International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 538
INVESTIGATION ON LATERAL- TORSIONAL BUCKLING
PERFORMANCE OF COLD-FORMED STEEL ‘C’ CHANNEL
SECTIONS
M. S. Deepak
1, R. Kandasamy
2 , Dr. R. Thenmozhi
3
1. P.G. Student- Government College of Technology, Coimbatore.
2. Head of the Department, Palani Andavaar Polytechnic college, Palani.
3 Associate Professor, Department of Civil Engineering, Thanthai Periyar Institute of
Technology, Vellore.
ABSTRACT The current cold formed steel sections such as C and Z sections are commonly used
because of their simple forming procedures and easy connections, but they suffer from certain
buckling modes. It is therefore important that these buckling modes are either delayed or
eliminated to increase the ultimate capacity of these members. In this paper, structural behavior
of cold-formed steel lipped „C‟ channel beams due to lateral buckling of beams and load carrying
capacity is evaluated. A unique test setup is fabricated for the transverse loading and testing.
Arrangements are made to define the restraint of warping and torsional boundary conditions, 3
specimens of 3m length with varying b/t and d/t ratios are tested for lateral- torsional buckling.
Vertical and lateral deflections are recorded using LVDT‟s and making use of the data
acquisition system. Strains are recorded using 350 ohms electrical resistance strain gauges at
both top and bottom lips, flanges and also in web portions at mid-span and quarter span.
Coupons are tested to determine the material properties. Load vs deflection curves are drawn.
This is followed through Finite Element Analysis using ANSYS software the experimental
results are compared with FEA results.
Key Words: Flexural-torsional buckling, Coupons test, Two point loading, Shear centre
Corresponding Author: M. S. Deepak
INTRODUCTION
Laterally stable steel beams can fail only by (a) Flexure (b) Shear or (c) Bearing,
assuming the local buckling of slender components does not occur. These three conditions are
the criteria for limit state design of steel beams. Steel beams would also become unserviceable
due to excessive deflection and this is classified as a limit state of serviceability.
Beams are used to support transverse loads and/or applied moment. Cold-formed steel
sections (CFS) such as, C-sections (channels), Z-shapes, angles, T-sections, hat sections, and
tubular members can be used as flexural members. In the design of cold-formed steel flexural
members, consideration should first be given to the moment-resisting capacity and the stiffness
of the member. It may be found that in many cases the moment of inertia of the section is not a
constant value but varies along the span length due to the non compactness of the thin-walled
section and the variation of the moment diagram.
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 539
The design method is discussed in this chapter follow the specifications as per AISI
S100. Second, the webs of beams should be checked for shear, combined bending and shear,
web crippling, and combined bending and web crippling.
In addition to the design features discussed above, the moment-resisting capacity of the
member may be limited by lateral-torsional buckling of the beam, particularly when the open
section is fabricated from thin material and laterally supported at relatively large intervals. For
this reason, flexural members must be braced adequately in accordance with the bracing
requirements prescribed in the North American Specification (NAS); otherwise a low design
moment has to be used. Furthermore, the design of flexural members can be even more involved
if the increase of steel mechanical properties due to cold work is to be utilized.
Fig. 1.1 Cold –Formed Sections used in Structural
Forming
In general, long-span, shallow beams are governed by deflection and medium-length
beams are controlled by bending strength. For short-span beams, shear strength may be critical.
Some of the main properties of cold- formed steel are as follows:
Lightness in weight and uniform quality
High strength and stiffness
Ease of prefabrication and mass production
Fast and easy erection and installation
More accurate detailing
Termite-proof and rot proof
Economy in transportation and handling
Advantages of CFS
More economical design can be achieved for relatively light loads thin sheet steel
products are extensively used in building industry.
Cross sectional shapes are formed to close tolerances and these can be consistently
repeated for as long as required. Unusual sectional configuration can be economically
produced by cold- forming operation.
Pre-galvanized or pre-coated metals can be formed, so that high resistance to corrosion.
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 540
Load carrying panels and decks can provide useful surfaces for floor, roof, and wall
constructions.
All conventional jointing methods, (i.e. riveting, bolting, welding and adhesives) can be
employed. They are usually light making it easy to transport and erect.
