Structures 30 (2021) 294–304
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Structures
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Flexural behaviour of cover plated CFS built-up beams composed of lipped
channels: Comparison of test and design strengths
M. Anbarasu a, M. Adil Dar b, Ahmad Fayeq Ghowsi c, A.R. Dar d, *
a
Department of Civil Engineering, Government College of Engineering, Salem, Tamil Nadu 636011, India
Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, 117576, Singapore
c
Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
d
Department of Civil Engineering, National Institute of Technology Srinagar, J&K 190006, India
b
A R T I C L E I N F O
A B S T R A C T
Keywords:
Cold-formed steel
Beams
Built-up section
Experiment
Flexural strength
Built-up members are efficient in developing adequate resistance against large load demands, and their efficiency
largely depends on how adequately the built-up sections are designed. This paper discusses the flexural
behaviour of cover plated cold-formed steel (CFS) built-up beams made up of lipped channels. Lipped channels
were placed at an adequate distance in the back-to-back arrangement and were connected at the flanges with
self-drilling screws by means of cover plates, on both the tension as well as the compression faces. Simply
supported end conditions were adopted in all the specimens. Both three-point loading as well as four-point
loading was considered to study the influence of moment gradient and constant moment loading of theses
built-up beam specimens. The sectional compactness of the channel section and the aspect ratio of the built-up
section were varied to assess the behavioural effect in the specimens with respect to the variations incorporated.
This study deals with the tests conducted to generate the test data. Prior to the testing of the specimens, tensile
coupon tests were carried out as per the relevant standards to acquire the actual material properties of the steel
used for the specimen fabrication. Both the European code as well as the North American Standards were used for
developing the theoretical strengths and were compared with the test results.
1. Introduction
Cold-formed steel (CFS) sections are being used extensively in the
primary framing elements of the structural systems, as they offer
numerous favourable features like light-weight construction, fast/
convenient installation, design flexibility with respect to availability of
large variety of cross-sectional shapes and sizes, and many more. To
overcome the limitation of the inherent local buckling instability in CFS
sections, many successful research attempts have delivered effective
solutions to the same [1,16,17,21–27].
Built-up members are gaining popularity in the construction sector,
particularly in CFS building segment, which is mainly due to the com­
bination of the favourable features in both CFS as well as in the adoption
of built-up members. Built-up members allow the cross-sectional
strength to be utilized in an effective manner, resulting in the efficient
utilization of steel, as a constructional material. The past research on
built-up flexural members has indicated immense potential in their
application. The web stiffening of the channel sections constructing the
flexural built-up members improved their bending strength by delaying
the local buckling failure [3,5,6,9]. The improvement in the stability of
the web resulted in the strength enhancement of such improved built-up
sections. However, the flexural stresses in the beams are always
maximum at the top compression flange particularly under four-point
loading. Therefore, the improvement in the flexural strength of such
improved built-up sections was not substantial [4,6,30,31] and needed
to be addressed differently. Many researchers attempted to address this
problem by working on the stiffening of the flange elements. Their
research identified that stiffening of the flange and around the flange
region enhances the flexural strength of the built-up beams
[7,15,28,29]. Furthermore, the stiffening of the flange improves the
performance of these beam sections under cyclic loading as well
[18–20]. All the measures to stiffen the individual elements improved
their local buckling resistance by a reasonable margin only, as the
thickness of the plate element (that could increase the sectional
compactness/flat width-to-thickness ratio) could not be increased
through these approaches. Also, the intermittent stiffening operation
* Corresponding author.
E-mail address: abdulrashid@nitsri.net (A.R. Dar).
https://doi.org/10.1016/j.istruc.2020.12.088
Received 23 August 2020; Received in revised form 24 November 2020; Accepted 21 December 2020
Available online 23 January 2021
2352-0124/© 2021 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
M. Anbarasu et al.
Structures 30 (2021) 294–304
Fig. 1. Details of the cross-section.
requires more efforts, quality workmanship to attain the desired per­
formance levels.
