icramid_59

ABSTRACT

Effective length factor of CFS lipped channel beams

subjected to flexure are given in AS/NSZ 4600, Euro code Part

1.3 and BS 5950, Part V taking into account their buckling

phenomena. The coefficients are given for boundary conditions

considering the effect of torsion and warping restraint. The effect

of torsion and warping restraints is treated by defining the range

of values for the coefficients. Lateral torsion buckling of the CFS

beams greatly influences the effective length factors. 16 CFS

lipped channel beams have been taken for the study with depth

of 100mm, flange width 50mm and lip size varies from 10mm to

20mm.Experimental investigation has been carried out to verify

the coefficients for the defined boundary conditions. The

influence of flange width and lip size on the buckling length has

been investigated. The results are compared with the Indian code

provisions for hot rolled beams.

Key words: Boundary Conditions, Effective length, Torsion and

Warping Restraints.

I. INTRODUCTION

Cold-formed sections (CFS) being thinner than hot rolled

sections, have different behaviors and different modes of failure.

Thin walled sections are characterized by local instabilities that do

not lead to normally lead to failure, but are helped by post-bucking

strength; hot rolled sections rarely exhibit local buckling. The

properties of CFS are altered by the forming process and residual

stresses are significantly different from hot rolled.

The thicknesses of individual plate element of CFS are

normally very small compared to their widths, so local buckling may

occur before section yielding. However, the presence of local

buckling of an element does not necessarily mean that its local

capacity has been reached. If such an element is stiffened by other

elements on its edges, it possesses still greater strength called “Post

buckling strength”. Local buckling is expected in most CFS’s and

often ensures greater economy than a heavier section that does not

buckle locally.

In case of unbraced beams, the possibility of lateral

torsional buckling arises, and this factor must be taken into account

while determining the strength of beams. Basis of Simple bending

theory with modifications to take into account of local buckling is

realistic and applicable over a wide range of beam design situations.

Beams having unsymmetrical Cross-Sections cannot be analyzed

with simple bending theory approach which does not have realistic

estimate of beam behavior. It such beams are not restrained

continuously along their lengths, these must be analyzed taken into

account the unsymmetrical nature of the behavior.

Fig.1. Beam of unsymmetrical Cross-Section

Due to the effective moments, Mx and My the stress at any

point on the Cross Section

σ=MxY/Ix+MyX/Iy ……………………………..…………... (1)

It is observed that if Ixy is zero, then x-z and y-y are the

Principal axes and the effective moments become equal to the real

moments. Bending tresses vary linearly with the distance normal to

this axis and deflections take place normal to the axis.

For the unsymmetrical beam, deflections are normal to the

Zero stress axis. It is interesting to observe that for this section, the

application of a vertical load produces a horizontal deflection greater

than the vertical deflection. If the load did not act through the shear

centre, or centre of twist, then torsion would arise and cause the

section to twist.

II. LOCAL BUCKLING

For Laterally stable beams, local buckling is the major

weakening effect. If the section is thin walled, then local buckling

can arise in the compression elements and to a lesser extent in the

webs.

Fig.2. Local buckling in a beam compression element

INDIAemail id: [email protected]

email id: [email protected]. Associate Professor, Dept of Civil Engineering, Government College of Technology, Coimbatore,

1. Research Scholar, Principal in-charge, Arulmigu Palaniandavar Polytechnic College, Palani-INDIA

Kandasamy.R1., Thenmozhi.R2

Restrained Boundary Conditions”

“Experimental Investigation of Buckling Lengthof CFS Lipped Channel Beams under

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International Conference on Recent Advances in Mechanical Engineering and Interdisciplinary Developments [ICRAMID - 2014]

ISBN 978-93-80609-17-1

Fig.3 Minimum buckling coefficients for a web under combined

axial load and bending

Fig 3.Shows the buckling coefficients of the plate elements

subjected to combined bending and axial loads, as occurs in the webs

of beam

For webs under pure bending, the minimum buckling

coefficient is approximately 23.9 as compared with four for a

uniformly compressed plate.

The expression of buckling stress, i.e.,

PCR = 185000 (t/b)2 ………………………….…………..….. (2)

Then the critical stress is equal to the yield stress in the

case of such a web if the web depth-to-thickness ratio is of the order

of 120. However, as in the case of uniformly compressed elements,

imperfections can cause web local buckling to have effects at around

half of this depth-to-thickness ratio. In BS5950: Part 5 a more simple

method is used, in which web stress is limited to a certain value

which reduces the section capacity to take account of the web local

buckling.

