Compression Tests of Cold-Reduced High Strength Steel Long Columns

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Department of Civil Engineering
Sydney NSW 2006
AUSTRALIA
http://www.civil.usyd.edu.au/
Centre for Advanced Structural Engineering
Compression Tests of Cold-Reduced High
Strength Steel Long Columns
Research Report No R816
Demao Yang BSc MEng
Gregory J Hancock BSc BE PhD
K.J.R Rasmussen MScEng, PhD
March 2002
Department of Civil Engineering
Centre for Advanced Structural Engineering
http://www.civil.usyd.edu.au/
Compression Tests of Cold-Reduced High Strength Steel
Long Columns
Research Report No R816
Demao Yang, BSc, MEng
Gregory J Hancock, BSc, BE, PhD
K.J.R Rasmussen MScEng, PhD
March 2002
Abstract:
This report describes a series of compression tests performed on long columns
fabricated from cold-formed high strength steel plates with nominal yield stress
of 550 MPa. The steel is classified as G550 to Australia Standard AS1397. The
test results presented in this report are the second stage of an Australian
Research Council research project entitled "Compression Stability of High
Strength Steel Sections with Low Strain-Hardening". A total of 28 long
columns, which were made from two thicknesses of sheet steel (0.42 mm and
0.6 mm), were tested. A box shaped section was between pinned ends over a
range of lengths.
This report shows the comparison of loads obtained experimentally with those
predicted on the basis of AS/NZS4600 and the AISI specification including
Supplement No.1, 1999. The finite element program, ABAQUS, was also used
to simulate the column behaviour. For sections which undergo local instability
at loads significantly less than the ultimate loads, the column design rules in
AS/NZS 4600 and the AISI Specification are unconservative if used in their
current form for G550 steel. Proposals for improved column design of high
strength slender sections are proposed in this report.
Keywords:
Long-column; High Strength Steel; Compression; Pin-ended; LB-
section; Local buckling; Overall buckling
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
2
Copyright Notice
Department of Civil Engineering, Research Report R816
Compression Tests of Cold-Reduced High Strength Steel Long Columns
© 2002 Demao Yang & Gregory J. Hancock & K.J.R Rasmussen
Email: D.Yang@civil.usyd.edu.au
G.Hancock@civil.usyd.edu.au
K.Rasmussen@civil.usyd.edu.au
This publication may be redistributed freely in its entirety and in its original
form without the consent of the copyright owner.
Use of material contained in this publication in any other published works must
be appropriately referenced, and, if necessary, permission sought from the
author.
Published by:
Department of Civil Engineering
The University of Sydney
Sydney NSW 2006
AUSTRALIA
March 2002
http://www.civil.usyd.edu.au
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
3
CONTENTS
INTRODUCTION.................................................................................................................................................5
1 TEST SPECIMENS...................................................................................................................................7
1.1 G
ENERAL
................................................................................................................................................7
1.2 L
ABELLING
.............................................................................................................................................8
1.3 G
EOMETRIC
I
MPERFECTION
M
EASUREMENTS
.........................................................................................8
1.4 M
ATERIAL
P
ROPERTIES
...........................................................................................................................9
2 LONG COLUMN TESTS.........................................................................................................................9
2.1 T
ESTING
..................................................................................................................................................9
2.2 M
EASUREMENT OF FLEXURAL RIGIDITY
(E*I).......................................................................................10
2.3 T
EST SPECIMEN BEHAVIOR AND ULTIMATE LOAD
-
CAPACITY
................................................................10
3 ANALYSES..............................................................................................................................................11
3.1 E
LASTIC LOCAL BUCKLING ANALYSES
..................................................................................................11
3.2 F
INITE
E
LEMENT
N
ONLINEAR
A
NALYSES
.............................................................................................12
3.2.1 Element type...................................................................................................................................12
3.2.2 Material behavior...........................................................................................................................12
3.2.3 Rigid body and Boundary conditions..............................................................................................13
3.2.4 Geometrical imperfections..............................................................................................................13
3.2.5 ABAQUS Results.............................................................................................................................13
3.3 T
EST
R
ESULTS AND
ABAQUS
RESULTS COMPARED WITH THE
D
ESIGN
S
TANDARDS
...........................14
3.3.1 General...........................................................................................................................................14
3.3.2 Test results comparisons with design standards.............................................................................15
3.3.3 ABAQUS results and comparisons with design standards.............................................................15
4 MODIFIED DESIGN CURVE...............................................................................................................16
5 CONCLUSIONS......................................................................................................................................16
6 ACKNOWLEDGEMENTS.....................................................................................................................18
7 REFERENCES.........................................................................................................................................19
8 NOTATION..............................................................................................................................................22
9 FIGURES..................................................................................................................................................23
10 TABLES....................................................................................................................................................43
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
4
A I
MPERFECTION
M
EASUREMENTS
................................................................................................................50
B L
OAD
-
SHORTENING
&
LOAD
-
DEFLECTION CURVES OF
LB-
SECTIONS IN
0.60
MM THICKNESS
....................73
C L
OAD
-
SHORTENING
&
LOAD
-
DEFLECTION CURVES OF
LB-
SECTIONS IN
0.42
MM THICKNESS
....................89
D E
CCENTRICITY
-
LOAD CURVES FOR
LB-
SECTIONS IN
0.60
MM THICKNESS
................................................112
E E
CCENTRICITY
-
LOAD CURVES FOR
LB-
SECTIONS IN
0.42
MM THICKNESS
................................................120
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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INTRODUCTION
Cold-formed sections used in steel framed houses as roof and wall structural
members are normally made from coil by means of roll-forming. The use of
high strength cold-reduced steels with yield stress values up to 550 MPa is
increasing rapidly, particularly for steel framed houses with sections as thin as
0.42 mm. Steels with high yield stress usually have little or no strain hardening
in the stress-strain curve, and low ductility unlike conventional 250 MPa and
350 MPa yield structural steels that are highly ductile and strain harden as
shown in Fig. 1. Strain hardening may be probably important in the stability of
thin-walled sections and so the high strength steels may have their stability
affected by the lack of strain hardening. In the design of thin-walled box
columns, an optimum choice of section must be made to ensure that the
maximum strength is obtained for a given weight of material.
It is customary to consider that a column may buckle in either one of two ways:
(a) by plate buckling of its component webs and flanges in shorter half-waves
(local or plate buckling) or (b) by deflection of the entire column in a half-wave
of length equal to the effective column length (overall buckling). For a given
column, buckling is supposed to occur at the lower of the two critical stresses,
local or overall. In reality, however, there is an interaction between these two
modes of buckling, so that the actual buckling stress will be smaller than either
of the buckling stresses. Imperfections play a significant role in interaction
buckling. Column strength is characterized by the maximum axial force that can
be supported without excessive lateral deformations. In view of the fact that
post-buckling strength of a flat plate is available for structural members to carry
additional load, cold-formed steel sections are normally designed on the basis of
the post-buckling strength of the plate elements rather than based on the local
buckling stress.
Columns and their strength and behaviour constitute a subject area that has
received much study and discussion over the years. Experimental and
theoretical investigations have been performed to study the interaction of local
and overall buckling. Bijlard and Fisher (1952) first studied the column strength
of square tubes in the post-buckling range of component plates. Graves-Smith
(1967) presented a theory for predicting the ultimate strength in compression of
thin-walled box columns which buckle locally. Van der Neut (1969) used a
mathematical model to study the interaction of local buckling and overall
buckling of thin walled compression members. Hancock (1981) used the finite
strip method to analyze the nonlinear response of box and I-sections under axial
compression and obtained the interaction buckling loads for them by a overall
bifurcation analysis of a locally buckled section.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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For high strength cold-reduced steel sections made from thin galvanized cold-
reduced steel to Australian Standard AS 1397-1993 and similar ASTM
Standards such as A792, no specific investigation has been performed. Mainly
due to lack of knowledge on their structural behavior, the 1996 Australian/New
Zealand Standard AS/NZS 4600 for Cold-Formed Steel Structures and the 1996
American Iron and Steel Institute (AISI) Specification for Cold-Formed
Structural Members have limited the design stress for high strength steels to 75
percent of their yield stress or tensile strength as applicable. The AISI
Specification has recently been revised in Supplement (1999) to allow values
higher than 75 percent for multiple web configurations, the value depending
mainly on plate slenderness, but excludes its use for structural members such as
columns.
A research project on these steels in tension, which was carried out by Rogers
and Hancock (1996), has shown that they have substantially reduced ductility
but this may not affect the net section strength of perforated sections. Steels of
this type are similar to Structural Grade 80 steels in the USA according to the
ASTM A653 (1997) Specification. A research project led by Professor W-W Yu
at the University of Missouri-Rolla to investigate the strength of these ASTM
steels when formed into decking sections and subject to bending has
demonstrated that their local and post-local buckling capacities may be
significantly influenced by the lack of strain hardening. In particular, the
ultimate moments of panels with slender sections (b/t>100) were lower than the
design moments calculated on the basis of a conventional effective section
model. However no significant definitive testing has been performed for
structural members composed of AS 1397 steel in compression. The AS 1397
steel may be zinc coated or aluminium-zinc coated. The steel studied in this
report is aluminium-zinc coated similar to ASTM A792 (1994).
Research on these steels as stub columns in compression, which was carried out
by Yang and Hancock (2002) as the first stage of this research has shown that
the greatest effect of the low strain hardening was for the stockier sections
where strain hardening play an important role. For the more slender sections
where elastic local buckling and post-local buckling are more important, the
effect of low strain hardening does not appear to be as significant which is
contrary to recent design proposals in the USA where it was believed that the
more slender sections had been also influenced. The aim of this report is to
present the second stage test results for long columns. The tests were performed
on lipped-box shaped specimens (LB-section) fabricated from G550 steel sheets
to AS1397 with 0.6 mm and 0.42 mm thickness similar to those in Yang and
Hancock (2002). In this report, two series of long columns tests (LB-section)
with pin-ends are described. The purpose of the tests was to investigate whether
high strength steel members with low strain hardening can be designed
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
7
according to existing standards of AS4600 or the AISI Specification or whether
these standards need to be modified for high strength steel.
1