Since easy fabrication is one of the key features of CFS construction,
there is a need to develop an easy and convenient fix to the local
buckling resistance enhancement of the compression flange of the builtup beam section that is more susceptible to local buckling. Reinforcing
the compression flange of the beam section by additional plates (also the
addition of cover plates) increase its flexural strength by improving the
local buckling strength (due to reduction in the compression flange plate
slenderness). It also improves the sectional modulus of the built-up
section. Very limited research work has been carried out on this type
of strengthening approach, which is mostly numerical [11–13]. This
clearly indicates the need for more research (particularly experimental
ones) on these types beam configurations.
Given the capital required for buying a cold-rolling machine that can
fabricate complex geometries of the sectional profiles and time required
for the fabrication of such built-up members, a simple cross-sectional
geometry (cover plated CFS built-up beams), with a simple fabrication
process would substantially improve the buckling resistance of these
beam sections, and thereby enhance the quality of CFS construction at a
much lower cost. This can boost the practice of safe, economical and
durable construction, particularly in the developing countries. With this
aim in consideration, the authors have made an attempt to bring out
built-up flexural members (as shown in Fig. 1) that can perform better
than the conventionally adopted built-up beams, i.e., two channels with
their webs in contact, screwed through their webs. This paper presents
the flexural behaviour of cover plated simply supported CFS built-up
beams made up of lipped channels. Lipped channels were placed at an
adequate distance in the back-to-back arrangement and were connected
at the flanges with self-drilling screws by means of cover plates, on both
the tension as well as the compression faces. To study the influence of
moment gradient and constant moment loading of theses built-up beam
specimens, both three-point loading and four-point loading were
considered. The sectional compactness of the channel section as well as
the aspect ratio of the built-up section was varied to evaluate the
behavioural effect in the specimen. Lastly, the European code as well as
the North American Standards were used for developing the theoretical
strengths and were compared with the test results.
Fig. 2. Plates welded at the ends to avoid warping failure.
2.1. Preparation of the test specimens
Six specimens were prepared to complete the experimental compo­
nent of this investigation. Each specimen comprised of two lipped
channel sections that were placed at an adequate distance in the back-toback arrangement. The channels as well as the cover plates were cut
from the steel sheets using a shearing machine. The cold forming of
lipped channels was carried out using a press brake that was based on
hydraulic operations. The corner radius at the flange-web junction and
at the flange-lip junction was 2 mm. Once the various components of the
built-up section were cut and cold-formed, the channels were connected
at the flanges with self-drilling screws of 6.4 mm diameter, by means of
cover plates (of thickness 1.6 mm), on both the tension as well as the
compression faces. The screws were connected at mid-point of the
flanges along the length of the beams at a spacing of 85 mm. Near the
supports the longitudinal spacing was reduced to avoid bearing failure.
At the end of the specimens, a plate of size equal to the width and depth
of the section was welded at the flange ends and the mid-point of the
cover plates, as shown in Fig. 2. The nominal thickness of this plate was
1.6 mm. The reason behind the incorporation of these plates was to
prevent warping of the cross-section. Additional plates were welded to
the top cover plate to reduce the stress concentration and ensure more
uniform distribution of forces, as shown in Fig. 3. Since one of the ob­
jectives of this investigation was to study the influence of moment
gradient and constant moment loading of theses built-up beam speci­
mens, both three-point loading as well as four-point loading were
considered accordingly. This resulted in the specimens being catego­
rized into two groups, first the three-point loading group, and second the
2. Experimental investigation
This section presents the various details of the experimental inves­
tigation, and is given in the sub-sections below.
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Structures 30 (2021) 294–304
Fig. 3. Location of the loading plates to avoid punching failure.