The limiting value of web stress given in BS 5950: Part 5 is

Po = [1.13 – 0.0019 D/t (Ys/280)2]Py………………………..... (3)

With the provision that Po cannot be greater than Py, This expression

is a modification of a similar type of expression used in the AISI

design code 1980.

Where Po = limiting web stress

Py = yield stress

D = Web depth

t = material thickness

the above equation is applicable if D/t ratio is large (i.e. D/t>68)

If D/t <68, and Py = 280 N/mm2, limiting stress becomes

greater than the yield stress, and yield stress is used in the analysis.

For large D/t ratios, the limiting stress becomes progressively smaller

than the yield stress as the D/t ratio increases, thus indicating more

severe local web buckling effects. This limiting stress is then used in

evaluation of the compression elements.

III. PROPENSITY FOR FLEXURAL BUCKLING

CFS sections are normally thin and consequently have a

low torsional stiffness. Many of the sections formed by cold-forming

are singly symmetric with their shear centres eccentric from their

centroids, as shown in Fig.4 (a). If a thin-walled beam loaded

through the shear centre produce flexural deformation without

twisting, any eccentricity of load from shear centre generally

produces considerable lateral–torsional deformations in a thin-walled

beam, as shown in Fig.4 (b). Hence, beams require torsional

restraints either at internals (or) continuously along them to prevent

lateral-torsional deformations.

Beams such as channel and Z sections and girts may

undergo lateral-torsional buckling because of their low torsional

stiffness. Hence, design equations to account for lateral-torsional

buckling of beams are described in section C3 of the AISI

specification.

Fig.4 (a) Torsional deformations: eccentrically loaded channel beam

Fig.4 (b) Torsional deformations: axially loaded channel column

IV. EVALUATION OF MOMENT CAPACITY

The moment capacity of the Cross-section is determined on

the basis that the maximum compressive stress on the section is Po.

This leads to two possible types of failure analysis depending on the

situation on the tension side of the Cross-Sections as indicated in

Fig.5

Fig.5 Failure criteria for Laterally Stable beams

(a) Failure by compression yield-tensile stress elastic

(b) Tensile stresses reach yield before failure-elastoplastic

stress distribution

If the geometry of the effective Cross-Section is such that the

compressive stress reaches Po, before the maximum tensile

stress reaches the yield stress, as indicated in fig 4(a), then the

moment capacity is evaluated using the product of compression

section modulus and Po, i.e.,

Mc = Po x Zc ………………………………………….. (4)

Where Zc = Compression section modulus of the effective

Cross-Section. This situation will occur in the case of members

which have wide tension elements or which have substantially in

effective compression elements. If on the other hand, the tensile

stresses reach before Po is attained on the compression side, as in Fig

4(b) the designer is allowed to take advantage of the plastic

redistribution of tension stresses and thus obtain higher predictions of

moment capacity then would be the case if first yield were taken as

the criterion.

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V. LITERATURE REVIEW

Lateral buckling, sometimes called lateral-torsional

buckling, generally occurs when a beam which is bent about its

major axis develops a tendency to displace laterally, i.e.,

perpendicularly to the direction of loading, and twist. This behavior

is shown in Fig.6

Fig.6 Lateral buckling of an I-section beam

Many beams used in Cold-Formed Construction are

restrained against lateral movement, in many cases continuously

restrained by roof (or) wall cladding. In other cases, restraint is

afforded by other members connected to the beam in question or by

bracing such as anti-sag bars. Such restraints reduce the potentiality

of lateral buckling, but do not necessarily eliminate the problem.

In general, sections do not have any axis of symmetry and

which are not laterally restrained are extremely complex to analyses

with respect to lateral buckling, and testing is the best method of

evaluating their behavior.

In design of flexural members, the moment capacity is not

only governed by the section strength of the cross section, but also

limited by the lateral-torsional buckling strength of the member.

The post buckling behavior of beam web was investigated

by John. T.Dewolf and Clinton J.Gladding[1] and observed that the

strength of beams can be considerably reduced by local buckling, by

as much as 60% for the beams studied. The beam capacities

calculated on the basis of the classical critical plate buckling stress

considerably underestimate the actual strength, by as much as 75%

for the tests reported. The deformations in the post bucking range re

not large so the full post-buckling strength should be utilized for

design.

