) the determination of the ‘initial flexural shape functions’. The derived formulation is then employed to investigate the local-plate, distortional and global buckling behaviour of (i) simply supported and fixed asymmetric E-section columns and (ii) simply supported I-section beams with unequal stiffened flanges. For validation purposes, several GBT-based results are compared with ‘exact’ values, obtained by means of finite strip or shell finite element analyses.
No abstract is provided for this article.
When compared with carbon steel, stainless steel exhibits a more pronounced non-linearity and no well-defined yield plateau, as well as appealing features such as aesthetics, higher corrosion resistance and lower life cycle cost. Due to its considerably high ductility/strength and cost, stainless steel structural solutions tend to be adopted mostly for slender/light structures, thus rendering the assessment of their structural behaviour rather complex, chiefly because of the high susceptibility to instability phenomena. The first objective of this paper is to present the main concepts and procedures involved in the development of a geometrically and physically non-linear Generalised Beam Theory (GBT) formulation and numerical implementation (code), intended to analyse the behaviour and collapse of thin-walled members made of materials with a highly non-linear stress-strain curve (e.g., stainless steel or aluminium). The second objective is to validate and illustrate the application of the proposed GBT formulation, by comparing its results (equilibrium paths, ultimate loads, deformed configurations, displacement profiles and stress distributions) with those provided by shell finite element analyses of two lean duplex square hollow section (SHS) columns previously investigated, both experimentally and numerically, by Theofanous and Gardner [1]. The stainless steel material behaviour is modelled as non-linear isotropic and the GBT analysis includes initial geometrical imperfections, but neglects corner strength enhancements and membrane residual stresses. It is shown that the GBT unique modal nature makes it possible to acquire in-depth knowledge concerning the mechanics of the column behaviour, by providing “structural x-rays” of the (elastic or elastic-plastic) equilibrium configurations: modal participation diagrams showing the quantitative contributions of the global, local, warping shear and transverse extension deformation modes moreover, this feature makes it possible to exclude, from future similar GBT analyses, those deformation modes found to play a negligible role in the mechanics of the behaviour under scrutiny, thus further reducing the number of degrees of freedom involved in a GBT analysis, i.e., increasing its computational efficiency.
In this paper, the mechanical behaviour of short rubberized concrete filled steel tubular (RuCFST) columns with square cross-section under cyclic loading is studied numerically. For this purpose, quasi-static analyses using commercial the finite element modeling package Abaqus/Explicit are performed. Firstly, a brief introduction and literature review on concrete filled steel tubes and rubberized concrete (RuC) are made. Then, the numerical models are described in detail with emphasis on the modelling of standard and rubberized concrete and of the steel under cyclic loading. An in-depth presentation of the numerical results is made which firstly includes a validation of the models by comparison with experimental results previously obtained by the authors and secondly a study on the effect of using RuC on the maximum strength and ductility of the columns. Finally, the main conclusions of the work are put forward.
The paper presents the formulation and illustrates the application of an asymptotic-numerical (semianalytical) method to analyze the geometrically nonlinear behavior of plane frames. The method adopts an “internally constrained” beam model and involves two distinct procedures: (1) an asymptotic analysis, which employs a perturbation technique to establish a sequence of systems of equilibrium differential equations and boundary conditions, and (2) the successive numerical solution of such systems, by means of the finite element method. This method can be applied to investigate the behavior of frames with arbitrarily complex configurations (member number and orientation) and leads to the determination of analytical expressions which provide: (1) the initial postbuckling behavior of perfect frames and (2) the nonlinear equilibrium paths of frames containing small initial imperfections or acted by primary bending moments, including the influence of eventual buckling mode interaction phenomena. In order to validate and illustrate the application and potential of the proposed method, several numerical results are presented, concerning (1) four validation examples (Euler column and three simple frames—two or three members), for which there exist some (perfect frame) analytical and numerical asymptotic results reported in the literature; (2) a single-bay pitched-roof frame with partially restrained column bases; and (3) a three-bay frame with two leaning columns. These results comprise (1) the initial postbuckling behavior of perfect frames (individual and coupled buckling modes) and (2) geometrically nonlinear equilibrium paths describing the behavior of frames containing initial geometrical imperfections or primary bending moments. In the latter case, most of the semianalytical results are compared with fully numerical values, yielded by finite element analyses performed in the commercial code ABAQUS.
No abstract is provided for this article.
Neste artigo apresenta-se uma formulacao da GBT para analises elasto-plasticas de 1a ordem e ilustra-se a sua aplicacao a uma viga simplesmente apoiada com seccao em I, constituida por um material elastico-perfeitamente plastico e submetida a cargas concentradas a meio vao. Os resultados da GBT sao validados por comparacao com os resultados obtidos atraves de um modelo de elementos de casca utilizando o programa ABAQUS. Constata-se uma excelente correlacao entre os resultados da GBT e do ABAQUS, em particular no que respeita a trajectorias de equilibrio e configuracoes deformadas. No que respeita a diagramas de tensoes, os resultados da GBT sao bastante satisfatorios no que respeita a tensoes axiais, de corte e de Von Mises, mas distintos dos resultados do ABAQUS no que diz respeito a tensoes normais transversais. No entanto, as distribuicoes 3D de tensoes normais transversais sao qualitativamente semelhantes em todo o dominio da barra.
This paper presents a novel progressive failure model for the 3D simulations of pultruded FRP structures which allows the modelling of the laminates as a homogeneous material. The failure initiation model proposed requires only the strength in each direction as input, combining them to retrieve in-plane and out-of-plane failure indexes. The damage propagation model can be divided in two main stages: (i) damage progression and (ii) constant stress beyond a limit strain. The former stage uses the in-plane and out-of-plane failure indexes to determine the damage progression, using different parameters in each direction to account for the different damage responses, while the latter is characterized by a constant stress after a limit strain is reached, also different for each direction. FE models were developed with the proposed damage propagation model, requiring as input the strengths obtained from standardize experimental material coupon testing, the results of which, namely the load/stress vs. displacement/strain curves, are used to calibrate all the parameters needed to established the model. The results show that the proposed damage propagation model, using a homogenized material, is well able to predict the experimental behaviour even for very complex cases such as interlaminar shear tests. Furthermore, in a companion paper the accuracy and limitations of the model are further assessed in the simulation of transverse compact tension and web-crippling tests.