EXPERIMENTAL INVESTIGATION
Tensile Coupons test The development of an appropriate analytical model to predict the behavior of Cold-
formed steel (CFS) structural members requires a correct representation of the corresponding
material characteristics.
The tensile coupons consisted of 5 standard flat coupons cut along the longitudinal
direction of the channel sections, length 140mm width 20mm. the standard flat coupons were
dimensioned according guidelines provided by IS 1608:2005 and ISO 6892:1998, “Metallic
materials – Tensile Testing at Ambient Temperature”
The tensile coupons were tested in a kN UTM machine. The coupons were mounted in
the testing machine using the gripping devices and aligned with vertical axis of the machine. The
axial load was applied at a constant rate. Strains were recorded using strain indicator. The
Engineering stress-strain curves for all tensile coupons are drawn. A typical graph is shown in
graph- 1 for strip no 5. The average results of the mechanical properties from such experimental
stress-strain curves have been presented in table-1.
Table-1: Coupons Test Results
S. N
o.
Len
gth
(m
m)
Wid
th (
mm
)
Th
ick
nes
s
(mm
)
Yo
un
g's
mo
dulu
s 'E
'
x 1
0 5
(Mp
a)
f y
(Mp
a)
(0.1
%)
f y
(Mp
a)
(0.2
%)
Yie
ldin
g
Ty
pe
1 140 20 1.6 2.05 290 428 G
2 140 20 2.0 2.07 292 402 G
3 140 20 2.0 2.06 290 402 G
4 140 20 2.5 2.0 325 450 G
5 140 20 2.5 2.01 322 431 G
*G- Good
Graph-1: Stress-Strain Curve Strip-5
0
200
400
600
800
1000
0 0.0005 0.001 0.0015
STR
ESS
(Mp
a)
STRAIN
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 541
A. Before test B. After test
Figure- 1 Coupons Test
TERMS AND DEFINITIONS Lateral-torsional buckling: Buckling mode of a flexural member involving deflection normal to
the plane of bending and simultaneously with twist about the shear centre of the cross section.
Local buckling: Limit state of buckling of a compression element within a cross section.
Ultimate tensile strength (UTS), often shortened to tensile strength (TS) or ultimate strength is the
maximum stress that a material can withstand while being stretched or pulled before necking,
which is when the specimen's cross-section starts to significantly contract called as local
buckling.
Transverse loading: Forces applied perpendicularly to the longitudinal axis of a member.
Transverse loading causes the member to bend and deflect from its original position, with internal
tensile and compressive strains accompanying change in curvature.
Shear centre: Shear centre is known as the elastic axis or torsional axis. It is an imaginary point
on a section, where a shear force can be applied without inducing any torsion. In general, the
shear centre is not the centroid. For cross-sectional areas having one axis of symmetry, the shear
centre is located on the axis of symmetry. For those having two axes of symmetry, the shear
centre lies on the centroid of the cross-section.
Specimen details
Table-2: Specimen Size and Ratios
‘C‟ Channel sections
Boundary conditions : Warping arrested @ ends
S.
no
SIZ
E
hw
xbfX
dl
(mm
)
Thic
knes
s
(mm
)
Len
gth
(m
)
Sel
f w
eight
(kg)
Ratios
h/t
b/t
d/t
C1 100X50X20 1.6 3 8.44 62.5 31.25 12.5
C2 100X50X20 2 3 10.5 50 25 10
C3 100X50X20 2.5 3 13.1 40 20 8
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 542
A Unique Test Setup It is important that loading in thin gauge cold-formed steel sections are not applied at
their shear centre since it does not coincide with the longitudinal axis of their sections. In order to
investigate the flexural-buckling performance of cold-formed steel sections (CFS) a unified setup
is fabricated in the structural dynamics laboratory according to the requirement. Boundary
conditions are defined as specified in IS 800-2007 code of practice for general steel. Warping and
torsion restraints are provided by welding 3mm thick plates at the sides and fixing with „T‟
sections at the ends of each specimen. Proper bolted connections are used as fasteners wherever
required. The welding of plates at sides make a complete rigid joint, so that both compression and
tension flanges are arrested against warping. The total height of this specific experimental setup is
1.2m excluding the specimen on top of it. Stay-cables are used to tie up at the ends which served
dually for both safety and stability for further continuation of the experiment.
