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Analysis and design of cold-formed steel channels subjected
to combined bending and web crippling
Wei-Xin Ren a,*, Sheng-En Fang a,b, Ben Young c
a Department of Civil Engineering, Central South University, Changsha, Hunan Province 410075, People’s Republic of Chinab E.T.S.de Ingenieros Industriales, Universidad Politecnica de Madrid, Madrid 28006, Spain
c Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China
Received 15 July 2005; received in revised form 7 March 2006; accepted 20 March 2006
Available online 4 May 2006
Abstract
The channel failures due to combined bending and web crippling may occur at the highly concentrated interior loading when there is no load
stiffener in cold-formed thin-walled steel beams. This paper presents accurate finite element models to predict the behavior and ultimate strengths
of cold-formed steel channels subjected to pure bending as well as combined bending and web crippling. Both geometric and material
nonlinearities are considered in the finite element analysis. The nonlinear finite element models are verified against experimental results of cold-
formed steel channels subjected to pure bending as well as combined bending and web crippling. The finite element analytical results show a good
agreement with the experimental results in terms of the ultimate loads and moments, failure modes and web load-deformation curves thus
validating the accuracy of the finite element models. The verified finite element models are then used for an extensive parametric study of different
channel dimensions. The channel strengths predicted from the parametric study are compared with the design strengths calculated from the North
American Specification for cold-formed steel structures. It is shown that the design rules in the North American Specification are generally
conservative for channel sections with unstiffened flanges having the web slenderness ranged from 7.8 to 108.5 subjected to combined bending
and web crippling. It is demonstrated that the nonlinear finite element analysis by using the verified finite element models against test results is an
effective way to predict the ultimate strengths of cold-formed thin-walled steel members.
q 2006 Elsevier Ltd. All rights reserved.
Keywords: Bending; Cold-formed steel channels; Design specification; Finite element analysis; Interaction; Nonlinearity; Thin-walled structures; Web crippling
1. Introduction
The failure of cold-formed steel channels subjected to
combined bending and web crippling may occur when there is
no load stiffener in cold-formed steel beams under highly
concentrated interior forces. The cold-formed channels without
transverse stiffeners against such loading are more susceptible
to failure because of the added bending moment, which may
obviously reduce the ultimate web crippling strengths of
channels [1]. Cold-formed steel sections are usually thinner
than hot-rolled sections and have modes of failure and
deformation, which are not commonly encountered in normal
structural steel design, and so corresponding design specifica-
tions are required to provide a guideline for the design of
0263-8231/$ - see front matter q 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tws.2006.03.009
* Corresponding author. Tel.: C86 731 2654349; fax: C86 731 5571736.
E-mail address: [email protected] (W.-X. Ren).
URL: http://bridge.csu.edu.cn (W.-X. Ren).
cold-formed thin-wall structural members [2]. The design rules
used in the Australian/New Zealand Standard [3] and the North
American Specification [4] for cold-formed steel structures
subjected to combined bending and web crippling are empirical
in nature based on a limited number of specimens tested in the
laboratory, and thus the design rules are only applicable for a
specific range of web slenderness and material properties. As
the appearance of new materials and the improvement of cold-
forming techniques, the material strength and sheet thickness
of cold-formed steel channels could be increased. Thus, the
applicability of the design rules to the cold-formed steel
channels subjected to combined bending and web crippling
needs to be investigated.
For that purpose, a series of tests on cold-formed high
strength steel channels subjected to combined bending and web
crippling were carried out by Young and Hancock [5]. The web
slenderness of the tested channels was stocky ranged from 15.3
to 45.0. The tests were conducted under the loading conditions
specified in the Australian/New Zealand Standard [3] and
American Specification [6] for cold-formed steel structures.
Thin-Walled Structures 44 (2006) 314–320
www.elsevier.com/locate/tws
Fig. 2. Comparison of failure modes under pure bending.
bf
t
dx
y
ri
Fig. 1. Geometry and symbol definition of cross-section of channel specimen.
W.-X. Ren et al. / Thin-Walled Structures 44 (2006) 314–320 315
The test results demonstrated that the design strengths
predicted by these specifications were generally conservative
for the tested channels.
Several tools are available when considering the analysis
and design of cold-formed sections such as testing, classical
methods based on explicit solutions of the governing
differential equations, finite element method, and finite strip
method [7]. Among these methods, the finite element method is
mostly used in dealing with both geometrical and material
nonlinearities. Finite element analysis (FEA) of cold-formed
steel structures is increasingly important in engineering
practice for its relatively inexpensive and time efficiency
compared with laboratory experiments, especially when a
parametric study of cross-section geometries is involved [8].