Fig. 4. Tensile coupons prepared for the material testing.
four-point loading group. In the three-point loading group, the crosssectional aspect ratio (B/D) was varied at 1.25, 1.5 and 1.75, with
constant width of the built-up section, while as the span was fixed at 1.2
m. In the four-point loading group, the sectional compactness of the
built-up section (that was governed by the slender web element of the
channel section) was varied as 50, 60 and 70, with a constant crosssectional aspect ratio of 1.5, while the span was fixed at 2.4 m. Three
values of sectional compactness were considered based on the limiting
value of sectional compactness being 60, proposed by the current stan­
dards [2,10]. The other two values were considered in such a way that
one value higher than the limited value, and the other lower than the
one. In both these cases, the moment span was fixed at 1.2 m. The
specimens were labelled such that each detail indicates the specimen
parameter affecting its behaviour, e.g., in the specimen 3PL-140-112-15,
3PL represents three-point loading, 140 indicates the depth of the built-
up section in mm, 112 indicates the width of the built-up section in mm
and 15 represents the depth of the lip in mm.
2.2. Coupon testing for material property assessment
IS 1608 – 2005 [14] was referred for obtaining the details regarding
the preparation of the tensile coupons, and three coupon specimens
were prepared as per the recommendation of the material testing stan­
dard, as shown in Fig. 4. Since the corner radius was small and press
braking operation was adopted for cold-rolling, the coupon specimens
were extracted longitudinally from the steel sheet. A similar procedure
has been adopted previously [4,8]. The material testing was carried out
in the Structural Engineering Laboratory of Government College of En­
gineering Salem. The flange region of the coupon was clamped between
the upper and lower clamp of the Computerized Universal Testing
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of CFS members. Accordingly, the geometric imperfections were
measured and noted, prior to the testing of specimens. The imperfections
were noted along the midpoint of the bottom cover plate and the web to
get these values in two orthogonal directions (both longitudinal as well
as transverse), as shown in Fig. 6. Table 1 presents the magnitudes of
imperfections noted. An optical theodolite along with a calibrated dig­
ital vernier caliper were used for the measuring the imperfections. The
maximum amplitude of the measured geometric imperfection at the
mid-span in the two said orthogonal directions viz., δ1 & δ2 were noted
as 1/2894 mm and 1/2913 mm, respectively. These imperfections
belonged to specimen 3PL-168-112-15. The minimum amplitude of the
measured imperfections at the same location and in the same directions,
belonged to the specimens 4PL-168-112-15 and 3PL-196-112-15, and
were noted as 1/3495 and 1/3724 respectively.
Fig. 5. Typical stress vs. strain plot obtained from the material testing.
2.4. Test setup and loading
A heavy-duty loading frame of 50 Tonnes capacity (as shown in
Fig. 7) was used for the testing of the specimens. Both four-point loading
tests as well as three-point loading tests were performed under the same
loading set-up. For transferring the single point load from the hydraulic
jack to the two loading points in the four-point loading, a rigid spreader
beam was used. Simply supported end conditions were considered for
the testing both these loading type specimens. To measure the vertical
displacement under the loading points as well as at the mid-point of the
beam specimens, LVDTs were used. The loading was applied by means of
a hydraulic jack and the loading was applied slowly, until the failure.
Width of loading plate and the bearing plate was 100 mm.
2.5. Test results and discussion
Fig. 8a shows the load vs. displacement plots of the three-point
loading group specimens. The specimen 3P-140-112-15 carried a peak
load of 18.75kN, and the corresponding displacement was noted as 2.81
mm. Predominant local buckling of the flange under and around the
loading point was observed, as shown in Fig. 9. However, minor local
buckling of the web portion near to the flange-web junction was also
noted. In specimen 3P-168-112-15, an ultimate load of 22.01kN against
the corresponding displacement of 2.17 mm was noted. Local bucking
failure like the previous case was observed, as shown in Fig. 10. Since
the web depth in this case was higher than the previous case, the
involvement of the web buckling was relatively higher. The specimen
3P-196-112-15 resisted a maximum load of 26.30kN, with the corre­
sponding displacement being 1.57 mm. Local buckling of both flange
and web was observed, as shown in Fig. 11. Clearly the web depth
influenced the involvement of the web buckling in the observed failure
modes. Also, the post peak branch of the plots got steeper, as the web
depth increased.