The bending strength of webs of Cold-Formed Steel beams

was studied by Roger A.Labouble and Wei-Wen Yu[2] and observed

that post buckling strength of web elements to be a function of web

slenderness ration, flat width to thickness ratio of the compression

flange, the bending stress ratio of the web, and the yield point of the

steel. A formula for post buckling strength factor was also derived

by the authors.

Elasto-Plastic interaction buckling of CFs channel columns

was investigated by Y.L.Guo and S.F.Chen[4] and observed that the

local buckling wavelength and its uniform distribution along the

length of the column are not changed significantly during the whole

loading process, which reveals that the effect of overall bending of

the column on then may be ignored.

Distorsional buckling of thin walled beams/panels was

examined by Reynaud L.Servettle and Teoman Pekoz[6] and

introduced two design methods to estimate the maximum moment

capacity of sections subject to an interaction of local and distorsional

buckling. Analytical expression was derived to compute distorsional

buckling stress which is identical to the present AISI specification

design method.

Lateral buckling studies on CFS RHS beams were carried

out by Xia-Ling Zhao, Gregory J.Hancock and Nicholas S.Trahair[5]

and included the effect of bending-moment distribution using

moment modification factor. The critical value of the moment

modification factor, beyond which the elastic lateral buckling will

control, was found to be 1.80.

The behavior of laterally braced CFS flexural members

with edge stiffened flanges was investigated by B.W.Schafer and

T.Pekoz[7] and found that two importantant buckling phenomena

namely local and distorsional have greatly influenced the buckling

behavior.

They concluded that Distorsional bucking has the ability to control

the final failure mechanism and has a lower post buckling capacity

than local buckling.

Lateral buckling behavior of CFS channel beams was

investigated by Bogdan M.Put, Yong-Lin Pi and N.S.Trahair[8] and

compared the test results with the predictions using AS/NZS 4600

design codes. It was observed that large deformations were

developed as the inelastic buckling loads were approached. It is

recommended that the lateral buckling design of thicker CFCs should

be made using the formulations of AS 4100 instead of those AS

4600.

Lateral buckling tests of CFS Z-beams were carried out by

Bogdan M.Put, Yong-Lin Pi and N.S.Trahair[9] and observed that

moments at failure were lower when the beam lateral deflections

increased the compression in the compression flange, lip, and higher

when they increased the compression in the flange-web junction.

They concluded that the design methods of AS 4600 for the section

capacities of thin-walled CFZS are thought to be superior to those of

AS 4100, and it is recommended that the section capacities of CFZS

should be determined using the methods of AS 4600.

Inclusion of inelastic reserve strength due to moment redistribution

was examined by Muzaffer Yener and Teoman Pekoz[3]and

observed that a considerable amount of reserve capacity due to

moment redistribution is possible which can be utilized to have a

economical section.

Lateral buckling strength of a new CFS beam, LSB,

Subject to moment gradient effect was examined by cyrilus Winaama

Kurniwan and Mathen Mahendran[10] and was found that strength

benefit of moment gradient for cases with high end moment ratios

(β>,0) is unfavorably influenced by LDB.

It is observed that the equivalent uniform moment factor (λm)

reaches the upper bound for LSBs with high beam slenderness (LTB)

but it reduces with lower beam slenderness due to the increasing

level of web distorsion associated with LDB, until other buckling

modes that precede the lateral buckling govern. It is found that the

current λm equations with its application in accordance with the

method in CFS codes are therefore safe for LSBs.

VI. MATERIAL PROPERTIES

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 CFS characteristics that are of interest

include mechanical properties (Uniaxial Stress – strain behavior,

including values for the proportional limit the yield and Ultimate

strengths; the extent of yielding plateau; and strain hardening

parameters) and built-in residual stress patters (initial state of

stress). In general, the non Uniformity of the Cold Work applied to

a CFS section results in different Mechanical properties and

different magnitudes of residual stresses at different locations across

the section.

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Equivalent yield stress is usually chosen as the 0.2% Proof

‘Stress, defined as the stress with a plastic strain of 0.2% as shown

in Fig. 7.

