Original Research
Behaviour of partly stiffened
cold-formed steel built-up beams:
Experimental investigation and
numerical validation
Advances in Structural Engineering
2019, Vol. 22(1) 172–186
Ó The Author(s) 2018
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DOI: 10.1177/1369433218782767
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M Adil Dar1 , N Subramanian2, A R Dar3,
M Anbarasu4 , James BP Lim5 and Mir Atif3
Abstract
To address the various instability problems in cold-formed steel members, many researchers have mainly focused on developing innovative sectional profiles wherein geometry of the section plays a vital role in enhancing the inherent resistance of such sections against
premature buckling. However, the process of forming such innovative shapes is not only complex and time-consuming but sometimes
such sections fail to mobilize their complete reserve strength. Hence, a stiffening arrangement of weaker zones for mobilizing the
untapped reserve strength is suggested. The contribution of this simple, effective and partly stiffening arrangements, aimed at eliminating/delaying the premature local buckling, is studied both experimentally and numerically and also compared with existing codes.
Experimental study was carried out on different simply supported cold-formed steel beams with judiciously proposed stiffening
arrangements under four-point loading. An equivalent hot-rolled steel beam was also tested to compare the efficiency of the coldformed steel beams. The cold-formed steel beams investigated had different width-to-thickness ratio, different geometries and different stiffening arrangements. The test strengths, failure modes, deformed shapes, load versus mid-span displacements and geometric
imperfections were measured and reported. The test strengths of the beam models are also compared with the design strength predicted by North American Standards and Eurocode for cold-formed steel structures. To validate the test results further, a numerical
study was carried out on such stiffened cold-formed steel beams using finite element software ABAQUS. All these results show that
the proposed strengthening system is efficient and economical and allow cold-formed steel beams to reach greater load carrying
capacity.
Keywords
cold-formed steel, experiment, numerical modelling, stiffening arrangements, structural behaviour
Introduction
In most of the developing countries, structural
designers face the global competition of designing fasttrack and cost-effective structural systems to meet the
huge deficit of various infrastructural systems. Such a
development is crucial for bringing such countries at
par with global standards of living. For this purpose,
cold-formed steel (CFS) sections provide the best
choice not only for cost-effective structural systems
but also an ideal choice for the desired fast-track construction (Anbarasu and Sukumar, 2013, 2014). The
main members in any structure need to have an adequate safety to avoid catastrophic or total collapse,
thus use of hot-rolled steel sections for such vital members are unavoidable, owing to their superior performance against premature buckling, thus can be
justified. However, use of hot-rolled steel sections for
moderate to lightly loaded members such as floor
beams and purlins generally remains under-utilized
(Keerthan et al., 2014; Wang et al., 2014; Wang and
1
Department of Civil Engineering, Indian Institute of Technology Delhi,
New Delhi, India
2
Consulting Structural Engineer, Maryland, USA
3
Department of Civil Engineering, National Institute of Technology,
Srinagar, Srinagar, India
4
Department of Civil Engineering, Government College of Engineering
Salem, Salem, India
5
Department of Civil and Environmental Engineering, The University of
Auckland, Auckland, New Zealand
Corresponding author:
Mohammad Adil Dar, Senior Research Fellow, Department of Civil
Engineering, Indian Institute of Technology Delhi, New Delhi 110016,
India.
Email: dar.adil89@gmail.com
Dar et al.
Young, 2016). Moreover, optimization techniques in
design are not fruitful because of the limited availability of rolled section in the market place (Subramanian
and Venugopal (1977). This contributes to the highly
conservative use of such a precious construction material with limited reserves. Keeping in view the importance of steel as an ideal construction material in
challenging situations, it is of paramount importance
to make the most optimum use of such vital construction material (Valsa Ipe et al., 2013). CFS provides an
ideal choice to avoid such a wasteful use of steel.
Unlike hot rolling, the cold forming process permits
an almost infinite variety of shapes to be produced
which can serve desired needs efficiently. Generally,
the width-to-thickness ratio of individual components
of CFS members is high, hence are prone to premature
buckling at moderate compressive stress levels
(much below the yield stress). This problem can be
tackled effectively either by developing innovative sectional profiles with intrinsic resistance against premature buckling and/or by appropriate stiffening
arrangement at vulnerable locations. Past research has
stressed mainly on the development of innovative
sections.
In the past decade, due to advances in the manufacturing technology, many attempts were made to make
changes in the cross section of the member in order to
attain economical and efficient sectional profiles
(Hancock, 2016; Schafer, 2011). SudhirSastry et al.