The load vs. displacement curves of the four-point loading group
specimens are presented in Fig. 8b. The ultimate load resisted by the
specimen 4P-120-80-15 was 11.48kN, with the corresponding
displacement of 12.32 mm. The displacements noted in four-point
loading cases were higher than the three-point loading cases, mainly
due to larger span in the former cases. The displacements in the fourpoint loading cases were nearly double of that of in the three-point
loading cases. Local buckling in the compression region of the built-up
section within the moment zone, prominent in the cover plate, in be­
tween the fasteners was noted, as shown in Fig. 12. In the specimen 4P144-96-15, a peak load with the corresponding displacement of 16.63kN
and 10.29 mm was noted. Like the previous case, local bucking halfwave lengths between the fasteners within moment zone was again
observed, as shown in Fig. 13. Since the depth of the built-up section was
higher, higher bending stresses were experienced, resulting in higher
degree of local buckling failure being observed. The maximum load
carried by the specimen 4P-168-112-15 was noted as 21kN, with the
corresponding displacement of 9.52 mm. The local buckling of the cover
Fig. 6. Details of the geometric imperfection measurement.
Table 1
Geometric imperfections measured.
Specimen
3PL-140–112-15
3PL-168–112-15
3PL-196–112-15
δ1/L
δ2/L
Specimen
δ1/L
δ2/L
1/3213
1/3367
4PL-120–80-15
1/3004
1/3325
1/2894
1/2913
4PL-144–96-15
1/3457
1/3337
1/3212
1/3724
4PL-168–112-15
1/3495
1/3215
Machine. The coupons were loaded until their fracture. The load vs. axial
elongation data obtained from the test was used to determine the stress
and strain data for the data plotting, as shown in Fig. 5. The average
values of the Young’s Modulus, yield stress, peak stress and elongation
obtained were 215GPa, 250 MPa, 364.33 MPa and 23.75% respectively.
2.3. Geometric imperfections
CFS sections due to their low wall thickness are susceptible to geo­
metric imperfections. Therefore, the measurement of these imperfec­
tions is important as they influence the local as well as global behaviour
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Fig. 7. Test set-up details (Four-point loading case).
Fig. 8. Load vs. displacement plots.
Fig. 9. Local buckling failure in 3P-140-112-15.
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Fig. 10. Local buckling failure in 3P-168-112-15.
Fig. 11. Local buckling failure in 3P-196-112-15.
Fig. 12. Local buckling failure in 4P-120-80-15.
Fig. 13. Local buckling failure in 4P-144-96-15.
plate, as observed in the previous two cases was observed in this case as
well. It was further noted that the magnitude of the local buckling in
between the fasteners within the moment zone was large and dropped
post the moment zone (within the shear zone), as shown in Fig. 14. The
magnitude of the local buckling wave between the fasteners was higher
due to constant moment within the moment zone. In the four-point
loading group specimens, a small deviation in the stiffness of the load
vs. displacement plots was observed, at around a displacement of
approximately 7 mm. This may be due to the formation of multiple local
buckling waves between the fasteners on the compression side cover
plate. Fig. 15 shows the three-point loaded specimens after failure.
role in governing its stability. It primarily controls the out-of-plane
displacement in flexural members. In the three-point loading cases, on
varying the aspect ratio from 1.25 to 1.5, the flexural strength changed
from 11.25kNm to 13.21 kNm, which resulted in a flexural strength
improvement of 17.42% as shown in Fig. 16a. On varying the aspect
ratio further from 1.5 to 1.75, the flexural strength changed to
15.78kNm, with a flexural strength improvement of 19.45%. The
improvement in the flexural strengths due to the variation in the aspect
ratio attributes to the increase in the width of the flexural members, that
improved their second moment of area, and thus improved their flexural
strengths. The percentage improvement in the flexural strength was
slightly higher in the latter case (when the aspect ratio was 1.75), as the
second moment of area was higher in that case. Also, the sectional
compactness in both these cases were constant.