TEST SPECIMENS
1.1

General
In the first stage report (Yang & Hancock, 2002), a series of stub column tests
was presented on sections fabricated from G550 steel sheets in 0.60 mm and
0.42 mm thickness. For cold-formed steel sections, which generally have thin-
walled plate elements, the stub-column test is aimed at determining the effect of
local buckling as well as the effect of cold-forming, residual stress and yielding
on the section capacity in compression.
In order to determine the capacity of long columns in compression, local and
overall buckling and the interaction between them should be considered. For the
high strength steel columns assembled from thin plates, the section
configuration is an important factor affecting their behaviour. Thin plate
elements will generally continue to carry load after local buckling into the post-
buckling range so that local buckling does not mean failure of the whole
column. However, a singly-symmetric section may have a neutral axis shift after
local buckling occurs resulting in an additional moment. To eliminate this
problem, in this test program, doubly-symmetric sections were chosen. These
sections are the LB-sections previously described by Yang & Hancock (2002)
for stub columns.
In this report, a long column is defined as a member whose length is
considerably larger than any of its cross-sectional dimensions and which is
subjected to compression in the longitudinal direction. A centrally loaded
column means that the resultant compressive force is approximately coincident
with its longitudinal centroidal axis (Galambos, 1988).
The tests were performed on closed sections brake pressed from
aluminium/zinc-coated Grade G550 structural steel sheet to AS1397 in 0.42 mm
and 0.6 mm thickness. The sections tested are shown in Fig. 2. Epoxy was used
to close the LB-sections. The lengths of the LB sections ranged from 450 to
1100 mm for the 0.6 mm sheet steel and 550 to 1700 mm for the 0.42 mm sheet
steel. The cross-section dimensions of the specimens are shown in Tables 1, for
the nomenclature shown in Fig. 3. The cross-section dimensions are the average
of the measured values. The base metal thickness (t
b
) was measured by
removing the zinc coating by acid-etching. The ends of each specimen were
milled flat and parallel to ensure full contact between specimens and end
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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bearing. Bolts & clamps were also used on the LB-sections as specified in Table
2 and shown in Fig. 4.
1.2

Labelling
The LB-sections were divided into two different series: one for the 0.6 mm
sheet steel and one for the 0.42 mm sheet steel. The test specimens were
labelled such that the thickness of steel sheet, type of section, nominal width of
specimen and specimen number were expressed by the label.
For example, the label “060LB20P450a” defines the following specimen:

The first three numbers indicate that the specimen is fabricated from 0.60
mm steel sheet.

Th fourth and fifth letters (LB) indicate that the specimen is a lipped box

The “20” indicates that the nominal width of specimen is 20 mm

The “P” indicates that the specimen is pin-ended

The "450" indicates that the nominal length of specimen is 450 mm

The last letter “a” indicates that the specimen was the first tested (alternative
b)
1.3

Geometric Imperfection Measurements
Geometric imperfections were measured for all of the specimens. Only minor
axis imperfections were measured and two methods were used. For the 0.60 mm
specimens, a small vertical scale was designed and moved along the specimens
and the scale was read optically. Readings were obtained using an optical level
at 20 mm intervals from end to end. For the 0.42 mm specimens, a more
accurate instrument was designed to measure the geometric imperfections as
shown in Fig. 5. The main components included a guide frame, a laser sensor, a
Datataker data logger and a synchronous motor. The laser sensor was attached
to a movable seat, which could move along two accurately levelled channels.
The seat was drawn by a synchronous motor in order to keep the laser sensor
moving smoothly. The laser sensor can move up and down along the upright
poles and from left to right using a screw adjuster. The specimen was positioned
on the seat in front of the frame using a clamp to make it firm and level. The
data was recorded using the Datataker data logger. Once the specimen was
properly positioned on the seat and fixed in position, the laser sensor was
moved along the specimen. The readings were taken at 15 mm or 20 mm
intervals. For each side of a specimen, the measurements were taken along three
lines in the longitudinal direction of the specimen, two along the corner
(approximately 5mm away from the corner or edge) and one along the centre.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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The results were used in the finite element modelling analysis. The full set of
measurements is given in Appendix A. The maximum imperfections are shown
in Table 5 and were computed relative to a straight line between the ends.
1.4

Material Properties
The material and its properties are fully described in Yang & Hancock (2002)
which is the companion report to this one. The proof stresses are given in Table
2.
2

LONG COLUMN TESTS
2.1

Testing
The test rig is shown in Fig. 6 and the test arrangement is shown in Fig. 7. The
rig consisted of the Sintech/MTS-300kN testing machine with pin-ended
bearings. The load and shortening were recorded using the Sintech data
acquisition system. The compressive deformation rate was 0.05 mm/min.
The measured specimen lengths are given in Table 1. The measured specimen
lengths (L) were different from the lengths of the pin-ended column (L
t
) were
obtained as the sum of the specimen length and the distance from the platen face
to the centre of the end bearings (L
t
=L+150 mm for the 0.60 mm series and
L
t
=L+108 mm for the 0.42 mm series). The first column was found to fracture
in the epoxy at loads very close to the ultimate load. It was therefore decided to
drill 3 mm holes in the corner lips and to place small diameter bolts and nuts to
ensure that the corners did not come apart for the first series. These bolts were
only located at the ends (four for each) and were only used for the 0.60 mm
sections. Clamps were used on the lips of 0.42 mm sections as shown in Fig. 4.
The central deflections were measured using two transducers on two opposite
sides of the LB-sections. Two strain gauges were attached at the centre of each
side of each column. The transducers and strain gauges were connected to the
SPECTRA data acquisition system.
During the test, the trial axial load which was 1/15 or 1/10 of the estimated
ultimate load was applied and readings of the strain gauges were. Based on a
calculation of the location of the initial central eccentricity (e) of the action line
as shown in Fig. 7, the location of the column was adjusted at each end. This
procedure was repeated until the value of the initial eccentricity (e) was
approximately equal to the nominal value of L/1000 which is the maximum
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
10
normally specified in structural design standards. The values are shown in Table
4 for the method in Appendix D.
2.2