(2015) carried out a numerical study to investigate the
effect of different flange configurations on the buckling of CFS channel beams. It was observed that the
beams with extended open flanges and rounded flanges
had enhanced critical buckling moments compared to
beams with dropped flanges. Obst et al. (2016) carried
out tests to study the behaviour of non-standard channel beams with single- and double-box flanges. Beams
with double-box flanges had higher capacities than the
ones with single-box flanges. It was also observed that
reinforced beams performed better than the unreinforced ones. Ye et al. (2018) conducted a study to optimize the CFS channel beam sections for higher energy
dissipation and ductility. It was found that by incorporating intermediate web and flange stiffeners to slender channel beams, there was a significant
improvement in their energy dissipating capacity.
However, in stockier channel beams, such introduction
of stiffeners did not help. Instead, increasing the crosssectional depth and decreasing the flange width helped
in attaining higher energy dissipating capacity. Paczos
and Wasilewicz (2009) tested anti-symmetrical CFS Ibeam sections fabricated out of a single steel sheet. It
was observed that there was quick loss in the stability
of beams that were loaded with a concentrated force at
the mid-span. Also, the critical loads for lipped beams
173
were higher than that of the non-lipped ones. Trahair
and Papangelis (2018) studied the lateral distortional
buckling in hollow flanged beams with corrugated web
plates. It was observed that the distortion in the hollow flanges resulted in the reduction of their torsional
rigidities as well as their lateral buckling resistance.
However, corrugation of web plate helped in preventing web distortion and significantly reduced the lateral
buckling resistance, which is generally observed in
beams with flat webs. Laı́m et al. (2015) conducted a
series of tests to study the flexural behaviour of CFS
beams with sigma profiles at ambient and elevated
temperatures. It was seen that the web stiffeners
behave differently under elevated temperatures and
that behaviour depends upon the sectional profile.
Axially unrestrained beams perform better than the
restrained ones. Under ambient temperature, chances
of excessive non-uniform compressive stress distribution are very likely compared to that in tension
regions. Ye et al. (2016) carried out a numerical study
to develop more efficient CFS channel sections under
flexure. Just by optimizing the relative dimensions of
flat plates and inclination of lips, the bending resistance can increase by nearly 30%. Double folded lips
can substantially improve the flexural resistance,
whereas intermediate web stiffeners may not necessarily improve flexural performance. Adequately
designed CFS channel beam sections have the potential to reach their plastic moment capacity (Kumar
and Sahoo, 2016). Siahaan et al. (2016a) studied innovative rectangular hollow flanged channel beams to
develop optimum sections which can delay the buckling failure in them. Dar et al. (2015a) investigated various innovative CFS beam sectional profiles under
flexure so as to find an ideal replacement for conventional hot-rolled steel sections. Wang and Young
(2015) carried out an experimental and numerical
investigation to study the local buckling and/or distortional buckling behaviour of the built-up open and
closed sections under flexure. All these studies indicate
that innovative profiles were successful in postponing
the buckling failures in CFS beams; however, the process of forming such innovative sections of complex
profiles requires a lot of time and effort, thus making
the process very difficult and time-consuming.
Appropriate stiffening of vulnerable zones is an effective alternate solution that can eliminate/delay premature buckling (Laı’m et al., 2013; Paczos, 2014; Moen
et al., 2013). Hence, there is an urgent need to develop
judicious stiffening arrangements that can be effectively used in simple CFS sections to overcome the
complex problem of premature buckling failure, thus
making CFS construction fast, simple and efficient.
The primary objective of this research is to conduct
experimental investigation on different simply
174
Advances in Structural Engineering 22(1)
Table 1. Model nominal and measured dimensions.
Model
I
II
III
IV
Weight
(kg/m)
Thickness
(mm)
Nominal (mm)
Measured (mm)
a
b
c
d
e
a
b
c
d
e
11.23
14.83
5.62
6.82
2
2
1
1
125
125
125
125
25
25
25
25
150
150
150
150
25
25
25
25
–
–
–
31.25
122.3
124.4
127.5
123.2
26.4
25.7
22.8
24.7
151.4
153.3
154.1
152.3
23.4
22.8
23.8
24.6
–
–
–
32.7
supported CFS beams with judiciously proposed stiffening arrangements under four-point loading. The
tests would compensate the lack of experimental data
on this form of construction and act as a data base for
numerical models to be developed. An equivalent hotrolled steel beam was also tested to compare the efficiency and the structural performance of these CFS
beams. The CFS beams investigated had different
width-to-thickness ratio, different geometries and different stiffening arrangements. The test strengths, failure modes, deformed shapes, load versus mid-span
displacements and geometric imperfections were measured and reported in this article. The test strengths of
the beam models are compared with the design
strength predicted by North American Specifications
and Eurocode for CFS structures. In order to validate
the test results, a numerical study was also carried out
on CFS beams using finite element software
ABAQUS.