2.5.1. Effect of aspect ratio on the flexural strength
The cross-sectional aspect ratio of the flexural member plays a vital
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Structures 30 (2021) 294–304
Fig. 14. Local buckling failure in 4P-168-112-15.
Fig. 15. Failed specimens of three-point loading cases.
Fig. 16. Effect on the flexural strength of the specimens.
2.5.2. Effect of sectional compactness on the flexural strength
The sectional compactness is a key parameter that significantly in­
fluences the behaviour in thin-walled members. It controls their local
buckling response, which mainly dominates the performance of such
members. In the four-point loading cases, on varying the sectional
compactness of the channel section from 50 to 60, the flexural strength
changed from 6.89kNm to 9.98kNm, that resulted in a flexural strength
enhancement of 44.84%, as shown in Fig. 16b. This enhancement in
flexural strength despite a small reduction in the sectional compactness
was primarily due to the increase in the depth of the beam cross-section,
that substantially improves its second moment of area, which drastically
enhances the flexural performance of these members. Also, the local
buckling occurs under compressive stresses, which occurs above the
neutral axis. This makes only half of the cross-section effective for the
local buckling effect. On varying the sectional compactness further from
60 to 70, the flexural strength changed to 12.6kNm, with a flexural
strength improvement of 26.25%. The reason behind this improvement
is the same as was in the previous case. However, the percentage
improvement in the flexural strength in the former case (when sectional
compactness was changed from 50 to 60) was about 1.75 times that of in
the latter case, and was mainly as the sectional compactness limit (60)
proposed by the current codes was exceeded.
2.5.3. Effect of aspect ratio on the stiffness characteristics
Stiffness characteristics are important features in structural mem­
bers, particularly in flexural members, essentially from serviceability
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Structures 30 (2021) 294–304
Fig. 17. Effect on the stiffness characteristics of the specimens.
improvement in the stiffness in the latter case (when sectional
compactness was changed from 60 to 670) was about 1.3 times that of in
the former case. Furthermore, the stiffness of three-point loading cases
was substantially higher than the four-point loading cases, primarily due
to smaller beam spans in the former cases.
2.5.5. Strength-to-weight ratio performance
The strength-to-weight ratio performance of CFS members is gener­
ally higher than the hot-rolled steel members, and for these reasons the
former is preferred over the latter, in moderately loaded structures. One
of the primary objectives in the CFS research is to improve the efficiency
of CFS sections by adopting different means to achieve the same. Fig. 18
shows the strength-to-weight comparison of different specimens. The
strength-to-weight ratio performance of the three-point loading cases
was better than the four-point loading cases, and was therefore, mainly
due to higher stiffness that was achieved due to lower beam spans, that
enabled them to carry higher loads. In the three-point loading cases, on
varying the aspect ratio from 1.25 to 1.5, the strength-to-weight ratio
changed from 1.04kNm/kg to 1.13 kNm/kg, which resulted in an
improvement of 8.65% as shown in Fig. 18. On varying the aspect ratio
further from 1.5 to 1.75, the strength-to-weight ratio changed to
1.26kNm/kg, with an improvement of 11.5%. The reason behind this
percentage enhancement and the order of enhancement is the same as
that of behind the flexural strength enhancement.
In the four-point loading cases, on varying the sectional compactness
of the channel section from 50 to 60, the strength-to-weight ratio
changed from 0.37kNm/kg to 0.48kNm/kg, that resulted in a perfor­
mance enhancement of 29.73%. On varying the sectional compactness
further from 60 to 70, the strength-to-weight ratio changed to 0.54kNm/
kg, with an improvement of 12.5%. The reason behind this percentage
enhancement and the order of enhancement is the same as that of behind
the flexural strength enhancement.
