A damage progression failure model for tridimensional finite element (FE) analyses has recently been proposed, allowing the simulation of composites as homogenized materials, greatly reducing computational costs. It is able to predict the damage and post-failure behaviour of composites, while its calibration can be performed with data derived from the standardized experimental characterization of the composite materials. This paper presents the calibration of that model for 5 new glass-FRP pultruded profiles, followed by the simulation of different application/design cases: (i) wide compact tension; (ii) compact compression; (iii) web-crippling; and (iv) bolted double-lap connection tests. While the results show that further investigation is needed to address the experimental characterization of the in-plane shear properties and the numerical simulation of bearing failure, overall the models were well able to predict the experimental strength, post-failure behaviour, failure modes and damage patterns, showing that the feasibility of using this damage progression model as a design tool.
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This paper reports an investigation aimed at developing a Direct Strength Method (DSM) approach to estimate the ultimate strength of lipped channel columns affected by local/distortional buckling mode interaction. Following a brief presentation of a few relevant aspects concerning the shell finite element analysis of the geometrically and materially non-linear behaviour of thin-walled members, one illustrates the methodology adopted to obtain a lipped channel column ultimate load “data bank” intended to be used in the development and assessment of a DSM design approach. Next, the current DSM expressions to predict the load-carrying capacity of columns failing in local and distortional modes are briefly reviewed, devoting special attention to an approach that takes into account the above mode interaction. Then, the results of a parametric study, carried out by means of the code Abaqus, are presented and discussed — this study involves the evaluation of the “exact” ultimate loads of 276 lipped channel columns with various geometries and two boundary conditions (pinned and fixed end supports), all exhibiting local/distortional interaction. Finally, these ultimate strength data are compared with the estimates provided by the available DSM expressions and, on the basis of this comparison, one identifies several features that a DSM approach successfully accounting for local/distortional interaction must incorporate.
The local post-buckling behaviour of elliptical hollow section (EHS) tubes under compression is analysed in this paper. It is found that EHS tubes with low to moderate aspect ratios can support loads up to their limit loads but are imperfection sensitive (shell-type behaviour), while EHS tubes with moderate to high aspect ratios can carry loads higher than their limits loads (plate-type behaviour) and are imperfection insensitive. For increasing EHS aspect ratio, it is found that the compressive stresses accumulate near the zones of minimum radius of curvature while the zones of maximum radius of curvature experience a relatively low compressive stress level. Thus, it is likely to apply the effective width concept to EHS tubes with moderate to high aspect ratio.
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The aims of this work are two-fold: (i) to present the results of a study concerning the elastic in-plane stability and second-order behaviour of unbraced single-bay pitched-roof steel frames and (ii) to propose, validate and illustrate the application of an efficient methodology to design this type of commonly used frame. After (i) characterizing the relevant frame buckling modes and P – Δ second-order effects, and (ii) addressing the exact and approximate calculation of the associated bifurcation loads and secondary bending moments, the paper deals with the incorporation of these concepts in the definition of an efficient design procedure. In particular, it is clearly shown that, due to the rafter slope, the geometrically nonlinear behaviours of orthogonal beam-and-column and pitched-roof frames are qualitatively different. Finally, the proposed concepts and methodologies are illustrated through the presentation and discussion of numerical results involving fixed and pinned-base frames.
This paper deals with the ultimate strength and design of fixed-ended lipped channel columns experiencing local-distortional buckling mode interaction. First, the paper reports the results of an experimental investigation involving a set of 26 columns with several cross-section dimensions and yield stresses that were tested to determine their failure loads and also to provide experimental evidence of the occurrence of local-distortional mode interaction. These results consist of the column geometries, material properties, initial geometric imperfections, nonlinear equilibrium paths, and ultimate strength values. Then, after comparing the experimental column ultimate loads with the estimates provided by the current direct strength method (DSM) design curves against local and distortional failures, which clearly show that they lead to inaccurate and often very unsafe ultimate strength estimates, the paper presents and assesses the quality of DSM-based design procedures based on approaches providing nominal strengths against local-distortional and distortional-local interactive failures. Next, an in-depth comparison is made between all the experimental ultimate strength results available in the literature and their estimates provided by the preceding DSM design procedures. Finally, the paper closes with design considerations and recommendations, motivated by the conclusions drawn from this investigation.