Experimental investigation
Test models
To achieve the well-defined objective of this study, four
CFS beam models have been fabricated with and without appropriate stiffening arrangements. The tested
CFS beams comprised two channel sections connected
back to back by black bolts of size 5 mm and class 4.6.
Two rows of bolts were provided with 100 mm centre
to centre spacing along the depth as shown in Figure 1
and 200 mm centre to centre spacing along the length
of the beam. To compare the efficiency and effectiveness of the proposed stiffening arrangements, one hotrolled steel section was tested. The dimensional details
of all the models are given in Table 1. A digital vernier
calliper was used to measure the dimensions of various
components of the models. The details of various models fabricated and tested are described below.
Model I: unstiffened model. The sectional geometry of this
model consisting of I shape using two-lipped channel
sections bolted back to back are shown in Figure 2(I).
A cold-formed sheet having a thickness of 2 mm only
Figure 1. Arrangement of bolts in the cross section.
has been used for the fabrication of this model. The
nominal and measured dimensions of the various elements of the model are shown Table 1. All the beams
had a span of 2.1 m.
Model II: angle-stiffened model. During the testing of
Model I, localized lip buckling failure on compression
side was observed at a low magnitude of loading.
Therefore, it was expected that effective stiffening of
compression area falling under high bending moment
zone would have arrested such localized buckling,
thereby considerably improving its structural performance. Accordingly, Model II, which is a modified
version of Model I was stiffened by attaching two hotrolled angle stiffeners (25 3 25 3 5) as shown in
Figure 2(II). This hot-rolled angle stiffener was placed
in the central 1.5 m length of the beam falling under
high bending moment zone. The steel angle stiffener
was welded to the inside of the compression flange lip
by using Shielded Metal Arc Welding process. Rest of
the details of Model II were kept strictly identical to
Model I so as to investigate the contribution of the
proposed variation in Model II towards improved
Dar et al.
175
Figure 2. Cross sectional details of the models.
Table 2. Dimensions of hot-rolled angle stiffener used in Model II.
Designation
Size (P 3 Q; mm 3 mm)
T (mm)
A (mm2)
W (kg/m)
Cxx = Cyy (mm)
exx = eyy (mm)
ISA 2525
25 3 25
5
225
1.8
7.9
17.1
Table 3. Dimensions of hot-rolled beam ISMB 150.
Designation
W
(kg/m)
A
(mm2)
D
(mm)
Wf (mm)
tf
(mm)
tw
(mm)
Ixx
(mm4)
Iyy
(mm4)
rxx
(mm)
ryy
(mm)
ISMB 150
14.9
1900
150
80
7.6
4.8
7.26°3106
5.26°3 105
61.8
16.6
structural performance. The dimensions of hot-rolled
angle stiffener used in Model II are given in Table 2.
Model III: unstiffened lightest model. Keeping in view the
importance of achieving steel economy, it was deemed
appropriate to fabricate lighter models using thinnest
possible steel sheets. Accordingly, Model III with symmetrical I shape (using two-lipped channel sections
back to back similar to Model I) involving simple fabrication was fabricated as shown in Figure 2(III). A
cold-formed sheet having a thickness of 1 mm only
was used for fabrication of this model.
Model IV: stiffened lightest model. During the testing of
Model III, localized lip buckling failure (similar to
Model I) on the compression side was observed in high
bending moment zone. It was again expected that
strengthening of flange lips in the compression zone
could have prevented/delayed such a failure.
Accordingly, Model IV which is a modified version of
Model III was fabricated by stiffening the compression
flange lips using a small-channel section as shown in
Figure 2(IV). The small-channel section was bolted to
the compression flange of the beam using 5 mm black
bolts of class 4.6. For each small-channel stiffener, a
single row of bolts were provided with centre to centre
spacing of 150 mm along the length.
By developing structurally efficient CFS beam sections, steel economy was the main consideration.