Fig. 18. Effect on the strength-to-weight ratio of the specimens.
consideration. The stiffnesses of the specimens were obtained as the
ratio of the load resisted by them until their linear part of the load vs.
displacement plots, to their corresponding displacements. In the threepoint loading cases, on varying the aspect ratio from 1.25 to 1.5, the
stiffness changed from 8.72kN/mm to 11.44 kN/mm, which resulted in
an improvement of 31.19% as shown in Fig. 17a. On varying the aspect
ratio further from 1.5 to 1.75, the stiffness changed to 19.14kN/mm,
with an improvement of 67.30%. The improvement in the stiffness due
to the variation in the aspect ratio attributes to the increase in the width
of the flexural members, that improved their stability, and thus
improved their stiffness characteristics. The percentage improvement in
the stiffness was more than double in the latter case (when the aspect
ratio was 1.75), as the second moment of area was higher in that case.
2.5.4. Effect of sectional compactness on the stiffness characteristics
In the four-point loading cases, on varying the sectional compactness
of the channel section from 50 to 60, the stiffness changed from 1.43kN/
mm to 1.95kN/mm, that resulted in a strength enhancement of 36.36%,
as shown in Fig. 17b. This enhancement in flexural strength despite a
small reduction in the sectional compactness was primarily due to the
increase in the depth of the beam cross-section, that substantially im­
proves its second moment of area, which drastically enhances the stiff­
ness characteristics of these members. On varying the sectional
compactness further from 60 to 70, the stiffness changed to 2.88kN/mm,
with an improvement of 47.69%. The reason behind this improvement is
the same as was in the previous case. However, the percentage
3. Design strengths
The comparison of the test strengths with the ones computed using
the current standards on CFS members was one of the key objectives of
this study. Accordingly, the design strengths of these built-up beams
were quantified for the same. Both American Standards as well as Eu­
ropean Standards were adopted. In the European Standard, the versatile
Effective Width Method was adopted, as that has been accepted
worldwide with good reliability. However, in the North American
Standard, the recently developed Direct Strength Method was imple­
mented, as the sections were open sections and were prismatic as well.
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The primary design equations used in these standards are given below.
3.3. For distortional buckling
3.1. Design equations specified in AISI-S100-16 [2] (Direct strength
Method)
The elastic distortional buckling moment resistance (Mcrd) shall be
determined as follows:
Mcrd = Sf *Fcrd
The procedure for the design strength determination of flexural
members is presented below:
For lateral torsional buckling of doubly symmetric sections (open
cross-section);
Fcre
Cb *π2 *E*d*Iyc
=
)2
(
Sf * Ky *Ly
Where
Fcrd = β
(1)
For λd > 0.673
[
)0.5 ](
)0.5
(
Mcrd
Mcrd
Mnd = 1 − 0.15
My
My
My
(3)
My = Sfy *Fy
3.4. Design equations specified in EN1993-1-3 (effective width method)
(4)
The critical elastic moment of the beam cross-section shall be
determined using the following equations, Mcr = Cb
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
(
)̅
√
2 EI
√ π 2 EI y
π
W
√(
(13)
)2 GJ +
(LKW )2
LKy
Where, Sf is the elastic cross-sectional modulus of the gross-section,
with reference to the extreme compression fibre, Fcrl is the local buck­
ling stress at compression fibre (extreme), and is given by
(5)
Where EIy, EIw and GJ are the flexural rigidity, warping rigidity and
torsional rigidity respectively, about the major axis. The factors ky and
kw are conservatively taken as unity. Also the constant Cb is considered
as unity.
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
3
Kσ = 0.5 + 0.83 (bp,c /bpl )2
√̅̅̅̅̅
f
b /t
λp = σyb = p √̅̅̅̅
Where, K is the plate buckling coefficient which is given in the Ap­
pendix 1 of the AISI [2], E = Young’s modulus of steel, t is the wall
thickness of the element, µ is the Poisson’s ratio of steel, w is the flat
width of the element.