Measurement of flexural rigidity (E*I)
For the LB sections in 0.60 mm thickness, the flexural rigidities (E*I) (minor
axis) were measured. The ends of each specimen were simply supported and sag
of the specimen between supports under self-weight was permitted. A point load
was then applied at mid-length. The mid-length deflections were measured with
increasing load. The measured flexural rigidities and values obtained from the
computer program THIN-WALL (Papangelis and Hancock, 1998) using the
measured dimensions are shown in Table 5.
It can be seen that the experimental results are in good agreement with the
theoretical results except for the 060LB40P450 specimen as detailed in Table 5.
This short wide section is very sensitive to a deviation of measured deflection,
which may be the main reason for the large difference between the experimental
results and theoretical results. The accurate rigidity measurements mean that the
epoxy was effective in causing the two hat-shaped halves to act in a fully
integral manner.
2.3

Test specimen behavior and ultimate load-capacity
The graphs in Fig. 8 & 9 and Appendices B&C show that initially the columns
remained elastic with slope of the load-shortening diagram approximately
constant after some initial take-up. The ultimate loads (P
t
) are given in Table 7
for each specimen. For the 060LB20 and 060LB30 series, the ultimate load (P
t
)
was less than the theoretical local buckling load (N
ol
) so that the slope kept
approximately constant until the ultimate load was reached. The 450 mm
specimens in 0.60 mm material and the 550 mm specimens in 0.42 mm material
buckled in-elastically soon after the ultimate load with a sudden drop in load.
The 900 mm specimens in 0.60 mm material and the 1100 mm and 1700 mm
specimens in 0.42 mm material generally had a more gradual decrease in load
until inelastic local buckling occurred at which point there was a sudden drop in
load as for the 450 mm specimens. Only the 042LB30P1100 specimens
appeared to inelastically locally buckle before the ultimate load caused by
overall deformation was reached. For the intermediate length columns in 0.42
mm thickness and the 060LB40P450 column, the slope reduced continuously
from the local buckling load to reaching the ultimate load.
By observation of the surface of the specimens, the local buckling behaviour
can be observed. Initially, elastic local buckling occurred with many half-
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
11
wavelengths occurring along the length of the specimens. Eventually the
columns entered the elastic-plastic state and a local plastic mechanism formed
accompanied by a sudden drop in load. The specimens (in 0.60 mm thickness)
with lower web slenderness (b/t) (from 33 to 50) developed roof-shaped
mechanisms. However, all the others developed the so-called flip-disc
mechanisms at about mid-length on one side as shown in Fig.10a. All of the test
columns are shown in Fig. 11.
The experimental local buckling loads were evaluated from the plots of load-
deflection and load-shortening. For the plots of load-deflection, the P-w
2
method (Ventaramaiah, K.R., Roorda, J.) was used to obtain the elastic local
buckling load. For the two series of pin-ended tests, the experimental local
buckling loads were obtained except for the 060LB20 and 060LB30 specimens
whose ultimate loads were lower than the elastic local buckling loads of the
section.
As shown in Figs. 10 (c) & (d) taken during the test, after the local buckling
load was reached, elastic local buckling can be observed on the concave side of
the columns. Due to the small eccentricity of the load, one side of the column
was in greater compression than the other and modulation of the local buckling
occurred on this side. Finally, interaction of local and overall buckling resulted
in failure of column.
It is noticeable that the column strength increases as the plate slenderness (b/t)
becomes larger and the overall slenderness becomes smaller for a given column
length as shown in Figs. 8 & 9. The column and plate slenderness values are
given in Table 6.
3

ANALYSES
3.1

Elastic local buckling analyses
The theoretical elastic local buckling loads (N
ol
) were obtained using the THIN-
WALL program (Papangelis and Hancock, 1998). The average measured cross-
section dimensions of the specimens for each series as well as the measured
values of base metal thickness and Young’s modulus taken from the coupon
tests were used to determine the theoretical local buckling loads. The theoretical
local buckling mode is shown in Fig.12. The theoretical local buckling loads
(N
ol
) are given in Table 7 where the ratios of the experimental to theoretical
local buckling loads (P
ol
/N
ol
) are computed.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
12
The mean ratio of the experimental local buckling loads (P
cr
) to the theoretical
local buckling loads (N
ol
) was approximately 1.06 and 0.95 respectively for the
two series. These results indicate that the THIN-WALL program was in good
agreement with the experimental local buckling load as detailed in Table 7.
3.2

Finite Element Nonlinear Analyses
The finite element non-linear analysis program “ABAQUS” was used to
simulate the behavior of the columns.
3.2.1

Element type
The 4-node doubly curved thin or thick shell, reduced integration, hour-glass
control, finite membrane strain element, type S4R, was used. The ratio of length
to width of element varied from about 2:1 to 6:1.
For the whole column, different mesh densities were adopted. In the
longitudinal direction of each column, the nodes are concentrated towards the
middle of the column so that the fine mesh can be obtained around the centre. In
the transverse direction, the finer mesh was used at the corners on the basis of
the concept of effective area. The details are given by Yang and Hancock
(2002).
The model consisted of 12848 nodes and 12212 elements. The mean mesh size
varied from 4.6 mm by 2.3 mm for the stockiest section to 14.2. mm by 2.3 mm
for the largest section.
3.2.2

Material behavior
Most of the plasticity models in ABAQUS are “incremental” theories are in
which the mechanical strain rate is decomposed into an elastic part and a plastic
(inelastic) part. ABAQUS also has a “deformation” plasticity model, in which
the stress is defined from the total mechanical strain. When performing an
elastic-plastic analysis at finite strains, ABAQUS assumes that the plastic
strains dominate the deformation and that the elastic strain is small. From load-
deflection graphs of column tests, this assumption can be adopted for G550
sheet steel. The data used in the ABAQUS model was obtained from the stress-
strain curves of coupon tests. The first point corresponded with the onset of
plasticity. Many points were used around the corner on the stress-strain curve in
order to simulate the true behaviour of the material.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
13
3.2.3

Rigid body and Boundary conditions
In order to simulate the pin-ended bearings, rigid bodies were used. The rigid
bodies were created by defining rigid elements (R3D4) that all share two rigid
body reference nodes. The top rigid body had both translational and rotational
degrees of freedom and bottom had only a rotational degree of freedom. The
lengths of the rigid bodies were 75 mm and 54 mm for the columns in 0.60 mm
thickness and in 0.42 mm thickness respectively. The rigid surfaces were also
defined to connect with the column. The reference nodes associating with each
rigid body were adopted to realize the rotation in the weak axis direction of the
cross-section. Eccentric loading was introduced. The values of eccentricity used
are the experimental values are shown in Table 4. The load was applied through
the top reference point.
In order to join the two hat-section parts, lips had to be used in the tests. To
simulate the connection between the lips, three ways were tried. One way was
that the entire lip was treated as double thickness. The others, Link and Pin,
used the Multi-Point Constraints method in ABAQUS to connect the lips. The
difference between results from the different methods was less than 2%. Here
the last method (pin) was used.
3.2.4

Geometrical imperfections
To introduce the local geometrical imperfection in the columns, two different
ways can be used, which are described in Yang & Hancock (2002). In this
report the initial imperfection was introduced based on an eigenvalue buckling
analysis to produce the imperfection model and Walker's suggested expression
for the amplitude as described in Yang & Hancock (2002).
The eccentricity of loading was also introduced in the ABAQUS model by
changing the location of the reference nodes. The mean values (e) obtained from
the calculations basing on the readings of the two strain gauges as shown in
Table 6. The plots are shown in Appendix D.
3.2.5