Thus, the numerical investigation based on nonlinear finite
element method is an effective way to solve engineering
problems. The key of numerical investigation is that the
validity of the finite element model. The material and
geometric nonlinearities as well as the complex boundary
conditions bring the difficulty to establish an accurate finite
element model.
The objective of this paper is intended to present analysis
and design of the cold-formed high strength steel channels
subjected to combined bending and web crippling. The finite
element program ANSYSw [9] was used to develop accurate
nonlinear finite element models for the numerical analysis. The
3D finite element models were established based on the
measured material properties obtained from tensile coupon
tests where the material nonlinearity is taken into account. The
developed finite element models were carefully calibrated
against the tests of channel sections in terms of the ultimate
loads, failure modes and load versus web deformation curves.
The verified finite element models were then used for an
extensive parametric study for a wide range of channel
dimensions with the web slenderness (h/t) ranged from 7.8 to
108.5. The results obtained from the numerical investigation
were compared with design predictions. The structural
behavior of cold-formed steel channels in terms of strength
and stiffness is quantified rationally for general design.
Consequently, the study provides understanding to the
structural performance of cold-formed steel channels subjected
to combined bending and web crippling.
2. Description of laboratory tests
A test program described by Young and Hancock [5,10]
provided the experimental ultimate loads and moments, failure
modes, load versus web deformation curves and interaction
curves for cold-formed steel channels subjected to pure
bending, pure web crippling as well as combined bending
and web crippling. The channel specimens were tested using
the loading conditions specified in the Australian/New Zealand
Standard [3] and American Specification [6] for cold-formed
steel structures. The test specimens were cold-rolled from
structural steel sheets having a nominal yield stress of
450 MPa, a nominal thicknesses ranged from 4 to 6 mm, a
nominal depth of the webs ranged from 75 to 300 mm, and
a nominal flange width ranged from 40 to 90 mm. The web
slenderness (h/t) values ranged from 15.3 to 45.0. The cross-
section geometry and symbol definition of channel specimens
are as shown in Fig. 1.
The test arrangement of pure bending is shown in Fig. 2(a)
where two channel specimens were used to provide the
symmetric loading. Hinge and roller supports were simulated
by half rounds and Teflon pads. The simply supported
specimens were loaded symmetrically at two points to the
load transfer blocks within the span using a spreader beam. The
pure in-plane bending of the specimens can be achieved
between two loading points without the presence of shear and
axial forces. The displacement transducers were used to
record the vertical deflections and curvatures of the specimens.
The specimens were labeled according to the test types and
their cross-section dimensions. For example, the label
‘BT100!50!4’ stands for a pure bending test of the specimen
Fig. 3. Comparison of failure modes under combined bending and web
crippling.
Table 1
Nominal and measured material properties
Channel Nominal Measured
d!bf!t
(mm)
E
(GPa)
s0.2(MPa)
s0.2(MPa)
su(MPa)
3f(%)
75!40!4 200 450 450 525 20
100!50!4 200 450 440 545 20
125!65!4 200 450 405 510 23
200!75!5 200 450 415 520 24
250!90!6 200 450 445 530 21
300!90!6 200 450 435 535 23
W.-X. Ren et al. / Thin-Walled Structures 44 (2006) 314–320316
having a nominal overall depth of the web of 100 mm, an
overall flange width of 50 mm, and a plate thickness of 4 mm.
The test arrangements and test results of the pure web
crippling under interior-one-flange (IOF) loading condition are
detailed in Young and Hancock [10,11]. The test results of the
cold-formed steel channels subjected to pure bending and pure
web crippling under IOF loading are herein used to
nondimensionalise the channels subjected to combined
bending and web crippling. Fig. 3(a) shows the test
arrangements of the cold-formed steel channels subjected to
combined bending and web crippling. Two channel specimens
were bolted to load transfer blocks at the end supports and a
bearing plate was poisoned at the mid-length of the specimens.
Hinge and roller supports were also simulated by half rounds
and Teflon pads. In addition, restraining frames were utilized to
prevent out-of-plane buckling of the long specimens. The web
deformations were measured between the bearing plate and the
bottom flanges of the specimens.
