INVESTIGATION ON LATERAL- TORSIONAL BUCKLING PERFORMANCE OF

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.



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.



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



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

http://en.wikipedia.org/wiki/Stress_%28mechanics%29

http://en.wikipedia.org/wiki/Necking_%28engineering%29

http://en.wikipedia.org/wiki/Cross_section_%28geometry%29



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.



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



Page 544

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



Page 545

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



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



Page 547

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



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



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)



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).



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).

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INVESTIGATION ON LATERAL- TORSIONAL BUCKLING PERFORMANCE OF