However, it was equally important to evaluate these
proposed CFS sections from structural performance
consideration too. Accordingly, Model V, that is,
ISMB-150 (hot-rolled steel section), was chosen as the
reference model for meaningful comparison with the
various CFS beam models. The dimensions of ISMB150 are given in Table 3.
Material properties
The test specimens were fabricated from locally available structural steel. Tensile coupon tests were used to
determine the mechanical properties of the same. Since
two categories of steel sheet thicknesses were used to
fabricate the models. Three coupons were prepared
from the centre of the flange in the longitudinal direction from each sheet. Various standards exist which
specify the requirements for testing of tensile specimens. However, the dimensions of the coupons, as conforming to the Indian Standards (IS1608:2005), were
used for material testing. A computerized universal
testing machine was used to conduct the tensile tests of
the coupons. The relevant material properties of the
steel obtained from the material testing are given in
Table 4. A typical stress–strain curve of CFS used in
this study is shown in Figure 3. Since hot-rolled steel
angle was used in Model II, three tensile test coupons
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Advances in Structural Engineering 22(1)
Table 4. Material properties of steel used.
Test
fn (MPa)
E (GPa)
fy (MPa)
fu (MPa)
d# (%)
1 (2 mm)
2 (2 mm)
3 (2 mm)
4 (1 mm)
5 (1 mm)
6 (1 mm)
Average
350
350
350
350
350
350
350
209
207
208
212
210
209
209
455
468
454
456
456
459
458
510
496
505
510
512
503
506
18
20
19
25
24
26
22
Table 5. Material properties of hot-rolled steel angle used.
Test
fn (MPa)
E (GPa)
fy (MPa)
fu (MPa)
d# (%)
1
2
3
Average
250
250
250
250
214
212
210
212
266
272
275
271
433
457
442
444
26
23
26
25
Figure 4. Directions of measured geometric imperfections.
Figure 3. Stress–strain curve of CFS used in this study.
were prepared from the flat portion of the angle along
the longitudinal portion. The relevant properties of this
hot-rolled steel angle are given in Table 5.
Table 6. The maximum geometric imperfection measured at the mid-length in d1 and d2 directions was 1/
2167 mm and 1/2131 mm, respectively, and found in
Model III. The minimum geometric imperfection measured at the mid-length in d1 and d2 directions was 1/
4112 and 1/4346, respectively. As a comparison, the
magnitude of the maximum and minimum imperfections measured by Yuan et al. (2015) was 1/100 and 1/
4856, respectively.
Geometric imperfections
Prior to testing, the initial overall geometric imperfections were measured. The imperfections were measured
at the bottom flange web junctions near the centre
both along the longitudinal as well as transverse directions. An optical theodolite and a calibrated vernier
calliper were used to obtain the readings at the midlength and near both ends of the models. The imperfections measured at the mid-lengths along the model
in two orthogonal directions (Figure 4) are given in
Test setup
The testing of models was carried out on a loading
frame of 500 kN capacity as shown in Figure 5. A
hydraulic loading jack of 500 kN capacity was used to
transmit load on a rigid spreader beam to ensure fourpoint loading as shown in Figure 6. Dial gauges of least
count of 0.01 and 75 mm travel were used to record the
vertical displacements. Identical bearing plates of size
Dar et al.
177
Table 6. Measured geometric imperfections at mid-length.
Model
I
II
III
IV
d1/L
d2/L
1/3221
1/4346
1/4112
1/3549
1/2167
1/2131
1/2654
1/2152
(Dar et al., 2015b, 2017). The supports were restrained
laterally at the supports.
Test results and discussions
Figure 5. Model mounted on the testing rig.
150 mm 3 150 mm 3 15 mm were placed under
concentrated loading points to prevent punching failure. To prevent web buckling under concentrated loading points, bearing stiffeners comprising two angles
ISA 50 3 50 3 6 (SP 6-1 :2003) back to back were
bolted to the web of the models on both sides. Simply
supported end conditions with one end hinged and the
other end pinned was adopted as shown in Figure 6.
The moment span was laterally unrestrained. To assess
the contribution of stiffening arrangements towards
favourable structural performance, it was important to
ensure strict uniformity of various parameters which
include span of the beam, support conditions, location
of applied point loads and bearing/stiffening arrangement under concentrated applied load/reaction points
Figure 6. Loading arrangement.