The loads were applied by means of bearing plate for the
combined bending and web crippling loading condition. They
were designed to act across the full flange widths of channels
excluding the rounded corners. The length of bearing (N) was
chosen to be the full and half flange widths of the channels. The
tests are detailed in Young and Hancock [5]. The specimens
were labeled such that the test type, web depth, interaction
factor and bearing length could be identified from the label. For
example, the label ‘C200K1.0N75’ defines the combined
bending and web crippling test specimen of 200 mm web depth
with an interaction factor of 1.0, and a bearing length of
75 mm. The pure bending test specimens had the same batch of
specimens as the web crippling tests as well as the combined
bending and web crippling tests. Hence, the material properties
of the test specimens for these tests were identical. Table 1
shows the material properties of the test specimens obtained
from tensile coupon tests.
3. Finite element modeling and analysis
3.1. General
The finite element (FE) package ANSYSw [9] was used in
this study to carry out the nonlinear finite element analysis and
simulate the tested cold-formed steel channels. It is aimed to
establish accurate finite element models for cold-formed steel
channels subjected to pure bending as well as combined
bending and web crippling. The FE models were calibrated
against the test data and performed an extensive parametric
study of channel geometries. The measured cross-section
dimensions, material properties and boundary conditions of the
tests were used in developing the FE models. The channel
sections of the FE models were based on the centerline
dimensions of the cross-sections together with the plate
thickness and rounded corners.
3.2. Element type and mesh
A thin shell element (Shell181 in ANSYS finite element
package) is used in the FE models. This is a four-node element
with six degrees of freedom at each node. The Shell181
element is suitable for thin to moderately thick structures with
powerful nonlinear capabilities such as large deflection, large
rotation, and large strain so that the web crippling deformation
and ultimate strength can be simulated. A 3D structural solid
element (Solid45) is utilized to model the load transfer blocks
and the bearing plates. The Solid45 element is suitable for the
3D modeling of structures with plasticity, stress stiffening,
large deflection, and large strain capabilities. The element is
defined by eight nodes having three translational degrees of
freedom at each node. The finite element mesh used in the
models has been investigated by varying the size of the
elements. The mesh sizes of approximately 15!15 mm or 9!9 mm (length by width) for both flange and web elements were
used to simulate the local deformation of channel web
crippling. The corresponding element aspect ratios (length-
to-width ratio) are chosen to be 1.0 for both flange and web of
the channel sections. A finer mesh is implemented at the
corners of channels due to its importance in transferring the
stress from flange to web. The typical finite element models of
W.-X. Ren et al. / Thin-Walled Structures 44 (2006) 314–320 317
cold-formed channels subjected to pure bending, and combined
bending and web crippling are shown in Figs. 2(b) and 3(b),
respectively.
3.3. Simulation of boundary conditions
The boundary conditions were carefully simulated in the FE
models. In the test setup, the channels were bolted to the load
transfer blocks. The coupled node method was herein used in
the region where the channel connected to the load transfer
blocks. The nodes at the x and y coordinates in the region were
coupled together by all degrees of freedom. For the regions
where the load applied through the bearing plates, the same
technique was implemented for the flanges connected to the
bearing plates. For the combined bending and web crippling
loading condition, the end load transfer blocks could only
rotate about the z-axis at the hinge support end, thus the nodes
on the z (vertical axis to web plane) symmetry axis of bottom
surface were restrained by x, y, z, rotx and roty five degrees of
freedom. As the load transfer blocks could also translate along
the x-axis at the roller support end, the translational degree of
freedom x was released in addition to the degree of freedom
rotz. The rest of the nodes were free to translate and rotate in
any directions.
3.4. Simulation of applied loading
The simulation of applied load in the finite element models
was identical to the tests. The displacement control method was
used. For the combined bending and web crippling loading
condition, the load was applied to the elements of the inner
strip at the flange corners. This is better than applying the
applied load on the bearing plate and then transferring the load
to the flange through contact elements [12]. For the pure
bending loading condition, the applied load was applied by
specifying a displacement to the two mid nodes at the top
surface of the load transfer blocks at the loading points. For the
interior-one-flange (IOF) loading condition of web crippling,
the model is detailed in Ren et al. [15].
3.5. Modeling of material properties
The measured material properties were used in the FE
models. The material properties of the test specimens were
determined by tensile coupon tests. The coupons were taken
from the center of the web plate of the untested specimens. The
tensile coupons were prepared and tested according to the
Australian Standard AS1391 [13] using 12.5 mm wide coupons
of gauge length 50 mm. Table 1 shows the material properties
of the test specimens.