ABAQUS Results
The ABAQUS results ultimate loads are given as AB in Table 7 where the
ratios AB/P
t
are computed. The average difference between the ABAQUS
results and test results is approximately 6%. It can be seen in Table 7 that for
most specimens the ABAQUS results are slightly higher than the test results.
The differences including variability are most likely related to assumed
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
14
imperfection in the ABAQUS model. Further investigation of the imperfection
to use in ABAQUS is required.
3.3

Test Results and ABAQUS results compared with the Design
Standards
3.3.1

General
The test results (P
t
), ABAQUS results (AB) and theoretical proposed column
strength N
cred
are given in Tables 7 where the ratios P
t
/N
cred
and AB/N
cred
show
the comparisons. The N
cred
values are the proposed column design strengths as
detailed later.
Figs. 13a-1, 13b-1 & 13c-1 show the test strength (P
t
) compared with a range of
design curves for the 30 mm, 40 mm and 50 mm sections in 0.42 mm material
respectively. Figs. 14a-1, 14b-1 & 14c-1 show same for the 20 mm, 30 mm and
40 mm sections in 0.60 mm material respectively. Similarly, Figs. 13a-2, 13b-2,
13c-2, 14a-2, 14b-2 & 14c-2 show the ABAQUS values (AB) compared with a
range of design curves. In Figs. 13 & 14, the test strengths (P
t
) have been non-
dimensionalised with respect to the squash load (P
y
) as computed for the
measured yield stress and dimensions in Table 1.
Dashed and dash-dotted curves are plotted in Figs. 13 & 14. The dashed curve is
the ratio of N
cRb
/P
y
against the column length (l
x
). N
cRb
was calculated using the
AISI Specification based on a yield stress R
b
f
y
as included in Section A3.3.2 of
the AISI Specification Supplement No.1(1999). The dash-dotted curve is the
ratio of N
c0.75
/P
y
against column length (l
x
). N
c0.75
was calculated based on
AS/NZS 4600 with a yield stress of 0.75f
y
as included in Clause 1.5.1.5(b) of
AS/NZS 4600.
The horizontal dashed line represents the ratio of the theoretical local buckling
load to the squash load (N
ol
/P
y
) against the column length (l
x
). the horizontal
solid line represents the ratio of the section capacity to the squash load
(N
s0.90
/P
y
) against the column length (l
x
). N
s0.90
was calculated based on AS/NZS
4600 with a yield stress of 0.90f
y
as proposed by Yang and Hancock (2002).
The curved solid curve is the ratio of Euler load to the squash load against the
column length (l
x
). The heavy dash-dot curve is the proposed design curve,
which is the ratio of the nominal reduced member capacity to the squash load
(N
cred
/P
y
) against the column length (l
x
). The proposed design method is
described in Section 5 following.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
15
Although each column in 0.60 mm thickness had 2 holes in the lips at both ends,
the effect of the holes on the ultimate load was not taken into account in the
calculation of the section or the member capacity.
3.3.2

Test results comparisons with design standards
It can be seen for all sections and lengths that when the elastic local buckling
loads (N
ol
) are generally lower than the test results (P
t
), the test results are lower
than the design curves at intermediate columns lengths where local and Euler
buckling interact.
As shown in Figs. 13a-1&13b-1&13c-1, for the columns in 0.42 mm thickness,
the results are lower than the curves based on AS/NZS 4600 and the AISI
Specification. The low values for the 060LB20P450 specimen is probably due
to a large load eccentricity. The test was repeated and gave a higher result.
For the sections of stockier cross-section (060LB20 and 060LB30), the AS/NZS
4600 design curve based on 0.75f
y
and the AISI design curve based on a stress
R
b
f
y
are generally slightly conservative.
The conclusion is that a modified design method is required for sections with
low local buckling loads as may occur in high strength steel columns with
slender plate elements.
3.3.3

ABAQUS results and comparisons with design standards
The ABAQUS results show a similar trend to the test results when compared
with the design curves although, as detailed above, they are slightly higher
probably due to assumption with the imperfections.
For the largest 50 mm section in 0.42 mm material, two more long columns
were simulated using ABAQUS in order to obtain a complete graph of variation
with length and to make up the shortage where no test could be performed on
such long columns. The lengths were 2400 mm and 3000 mm. The dimensions
of cross-section used are the same as 042LB50P1700 as detailed in Table 1. The
ABAQUS results are 7.27 kN and 5.42 kN for 2400 mm and 3000 mm
respectively. It can be seen that the results are 7% and 4% lower than the curves
based on AS/NZS 4600 and AISI Specification. The longer the column, the less
the difference becomes for a given size of cross-section.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
16
4

MODIFIED DESIGN CURVE
The effect of local buckling on overall buckling behaviour has been studied in
several research projects. On the basis of tests and analytical studies, DeWolf,
Pekoz, Winter (1974) and Kalyanaraman, Pekoz, Winter (1977) conclude that a
satisfactory approach is to calculate the overall buckling load using the effective
radius of gyration and the effective area, both calculated at the overall buckling
stress. The unified approach proposed by Pekoz (1986) was adopted by the AISI
Specification (1986, 1991, 1996) and AS/NZS 4600 (1996) to determine the
strength of columns where local and Euler buckling interact. This proposed
approach does not take account of the reduction of the radius of gyration
(flexural rigidity) resulting from local buckling which was proposed by the
earlier researchers. However, for the high strength steel sections, the effect of
the reduction in the radius of gyration on the interaction of local buckling and
overall buckling is significant, especially buckling of these very slender sections
at loads above the local buckling load.
To fit the test data, a new design approach is proposed. The proposed approach
consists of two steps. Firstly, the reduced yield point 0.90f
y
, which was
determined by Yang and Hancock (2002) for stub columns, is used to replace
the yield stress in Clause 3.4 of AS/NZS 4600 and Section C4 of the AISI
specification. Secondly, a reduction factor γ is applied to the radius of gyration
as defined in Eq.1. It is a function of the length varying from some limit γ
0
at
length l
x
=0 (here γ
0
taken as 0.65) to 1.0 at length l
x
=1.10*l
x0
. Here, l
x0
is the
length where the local buckling load equals the Euler buckling load as defined
by Eq. 2. The reduction factor γ accounts for the loss of flexural rigidity due to
local buckling. The value of reduced radius of gyration γ*r
x
is used in Clause
3.3.3.2(a) of AS/NZS 4600 to replace the normal radius of gyration r
x
(Section
C3.1.2, Eq. C3.1.2-8 of the AISI Specification). It can be seen in Figs 13 & 14
that the proposed design curves based on the reduced the radius of gyration γ fit
the test data well.
γ=γ
0
+(1-γ
0
)*l
x
/(1.1*l
x0
) (1)
l
x0
=
olx
fEr
/**π
(2)
5

CONCLUSIONS
Pin-ended column tests with box-sections and constructed from high strength
G550 steel have been successfully performed. The plate slenderness (b/t) ranged
from 33 to 119 and the column slenderness (L/r
x
) ranged from 27 to 148. A load
eccentricity which produced a column response equivalent to L/1000 was used
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
17
for all tests. ABAQUS simulations of the test results with local imperfections
and overall eccentricity were made.

The ABAQUS results (AB) were generally in good agreement with the test
results (P
t
). The difference was on average less than 6% for all columns
although the ABAQUS results were higher. More detailed investigation of
imperfections to use in ABAQUS is required.

The columns with stockier plate elements, which had high local buckling
stresses (f
ol
), failed by overall buckling. The test results and the ABAQUS
results were close to the curves based on AS/NZS 4600 and the AISI
Specification. For very long columns with slender plate elements which had
lower local buckling stresses (f
ol
), failure was still governed by overall
buckling although local buckling occurred. However, for the intermediate
length columns, the failure mode was governed by the interaction of local
and overall buckling. The interaction of local and overall buckling reduced
the column strength and made the test results lower than the design curves.
The worst case had a difference between test results and the results based on
AS/NZS 4600 and the AISI Specification of about 14%, which means that
for the slender sections AS/NZS 4600 and the AISI method are
unconservative.