Sometimes, semi-log curves are plotted for better interpretation of results (Dar et al., 2018; Manikandan
et al., 2014). Figure 7 shows the log of load versus displacement (at mid-span) curve of various models. The
Model I resisted the load until it experienced premature local buckling failure (as seen in Figure 8) in the
lip within the central one-third span with the maximum bending moment. The said failure was noticed
corresponding to a maximum load of 44.1 kN and
mid-span displacement of 11.67 mm.
Except a localized lip failure confined to a smalllength segment, rest of the model was in sound condition and still possessed enough reserve strength. To
exploit this reserved strength, appropriate stiffening
arrangement (as mentioned earlier) was introduced in
Model II. The Model II resisted a higher load
(68.3 kN) compared to Model I. The extra load carried
by Model II was partly due to reserve capacity of the
section and partly due to strain hardening. The mode
of failure was initiated with local buckling of a compression flange shown in Figure 9 falling within the
central one-third length and was under highest compressive stress corresponding to a failure load of
68.3 kN and a maximum deflection of 20.9 mm at
mid-span. It is worth highlighting here that the stiffening arrangement adopted over a full length of the
vulnerable zone has greatly contributed to a muchimproved load carrying capacity from 44.1 to 68.3 kN
178
Advances in Structural Engineering 22(1)
Figure 7. Combined load–displacement curves of various models.
Figure 8. Lip buckling of Model I.
Figure 10. Lip buckling failure in Model III.
Figure 9. Compression flange buckling in Model II.
(i.e. an increase of 39%). This encouraging experimental result confirms the important role of judiciously
provided stiffening arrangements in CFS construction.
The Model III experienced premature local lip buckling failure within the middle third zone of the maximum bending moment as shown in Figure 10. The said
failure was observed at a lower load of 12.7 kN and
mid-span displacement of 5.0 mm. At this stage, the
model suddenly stopped resisting any further load;
hence, the model was said to have reached its limit
state. Except localized lip failure confined to a small
length, the rest of the model seemed in good condition
and expected to possess appreciable reserve strength.
To exploit this reserved strength, appropriate stiffening
(as mentioned earlier) was introduced in Model IV.
Dar et al.
179
Figure 11. Lip buckling failure in Model IV.
Figure 12. Lateral buckling in ISMB-150.
The stiffened model (Model IV) failed at a load of
15 kN against 12.7 kN resisted by the unstiffened
model (Model III; i.e. only a meagre increase of
2.3 kN). The mode of failure was again local lip buckling within the middle third zone of high bending
moment and is prominently noticeable as seen in
Figure 11. It is therefore concluded that using thin
sheets with a thickness of 1 mm for the fabrication of
CFS beams is highly vulnerable to premature buckling
at very low loads even after adopting some stiffening
arrangements; hence, such thin cold-formed sheets are
not recommended. During testing of specimens, no
distortional and lateral torsional buckling was visually
observed in any of the selected cross sections.
As mentioned earlier, it would be appropriate to
have experimental results of a comparable hot-rolled
section for meaningful comparison. Accordingly, a
hot-rolled beam of ISMB-150 at 15 kg/m, named
Model V, was chosen as the only reference beam
model, with all other conditions remaining identical.
The curve for ISMB-150 shows a linear response till it
experienced lateral buckling as seen in Figure 12 corresponding to failure load of 83.65 kN and mid-span displacement of 16 mm. It needs to be highlighted here
that the promising results of partly stiffened CFS
Model II are comparable with reference hot-rolled section (i.e. Model V), thus confirming the vital role of
proper stiffening arrangements in enhancing the structural performance of CFS construction. Hence, judiciously selected stiffening arrangements can be adopted
with confidence in new CFS construction as well as in
the strengthening of existing CFS structures (which
demand upgradation).
The flat-width-thickness ratio of the flange had an
effect on both strengths as well as stiffness as shown in
Figure 13. The stiffness of beams was calculated by the
method adopted by Deepak and Shanthi (2018). The
effect of stiffening on the strength and initial stiffness
of CFS beams is shown in Figure 14. As the flat-widththickness ratio (b/t) of the flange reduced from 62.5 to
31.25 in unstiffened beams and from 31.25 to 18.75 in
stiffened beams, the strength increased by 228% and
354%, respectively, as shown in Figure 13(a). For the
same reduction in flat-width-thickness ratio (b/t) of the
flange, the initial stiffness increased by 35% and 106%
for unstiffened and stiffened beams, respectively, as
shown in Figure 13(b).
Design rules
Since one of the objectives of this research was to
assess the strengths of the CFS beams against the current design standards. Accordingly, the un-factored
design strengths predicted by European code and
North American Standards were calculated and are
summarized in Table 7.