The material of the channels behaves nonlinear when loaded
to the ultimate load-carrying capacity. The large strain
behavior of the material was implemented by using the
Isotropic Hardening material model. The material nonlinearity
behavior was herein incorporated with the true stress–strain
curve defined by true stress and logarithmic (true) strain
calculated from the coupon test data. The relationships
between true and engineering stresses or strains are given in
ANSYSw [9].
It should be noted that the cold-forming process enhances
the yield stress, but reduces the ductility of the material. This
influence is significant in the case of the corner material that the
yield stress increased by approximately 50% compared to the
flat material as shown in the tests conducted by Popovic et al.
[14]. Therefore, the corners material properties of the channels
were considered in the FE models. Ren et al. [15] detailed the
modeling of corners material properties of cold-formed steel
channels.
4. Verification of FE model
4.1. General
The FE models were verified against the experimental
results in terms of failure modes, web deformation, and
ultimate loads and moments. A nonlinear finite element
analysis by incorporating material nonlinearity was performed
using Newton–Raphson iteration method and displacement-
based convergent criterion.
4.2. Small strain and large strain
As mentioned earlier, the cold-formed steel channels
subjected bending, web crippling, and combined bending and
web crippling may experience large strains. Ren et al. [15]
investigated the effects of large strain on the web crippling
strength of the channels, where both small and large strain
analyses involved material nonlinearity were carried out. It is
shown that the small strain analysis slightly under-estimates
the web crippling strength of the channels, and the large strain
analysis provided a much better prediction of web deformation
and ultimate strength. Subsequently, the large strain analysis is
employed in the finite element analysis.
4.3. Failure modes
The failure modes of the cold-formed steel channels
subjected to pure bending as well as combined bending and
web crippling were simulated using the FE models. Figs. 2(b)
and 3(b) show the failure modes of the FE predictions for pure
bending, and combined bending and web crippling, respect-
ively. It is demonstrated that the FE predictions are in good
agreement with the failure modes observed from the tests.
4.4. Web deformation
Figs. 4 and 5 show the comparison of the web deformation
curves for channel specimens subjected to pure bending and
combined bending and web crippling, respectively. In general,
the web deformation curves predicted by the finite element
analysis agree well with the test curves. Therefore, the FE
models using large strain analysis are capable to predict the
web deformations of the cold-formed steel channels.
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
90
Test curveFEA curve
Mom
ent (
kNm
)
Web deformation (mm)
Fig. 4. Comparison of web deformation curves for specimen BT250!90!6
under pure bending.
W.-X. Ren et al. / Thin-Walled Structures 44 (2006) 314–320318
4.5. Ultimate load-carrying capacity
The ultimate load-carrying capacities of moments [Mb-Exp
and Mb-FEA for channels subjected to pure bending are
shown in Table 2. The ultimate load-carrying capacities of
loads Pc-Exp and Pc-FEA as well as moments Mc-Exp and Mc-FEA
for channels subjected to combined bending and web crippling
are shown in Table 3.
The ultimate strengths predicted by the nonlinear FEA are
compared in Tables 2 and 3 with the experimental ultimate
strengths for pure bending as well as combined bending and
web crippling, respectively. The mean value of experimental-
to-FEA strength ratios Mb-Exp/Mb-FEA and Mb-Exp/Mb-FEA are
0.97 and 1.09 with the corresponding coefficients of variation
(COV) of 0.046 and 0.041 for pure bending, and combined
bending and web crippling, respectively. Fig. 6 illustrates the
moment-load interaction curves obtained from laboratory tests
with those predicted by the finite element analysis for different
size of channels subjected to combined bending and web
0 1 2 3 4 5 6 7 60
10
20
30
40
50
60
Web deformation (mm)
Loa
d (k
N)
Test curveFEA curve
Fig. 5. Comparison of web deformation curves for specimen C200K1.5N37
under combined bending and web crippling.
crippling. In most cases, the ultimate strengths of the channels
predicted by the nonlinear FEA are slightly less than the
experimental results, which indicate the FE predictions are
slightly conservative.
5. Parametric study
The calibrated FE models of the cold-formed steel
channels subjected to pure bending as well as combined
bending and web crippling were used to carry out an
extensive parametric study of different channel dimensions.