To account for the loss of flexural rigidity due to local buckling for the
slender sections, a reduction of the radius of gyration is needed to take
account of interaction buckling in the design curve. The proposed design
curve based on a reduction factor (γ) fits the test data well. So the reduced
radius of gyration
γ*r
x
may be used in the design curve for the slender
sections.

Since ABAQUS results were in reasonably good agreement with test results,
ABAQUS can be used to simulate long column tests which could not be
performed in the available machine.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
18
6

ACKNOWLEDGEMENTS
This report forms a part of an ARC Research project entitled “Compression
Stability of High Strength Steel Sections with Low Strain-Hardening” being
carried out in the Department of Civil Engineering at the University of Sydney.
The authors would like to thank the Australian Research Council and BHP
Coated Steel Australian for their financial support for these projects performed
at the University of Sydney. The tensile specimens were milled in the Willam
and Agnes Bennet Supersonics Laboratory in the Department of Aeronautical
Engineering. The compression specimens were fabricated in the J.W. Roderick
Laboratory for Materials and Structures in the Department of Civil Engineering.
The authors would like to thank Mr. Todd Budrodeen for fabricating all the
specimens and setting up the rig for the imperfection measurements. The first
author is supported by a joint Department of Civil Engineering and Centre for
Advanced Structural Engineering Scholarship.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
19
7

REFERENCES
American Iron and Steel Institute. (1997). "1996 Edition of the Specification for
the Design of Cold- Formed Steel Structural Members", Washington, DC, USA.
American Iron and Steel Institute. (2000). "1996 Edition of the Specification for
the Design of Cold-Formed Steel Structural Members, Supplement 1, July 1999”,
Washington, DC, USA.
American Society for Testing and Materials A611. (1997). "Standard Specification
for Steel Sheet, Carbon, Cold-Rolled, Structural Quality", Philadelphia, PA, USA
American Society for Testing and Materials A653. (1997). "Standard Specification
for Steel Sheet, Zinc-Coated (Galvanized) or Zinc-Iron Alloy-Coated
(Galvannealed) by the Hot-Dip Process", Philadelphia, PA, USA.
American Society for Testing and Materials A792. (1994). "Standard Specification
for Steel Sheet, 55% Aluminium-Zinc Ally-Coated by the Hot-Dip Process",
Philadelphia, PA, USA
Bijlaard P.P., and Fisher G.P., "Interaction of column and local buckling in
compression members", NACA TN2640 1953.
Dewolf, J.T., Pekoz, T., and Winter, G., “Local and overall buckling of cold
formed steel members”, Journal of the Structural Division, ASCE, Oct., 1974.
Galambos, T.V., “Guide to stability design criteria for metal structures”, John
Wiley & Sons, Inc., 1988.
Graves-Smith, T.R., "The ultimate strength of columns of arbitrary length",
Symposium on thin -walled steel structures, Swansea, 1967.
Hancock, G.J., "Nonlinear analysis of thin sections in compression" Journal of
Structural Engineering, Vol.107, No.ST3, 1981
Hibbitt, Karlsson & Sorensen, Inc., “ABAQUS/Standard User’s Manual”, Ver.
5.7, 1997
Kalyanaraman, V., Pekoz, T., and Winter, G., “Unstiffened compression
elements”, Journal of the Structural Division, ASCE, Sept., 1977.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
20
Levy, S. Wooley, R.M., and Kroll, W.D., "Instability of simply supported
square plate with reinforced circular hole in edge compression", Research Paper
RP1849, Vol.39, Dec. 1947
Mathcad 2000 Professional, (1999), ©1989-1999 Mathsoft Inc.
McAdam, J.N, Brockenbrough, R.A., LaBoube, R.A., Pekoz, T, and Schneider,
E.J., “Low strain hardening ductile steel cold-formed members”, 9
th
International
Specialty Conference on Cold-Formed Steel Structures, St Louis, Missouri, Nov
1988.
Miller T.H., Pekoz T., “Unstiffened strip approach for perforated wall studs”,
Journal of Structural Engineering, Vol.120, No.2, 1994
Papangelis, J.P., Hancock, G.J. THIN-WALL 2.0 (1998), Center for Advanced
Structural Engineering, Department of Civil Engineering, University of Sydney.
Pekoz, T., “Development of a unified approach to the design of cold-formed
steel members”, Research Report, American Iron and Steel Institute, 1986.
Pekoz, T., “Development of a unified approach to the design of cold-formed
steel members”, 8
th
International Specialty Conference on Cold-Formed Steel
Structures, St. Louis, Missouri, Nov., 1986
Rogers, C.A., Hancock, G.J. (1997), "Ductility of G550 sheet steels in tension",
Journal of Structural Engineering, ASCE, Vol. 123, No. 12, 1586-1594.
Rhodes J., Harvey J.M., “Examination of plate post-buckling behaviour”, Journal
of the Engineering Mechanics Division, Vol.103, No. EM3, June, 1977.
Roger, C.A., Hancock, G.J., " Ductility of G550 sheet steels in tension-elongation
measurements and perforated tests", Research Report No. R735, School of Civil
and Mining Engineering, University of Sydney
Shanmugam, N.E. Chiew S. and Lee S., “Strength of thin-walled square steel box
columns”, Journal of Structural Engineering, ASCE, Vol. 113, No. 4, 818-831.
Standards Australia / Standards New Zealand. (1996). "Cold-formed steel
structures - AS/NZS 4600", Sydney, NSW, Australia
Standards Australia. (1993). "Steel sheet and strip - Hot-dipped zinc-coated or
aluminium/zinc coated - AS 1397", Sydney, NSW, Australia
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Department of Civil Engineering
Research Report No R816
21
Van der Neut, A., "The interaction of local buckling and column failure of thin-
walled compression members", Proceedings, 12
th
International congress applied
mechanics, Springerverlag, Germany, 1969.
Walker, A. C., “Design and analysis of cold-formed sections”, International
Textbook Company Limited, 1975
Wu, S., Yu, W.W, and LaBoube, R.A. (1996a), “Strength of flexural members
using structural Grade 80 of A653 steel (deck panel tests)”, Second Progress
Report, Department of Civil Engineering, University of Missouri-Rolla,
November.
Wu, S., Yu, W.W, and LaBoube, R.A. (1996b), “Flexural members using
structural Grade 80 of A653 steel (deck panel tests)”, 13
th
International Specialty
Conference on Cold-Formed Steel Structures, St Louis, Missouri, Oct 1996, pp.
255-274.
Yang, D., Hancock, G.J., "Compression tests of cold-reduced high strength steel
stub column", Research Report No. R815, School of Civil and Mining
Engineering, University of Sydney, 2002.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
22
8

NOTATION
A cross-sectional area (mm
2
)
AB ultimate load of ABAQUS (kN)
b web width (mm)
d lip width (mm)
e eccentricity (mm)
E Young's modulus of elasticity (MPa)
f
ol
elastic buckling stress (MPa)
f
y
yield stress (MPa)
h flange width (mm)
hl glued lips thickness (mm)
l
x
, l
x0
length of column (mm)
L length of column (mm)
L
t
length of pin-ended column (mm)
N
cred
reduced member capacity (kN)
N
ol
elastic buckling load (kN)
N
s
nominal section compression capacity (kN)
P
cr
elastic buckling load of test (kN)
P
e
Euler load (kN)
P
t
ultimate load of test (kN)
P
y
squash load (kN)
r radius of corner (90
o
) (mm)
r
x
radius of gyration of the cross-section (mm)
R radius of corner (135
o
) (mm)
t thickness (mm)
t
b
thickness of base metal (mm)
t
c
thickness of coated metal (mm)
γ
0
, γ
reduction factor of radius of gyration
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
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9

