Figure 1
CFS lipped channel column and its buckling modes: (a) local L; (b) distortional D; (c) global G or FT (flexural-torsional); (d) global G or F (flexural).
Figure 2
Finite Element Model description of steel lipped channel cold-formed column: (a) shell finite element mesh of CFS member and thick steel plate at the fixed-end; (b) boundary condition and axial loading; (c) shell finite element mesh along the column; (d) restriction to longitudinal displacement at mid span; (e) boundary condition and axial loading.
Figure 3
Detail of the end plate, showing the type of possible mesh occurrences, quadrilateral and triangular shell element.
Figure 4
Geometry and initial geometric imperfections generation (IGI): (a) amplified 3D buckling mode obtained by the FStr Computer Application; (b) KEYPOINTS location in ANSYS, generated from the buckling mode; (c) non-planar surfaces, connecting 4 nearby KEYPOINTS; (d) mesh automatic generation (5 by 5 mm); (e) final model in ANSYS with IGI.
Figure 3
Detail of the end plate, showing the type of possible mesh occurrences, quadrilateral and triangular shell element.
Figure 4
Geometry and initial geometric imperfections generation (IGI): (a) amplified 3D buckling mode obtained by the FStr Computer Application; (b) KEYPOINTS location in ANSYS, generated from the buckling mode; (c) non-planar surfaces, connecting 4 nearby KEYPOINTS; (d) mesh automatic generation (5 by 5 mm); (e) final model in ANSYS with IGI.
Figure 5
Stress-Strain models from Heva (2009)HEVA, Y. B. Behaviour and design of cold- formed steel compression members at elevated temperatures, 2009. Thesis, School of Urban Developments Queensland University of Technology. for (a) 1.95mm and 250 MPa, (b) 1.90mm and 450 MPa and (c) 0.95mm and 550 MPa cold-formed steel.
Figure 6
Load versus displacement out of plane in the middle top flange at the column mid span of models (a) G250-1.95-1800 and (b) G550-0.95-1800 (both for room temperature 20oC).
Figure 7
Results from model G450-1.90-1800: (a) comparison of flexural-torsional failure mode for (a.1) the present numerical model, (a.2) the laboratory test from Heva (2009)HEVA, Y. B. Behaviour and design of cold- formed steel compression members at elevated temperatures, 2009. Thesis, School of Urban Developments Queensland University of Technology. and (a.3) numerical model from Heva (2009)HEVA, Y. B. Behaviour and design of cold- formed steel compression members at elevated temperatures, 2009. Thesis, School of Urban Developments Queensland University of Technology.; (b) load versus displacement out of plane in the middle top flange at the column mid span.
Figure 8
Lipped Channel specimen by Salles (2017)SALLES, G. C. Investigação Analítica, Numérica e Experimental do Modo de Flambagem Distorcional em Perfis Formados a Frio, 2017. Dissertação de Mestrado, Universidade Federal do Rio de Janeiro, COPPE.: (a) LC geometry (out-of-section measurements) and displacement transducers location; (b) load versus displacement of the web extremities D1 and D3 at mid span of test and numerical FEM results for the present study.
Figure 9
Displacement D4 along the column’s length, with 5 load steps of numerical FEM results of the present study and experimental results Salles (2017)SALLES, G. C. Investigação Analítica, Numérica e Experimental do Modo de Flambagem Distorcional em Perfis Formados a Frio, 2017. Dissertação de Mestrado, Universidade Federal do Rio de Janeiro, COPPE..
Figure 10
Displacement D5 along the column’s length, with 5 load steps of numerical FEM results of the present study and experimental results Salles (2017)SALLES, G. C. Investigação Analítica, Numérica e Experimental do Modo de Flambagem Distorcional em Perfis Formados a Frio, 2017. Dissertação de Mestrado, Universidade Federal do Rio de Janeiro, COPPE..
Figure 11
Critical load vs. for LC 100x70x15x2.70 mm, illustrating SGI, TI, and SDI regions in all mode analysis (signature curve) and pure mode analysis ( gives , gives and gives ).
Figure 12
Analogy of modal shape initial imperfection combination in function of initial imperfection parameter (modal shapes amplified 10 times).
Figure 13
LC columns results for =345 MPa (): (a) FEM ultimate load versus parameter; (b) maximum vector displacement at the limit load (or column strength) step for to , incremented by .
Figure 14
Post-buckling equilibrium paths, load steps vs. out-of-plane displacement: (a) NT1, with and () at , from (a.1) and (a.2) ; (b) NT2, with and () at , from (b.1) and (b.2) .
Figure 15
Post-buckling equilibrium paths, load steps vs. out-of-plane displacement: (a) NT3, with and () at , from (a.1) and (a.2) ; (b) NT4, with and () at , from (b.1) and (b.2) .
Figure 16
Post-buckling equilibrium paths, load steps vs. out-of-plane displacement (a) NT5, with and () at , from (a.1) and (a.2) , as well as (b) the displacements nomenclature and reference.
