A proposal for beam-column interaction formulae

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Ultimate capacity of I-sections under combined loading – Part 1: Experiments and FE model validation

An experimental and numerical study of hot-rolled steel I-sections under combined compression and bending moment is presented herein. A total of two stub column tests and 12 mono-axial or bi-axial eccentric compression tests on HEB 160 cross-sections with two different material grades (S235 and S355) were carried out. The tested cross-sections were of stocky proportions to enable the influence of material strain hardening on the strength and behaviour of hot-rolled steel I-sections to be investigated. The loading eccentricities for the eccentric compression tests were varied in order to achieve different axial compression-to-bending moment ratios. Measured geometric and material properties, together with the full load-deformation histories from the test specimens, were reported. Finite element (FE) models were developed and validated against the experimentally obtained load-deformation curves, as well as the failure modes. The FE results successfully captured the experimental structural performance of hot-rolled steel I-sections and the validated FE models were then used for parametric studies in the companion paper to generate additional numerical results, considering different cross-section slendernesses, material grades and combinations of loading. The experimental and numerical results are employed in the companion paper for the assessment of the design rules given in EN 1993-1-1 (2005) and AISC-360-16 (2016) and for the extension of the deformation-based continuous strength method to the case of hot-rolled steel I-sections under combined loading

Ultimate capacity of I-sections under combined loading – Part 2: Parametric studies and CSM design

The second part of the study on the ultimate capacity of hot-rolled steel I-sections under combined compression and bending moment, focussing on parametric studies and design, is presented herein. An extensive numerical parametric study was carried out, using the verified finite element (FE) models from the companion paper, to generate further structural performance data for specimens with different steel grades, cross-section slendernesses and loading cases. The numerical results together with the experimental results were then used to assess the accuracy of two codified design methods: the European Standard EN 1993-1-1 (2005) and the American Specification AISC-360-16 (2016). The design strengths predicted by the current design standards were found to be generally rather conservative and scattered when applied to non-slender cross-sections, owing principally to the neglect of material strain hardening and reserve capacities between the classification limits. To improve the accuracy and efficiency of the design rules, the continuous strength method (CSM) – a deformation-based design approach which relates the resistance of a cross-section to its deformation capacity – was extended to cover the design of hot-rolled steel I-sections under combined loading, underpinned by both the experimentally and numerically derived ultimate capacities. Overall, the CSM was shown to offer more accurate and consistent predictions than the current design provisions. Finally, reliability analysis was performed to evaluate the reliability level of the design rules

A non-linear 3D beam finite element for the study of steel frames with tapered members

peer reviewedThis paper presents the essentials of an original geometrically and materially nonlinear 3-D tapered beam finite element. The theoretical bases of the element are described, with particular attention paid to the choice of an appropriate displacement field and to the corresponding non-linear axial strains. Specific numerical problems met in the development of the finite element are examined, concerning mainly shear and membrane locking and the handling of rigid body motions. Worked examples on isolated members are presented for various types of analyses: elastic linear, elastic critical and geometrically and materially non-linear analyses. Good accuracy with reference to numerical results is shown, as well as good convergence properties. It is also demonstrated – analytically and numerically – that the use of prismatic beam finite elements for the analysis of tapered beams (segmentation technique) may lead to significant discrepancies when the behaviour is influenced by torsional aspects. Then, the behaviour of two different portal frames with tapered members is proposed, and the results obtained using shell elements, tapered beam elements and prismatic beam elements are compared. This comparison shows that the use of tapered elements leads to results in close agreement with those obtained by shell elements, unlike the prismatic ones. The convenience of the tapered beam element is also highlighted since the total number of degrees of freedom required is significantly reduced compared to a shell modelling, leading to easier meshing, shorter computation time and easier interpretation of results

An investigation on the use of GBT for the study of profiles with branched cross section

peer reviewedThis paper presents a formulation allowing the application of generalised beam theory (GBT) to the analysis of thin-walled members with branched open cross section. It is then applied to a simple example and compared with results obtained by the use of classical FE-models (beam elements or shell elements)

A new spatial thin-walled beam finite element for tapered members

peer reviewedThis paper presents the essentials of an original geometrically and materially non-linear 3-D tapered beam finite element. The theoretical bases of the element are described, with particular attention paid to the choice of an appropriate displacement field and to the corresponding non-linear axial strains. Specific numerical problems met in the development of the finite element are examined, concerning mainly shear and membrane locking and the handling of rigid body motions. Worked examples on isolated members are presented for various types of analyses: elastic linear, elastic critical and geometrically and materially non-linear analyses. Good accuracy with reference to numerical results is shown, as well as good convergence properties. It is also demonstrated – analytically and numerically – that the use of prismatic beam finite elements for the analysis of tapered beams (segmentation technique) may lead to significant discrepancies when the behaviour is influenced by torsional aspects

Analysis of tapered steel frames using beam elements and comparison with shell elements

peer reviewedThis paper deals with the consequences of modelling a tapered steel frame with beam elements rather than shell elements. It starts by presenting a specific beam element accounting for the tapering that allows performing geometrically as well as materially non-linear analysis. Then, several kinds of analyses are carried out on two different frames and the results obtained using shell elements, tapered beam elements and prismatic beam elements are compared. This comparison shows that the use of tapered elements leads to results in close agreement with those obtained by shell elements, unlike the prismatic ones. The paper aims at showing that resorting to a so-called segmentation technique should be decided carefully. It also intends at showing the accuracy and convenience of tapered elements when compared to shell models: the total number of degrees of freedom is indeed significantly reduced, leading to easier meshing, shorter computation time and easier interpretation of results

Experimental and numerical study of flange class 3 cross-section members

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