Design rules specified in EC3
The unfactored design strength of flexural members
depends on the minimum effective section modulus
depending upon the position of the neutral axis.
According to EC3 (BS-EN1993-1-3), the unfactored
design strength (MEC3) is calculated as follows
MEC3 = Weff, y *fyb
ð1Þ
where fyb is the basic yield strength and Weff,y is the
effective section modulus given by
Weff, y = min Weff, y, c , Weff, y, t
ð2Þ
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Advances in Structural Engineering 22(1)
Figure 13. Effect of flange’s flat-to-width ratio on ultimate load and stiffness: (a) ultimate load variation and (b) stiffness variation.
Figure 14. Effect of stiffening on ultimate load and stiffness: (a) ultimate load variation and (b) stiffness variation.
Table 7. Summary of all model results.
Models
lLT
PTest
(kN)
PEC
(kN)
PNAS
(kN)
PTest/PEC
PTest/PNAS
MNAS
(kN m)
MEC
(kN m)
Mcr
(kN m)
My
(kN m)
I
II
III
IV
0.193
0.18
1.04
0.75
44.1
68.3
12.7
15.0
34.71
54.78
11.98
22.04
35.95
52.86
13.13
19.20
1.27
1.24
1.06
0.68
1.23
1.29
0.97
0.78
12.58
18.50
4.60
6.72
12.15
19.17
4.19
7.71
326.55
591.46
180.88
225.70
28.66
32.04
15.06
15.55
Weff, y =
Ieff, y
Z
ð3Þ
where Weff, y,c and Weff, y,t are the section moduli with
regard to compression and tension flanges, respectively; Z is the position of neutral axis from respective
flange and Ieff,y is the second moment of area of the
effective section.
The effective section properties are calculated by
using a reduction factor for elements in compression
heff = r*hc
r=
lp, h 0:055ð3 + cÞ
2
lp, h
ð4Þ
ð5Þ
lp, h =
hp =t
pffiffiffiffiffiffiffi
28:4e Ks
Ks = 7:81 6:29c + 9:78c2
c=
h c hp
hc
ð6Þ
ð7Þ
ð8Þ
where r is the width reduction factor, lp,h is the
relative slenderness, Ks is the buckling factor, c is the
stress ratio, hp is the nominal dimension of crosssectional element and hc is the distance of the point of
maximum compressive stress in element from neutral
axis.
Dar et al.
181
Design rules specified in AISI-S100
The unfactored design strength (Mn) of flexural members using the AISI specification (2016) is calculated as
follows
Mn = Se *Fy
Se =
Ix
ycg
ð9Þ
ð10Þ
where Fy is the nominal yield strength, Se is the elastic
section modulus relative to top fibre, ycg is the depth of
neutral axis with respect to the compression flange and
Ix is the second moment of area of the effective section,
determined by using a reduction factor, given by
w for l ł 0:673
rw for l.0:673
rffiffiffiffi
1:052 w f
l = pffiffiffi
E
k t
beff =
r=
1 0:22=l
ł1
l
ð11Þ
ð12Þ
ð13Þ
where beff is the effective design width, w is the width
of compression element, r is the reduction factor, k is
the plate buckling co-efficient, t is the thickness of
compression element, E is the modulus of elasticity
and f is the maximum compressive edge stress in the
element.
Comparison with design rules
Figure 15 shows the comparison between test strengths
and design strength predictions of North American
Standards and Eurocode. From Table 4 and Figure 15,
it can be concluded that North American Standards
are conservative for beams with a wall thickness of
2 mm, but un-conservative for the stiffened CFS beam
with a wall thickness of 1 mm. A similar behaviour
Figure 15. Comparison between test and design strengths for
CFS beams.
was indicated by Eurocode, except for Model III
(where a slight degree of unconservativeness was
observed). In all the four models, non-dimensional
slenderness for lateral torsional buckling is less than
limiting slenderness 0.4; therefore, there is no possibility of occurrence of lateral torsional buckling.