FIGURES
0.2
f
y
f
y
Strain-hardening range
f
u
f
u
High strength cold-reduced steel G550
300
600
Strain
Fully annealed steel G300
Fig.1 Stress-Strain Curve
Stress (MPa)
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
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Epoxy
Epoxy
Bolt in some sections,
clamps in others
Lipped-Box Section (LB)
Fig.2 Tested Sections
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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Fig.3 Cross-Section Dimensions
d
b
r
t
R
h
t
d
b
r
R
Lipped-Box Section
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
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(a) Lipped-Box Section (LB) with Clamps (b) Lipped-Box Section (LB) with Bolts at ends
Fig.4 Bolting & Clamping Configurations of Test
Specimens of LB section
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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Fig.5 Rig for Imperfection Measurement
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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Fig.6 Test Specimen in Test Rig
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
29
Fig. 7 Test Arrangement
e
Pin-ended bearing
Pin-ended bearing
Location of transducers
& strain gauges at
column mid-height
End plate
Test long column
End plate
Test machine centre line
Specimen centre line
Fixed base
Cross head
P
L
L
t
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
30
0
5
10
15
20
25
30
35
0 0.5 1 1.5 2 2.5
Axis Shortening (mm)
Load
FIG. 8a. Load- Shortening of 060LB450 Series
FIG. 8b. Load- Shortening of 060LB900 Series
0
5
10
15
20
25
30
35
40
45
50
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Axis Shortening (mm)
Load
060LB20P450
060LB30P450
060LB40P450
060LB40P900
060LB20P900
060LB30P900
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
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FIG. 9a. Load- Shortening of 042LB550 Series
FIG. 9b. Load- Shortening of 042LB1100&1700 Series
0
5
10
15
20
25
0 0.5 1 1.5 2 2.5
Axis Shortening (mm)
Load
0
5
10
15
20
25
0 0.5 1 1.5 2 2.5 3 3.5 4
Axis Shortening (mm)
Load
042LB50P550
042LB30P550
042LB40P550
042LB50P1100
042LB40P1700
042LB40P1100
042LB50P1700
042LB30P1100
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
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Fig.10 Buckling Mode
(a) Local buckle at failure (b) Overall buckle
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
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Fig.10 Buckling Mode (continued)
(a) Local & Overall buckling (Bolts at ends) (b) Local & Overall buckling (Clamps)
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
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Fig. 11a Tested specimens of 060LB450&900 series
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
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Fig. 11b Tested specimens of 042LB550&1100 series
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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Fig. 11c Tested specimens of 042LB1700 series
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
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Fig.13a-1 Comparison of Test Results with Design Standard (0.42mm), 30x30 mm Sections
Fig.13a-2 Comparison of ABAQUS Results with Design Standard (0.42mm), 30x30 mm Sections
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
Test Results
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
ABAQUS Results
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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Fig.13b-1 Comparison of Test Results with Design Standard (0.42mm), 40x40 mm Sections
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
Test Results
Fig.13b-2 Comparison of ABAQUS Results with Design Standard (0.42mm), 40x40 mm Sections
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
ABAQUS Results
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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Fig.13c-1 Comparison of Test Results with Design Standard (0.42mm), 50x50 mm Sections
Fig.13c-2 Comparison of ABAQUS Results with Design Standard (0.42mm), 40x40 mm
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
Test Results
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
ABAQUS Results
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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Fig.14a-1 Comparison of Test Results with Design Standard (0.60mm), 20x20 mm Sections
Fig.14a-2 Comparison of ABAQUS Results with Design Standard (0.60mm), 20x20 mm Sections
0
0.25
0.5
0.75
1
1.25
1.5
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
Test Results
0
0.25
0.5
0.75
1
1.25
1.5
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
ABAQUS Results
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
41
Fig.14b-1 Comparison of Test Results with Design Standard (0.60mm), 30x30 mm Sections
Fig.14b-2 Comparison of ABAQUS Results with Design Standard (0.60mm), 30x30 mm Sections
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
Test Results
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
ABAQUS Results
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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Fig.14c-1 Comparison of Test Results with Design Standard (0.60mm), 40x40 mm Sections
Fig.14c-2 Comparison of ABAQUS Results with Design Standard (0.60mm), 40x40 mm Sections
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
Test Results
0
0.25
0.5
0.75
1
0 500 1000 1500 2000 2500 3000
Length (mm)
Dimsionless Load
AS/NZS 4600
AISI, NcRb
Euler Curve
Section Capacity, Ns0.90
Local buckling Load
Proposed Design Curve, Ncred
ABAQUS Results
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
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10

