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Metwally Abu-Hamd
Cairo University, Egypt
Cairo University
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Outline
2
1- Introduction
2- FEM Model
3- Comparison with Test Results
4- Parametric Study
5- Conclusions
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3
Common Applications
Door Framing Bracings
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Failure Modes
Global BucklingLocal Buckling
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Design Provisions
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AISI Section C4
Pn= smaller of (Pne, Pnd)
Pne
= Nominal strength for yielding, flexural,
flexural-torsional, and torsional buckling
according to section C4.1,
Pnd= Nominal distortional buckling strengthaccording to section C4.2.
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up Members-Provisions for Built
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Section D1.2
=
(a/ri) is not to exceed 0.5*(KL/r)o
(KL/r)o: overall (unmodified) slenderness ratio
a : longitudinal spacing between intermediate fasteners
ri: minimum radius of gyration of the full unreduced
cross-section of the individual component
Modified Slenderness:
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Previous Work
Objective of Present Work
Develop a numerical model that can be used
to calculate the axial capacity of cold-formed
built-up I-sections.
Stone and LaBoubes (2005)
Whittle (2007) and Biggs (2008)
Piyawat (2011): Distortional Buckling
Brueggen and Ramseyer (2003)
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FEM Analysis
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Numerical Model
1- Eigenvalue analysis: Buckling modes and buckling
frequencies are the solutions to an eigenvalue
problem. Elastic material behavior and perfectmember geometry are assumed.
2- Nonlinear loaddisplacement analysis of the real
member under the action of applied loads in thepresence of initial geometrical imperfections, residual
stresses and material nonlinearity.
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Numerical Model
4-node finite strain shell element of ANSYS
mesh size: 25 mm10 mm at flat portions
finer mesh was used at the corners
material behavior elastic-plastic.
slope of plastic part assumed at 5 %.
Von-Mises yield criteria with isotropic hardening.
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Geometric Imperfections
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Modeled as a linear combination of the first localand global
buckling modesusing a suitable magnitude for each mode
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Residual Stresses due to Manufacturing Processes
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Idealized as a summation of two types:Membrane and Flexural:
1- Membrane Stresses
about 8 % Fyat cornersabout 4% Fyfor flat parts
Opposing this effect, yield stress is increased
at corner regions by about 15 % due to cold
work of forming
Effect on axial buckling strength < 1 %
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Residual Stresses
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2- Flexural residual stresses
Show a large degree of variation
Considering these stresses in the FE model
complicates the analysis considerably as it requiresdefining the through thickness stresses for each layer.
As the main interest in this paper is to find the
ultimate axial load capacity, the present analysis
neglects the effect of flexural residual stresses.This assumption would not be correct when
considering the deformation behavior and stress
distribution across the section.
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Boundary Conditions
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Both column ends modeled as hinged ends except for thedisplacement at the loaded end in the direction of the
applied load.
Nodes other than the two ends were free to translate and
rotate in any directions.
Displacements of the two components coupled at the
locations of the connecting screws.
The load was applied as an axial concentrated load at the
section centeroid at the loaded end.
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Comparison with Test Results
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Axial load capacity of 32 cold-formed columnstested by Stone and Laboube (2005):
12 Sections 152.4x1.372
6 Sections 92.1x1.155
8 Sections 92.1x0.88
6 Sections 152.4x0.841
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0.00
0.10
0.20
0.30
0.40
1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10
Nom
inalAxialStrengthFn/Fy
Nominal Axial Strength Fn/Fy
TEST
AISI
FE
12 Sections 152.4x1.372
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6 Sections 92.1x1.155
0.00
0.10
0.20
0.30
0.40
0.50
0.60
1.30 1.35 1.40 1.45 1.50 1.55 1.60
NominalAxialStrengthFn/Fy
Slenderness Parameter : c
TEST
AISI
FE
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8 Sections 92.1x0.88
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
1.10 1.15 1.20 1.25 1.30
NominalAxialStre
ngthFn/Fy
Slenderness Parameter : c
TEST
AISI
FE
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6 Sections 15.42x0.841
0.00
0.10
0.20
0.30
0.40
0.50
1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70
NominalAxialStrengthFn/Fy
Slenderness Parameter : c
TEST
AISI
FE
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StudyParmetric
Variations in Design Parameters:0.5 < c < 2.5
Presented Results for Six typical SSMA cross
sections:400S137-33, 400S137-68, 600S162-33,
600S162-97, 800S200-33, 800S200-97
Amplitude of geometric imperfections at 25%
and 75 %.
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Section 400S137-33
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.50 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50
NominalAxialStre
ngthFn/Fy
Slenderness Parameter : c
AISI
ANSYS 75%
ANSYS 25%
400S137-33
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Section 400S137-68
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.50 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50
NominalAxialStrengthFn/Fy
Slenderness Parameter : c
AISI
ANSYS 25%
ANSYS 75%
400S137-68
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Section 600S162-33
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.50 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50
NominalAxialStrengthFn/Fy
Slenderness Parameter : c
AISI
ANSYS 75%
ANSYS 25%
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Section 600S162-97
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.50 1.00 1.50 2.00 2.50
Nom
inalAxialStrengthFn/Fy
Slenderness Parameter : c
AISI
ANSYS 25%
ANSYS 75%
600S162-97
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Section 800S200-33
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.50 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50
NominalAxialStre
ngthFn/Fy
Slenderness Parameter : c
AISI
ANSYS 75%
ANSYS 25%
800S200-33
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Section 800S200-97
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.50 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50
Nom
inalAxialStrengthFn/Fy
Slenderness Parameter : c
AISI
ANSYS 25%
ANSYS 75%
800S200-97
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This paper presents a finite element procedurefor calculating the axial buckling strength of cold-
formed built up I-sections.
The initial local and overall geometric
imperfections, nonlinear material properties havebeen included in the model.
A parametric study of 60 columns was performed
to investigate the effect of major design parameters
on the behavior.AISI design rules are generally conservative for
medium and long members but may overestimate
the capacity for short members.
Conclusions
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Cairo University
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