Twelve series of different channel sizes of cold-formed steel
channels were investigated with a wide range of web
slenderness h/t from 7.8 to 108.5. The channels for
parametric study have the plate thickness t of 4 and 6 mm
as well as the inside corner radius ri of 4 and 8 mm,
respectively. The overall depth of the web ranged from 75 to
450 mm, and the overall flange width ranged from 40 to
120 mm. The channel lengths were remained at 1270 mm for
the pure bending loading condition and ranged from 462 to
8590 mm for the combined bending and web crippling
loading condition. The bearing length (N) ranged from 20 to
120 mm, which was chosen to be the full and half flange
widths of the channels.
The total number of specimens in the parametric study is 12
for pure bending loading condition and 123 for combined
bending and web crippling loading condition. The finite
element analysis of cold-formed steel channels subjected to
pure web crippling has been carried out by Ren et al. [15]. In
the parametric study, the material properties of channels with
plate thickness of 4 mm are identical to those of the tested
channel section 75!40!4, and the channels with plate
thickness of 6 mm are identical to those of the tested channel
section 250!90!6 as shown in Table 1. The element aspect
ratio (length to width) of finite element mesh is approximately
1.0 for the flange and web of the channel sections. The element
meshes are 15!15 mm and 9!9 mm (length by width)
depending on the channel size. The loading method and the
boundary conditions of the parametric study are identical to
those used in the FE models calibration against the laboratory
tests.
6. Design rules
The design strengths obtained from the interaction equation
specified in the North American Specification (NAS) for cold-
formed steel structures [4] is used to compare with the
numerical results obtained from the parametric study for
channels subjected to combined bending and web crippling.
The design equation is empirical based on the limited test
results carried out by different researchers, where the
geometries and material properties of the tested channels are
limited. The design interaction equation specified in the NAS
Specification is herein further examined by the extensive
parametric study using finite element analysis. The unfactored
design strengths of channel sections having single unreinforced
webs were calculated using the following interaction equation
Table 2
Comparison of pure bending test strengths with FEA strengths
Specimen Web
d (mm)
Flanges
bf (mm)
Thickness
t (mm)
Radius
ri (mm)
Length
L (mm)
Exp. Ult. moment
per channel
Mb-Exp (kNm)
FEA moment per
channel
Mb-FEA (kNm)
Ratio
Mb-Exp/Mb-FEA
BT75!40!4 74.4 40.3 3.85 3.9 1267.9 6.44 6.68 0.96
BT100!50!4 99.2 50.4 3.83 4.1 1269.6 11.64 11.22 1.04
BT125!65!4 124.9 65.5 3.84 3.9 1269.2 16.20 16.51 0.98
BT200!75!5 198.8 75.9 4.70 4.2 1271.9 40.48 43.44 0.93
BT250!90!6 249.4 90.1 6.01 7.9 1269.5 79.90 80.28 1.00
BT300!90!6 298.7 91.2 6.00 8.4 1270.7 92.89 101.50 0.92
Mean 0.97
COV 0.046
W.-X. Ren et al. / Thin-Walled Structures 44 (2006) 314–320 319
for cold-formed steel channels subjected to combined bending
and web crippling,
1:07P
PFEA
� �C
M
MFEA
� �%1:42 (1)
The numerical results obtained from the parametric study
are plotted in Fig. 7 and the interaction curve of NAS
Specification are also plotted. For the purpose of comparison,
the design strengths have been nondimensionalised
with respect to the numerical results PFEA for pure web
crippling and MFEA for pure bending loading conditions.
Therefore, Pc-FEA/PFEA and Mc-FEA/MFEA were plotted for the
combined bending and web crippling as shown in Fig. 7. It can
be observed from Fig. 7 that the design strengths predicted by
the NAS Specification for channel sections with unstiffened
flanges are generally conservative.