Numerical calibration
The finite element analysis using ABAQUS (2004) version 6.14 was conducted to simulate an experimental
behaviour of CFS lipped channel beams under fourpoint loading as shown in Figure 16. Nominal crosssectional dimensions, material imperfections and initial
geometric imperfections of the test specimens were
incorporated. S4R5 shell element was selected to
develop the finite element model. This element is thin,
shear flexible, isometric quadrilateral shell with four
nodes and five degrees of freedom per node, utilizing
reduced integration and bilinear interpolation scheme
(Ammash, 2017; Anbarasu, 2016; Keerthan and
Mahendran, 2013). Mesh convergence study was carried out to find the optimum mesh size. The model
with 5 mm mesh size provided reasonable accuracy
and was hence used in all the finite element models
(FEMs). The size of the element adopted was 5 mm
3 5 mm (25) mm2. Elastic perfectly plastic model
with a modulus of elasticity of 210 GPa and yield
stress of 450 MPa was used in this study. To ensure
proper distribution of concentrated forces on to the
beams, the load was applied at the centre of the rigid
plate attached to the beams as shown in Figure 16.
Idealized simply supported end condition was modelled by restraining the displacements in x, y and z
directions and rotations in z directions at the pinned
support. The displacements were restrained in y and z
directions and rotations in z directions at the roller
support. To avoid contact problems in-between the
Figure 16. Numerical model used in the finite element
analysis.
182
Advances in Structural Engineering 22(1)
Figure 17. Comparison of test and FEM results.
layers, general hard surface contact was adopted. In
the assembly, various instances of master–slave surfaces were created between the surfaces. Frictionless
hard contact was adopted. One major problem while
meshing sections with contact faces is that there are
penetrations of layers during analysis. From various
trials, it was found that square mesh of size 5 mm
3 5 mm can be adopted for modelling all parts of the
assembled sections to avoid any penetrations (Deepak
and Shanthi, 2018). Residual stresses have a negligible
effect on the strength (Schafer and Pekoz, 1998) and
hence were ignored. Local, distortional and global
Dar et al.
183
1998). In the nonlinear analysis, RIKS method was
used.
The comparison of load versus deflection curves for
test and FEM studies is shown in Figure 17. The mean
value of the (PTest/PFEM) ratio is 0.987 with the corresponding standard deviation of 0.037, as shown in
Table 8 and is also presented in Figure 18. Figure 19
shows the comparison of deformed shapes (test vs
FEM) in Model II and Model III. Table 5 and Figures
17 to 19 indicate that the FEM-predicted results are in
good agreement with test results, thus confirming the
accuracy of the experimental results.
Conclusion
Figure 18. Verification of test results.
geometric imperfections were incorporated in the
model. The maximum magnitude of local, distortional
and global imperfections adopted was 0.34 3 t,
0.94 3 t and L/1000, respectively (Schafer and Pekoz,
Based on experimental as well as numerical investigations carried out to study the effectiveness of stiffening
arrangements in mobilizing the untapped reserve
strength in CFS beams (comprising two channel sections connected back to back by bolts), the following
important conclusions are drawn:
The judiciously provided steel angle stiffener
which was welded to the inside of the compression flange lip only over the vulnerable zone
considerably improved the load carrying
Figure 19. Comparison of deformed shapes (test vs FEM): (a) Model II and (b) Model III.
184
Advances in Structural Engineering 22(1)
Table 8. Summary of all test and FEM results.
Models
PTest
(kN)
PFEM
(kN)
PTest/PFEM
dTest
(mm)
dFEM
(mm)
MTest
(kN m)
MFEM
(kN m)
(P/d)Test
(kN/mm)
(P/d)FEM
(kN/mm)
Failure
mode
I
II
III
IV
44.1
68.3
12.7
15.0
42.92
69.39
13.35
15.28
1.03
0.98
0.96
0.98
11.7
20.9
5.00
6.20
12.1
20.5
5.10
6.10
15.4
23.9
4.44
5.25
14.8
24.2
4.67
5.35
3.51
5.58
2.61
2.71
3.51
5.59
2.62
2.72
LB
FB
LB
LB
FEM: finite element model.
Average = 0.987.
Standard deviation = 0.037.
capacity from 43 to 67.8 kN (i.e. increase in
strength by 40%) and the initial stiffness from
3.58 to 5.71 kN/mm (i.e. increase by 60%).
Hence, instead of using a heavy hot-rolled section or larger CFS section, a suitable smaller
CFS section can be partially stiffened in the
compression zone to avoid premature local
buckling. This type of stiffening can be adopted
both in existing structures (which demand stiffening) as well as in the structures to be built to
obtain economy.
The stiffening of the compression flange lips in
sections with flat width-to-thickness ratio of
compression flange greater than 62.5 using
small-channel section did not perform satisfactorily. It shows that the proposed stiffening
arrangement may be suitable only when the flat
width-to-thickness ratio of compression flange
is not greater than 32.5.