The nominal flexural resistance (Mnl) that considers the local
buckling and global buckling interaction shall be determined by using
the following equations:
For λl ≤ 0.776
Mnl = Mne
For λl > 0.776
[
(
)0.4 ](
)0.4
Mcrl
Mcrl
Mnl = 1 − 0.15
Mne
Mne
Mne
(12)
Sfy is the section modulus (elastic) of gross cross-section, relative to
the extreme fibre in the first yielding.
The beam’s local buckling moment resistance (Mcrl) shall be gov­
erned by the lowest buckling stress among the cross-sectional elements,
with reference to the extreme compression fibre, as follows:
π2 *E ( t )2
12(1 − μ2 ) w
(11)
Where
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
λd = My /Mcrd
3.2. For local buckling
Fcrl = K
(9)
(10)
Mnd = My
Where, Mcre is the critical lateral-torsional buckling moment resistance,
My is the yield moment resistance, Mp is the plastic moment resistance,
Zf is the plastic modulus of the beam cross-section.
Mcrl = Sf *Fcrl
Kφfe + Kφwe + Kφ
Kφfg + Kφwg
β is conservatively considered as unity; Kфfe is the rotational stiffness
provided to the flange-web junction by the flange, Kфwe is the rotational
stiffness provided to the flange-web junction by the web, Kф is the
rotational stiffness to the flange-web junction provided by any
restraining element like brace, panel, sheathing, Kфfg is the geometric
rotational stiffness demand of flange from the flange-web junction,
Kфwg is the geometric rotational stiffness demand of the web from the
flange/web junction.
The nominal flexural resistance (Mnd,) shall be determined as
follows:
For λd ≤ 0.673
Where, Fcre is the elastic buckling stress, Cb is the constant that is
conservatively considered as unity, d is the sectional depth, Iyc is the
second moment of area of the full cross-section’s compression region
about the centroidal axis, E = Young’s modulus of steel, Ky = effective
length factor, Ly = unbraced member length for flexure about y axis.
The nominal strength [resistance], Mne, considering inelastic flex­
ural reserve capacity is given by
For Mcre > 2.78My ,
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
̅
/
) My Mcre − 0.23
(
Mne = Mp − Mp − My
(2)
0.36
For 2.78My > Mcre > 0.56My ,
(
)
10
10My
Mne = My 1 −
9
36Mcre
(8)
cr
28.4ε
kσ
λp,b − 0.055(3+Ψ)
ρ=
(6)
λp,b
2
Mrd
Mb,Rd = χltγm1
= χlt Wy
fy
γm1
(7)
(14)
In which χlt is defined as follows:
If λlt ≤0.4, χ lt = 1.0
If λlt >0.4, χ lt = 1.0/(φLT+(φ2LT + λ2LT )0.5)Where,
φLT = 0.5(1+ɑ(λlt -0.2) + λ2LT )
λ2LT =(Wy fy /Mcr)0.5Where, Wy is the appropriate elastic sectional
modulus depending on its class, Wel for class 3 and effective section
Where
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
λl = Mne /Mcrl
Mne is the nominal flexural resistance for lateral-torsional buckling,
Mcrl is the critical local buckling moment resistance.
302
M. Anbarasu et al.
Structures 30 (2021) 294–304
and the aspect ratio of the built-up section were varied to assess the
behavioural effect in the specimens with respect to the variations
incorporated. Both the European code as well as the North American
Standards were used for developing the theoretical strengths and were
compared with the test results. Some prominent results are given below:
Table 2
Comparison of test results and FEA results.