Table 3
Comparison of combined bending and web crippling test strengths with FEA stren
Specimen Bearing
N (mm)
Web
d (mm)
Flanges
bf (mm)
Thickness
t (mm)
Radius
ri (mm)
Le
L (
C100K0.7N50 50.0 99.4 50.5 3.84 4.1 65
C100K1.0N50 50.0 99.6 50.5 3.83 4.1 89
C100K1.5N50 50.0 99.5 50.5 3.83 4.1 12
C100K0.7N25 25.0 99.4 50.5 3.84 4.1 66
C100K1.0N25 25.0 99.5 50.4 3.83 4.1 91
C100K1.5N25 25.0 99.5 50.4 3.84 4.1 13
C200K0.5N75 75.0 198.7 75.9 4.72 4.2 94
C200K1.0N75 75.0 198.8 75.9 4.71 4.2 18
C200K1.5N75 75.0 198.7 75.9 4.73 4.2 26
C200K0.5N37 37.5 198.4 75.8 4.71 4.2 97
C200K1.0N37 37.5 198.5 75.7 4.70 4.2 18
C200K1.5N37 37.5 198.6 75.7 4.72 4.2 26
C300K0.5N90 90.0 298.5 91.2 6.01 8.4 13
C300K1.0N90 90.0 298.5 91.2 6.01 8.4 26
C300K0.5N45 45.0 298.1 91.4 6.00 8.4 14
C300K1.0N45 45.0 298.2 91.3 6.01 8.4 28
Mean
COV
7. Conclusions
A nonlinear finite element analysis of cold-formed steel
channels subjected to pure bending as well as combined
bending and web crippling has been presented. The finite
element models have been verified against experimental
results. The failure modes, web deformations and ultimate
strengths of the channels have been simulated. The failure
modes predicted by the finite element analysis are in good
agreement with the failure modes observed in the tests for
pure bending as well as combined bending and web
crippling loading conditions. The ultimate strengths of the
channels predicted by the nonlinear finite element analysis
are generally agreed with the test results. The calibrated
finite element models were used to perform an extensive
parametric study for a wide range of channel dimensions
with unstiffened flanges having the web slenderness ranged
from 7.8 to 108.5. The ultimate strengths predicted by the
finite element analysis were compared with the design
strengths calculated using the North American Specification
gths
ngth
mm)
Exp. Ult. load per
channel
Ratio
Pc-Exp/
Pc-FEA
Exp. Ult. moment per
channel
Ratio
Mc-Exp
Pc-Exp
(kN)
Pc-FEA
(kN)
Mc-Exp
(kNm)
Mc-FEA
(kNm)
Mc-FEA
3.0 54.2 49.2 1.10 7.63 6.93 1.10
3.4 44.0 41.1 1.07 8.83 8.25 1.07
97.0 34.6 31.4 1.10 10.44 9.47 1.10
8.7 48.9 41.9 1.17 7.07 6.06 1.17
4.7 40.7 35.8 1.14 8.38 7.37 1.14
31.8 31.6 28.5 1.11 9.80 8.84 1.11
7.0 91.8 87.4 1.05 19.66 18.72 1.05
04.8 68.5 65.7 1.04 29.39 28.19 1.04
62.1 53.0 50.2 1.06 34.08 32.28 1.06
7.4 82.9 72.3 1.15 18.38 16.03 1.15
66.5 61.4 57.8 1.06 27.26 25.66 1.06
54.1 49.1 48.9 1.00 31.46 31.33 1.00
84.7 138.4 123.7 1.12 44.79 40.03 1.12
79.0 107.6 99.4 1.08 69.65 64.34 1.08
69.8 124.2 111.4 1.11 42.85 38.43 1.11
48.0 90.2 86.8 1.04 62.22 59.87 1.04
1.09 1.09
0.041 0.041
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Non
-dim
ensi
onal
ised
mom
ent,
M/M
Exp
Non-dimensionalised load, P/PExp
N=50.0mm (test) N=25.0mm (test) N=50.0mm (FEA) N=25.0mm (FEA) NAS 2001
(a) channel 100×50×4
Non
-dim
ensi
onal
ised
mom
ent,
M/M
Exp
Non-dimensionalised load, P/PExp
(b) channel 200×75×5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
N=75.0mm (test) N=37.5mm (test) N=75.0mm (FEA) N=37.5mm (FEA) NAS 2001
Non
-dim
ensi
onal
ised
mom
ent,
M/M
Exp
Non-dimensionalised load, P/PExp
(c) channel 300×90×6
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
N=90.0mm (test) N=45.0mm (test) N=90.0mm (FEA) N=45.0mm (FEA) NAS 2001
Fig. 6. Test and FEA results for combined bending and web crippling.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Non
-dim
ensi
onal
ised
mom
ent,
M/M
FEA
Non-dimensionalised load, P/PFEA
FEA NAS 2001
Fig. 7. Comparison of FEA results with design curve for cold-formed steel
channels subjected to combined bending and web crippling.
W.-X. Ren et al. / Thin-Walled Structures 44 (2006) 314–320320
for cold-formed steel structures for channels subjected to
combined bending and web crippling. It is observed that the
interaction equation specified in the North American
Specification are generally conservative for cold-formed
steel channels with web slenderness ranged from 7.8 to
108.5.
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