Geometrically non-linear generalised beam theory for elastoplastic thin-walled metal members

Gonçalves, Rodrigo; Camotim, Dinar

doi:10.1016/j.tws.2011.10.006

Cited by 87 publications

(39 citation statements)

References 16 publications

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“…The observation of these results prompts the following remarks: (ii) Fig. 4 shows the relevance of the quadratic transverse extension modes in capturing accurately the beam post-buckling behavior, thus confirming the findings of Gonçalves & Camotim (2012). In fact, when these modes are excluded from the analysis (solution 1-57 in Fig.…”

Section: Gbt Post-buckling Behavior Of Beams Experiencing L-d Interacsupporting

confidence: 81%

“…The deformation modes obtained can be divided into three main sets/families, namely the (i) conventional (or Vlasov modes), (ii) shear modes and (iii) transverse extensions modes. These deformation mode sets are also adopted in this work, together with an additional family of quadratic transverse extension modes, which play an essential role in capturing the Poisson effects that develop in the deformed configurations occurring in the advanced post-buckling stages, which involve heavy crosssection in-plane deformation and, therefore, in precluding the determination of overly stiff solutions (Gonçalves & Camotim 2012)  the aforementioned Poisson effects will be addressed in Section 4. . It should be mentioned that the number of deformation modes considered in this work is almost twice that required to analyze lipped channel columns experiencing L-D interaction 7  this is because of the lack of symmetry of the beam cross-section deformation patterns, which did not occur in the columns.…”

Section: Cross-section Analysismentioning

confidence: 99%

“…These authors adopted a total Lagrangian kinematic description and an additive decomposition of the strain terms into Green-Lagrange membrane strains and small-strain bending. The main novelty of the formulation developed in this paper is the consideration of the whole set of non-linear membrane strain terms, which is equivalent (but not similar) to the formulation recently proposed by Gonçalves & Camotim (2012). The strain-displacement relationships adopted read 3 s (v) x(u) z (w) s (v) x(u) z (w) s (v) x(u) z(w) t s (v) x(u) z (w) s (v) x(u) z (w) s (v) x(u) z(w) t Figure 1: Arbitrary prismatic thin-walled member, local coordinate system and displacement components     2 2 2 2 2 2 , , , …”

Section: Introductionmentioning

confidence: 99%

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On the mechanics of local-distortional interaction in thin-walled lipped channel beams

Martins

Camotim

Gonçalves

et al. 2018

Thin-Walled Structures

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This paper investigates the elastic post-buckling behavior of simply supported thin-walled lipped channel beams undergoing local-distortional (L-D) interaction. The beams are uniformly bent about the major-axis and experience flange-triggered local buckling (most common situation in practice). Three beams are analyzed, each exhibiting a different type of L-D interaction, namely (i) "true L-D interaction" (close local and distortional critical buckling moments), (ii1) "secondary local-bifurcation interaction" and (ii2) "secondary distortional-bifurcation interaction" (critical distortional/local buckling moments and high enough yield stresses). The results presented and discussed are obtained through geometrically non-linear Generalized Beam Theory (GBT) analyses and provide the evolution, along given equilibrium paths, of the beam deformed configuration (expressed in GBT modal form) and relevant displacement profiles, making it possible to acquire in-depth knowledge on the beam L-D interaction mechanics. Particular attention is devoted to interpreting the quantitative and qualitative differences exhibited by the beam post-buckling behaviors associated with the three aforementioned L-D interaction types.

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Section: Gbt Post-buckling Behavior Of Beams Experiencing L-d Interacsupporting

confidence: 81%

Section: Cross-section Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the mechanics of local-distortional interaction in thin-walled lipped channel beams

Martins

Camotim

Gonçalves

et al. 2018

Thin-Walled Structures

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“…A standard incremental/iterative scheme with Newton-Raphson's method and displacement control is implemented. [22], (b) reinforced concrete column [23,24], (c) SHC-1 concrete-filled steel box column [25,16], (d) high-strength concretefilled steel circular hollow section column [26,16] and (e) partially encased I-section steel column.…”

Section: Formulationmentioning

confidence: 99%

“…The first example is taken from [22] and concerns the simply supported steel column shown in Fig. 3(a).…”

Section: Steel Columnmentioning

confidence: 99%

An efficient geometrically exact beam element for composite columns and its application to concrete encased steel I-sections

Gonçalves

Carvalho

2014

Engineering Structures

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Analysis of pallet rack beam members through a nonlinear GBT formulation with sectional constraints

Bonada¹,

Ribera²,

Fernández³

et al. 2021

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Thin‐walled open cross‐sections are commonly used in steel storage pallet rack structures. In some cases, open sections are employed as beam members. These beam members usually have weld spots along their length in order to reduce the distortional deformation under a flexural load. On the other hand, beam members are typically connected to columns by means of claws, which typically exhibit a nonlinear moment ‐ rotation relationship. These two characteristic should be taken into account in order to properly reproduce their structural response. In this paper, the Generalised Beam Theory (GBT) is used to perform a geometrical nonlinear analysis of a pallet rack beam members taking weld spots and the beam‐to‐column connection behavior into account. The influence of the number and location of weld spots, as well as the beam‐to‐column connection behavior, in the distortional deformation of a beam member is evaluated by means of GBT nonlinear analyses. The results show that the use of a small number of weld spots could be enough to minimize the beam distortional deformation. Moreover, the stiffness of the beam‐to‐column connection also has influence on the beam distortional deformation. Finally, GBT results are successfully compared with shell finite element analyses.

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Geometrically non-linear generalised beam theory for elastoplastic thin-walled metal members

Cited by 87 publications

References 16 publications

On the mechanics of local-distortional interaction in thin-walled lipped channel beams

On the mechanics of local-distortional interaction in thin-walled lipped channel beams

An efficient geometrically exact beam element for composite columns and its application to concrete encased steel I-sections

Analysis of pallet rack beam members through a nonlinear GBT formulation with sectional constraints

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