Loading frame and loads used The beam is to be loaded transversely at every 1/3
rd span, so at first a special frame is
designed that could be assembled every time to provide point loading in the beam, it could be
dismantled after each experiment. „S‟ shaped hook is used for hanging the loading platform
vertically downward. Third part is the loading platform a specially fabricated box that
accommodates the steel discs (loads). Those loading plates are of different weights likewise 50N,
100N, 150N and 200N. The end conditions are as defined in IS 800- 2007.
Procedure
The space requirements for conducting the test are ensured first. The schematic procedure of the
experiment of CFS beams for flexural-torsion buckling of beam is as follows, Simply supported
condition
Initially the flanges are warping arrested by welding 3mm thick flats at ends.
The surface of the specimen is cleaned for any dust and rust that may be present in it may
affect while strapping the strain gauges onto it. The one end of the wires is fixed to the
strain gauge terminals by careful soldering and the other ends are connected to the knobs
of the strain indicator.
Electrical resistance strain gauges at both top and bottom lips, flanges and also in web
portions at mid-span and quarter span. 5 parts.
The two point loading is important to get the constant moment and shear free zone.
The LVDT‟s are positions at 4 places
For vertical deflection
1. At the bottom side of the centre of the mid-span of the beam
2. 1/3rd
span of the beam
Similarly, for the lateral deflection
1. At the horizontal face side of the mid-span of the beam
2. 1/3rd
span of the beam
Now, loading is done, the starter of loading is with the loading box that it weighing
around 700N deflections is observed. The second stage of increment of loading is done
by adding steel discs (50N, 100N, 150N and 200N). Similarly the experiment is repeated
with increment of loads.
FEA is done using ANSYS workbench.
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 543
Calculations
With the dimensions of the specimen beams the depth of horizontal centroidal axis (y),
moment of inertia (Ix) and the section modulus (Sx) is calculated. Allowable bending moment
about X axis Mx = Sx * F
The geometric limitations are,
1. h/t < 183
2. b/t < 60
3. 0 < d/t < 20
4. 470 < θ < 90
0
5. 0.18 < d/t < 0.37
Loading scheme
Figure2- Line Diagram
Figure2- Warping And Torsion Restraints
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
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Figure3- Lateral- Torsional Buckling Of Beam Due To The Application Of Loads At Two Points
Figure4- Flexural- Torsion Buckling Failure of Beam
Flexural- torsion buckling tests on CFS channel sections (1.6mm) BEAM-C1
Specimen details
Span, L = 3 m
Depth of web, Dw = 100 mm
Breadth of flange, Bf = 50 mm
Depth of lip, Dl = 15 mm
Thickness,
Deflection measurements
T = 1.6 mm
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
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Table3 Deflection Readings (C1)
S
.No
S.