In this paper, one investigates the local-plate, distortional and global buckling behavior of thin-walled steel beams subjected to non-uniform bending moment diagrams, i.e. under the presence of longitudinal stress gradients. One begins by deriving a novel formulation based on Generalized Beam Theory (GBT), which (i) can handle beams with arbitrary open cross-sections and (ii) incorporates all the effects stemming from the presence of longitudinally varying stress distributions. This formulation is numerically implemented by means of the finite element method: one (i) develops a GBT-based beam finite element, which accounts for the stiffness reduction associated to applied longitudinal stresses with linear, quadratic and cubic variation, as well as to the ensuing shear stresses, and (ii) addresses the derivation of the equilibrium equation system that needs to be solved in the context of a GBT buckling analysis. Then, in order to illustrate the application and capabilities of the proposed GBT-based formulation and finite element implementation, one presents and discusses numerical results concerning (i) rectangular plates under longitudinally varying stresses and pure shear, (ii) I-section cantilevers subjected to uniform major axis bending, tip point loads and uniformly distributed loads, and (iii) simply supported lipped channel beams subjected to uniform major axis bending, mid-span point loads and uniformly distributed loads — by taking full advantage of the GBT modal nature, one is able to acquire an in-depth understanding on the influence of the longitudinal stress gradients and shear stresses on the beam local and global buckling behavior. For validation purposes, the GBT results are compared with values either (i) yielded by shell finite element analyses, performed in the code ANSYS, or (ii) reported in the literature. Finally, the computational efficiency of the proposed GBT-based beam finite element is briefly assessed.
This paper presents the formulation of a generalized beam theory (GBT) to analyze the vibration behavior of composite thin-walled prismatic members displaying straight axis, open-section, and arbitrary orthotropy. It accounts for the effects of (1) the cross section in-plane deformation, (2) geometric and material couplings, (3) primary and secondary warping, and (4) rotary inertia. First, the GBT equilibrium equations and boundary conditions are derived, and their terms are physically interpreted, i.e., related to the member mechanical properties. Then, a few remarks on the cross-section mechanical properties appearing in the linear stiffness and inertia terms are presented. Finally, to clarify the concepts involved in the proposed GBT formulation and illustrate its application and capabilities, an in-depth study concerning the local and global vibration behavior of lipped channel members with (1) simply supported end sections and wall cross-ply orthotropy and (2) fixed (clamped) end sections and wall nonaligned orthotropy are presented and discussed in detail.
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This paper presents a study on the buckling behaviour of curved panels under pure compression using the Generalised Beam Theory (GBT). A GBT formulation is presented first, based on its natural degrees-of-freedom (i.e. modes) and some explanations are given about the discretization of panel section and its influence on the deformation mode nature. Then, the GBT formulation is applied and illustrated by means of three studies. In the first study, the influence of the deformation mode (global, distortional, local, warping shear, transverse extension) on the buckling load and buckling mode of an unstiffened panel with moderate curvature is investigated. Then, in the second and third studies, the effects of the curvature and of the number of stiffeners on the buckling behaviour of the panels are assessed. It is concluded that accurate predictions of buckling loads and modes of curved panels can only be achieved by considering all modes (conventional, warping shear and transverse extension) in GBT analyses. Both warping shear and transverse extension modes appear naturally due to the panel curvature. However, their participation drops with decreasing curvature of the panel – in the limit case (flat panel, i.e., plate) their contribution is null and only conventional modes participate in the buckling mode (minor axis bending and distortional modes tend to equal participations, 50% each). Finally, an increase of the number of stiffeners leads to a decrease of the global mode participation and to an increase of the distortional mode participation.
In this paper, the lateral–distortional buckling (LDB) of hollow tubular flange plate girders (HTFPGs) with slender unstiffened webs is investigated. Firstly, shell finite element analyses are performed in order (i) to study the elastic buckling behaviour of simply supported HTFPGs under uniform bending and (ii) to compare it with the behaviour of I-section plate girders (IPGs) with unstiffened and stiffened webs. The results show that HTFPGs (without stiffeners) have much higher critical moments than IPGs (with stiffeners). Secondly, the LDB behaviour of HTFPGs is investigated using finite strip analyses and the results show the girder length range in which LDB is relevant. After that, an analytical model to estimate the critical LDB moment is proposed and validated by comparison between analytical and numerical values. Thirdly, the investigation is extended to the inelastic domain and non linear shell finite element analyses are performed to evaluate the ultimate strengths of the HTFPGs. Several remarks regarding the flexural strength of HTFPGs are presented. Finally, the predictions given by Eurocode 3 are compared with the numerical results and it is found that the predictions given by the design equations are unconservative. Therefore, it is recommended to use the European specifications by adopting the proposed expression to estimate the critical LDB moment.
