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 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 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.
Propoe-se neste trabalho uma formulacao inelastica de 2a ordem da Teoria Generalizada de Vigas (GBT), baseada na teoria de escoamento J2, e que constitui uma promissora alternativa ao MEF de casca. A sua aplicacao e ilustrada na analise de uma viga em I e de uma coluna em C-reforcado. Sao validados resultados da GBT por comparacao com os obtidos atraves do Abaqus (trajectorias de equilibrio, configuracoes deformadas e perfis de deslocamentos), tendo-se concluido que a natureza modal da GBT permite (i) obter resultados precisos com apenas 22% do numero de graus de liberdade usado no Abaqus, bem como (ii) compreender a mecânica comportamental do elemento em qualquer regime elasto-plastico (atraves da analise dos diagramas de participacao modal).
This paper reports the results of a numerical investigation concerning the elastic and elastic–plastic post-buckling behaviour of cold-formed steel lipped channel columns affected by local-plate/distortional buckling mode interaction. The results presented and discussed were obtained through analyses performed using the finite element code Abaqus and discretising the columns by means of fine 4-node shell element meshes. The columns analysed (i) are simply supported (end sections locally/globally pinned and free-to-warp), (ii) have cross-section dimensions that ensure equal local-plate and distortional critical buckling stresses, thus maximising the local-plate/distortional mode interaction effects, and (iii) contain critical-mode initial geometrical imperfections that exhibit different shapes but share the same combined amplitude. The numerical post-buckling results reported consist of (i) elastic and elastic–plastic non-linear equilibrium paths, (ii) curves and figures describing how the column deformed configuration (expressed as a linear combination of its local-plate and distortional components) evolves along the elastic post-buckling equilibrium paths and (iii) figures providing a clear visualisation of the (iii1) evolution of the elastic–plastic column deformed configurations, (iii2) the growth of the plastic strains and (iii3) failure mechanisms exhibited by a fairly large portion of the elastic–plastic columns that were analysed in this work.
No abstract is provided for this article.
Glass fiber–reinforced polymer (GFRP) pultruded profiles are prone to web buckling and/or crushing when subjected to concentrated loads in the direction transverse to the pultrusion axis due to their low elastic and strength properties. Based on a recent work in which it was concluded that the Tsai-Hill criterion does not succeed in providing reasonable estimates of the web-crippling capacity of GFRP profiles, in the present work another progressive damage model is implemented into a finite-element (FE) model for web-crippling analysis. First, previous web crippling experiments on I-section GFRP profiles are summarized. Then the basis of the FE model is presented (element types, failure initiation criteria, and damage model) and results of preliminary analyses (mesh size and viscous regularization) are discussed. Subsequently, the load versus displacement curves, damage zones, and failure modes of GFRP profiles under different load configurations and bearing lengths are presented. Finally, the model sensitivity to different parameters (transverse compressive strength, in-plane shear strength, matrix compressive fracture energy, modeling of web-flange rounded corner) is analyzed. The proposed model is shown to be much more accurate than those based on Tsai-Hill criterion. It is also shown that the in-plane shear strength governs failure initiation, while the transverse compressive strength is more influential to the profiles' ultimate behavior. This study also highlights the major impact of fracture energy in the behavioral response of GFRP profiles subjected to transverse concentrated loads.
This paper begins by presenting a Generalized Beam Theory (GBT) formulation for analyzing the vibration behavior of loaded composite thin-walled members, which accounts for the effects of (i) cross-section in-plane deformation, (ii) shear deformation, (iii) geometric and material coupling, (iv) primary, secondary and non-linear warping, and (v) rotary inertia. This formulation is then used to investigate the local and global vibration behavior of lipped channel columns and beams displaying cross-ply orthotropy, focusing on issues dealing with the variation of the fundamental frequency and vibration mode nature with the member length and applied stress level. For validation purposes, some GBT-based results are also compared with values obtained by means of 4-node shell finite element analyses using ABAQUS. Some relevant conclusions are drawn concerning the dependence of the member vibration mode shape (wave number) on the compression/bending level (applied-to-critical ratio).
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.
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 an experimental study about the fire resistance behaviour of pultruded glass fibre reinforced polymer (GFRP) beams. The main objectives of the study were to evaluate the influence on the fire resistance of GFRP beams of (i) the number of sides exposed to fire; (ii) the load level applied, and (iii) using different fire protection systems. To this end, a total of 12 GFRP tubular beams were exposed to the time-temperature curve of ISO 834, in either one or three sides, and simultaneously subjected to two different load levels corresponding to mid-span deflections of L/400 or L/250, L being the span. Different passive and active fire protection systems were assessed, including thick insulation boards, intumescent products and water-cooling. The results obtained show that three-side exposure causes a remarkable reduction of fire resistance, compared to one-side exposure, for both unprotected and protected profiles, highlighting the importance of adopting a building architecture with GFRP beams integrated in the floors. The efficacy of water-cooling for one-side exposure was confirmed; however, for three-side exposure it is shown that only passive protection is able to significantly extend the fire endurance of GFRP pultruded profiles. As expected, increasing the load level caused a (moderate) reduction of fire resistance.
The mechanical behavior of light steel framing (LSF) walls under horizontal (shear) loadings is reported and assessed in this paper. In total, an experimental program with twelve LSF walls (six under monotonic and six under cyclic loading) was conducted, and the main parameters investigated were (i) the thickness and (ii) the material used as the cladding (OSB, a plasterboard, and a steel sheet), (iii) the spacing between fasteners (150 or 75 mm), and (iv) the influence of using steel bracing elements. It is concluded that doubling the number of fasteners and increasing the thickness of OSB by 80% lead to increases in ultimate loads, respectively, of 33 and 13%. The ductility index of the walls with steel sheets was 50 to 75% lower than those of the remaining walls. The wall with the steel strap x-bracing system presented (i) the lowest initial rigidity (a diaphragm effect could not be triggered with these elements) and (ii) the highest damage extent at the end of testing (a damage parameter of 0.85, due to damage of the steel strap-to-steel structure connection). It is confirmed that the results obtained with testing of the walls under a monotonic load can be good predictors of their behavior under cyclic loading as, for instance, the ultimate loads of walls under both loading cases present an average difference of 4%.
This paper presents a formulation of Generalised Beam Theory (GBT) intended to perform first-order elastic–plastic analyses of thin-walled members experiencing arbitrary deformations and made of non-linear materials exhibiting isotropic hardening. After presenting the GBT fundamental assumptions and kinematic relationships, the member non-linear equilibrium equations are derived and a non-linear one-dimensional (beam) finite element is formulated. The arc-length control technique is adopted in the numerical solution of the non-linear equations and J2-flow theory is used to model plasticity in conjunction with the Backward Euler return-mapping algorithm. In order to show the capabilities and potential of the implemented formulation, a set of numerical illustrative examples are presented and discussed. For validation purposes, most of the GBT results obtained (equilibrium paths, modal participation diagrams, displacement profiles, stress distributions and deformed configurations) are compared with values yielded by Abaqus shell finite element analyses.
No abstract is provided for this article.
