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1

Metwally Abu-Hamd

Cairo University, Egypt

Cairo University

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Outline

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1- Introduction

2- FEM Model

3- Comparison with Test Results

4- Parametric Study

5- Conclusions

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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



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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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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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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


TEST

AISI

FE

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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



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


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



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



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



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


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



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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Abu-hamd Ssrc 2013 p1306