TABLES
Flange Web Thickness Radius Lip
Thickness
of Lip
Length
Specimen
h (mm) b (mm) t
b
(mm) t
c
(mm) r (mm) R (mm) d (mm) hl (mm) L (mm)
060LB20P450a
10.5 22.3 0.60 0.65 0.60 0.60 6.0 1.5 448.5
060LB20P450b
10.3 20.6 0.60 0.65 0.60 0.60 5.8 1.6 449.0
060LB20P900a
10.7 21.4 0.60 0.65 0.60 0.60 5.2 1.9 896.5
060LB20P900b
11.5 20.5 0.60 0.65 0.60 0.60 5.9 1.6 896.0
060LB30P450a
15.5 32.0 0.60 0.65 0.60 0.60 8.2 1.7 448.8
060LB30P450b
15.1 31.4 0.60 0.65 0.60 0.60 8.1 1.4 449.0
060LB30P900a
15.8 30.8 0.60 0.65 0.60 0.60 8.7 1.5 898.3
060LB30P900b
15.2 30.8 0.60 0.65 0.60 0.60 8.5 1.6 897.5
060LB40P450a
19.8 41.9 0.60 0.65 0.60 0.60 10.8 1.6 448.8
060LB40P450b
20.0 41.9 0.60 0.65 0.60 0.60 10.7 1.5 448.6
060LB40P900a
19.8 41.5 0.60 0.65 0.60 0.60 11.4 1.7 897.5
060LB40P900b
19.8 41.2 0.60 0.65 0.60 0.60 11.1 1.6 898.5
Table 1a Measured Dimensions of Long Columns (0.60mm)
Flange Web Thickness Radius Lip
Thickness
of Lip
Length
Specimen
h (mm) b (mm) t
b
(mm) t
c
(mm) r (mm) R (mm) d (mm) hl (mm) L (mm)
042LB30P550a
15.4 32.5 0.41 0.45 0.60 0.60 5.8 1.1 550.1
042LB30P550b
15.9 32.4 0.41 0.45 0.60 0.60 5.8 1.2 550.0
042LB30P1100a
15.7 32.7 0.41 0.45 0.60 0.60 6.1 1.1 1099.8
042LB30P1100b
15.8 32.6 0.41 0.45 0.60 0.60 5.9 1.2 1100.1
042LB40P550a
21.2 41.5 0.41 0.45 0.60 0.60 5.9 1.0 550.0
042LB40P550b
21.3 41.2 0.41 0.45 0.60 0.60 5.9 1.1 549.5
042LB40P1100a
21.3 41.4 0.41 0.45 0.60 0.60 6.1 1.4 1099.8
042LB40P1100b
21.2 41.6 0.41 0.45 0.60 0.60 6.0 1.2 1099.5
042LB40P1700a
20.4 41.2 0.41 0.45 0.60 0.60 6.0 1.3 1698.0
042LB40P1700b
20.5 41.4 0.41 0.45 0.60 0.60 5.9 1.1 1697.0
042LB50P550a
26.4 51.0 0.41 0.45 0.60 0.60 5.9 1.2 550.0
042LB50P550b
26.5 50.8 0.41 0.45 0.60 0.60 6.2 1.2 550.0
042LB50P1100a
26.5 50.3 0.41 0.45 0.60 0.60 6.6 1.5 1099.8
042LB50P1100b
26.5 50.7 0.41 0.45 0.60 0.60 6.2 1.3 1100.1
042LB50P1700a
25.3 52.0 0.41 0.45 0.60 0.60 6.2 1.2 1697.0
042LB50P1700b
25.4 51.7 0.41 0.45 0.60 0.60 6.0 1.2 1698.0
Table 1b Measured Dimensions of Long Columns (0.42mm)
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
44
Specimen
Dimensions
Table
Hole/Clamping 0.2% Proof Stress
060LB20P450a~~060LB40P900b
1a
4 Holes at ends for each 711
042LB30P550a~~042LB50P1100b
042LB40P1700a~~042LB50P1700b
1b
Clamps 690
Table 2 Hole/Clamping Configuration and Proof Stresses
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
45
Specimen
Side1 Max
(mm)
Side2 Max
(mm)
060LB20P450a -0.18 0.14
060LB20P450b 0.12 -0.15
060LB20P900a -0.51 -0.33
060LB20P900b -0.97 0.19
060LB30P450a 0.19 -0.25
060LB30P450b 0.06 -0.12
060LB30P900a -0.75 0.79
060LB30P900b -0.33 -0.46
060LB40P450a 0.19 -0.21
060LB40P450b 0.13 0.19
060LB40P900a 1.27 0.99
060LB40P900b 0.85 0.81
Table 3a Measured Imperfections of LB sections(Longitudinal)
Side1 Max (mm) Side2 Max (mm)
Specimen
Ed11 Ce10 Ed12 Ed21 Ce20 Ed22
042LB30P550a 0.448 0.19 -0.556 -0.435 -0.427 0.452
042LB30P550b -0.538 -0.376 -0.894 -0.4 -0.59 -0.399
042LB30P1100a 0.496 -0.75 -0.812 -0.75 -1.071 -1.55
042LB30P1100b 0.317 -1.04 -1.26 -0.441 -0.678 -0.37
042LB40P550a -0.589 -0.397 -0.367 -0.81 0.674 0.458
042LB40P550b 0.708 -0.482 -0.385 0.413 -0.596 -0.571
042LB40P1100a -0.768 -0.803 -0.35 -0.642 -0.498 0.53
042LB40P1100b 0.419 -0.47 0.606 -0.64 -0.91 -1.01
042LB40P1700a -0.38 -0.65 -0.98 -0.78 -1.41 -1.39
042LB40P1700b -1.59 -1.63 -1.36 -1.25 -1.58 -1.25
042LB50P550a 0.568 1.35 -0.543 0.562 -0.666 -0.329
042LB50P550b 0.453 0.414 -0.373 0.378 -1.052 -0.365
042LB50P1100a -0.443 -0.424 -0.723 -0.352 -0.555 0.54
042LB50P1100b -0.682 -0.443 -0.455 0.674 -0.907 0.408
042LB50P1700a -2.19 -2.5 -1.8 -1.17 -1.32 -0.82
042LB50P1700b -1.55 -1.63 -1.32 -1.25 -1.59 -1.56
Table 3b Measured Imperfections of LB sections(Longitudinal)
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
46
Specimen
e (mm)
Average
060LB20P450a
0.277
060LB20P450b
0.046
060LB20P900a
0.828
060LB20P900b
0.072
060LB30P450a
0.3960
060LB30P450b
0.049
060LB30P900a
0.143
060LB30P900b
0.773
060LB40P450a
0.486
060LB40P450b
0.071
060LB40P900a
0.632
060LB40P900b
0.062
Table 4a Measured Eccentricity of LB sections (0.60 mm)
Specimen
e (mm)
Average
042LB30P550a
0.122
042LB30P550b
0.072
042LB30P1100a
0.166
042LB30P1100b
0.099
042LB40P550a
0.609
042LB40P550b
0.429
042LB40P1100a
0.879
042LB40P1100b
0.764
042LB40P1700a
1.165
042LB40P1700b
0.9325
042LB50P550a
0.481
042LB50P550b
0.346
042LB50P1100a
0.263
042LB50P1100b
0.573
042LB50P1700a
N/A
042LB50P1700b
1.450
Table 4b Measured Eccentricity of LB sections (0.42 mm)
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
47
Specimen
E*I (m
2
N)
from beam tests
E*I (m
2
N)
from Thin-Wall
(E*I)
m
/(E*I)
tw
060LB20P450a
587.4 552.6
1.06
060LB20P450b
663.0 665.6
1.00
060LB20P900a
847.4 895.5
0.95
060LB20P900b
810.2 762.5
1.06
060LB30P450a
2164 1960
1.10
060LB30P450b
2152 1963
1.10
060LB30P900a
2178 2155
1.01
060LB30P900b
2178 2180
1.00
060LB40P450a
5048 3791
1.33
060LB40P450b
5054 3744
1.35
060LB40P900a
4874 4607
1.06
060LB40P900b
4976 4568
1.09
Table 5 Measurement of E*I of LB Sections (0.60mm)
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
48
Slenderness
L/r
x
Overall Slenderness
L(mm)
550 1100 1700
b/t
Plate Slenderness
042LB30
48 95 148 71
042LB40
35 70 108 95
042LB50
27 55 85 119
Table 6a Slenderness of Sections in 0.42 mm Thickness
Slenderness
L/r
x
Overall Slenderness
L(mm)
450 900
b/t
Plate Slenderness
060LB20
63 126 33
060LB30
43 85 50
060LB40
32 63 67
Table 6b Slenderness of Sections in 0.60 mm Thickness
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
49
A
(mm
2
)
b/t
f
y
(MPa)
P
y
(kN)
N
cred
(kN)
P
t
(kN)
P
t/
/N
cred
AB
(kN)
AB/N
cred
AB/P
t
f
ol
(MPa)
P
cr
(MPa)
N
ol
(kN)
P
cr
/N
ol
060LB20P450a
60.97 33.3 711 43.35 15.7 16.4 1.04 22.88 1.46 1.40 954.6 N/A 58.20 N/A
060LB20P450b
60.41 33.3 711 42.95 15.7 21.3 1.36 22.88 1.46 1.07 954.6 N/A 57.67 N/A
060LB20P900a
61.93 33.3 711 44.03 5.2 8.1 1.56 7.43 1.43 0.92 954.6 N/A 59.12 N/A
060LB20P900b
62.12 33.3 711 44.17 5.2 N/A N/A 7.43 1.43 0.49 954.6 N/A 59.30 N/A
060LB30P450a
90.78 50.0 711 64.54 29.0 N/A N/A 37.86 1.31 N/A 411.7 N/A 37.37 N/A
060LB30P450b
90.37 50.0 711 64.25 29.0 35.5 1.22 37.86 1.31 1.07 411.7 N/A 37.21 N/A
060LB30P900a
91.39 50.0 711 64.98 16.4 21.9 1.34 19.50 1.19 0.89 411.7 N/A 37.63 N/A
060LB30P900b
90.32 50.0 711 64.22 16.4 20.3 1.24 19.50 1.19 0.96 411.7 N/A 37.18 N/A
060LB40P450a
120.77 66.7 711 85.87 39.26 47.6 1.21 50.17 1.28 1.05 225.6 31.6 27.25 1.16
060LB40P450b
120.66 66.7 711 85.79 39.26 45.5 1.16 50.17 1.28 1.10 225.6 32.6 27.22 1.20
060LB40P900a
120.92 66.7 711 85.97 25.3 28.7 1.13 31.76 1.26 1.11 225.6 24.4 27.28 0.89
060LB40P900b
120.51 66.7 711 85.68 253 30.1 0.12 31.76 0.13 1.06 225.6 27.3 27.19 1.00
Table 7a Summary of Results for LB Sections (0.60mm)
A
(mm
2
)
b/t
f
y
(MPa)
P
y
(kN)
N
cred
(kN)
P
t
(kN)
P
t/
/N
cred
AB
(kN)
AB/N
cred
AB/P
t
f
ol
(MPa)
P
cr
(MPa)
N
ol
(kN)
P
cr
/N
ol
042LB30P550a
60.14 71.4 690 41.50 16.1 17.50 1.09 18.66 1.16 1.07 183.6 10.1 11.04 0.91
042LB30P550b
60.50 71.4 690 41.75 16.1 17.38 1.08 18.66 1.16 1.07 183.3 9.7 11.09 0.87
042LB30P1100a
60.45 71.4 690 41.71 8.1 10.78 1.33 10.58 1.31 0.98 192.8 9.9 11.65 0.85
042LB30P1100b
60.38 71.4 690 41.66 8.1 11.70 1.44 10.58 1.31 0.90 182.3 10.4 11.01 0.94
042LB40P550a
79.90 95.2 690 55.13 20.1 20.90 1.04 23.30 1.16 1.11 108.0 9.2 8.63 1.07
042LB40P550b
76.95 95.2 690 53.10 20.1 23.00 1.14 23.30 1.16 1.01 109.0 9.6 8.39 1.14
042LB40P1100a
76.93 95.2 690 53.08 13.9 15.00 1.08 16.81 1.21 1.12 108.7 8.8 8.36 1.05
042LB40P1100b
77.12 95.2 690 53.21 13.9 14.20 1.02 16.81 1.21 1.18 107.4 8.5 8.28 1.03
042LB40P1700a
75.80 95.2 690 52.30 8.0 8.40 1.05 8.09 1.01 0.96 116.3 6.2 8.82 0.70
042LB40P1700b
75.74 95.2 690 52.26 8.0 8.79 1.10 8.09 1.01 0.92 116.3 7.6 8.81 0.86
042LB50P550a
93.25 119.0 690 64.34 22.5 23.40 1.04 24.50 1.09 1.05 70.57 6.6 6.58 1.00
042LB50P550b
93.53 119.0 690 64.54 22.5 23.60 1.05 24.50 1.09 1.04 71.18 6.8 6.66 1.02
042LB50P1100a
93.79 119.0 690 64.72 17.5 19.70 1.13 20.21 1.15 1.03 72.24 7.2 6.78 1.06
042LB50P1100b
93.26 119.0 690 64.35 17.5 17.50 1.00 20.21 1.15 1.15 85.96 6.5 8.02 0.81
042LB50P1700a
92.14 119.0 690 63.58 10.4 11.2 1.08 10.53 1.01 0.94 73.98 6.5 6.82 0.96
042LB50P1700b
91.88 119.0 690 63.40 10.4 10.7 1.03 10.53 1.01 0.98 73.98 6.2 6.80 0.91
Table 7b Summary of Results for LB Sections (0.42mm)
042LB30 042LB40 042LB50 060LB20 060LB30 060LB40
f
y
(MPa)
634 634 634 711 711 711
N
s
(kN)
26.88 28.08 28.12 39.60 52.80 60.89
P
t
(kN)
24.15 25.05 26.10 37.50 48.70 53.01
AB (kN)
26.20 26.42 26.62 42.51 50.01 55.32
(0.42mm & 0.60mm)
Table 7d Average Results for Stub Column of LB Sections
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
50
APPENDIX
A Imperfection Measurements
Appendix ‘A’ contains measured imperfection data of long columns. This
measurement of imperfection was for three series of long columns. The
instrument shown in Fig. 5 was designed for this purpose.
The part includes the graphs of longitudinal measurement.
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
51
FIG. A-1. Local Geometric Imperfection for 060LB20P450a
FIG. A-2. Local Geometric Imperfection for 060LB20P450b
0 50 100 150 200 250 300 350 400 450
2
1
0
1
2
Side1
Side2
Length (mm)
Deformation (mm)
1.4
1.833