Specimen
Test
PuTest
3P-140-11218.75
15
3P-168-11222.01
15
3P-196-11226.3
15
4P-120-8011.48
15
4P-144-9616.63
15
4P-168-11221
15
Mean
Standard deviation
FEA
MtTest/
W
MtTest
PuFEA
MtFEA
MtTest/
MtFEA
11.25
19.53
11.72
0.96
1.04
13.211
23.35
14.01
0.94
1.13
15.78
27.54
16.52
0.96
1.26
6.89
12.35
7.41
0.93
0.37
9.98
17.35
10.41
0.96
0.48
22.09
13.25
0.95
0.54
12.6
• Both the aspect ratio (by varying the transverse spacing between
channels at constant depth) as well as the sectional compactness of
the channel sections (by varying the sectional depth at aspect ratio)
influence the flexural behaviour of cover plated CFS built-up beams.
• The sectional compactness effects the flexural strength more than the
aspect ratio. However, the influence of the sectional compactness is
dominant provided the sectional compactness doesn’t exceed the
limiting value recommended by the current codes.
• The stiffness characteristics are affected by both the variation in the
aspect ratio as well as the sectional compactness, and this relation­
ship is proportional.
• Local buckling in the compression zone was the primary mode of
failure observed in the cover plated CFS beam specimens, and was
noted near the loading points.
• The aspect ratio influences the stiffness characteristics more
compared to the sectional compactness. This is primarily due to
involvement of local buckling behaviour on the sectional compact­
ness of the built-up section that controls the structural behaviour of
thin-walled members.
• Both the strength as well as the stiffness in three-point loading cases
were higher than that of the four-point loading cases. This behaviour
was observed mainly due to the moment gradient in the former cases
and constant moment in the latter cases. The stiffness was higher in
the three-point loading cases, primarily due to smaller spans.
• The strength-to-weight ratio in the three-point loading cases was
higher than the four-point loading cases, and again attributed to
0.95
0.01
modulus Weff, for class 4 cross-sections, fy is the yield strength of steel,
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
kσ is the relative buckling factor, ε is the ratio 235/fyb with fyb in N/
mm2, Ψ is the stress ratio, t is the sectional thickness, σcr is the elastic
critical buckling stress of the plate element.
The comparison of the test strengths with the strengths predicted by
the current codes are given in Table 2 and Fig. 19. Both Table 3 and
Fig. 19 indicates that both current codes are unconservative in pre­
dicting the flexural strengths of the cover plated CFS beams comprising
of lipped channel sections. One of the reasons behind such an uncon­
servative prediction may be that the role of the transverse spacing be­
tween the two lipped channel sections could not be considered in the
design. Also, the interaction of the cover plate with the flange was not
accounted for in the design strengths quantified as per the current codes.
Both these reasons behind the unconservative design strength pre­
dictions need to be assessed individually and collectively. Furthermore,
the extent of un-conservativeness was higher in the European code, as
their design approach is different from that of the North American
Standard.
Table 3
Comparison of test strengths and design strengths.
4. Conclusions
This study discussed the flexural behaviour of cover plated CFS builtup simply supported beams made up of lipped channels, under both
three-point as well as four-point loading. The influence of moment
gradient and constant moment loading on theses built-up beam speci­
mens was investigated. The sectional compactness of the channel section
Specimen
Test
EC3 [10]
NAS
Test/EC3
Test/NAS
3P-140-112-15
3P-168-112-15
3P-196-112-15
4P-120-80-15
4P-144-96-15
4P-168-112-15
Mean
Standard deviation
11.25
13.21
15.78
6.89
9.98
12.6
12.34
16.72
20.39
8.46
12.25
16.72
11.41
14.06
18.24
7.45
10.27
13.44
0.91
0.79
0.77
0.81
0.81
0.75
0.81
0.06
0.99
0.94
0.87
0.92
0.97
0.94
0.94
0.04
Fig. 19. Effect on the stiffness characteristics of the specimens.
303
M. Anbarasu et al.
Structures 30 (2021) 294–304
larger flexural strengths and smaller spans in the former cases
compared to the latter one.
• Both the European code as well as the North American Specification
over predicted the strengths of these beam specimens and was so as
the transverse spacing is not accounted for in the design strength
approach.
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The authors are currently working on the parametric study on the
similar configuration to develop a large pool of data for the development
of reliable design equations.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
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