The finite element models developed were in
good agreement with the experimental results.
The ratio of FEM-predicted strengths and test
results had an average PTest/PFEM of 0.987 and
standard deviation of 0.037. It shows that
ABAQUS software can be used to predict the
behaviour of such partly stiffened CFS beams.
Design strengths computed as per North
American Specifications and European Code
for CFS structures were found to be conservative, except for the stiffened CFS beam with a
wall thickness of 1 mm. Hence, these provisions
can be safely used for the design of such CFS
beams.
Lip buckling and flange buckling in the compression zone were the primary types of
observed failures, which can be effectively controlled by the proposed stiffening.
The minimum and maximum geometric imperfections observed at mid-lengths in the various models were 1/4346 mm and 1/2131 mm, respectively.
It has to be noted that in this study, angles were
used to stiffen the compression flange of CFS beams.
However, we can optimize the dimensions of the stiffener in order to obtain economy. On this aspect, a
parametric study being carried out by the authors is
under progress.
Acknowledgements
The authors would like to thank the Civil Engineering
Department of National Institute of Technology Srinagar
for their support by permitting the testing of the models in
their Structural Engineering Laboratory. Prior to joining IIT
Delhi, M. Adil Dar was working as an MTech scholar in
Structural Engineering at Kurukshetra University and wishes
to thank the University for their support.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship and/or publication of this
article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this
article: The experimental work described in this paper has
been supported by a grant from Consulting Engineers, PVT.
LTD (Project No. CES2015/8360).
ORCID iDs
M Adil Dar
M Anbarasu
https://orcid.org/0000-0003-2782-9225
https://orcid.org/0000-0002-7144-6195
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Appendix 1
Notation
a
A
b
beff
b/t
c
CFS
Cxx, Cyy
d
D
e
exx, eyy
E
fn
fy
fyb
fu
FB
hp
hc
Ieff,y
Ixx, Iyy
Ix
k
Ks
LB
Mcr
MFEM
width of top compression flange
cross-sectional area
depth of compression flange lip
effective design width
ratio of spacing between bolts in the web
along the depth to the thickness of the
web
depth of the section
cold-formed steel
centroid of the section of hot-rolled angle
stiffener in X and Y directions
depth of the tension flange lip
depth of hot-rolled beam ISMB 150
width of compression flange stiffener
distance of extreme fibre in the section of
hot-rolled angle stiffener in X and Y
directions
modulus of elasticity
nominal yield strength
yield strength
basic yield strength
ultimate strength
flange buckling
nominal dimension of cross-sectional
element
distance of the point of maximum
compressive stress in element from neutral
axis
second moment of area of effective section
moment of inertia about major and minor
axis
second moment of area of the effective
section
plate buckling co-efficient
buckling factor
lip buckling
elastic critical moment
ultimate FEM-predicted moment in the
central mid-third portion
MEC
MNAS
MTest
PNAS
PEC
PTest
PFEM
(P/d)Test
(P/
d)FEM
P, Q
rxx, ryy
Se
tf
tw
T
W
Wf
Weff,y
Weff, y,c,
Weff, y,t
ycg
Z
dTest
dFEM
d1
d2
d#
lp,h
lLT
r
C
design moment resistance predicted by
EC-1993-3
design moment resistance predicted by
AISI-S100
ultimate test moment in the central midthird portion
design strength predicted by AISI-S100
design strength predicted by EC-1993-3
ultimate test strength
ultimate FEM-predicted strength
initial stiffness observed during the test
initial stiffness predicted by FEM
outstand elements of hot-rolled angle
stiffener
minimum and maximum radius of
gyration
elastic section modulus relative to top
fibre
thickness of flange of hot-rolled beam
ISMB 150
thickness of web of flange of hot-rolled
beam ISMB 150
wall thickness of hot-rolled angle stiffener
weight per metre length
width of flange of hot-rolled beam ISMB
150
effective section modulus
section moduli with regard to
compression and tension flanges,
respectively
depth of neutral axis with respect to the
compression flange
position of neutral axis from respective
flange
maximum deflection at the mid-span in
the model tests
maximum deflection at the mid-span
predicted by FEM
maximum imperfection at the mid-span in
the transverse direction
maximum imperfection at the mid-span in
the longitudinal direction
elongation (tensile strain) after fracture
based on gauge length of 50 mm
relative slenderness
non-dimensional slenderness for lateral
torsional buckling
width reduction factor
stress ratio