Ed11 L( )
Ed12 L( )
450
0
L
0 50 100 150 200 250 300 350 400 450
2
1
0
1
2
Side1
Side2
Length (mm)
Deformation (mm)
1.2
1.5

Ed21 L( )
Ed22 L( )
450
0
L
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
52
FIG. A-3. Local Geometric Imperfection for 060LB20P900a
FIG. A-4. Local Geometric Imperfection for 060LB20P900b
0 100 200 300 400 500 600 700 800 900
6
4
2
0
2
Side1
Side2
Length (mm)
Deformation (mm)
1.122
5.133

Ed11 L( )
Ed12 L( )
900
0
L
0 100 200 300 400 500 600 700 800 900
10
5
0
5
Side1
Side2
Length (mm)
Deformation (mm)
1.944
9.733

Ed21 L( )
Ed22 L( )
900
0
L
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
53
FIG. A-5. Local Geometric Imperfection for 060LB30P450a
FIG. A-6. Local Geometric Imperfection for 060LB30P450b
0 50 100 150 200 250 300 350 400 450
4
2
0
2
Side1
Side2
Length (mm)
Deformation (mm)
2
2.567

Ed11 L( )
Ed12 L( )
450
0
L
0 50 100 150 200 250 300 350 400 450
1.5
1
0.5
0
0.5
Side1
Side2
Length (mm)
Deformation (mm)
0.189
1.189

Ed21 L( )
Ed22 L( )
450
0
L
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
54
FIG. A-7. Local Geometric Imperfection for 060LB30P900a
FIG. A-8. Local Geometric Imperfection for 060LB30P900b
0 100 200 300 400 500 600 700 800 900
10
5
0
5
10
Side1
Side2
Length (mm)
Deformation (mm)
7.889
7.5

Ed11 L( )
Ed12 L( )
900
0
L
0 100 200 300 400 500 600 700 800 900
6
4
2
0
2
Side1
Side2
Length (mm)
Deformation (mm)
1.489
4.567

Ed21 L( )
Ed22 L( )
900
0
L
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
55
FIG. A-9. Local Geometric Imperfection for 060LB40P450a
FIG. A-10. Local Geometric Imperfection for 060LB40P450b
0 50 100 150 200 250 300 350 400 450
4
2
0
2
Side1
Side2
Length (mm)
Deformation (mm)
1.9
2.122

Ed11 L( )
Ed12 L( )
450
0
L
0 50 100 150 200 250 300 350 400 450
1
0
1
2
Side1
Side2
Length (mm)
Deformation (mm)
1.867
0.156

Ed21 L( )
Ed22 L( )
450
0
L
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
56
FIG. A-11. Local Geometric Imperfection for 060LB40P900a
FIG. A-12. Local Geometric Imperfection for 060LB40P900b
0 100 200 300 400 500 600 700 800 900
0
5
10
15
Side1
Side2
Length (mm)
Deformation (mm)
12.744
0
Ed11 L( )
Ed12 L( )
900
0
L
0 100 200 300 400 500 600 700 800 900
0
5
10
Side1
Side2
Length (mm)
Deformation (mm)
8.478
0
Ed21 L( )
Ed22 L( )
900
0
L
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
57
FIG. A-13a. Local Geometric Imperfection for 042LB30P550a (Side1)
FIG. A-13b. Local Geometric Imperfection for 042LB30P550a (Side2)
0 100 200 300 400 500
1
0.5
0
0.5
Edge1
Center
Edge2
Length (mm)
Deformation (mm)
0.448
0.556

Ed11 L( )
Ce10 L( )
Ed12 L( )
5500
L
0 100 200 300 400 500
0.5
0
0.5
Edge1
Center
Edge2
Length (mm)
Deformation (mm)
0.453
0.435

Ed21 L( )
Ce20 L( )
Ed22 L( )
5500
L
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
58
FIG. A-14a. Local Geometric Imperfection for 042LB30P550b (Side1)
FIG. A-14b. Local Geometric Imperfection for 042LB30P550b (Side2)
0 100 200 300 400 500
1
0.5
0
0.5
Edge1
Center
Edge2
Length (mm)
Deformation (mm)
0.236
0.894

Ed11 L( )
Ce10 L( )
Ed12 L( )
5500
L
0 100 200 300 400 500
1
0.5
0
0.5
1
Edge1
Center
Edge2
Length (mm)
Deformation (mm)
0.592
0.59

Ed21 L( )
Ce20 L( )
Ed22 L( )
5500
L
Compression Tests of Cold-Reduced High Strength Steel Long Columns March 2002
Department of Civil Engineering
Research Report No R816
59
FIG. A-15a. Local Geometric Imperfection for 042LB30P1100a (Side1)