No
Wei
ght
(kg)
Load
(N
)
Deflection
measurements(mm)
Vertical Lateral
Mid span 1/3rd
span Mid span 1/3rd
span
0 0 0 0 0 0
1 40 392 5 3 2 1
2 80 785 11 6 5 3
3 120 1177 18 9 9 4
4 160 1570 24 12 11 6
5 180 1766 27 14 13 7
6 200 1962 29 15 14 7
7 210 2060 30 15 15 8
8 230 2256 33 17 16 9
9 250 2453 36 20 19 10
10 270 2649 45 22 20 11
11 290 2845 49 26 32 21
Table4- Strains at Various Sections
Section modulus calculation
E= f/ε fy= 428 Mpa
M= f x
Z
H= 100 mm
R= 4.76 mm
t= 1.6 mm
bf= 50 mm
d= 20 mm
R+ t= 6.36 mm
Beam-C1 Strain observations
@ 1/3rd
span @ Centre
fc w ft Lt lc fc w Ft
-7 10 -23 -36 -28 42 30 -21
-9 18 -43 -49 -63 51 70 -33
-11 35 -70 -50 -107 56 85 -57
-13 49 -94 -57 -154 60 90 -71
-17 56 -111 -65 -167 68 96 -84
-27 68 -121 -92 -176 73 99 -90
-61 80 -137 -96 -177 81 108 -103
-68 91 -142 -135 -188 87 118 -108
-89 96 -155 -226 -209 92 127 -113
-104 107 -160 -327 -236 95 136 -126
-116 127 -175 -695 -263 101 140 -144
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 546
Effective design width of the compression flange
F= 0.60x fy = 256.8 Mpa
W= H-2(R+t) = 87.28 Mm
W/t= 54.55
(Wx 2/t)(limit)= 6.81 < W/t
Use effective design width computed as follows,
b/t= 253/(f)0.5
x [1-(55.3/((W/t)(f)0.5
)
b/t= 14.79
∑Ay2= 1158827.88 mm
4
I (lips)= 676.352380 mm4
I (web)= 88635.6245 mm4
∑Ay(c-g)2= 783828.601 mm
4
Ix= 464311.26 mm4
Table5- Depth Of Neutral Axis
Element Area mm2
y'
mm
y2
mm2
Ay
mm3
Ay2
mm4
Top Flange 60 1 1 48 38
Top Corners 15 2 3 28 53
Top Lip 22 13 174 288 3791
Web 140 50 2500 6982 349100
Bottom
Corners 15 97 9374 1462 141587
Bottom Lip 22 99 9841 2165 214723
Bottom
Flange 60 87 7537 5178 449536
Total 333 16150 1158828
y= 49 mm
y=48.5377mm
Sx= 9566.872626
mm3
Allowable bending moment about X axis
Mx = Sx x F =2456772.89Nmm = 2.46 kNm
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
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Typical- Load vs Deflection graphs
Graph- 2: Graphs Showing Deflections During Increment Of Loads (Beam-1)
Figure-5: Y- Displacement
Figure-6: Z- Displacement
0
500
1000
1500
2000
2500
3000
0 50 100
Load
(N)
Deflection (mm)
VERTICAL DEFLECTION
middle
1/3rd span0
500
1000
1500
2000
2500
3000
0 10 20 30
Load
(N)
Deflection (mm)
LATERAL DEFLECTION
middle
1/3rd span
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 548
Figure-7: Von Mises Equivalent Stress
RESULTS
Table6- Maximum Deflection Results
LOAD AND
DEFLECTION EXPERIMENT
ANSYS
(RELIABLE)
S.
no
Ultimate
load (kg)
Ultimate
load (N)
Maximum Vertical
Deflection (mm)
Maximum Lateral
Deflection (mm)
Maximu
m
Vertical
Deflectio
n (mm)
Maximu
m Lateral
Deflectio
n (mm)
Mid
span
1/3rd
span
Mid
span
1/3rd
span Mid span Mid span
C1 290 2844.9 49.4 26 32 21 42.164 38.7
C2 460 4512.6 53.9 43.5 39 28.1 50.62 40.02
C3 760 7455.6 66 49 53 32 58.75 56.12
Table7-Maximum Strain Results
Maximum Strain
S.
