Generalised Beam Theory (GBT) for stiffened sections

Taig, Gerard; Ranzi, Gianluca

doi:10.1007/s13296-014-2017-x

Cited by 14 publications

(3 citation statements)

References 30 publications

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“…In the spirit of the dynamic GBT approach [73][74][75][76][77][78][79][80][81], the deformation modes will be determined from the free dynamics of an unrestrained planar frame model, representing the cross-section with its plates located at their mid-lines. In this context, two eigenvalue problems will be considered, namely (a) the planar eigenvalue problem and (b) the warping eigenvalue problem, which are aimed at the identification of the conventional and extension modes, and of the warping eigenmodes, respectively.…”

Section: Cross-sectional Analysismentioning

confidence: 99%

“…Its novelty relies on the ability to account for both longitudinal and transverse partial interaction taking place within the plane of the shear connection interface in the evaluation of the GBT deformation modes, therefore extending the applicability of a longitudinal partial interaction model developed by the authors [73]. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section [74][75][76][77][78][79][80][81]. The transverse partial interaction is described by means of shear deformable spring elements and is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses.…”

Section: Introductionmentioning

confidence: 99%

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Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction

Taig

Ranzi

2016

Mathematics and Mechanics of Solids

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This paper presents a Generalised Beam Theory formulation to study the partial interaction behaviour of two-layered prismatic steel–concrete composite beams. The novelty of the proposed approach is in its capacity to handle the deformability of the shear connections at the interface between the slab and steel beam in both the longitudinal and transverse directions in the evaluation of the deformation modes. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section. In this context, the shear connections are modelled using shear deformable spring elements. As a result, the in-plane partial shear interaction behaviour is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses. In the case of the conventional modes, the longitudinal slip is accounted for in the post-processing stage where the warping displacements are determined. A numerical example of a composite box girder beam is presented and its structural response investigated for different levels of shear connection stiffness in both the longitudinal and transverse directions. The accuracy of the numerical results is validated against those obtained with a shell finite element model implemented in ABAQUS/Standard software.

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Section: Cross-sectional Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction

Taig

Ranzi

2016

Mathematics and Mechanics of Solids

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“…Since then, different academic groups have contributed to its development -e.g. Simão & da Silva [11], the group around Camotim [12,13,14,15,16,17], or by Ranzi and his colleges [18,19] just to mention some of the many contributors. The general idea of GBT is to represent and discretise the cross-section along the wall centre line to find distortional transverse displacement modes that have orthogonal warping modes.…”

Section: Introductionmentioning

confidence: 99%

A thin-walled beam element based on semi-analytical solution modes

Hansen

Jönsson

2019

Thin-Walled Structures

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Using energy principles, a thin-walled beam element is introduced for the analysis of beams with deformable crosssections that are prone to distortion. The beam element is based on previously attained semi-analytical displacement solution modes of an advanced thin-walled beam model. The first-order beam element for linear analysis handles shear deformations related to both Timoshenko and Mindlin-Reissner type deformations, warping effects of torsion, crosssection distortion including associated warping effects, as well as the transverse displacement effect from normal stress. The formulation can handle both open and closed cross-sections without special attention. The formulation of the displacement solution modes and the stiffness integration of the products of the advanced displacement modes using the Hadamard product are described. The paper also presents the transformations between modal degrees of freedom and element displacement degrees of freedom. Four examples show the beam element capabilities and good agreement with results obtained using the shell and solid elements of a commercial finite element program. The kinematic assumptions that the thin-walled beam model accommodates leads to local shear stress transfer at corners. This transfer of shear stresses is not normally seen in thin-walled beam formulations or shell models. However, the shear transfer is verified through examination of a finite element model using solid elements.

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