Figure 17
Failure modes with von Mises's yield criterion distribution for (a.1) 1G+0D, (b.1) 0.5G+0.5D, and (c.1) 0G+1D initial imperfection and post-buckling equilibrium paths ( vs. of displacement NT5 at ) for different ratios of , for (a.2) 1G+0D, (b.2) 0.5G+0.5D, and (c.2) 0G+1D IGI, where and .
Figure 18
vs. of columns under different IGI combination, and with yield stress of 345 MPa, 508 MPa, 1016 MPa, and 1523 MPa.
Figure 19
Numerical-to-DSM-based ultimate loads vs DG slenderness ratio, for global
Eq. (1), distortional
Eq. (2), distortional-global Eq. (3), and global-distortional Eq. (4) DSM equations, with yielding stress of: (a) 345 MPa and (a.1) 0.5G+0.5D and (a.2) 1G+0D IGI; (b) 508 MPa and (b.1) 0.5G+0.5D and (b.2) 1G+0D IGI; (c) 1016 MPa and (c.1) 0.5G+0.5D and (c.1) 1G+0D IGI.
Figure 20
FEM ultimate Load over DSM Nominal Axial Strength versus DG slenderness ratio, considering (a) 50% global + 50% distortional initial imperfection and (b) 100% global initial imperfection.
Figure 21
FEM column strength over Squash Load (
) results, with different yield stress and IGI, compared with: (a) the DSM equations (
); (b) the global DSM equation
Eq. (1) and Euler
curve.
Figure 22
FEM ultimate Load over DSM-based Nominal Axial Strength versus DG slenderness ratio for distortional-global
Eq. (3) and global-distortional
Eq. (4) equations taking (a) 50% global + 50% distortional IGI and (b) 100% global IGI.
Figure 12
Analogy of modal shape initial imperfection combination in function of initial imperfection parameter (modal shapes amplified 10 times).
Figure 13
LC columns results for =345 MPa (): (a) FEM ultimate load versus parameter; (b) maximum vector displacement at the limit load (or column strength) step for to , incremented by .
Figure 14
Post-buckling equilibrium paths, load steps vs. out-of-plane displacement: (a) NT1, with and () at , from (a.1) and (a.2) ; (b) NT2, with and () at , from (b.1) and (b.2) .
Figure 15
Post-buckling equilibrium paths, load steps vs. out-of-plane displacement: (a) NT3, with and () at , from (a.1) and (a.2) ; (b) NT4, with and () at , from (b.1) and (b.2) .
Figure 16
Post-buckling equilibrium paths, load steps vs. out-of-plane displacement (a) NT5, with and () at , from (a.1) and (a.2) , as well as (b) the displacements nomenclature and reference.
Figure 17
Failure modes with von Mises's yield criterion distribution for (a.1) 1G+0D, (b.1) 0.5G+0.5D, and (c.1) 0G+1D initial imperfection and post-buckling equilibrium paths ( vs. of displacement NT5 at ) for different ratios of , for (a.2) 1G+0D, (b.2) 0.5G+0.5D, and (c.2) 0G+1D IGI, where and .
Figure 18
vs. of columns under different IGI combination, and with yield stress of 345 MPa, 508 MPa, 1016 MPa, and 1523 MPa.
Figure 17
Failure modes with von Mises's yield criterion distribution for (a.1) 1G+0D, (b.1) 0.5G+0.5D, and (c.1) 0G+1D initial imperfection and post-buckling equilibrium paths ( vs. of displacement NT5 at ) for different ratios of , for (a.2) 1G+0D, (b.2) 0.5G+0.5D, and (c.2) 0G+1D IGI, where and .
Figure 18
vs. of columns under different IGI combination, and with yield stress of 345 MPa, 508 MPa, 1016 MPa, and 1523 MPa.
Figure 19
Numerical-to-DSM-based ultimate loads vs DG slenderness ratio, for global
Eq. (1), distortional
Eq. (2), distortional-global Eq. (3), and global-distortional Eq. (4) DSM equations, with yielding stress of: (a) 345 MPa and (a.1) 0.5G+0.5D and (a.2) 1G+0D IGI; (b) 508 MPa and (b.1) 0.5G+0.5D and (b.2) 1G+0D IGI; (c) 1016 MPa and (c.1) 0.5G+0.5D and (c.1) 1G+0D IGI.
Figure 20
FEM ultimate Load over DSM Nominal Axial Strength versus DG slenderness ratio, considering (a) 50% global + 50% distortional initial imperfection and (b) 100% global initial imperfection.
Figure 21
FEM column strength over Squash Load (
) results, with different yield stress and IGI, compared with: (a) the DSM equations (
); (b) the global DSM equation
Eq. (1) and Euler
curve.
Figure 22
FEM ultimate Load over DSM-based Nominal Axial Strength versus DG slenderness ratio for distortional-global
Eq. (3) and global-distortional
Eq. (4) equations taking (a) 50% global + 50% distortional IGI and (b) 100% global IGI.
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