no
Mid span 1/3rd
span
Top
Lip
Top
Flange Web
Bottom
flange
Bottom
lip
Top
Lip
Top
Flange Web
Bottom
flange
Bottom
lip
C1 -339 182 185 -367 -304
-
297 51 178 -218 -101
C2 -246 276 348 -299 -231
-
194 264 272 -156 -223
C3 -324 248 257 -349 -749
-
185 252 199 -381 -302
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 549
Table-8: Maximum Moments Obtained
No BEAM SIZE (mm) LENGTH
(mm)
ULTIM
ATE
LOAD
(N)
SECTION
MODULU
S Sx (mm3)
THEORITIC
AL
ALLOWABL
E BENDING
MOMENT
(KNm)
MAXIMUM
BENDING
MOMENT
DUE TO
WARPING
@ ENDS
(KNm)
1 100 X 50 X 20 X
1.6 3000 2844.9 9566.8726 2.45 2.85
2 100 X 50 X 20 X
2.0 3000 4512.6 11460.923 2.77 4.51
2 100 X 60 X 20 X
2.5 3000 7455.6 13668.77 3.53 7.46
Bar Chart -1 Showing The Increase In Load Carrying Capacities For Various Dl/T Ratios Of All
3 Beams
Bar Chart -2 Showing The Increase In Deflections At Mid-Span And 1/3
rd Span Both In Vertical
And Lateral Directions Of All 3 Beams
1 2 3
ULTIMATE LOAD (N)
2844.9 4512.6 7455.6
0
1000
2000
3000
4000
5000
6000
7000
8000
Load
(K
g)
ULTIMATE LOAD
0
20
40
60
80
1 2 3
Def
lect
ion
(mm
)
Specimen
DEFLECTION
MAXIMUM VERTICAL DEFLECTION @ MID SPAN (mm)
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 550
Inferences
The results from table-1 show that in tensile coupons the yield strength (@0.2% strain) is
around 400 Mpa for cold-formed steel sections which is comparatively more to that of the
hot rolled sections.
From table 5 it is clear that the specimens having different dl/t (i.e., depth of lip to thickness
ratio) and, same span length have greater load carrying capacities with greater deflections.
The Finite Element Analysis using ANSYS workbench software is reliable.
Table- 6 shows the maximum strain variations at various portions of the beam
The theoretical moment is calculated and the experimental moment is obtained.
Conclusion
The decrease in dl/t ratio show increase in load carrying capacity. And also there is increase
in deflection of beams.
Beam C3 have the maximum ultimate load carrying capacity
From table- 6 the mid span of the section when subjected to two point loading under flexure
have the maximum lateral-torsional buckling with more strain than the one- third span.
The failure of the beam is at the critical sections where the stresses are maximum, at points
of loading.
The optimum value to increase the depth of the lip section is 20mm by Effective Width
method.
The moment carrying capacity increases almost 40-45% by warping at ends. The load
carrying capacity is also increased up to 25-35% due to this warping.
Warping reduces the lateral buckling effect.
By trials very thin sections of 1.6mm thickness,10mm lip depth, 100mm web height and
60mm breadth of flange is not much satisfactory because the specimen failed due to web
crippling effect prior to lateral buckling because of its slenderness.
References [1] IS 801-1975 Code of practice for use of Cold-formed light gauge steel structural
members in general building construction.
[2] IS 811-1987 Specification for Cold-formed light gauge structural steel sections.
[3] IS 800-2007 Code of practice for general construction in steel.
[4] SP 6 (5) -1980 cold formed light gauge steel structures hand book.
[5] Anapayan, M. Mahendran, D. Mahaarachchi, T. „Lateral distortional buckling tests of a
new hollow flange channel beam‟, Thin-Walled Structures (2011)
[6] Ben young and Gregory J. Hancock. „Web Crippling Behaviour of Channels with Flanges
Restrained‟, Fifteenth International spaciality conference on Cold- formed steel
structures, Oct 19, 20 (2000).
[7] Roberto Martins Goncalves, Maximiliano Malite, carlos Eduardo javarom, „A theoretical
and experimental analysis of cold –formed steel shapes subjected to bending–channel and
simple lipped channel‟. Fifteenth International spaciality conference on Cold-formed
steel structures, Oct 19, 20 (2000).
[8] Xiao-ting Chu, Roger Kettle and Long-yuan L. „Lateral-torsion buckling analysis of
partial-laterally restrained thin-walled channel-section beams‟,
[9] Xiao-ting Chu, Roger Kettle and Long-yuan L. Journal of Structural Engineering (2006).
International Journal of Emerging trends in Engineering and Development
Issue 2, Vol.4 (May 2012) ISSN 2249-6149
Page 551
Cheng Yu- Weiming Yan ,Journal - Effective width method for determining distorsional
buckling strength of cold formed steel Flexural C and Z section‟. Thin Walled Structures
2011.
[10] G. J. Hancock. „Cold-formed steel sections to AISI specifications category‟
[11] Wen Yu, Ph. D., „Cold-formed steel structures design, analysis and construction‟ Wei
Tata Mc craw Hill Book Company (2002).