It is also a common practice to represent the Stress-Strain

curve by a Ramberg-Osgood curve, which is defined in terms of the

initial elastic modulus (Eo), a proof and a parameter (n) that defines

the sharpness of the Knee of the stress-strain curve. If the proof

stress is chosen as the 0.2 % proof stress ( 0.2), the Ramberg-

Osgood takes the form

often the proportionality stress (p) is defined as the 0.01%

Proof stress (0.01), as shown in Fig. 7.

Fig 7 Bending Moment Distribution

The n-parameter can then be determined by requiring that

the Ramberg-Osgood curve coincides with the measured stress-

strain curve at the 0.01 and 0.2% proof stress

The Ramberg-Osgood curve is known to accurately

represent actual stress-strain curves for stress less than the 0.02%

proof stress when n is determined using Eq. (6).

Tensile Test specimens including two specimens from each

steel thickness were taken from the same steel batch that that was

used in the section and member capacity tests. This allowed the

determination of an accurate stress-strain relationship for each steel

thickness used in the tests that can be used in the section and

member capacity calculations of CFS lipped channel beams. Tensile

specimens for this test program were prepared in accordance with

the Indian Standard “1608-2005 & ISO 6892-1998” A typical

tensile test specimen used in this test program is shown in Fig 9 (a)

and 9 (b).

Fig.9.(a). Specimen Fig .9(b). Failure

PATTERN

The stress-strain curves for different thicknesses are shown in fig.10

Fig.10. Stress-Strain Curve

The material properties derived from coupon test are tabulated in

table. 1

TABLE.1. MATERIAL PROPERTIES

Sl.

No.

Thickness

(t)

mm

Specimen

ID

Fy

N/mm2

Fu

N/mm2

E

N/mm2

1 1.6 CFS 1.6 428 478 2.01 x 105

2 2.0 CFS 2.0 402 492 2.01 x 105

3 2.5 CFS 2.5 431 565 2.01 x 105

4 3.0 CFS 3.0 408 463 2.01 x 105

VII.BOUNDARY CONDITIONS Beams considered for studies are simply supported and its

boundary conditions for warping and torsion restraints are tabulated

and shown in Fig 11.

Fig.11. Boundary Conditions

A. DETERMINATION OF ELASTIC LATERAL

BUCKLING RESISTANCE MOMENT

In BS 5950: Part 5, the rules for determination of the

elastic lateral buckling resistance are limited to four specified

sections, such as I, C, Z and T beams as shown in Fig.12.These thin

elements may buckle locally at a stress level lower than the yield

stress of steel when they are subject to compression in flexural

bending, axial compression, shear or bearing.

Fig.12.Cross Section covered by the Lateral buckling clauses of BS

5950 Part 5

Fig.11 illustrates local buckling patters of certain beams

and columns, where the line junctions between elements remain

straight and angles between elements do not change

………………….…………. (5)

……………………............….. (6)

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B. ELASTIC LATERAL BUCKLING RESISTANCE

MOMENT In BS 5950, Part 5 Elastic critical moment, ME, for such a beam of

Length L bent in the plane of web is given by the expression for an I-

beam.

Using the relationships

I1= B3t/6 = Ary2, Cw = I1 x D2/4

G = E/2 (1-) = E/2.6, J = At2/3 Hence, the above equation can be

rearranged to give

The term 4/7.82 is very close to 1/20 and this form the

basis of the elastic lateral buckling resistance moment used in BS

5950: part 5 for I-section. The buckling resistance moment for

Channels or I section in BS 5950: parts is therefore

Cb= 1.75 – 1.05 β+ 0.3β2 2.3 ……….…………………………. (9)

C.EXPERIMENTAL INVESTIGATION

In order to investigate the (Lateral Flexural – Torsion

Buckling) buckling and ultimate strength behavior of CFS lipped

channel beams used as flexural members, a full scale bending test

rig was designed, fabricated and built in the GCT structural

dynamics Engineering Laboratory. The test required special

support conditions that prevented in-plane and out-of plane

deflections and twisting rotation without restraining in-plane and

out-of plane rotations and warping displacements. The test rig used

for lateral distortional buckling tests included a support system and

a loading system, in which support system were rigidly fixed in the

floor of dynamics laboratory.

D.SUPPORT SYSTEM

Specially designed two supports of 1.2m high were

fabricated and installed at a spacing of 3 meter in the floor of

dynamics Laboratory to support the test beams. The height of the

support was fixed in order to provide space for loading platform

which will be attached to the beam so that loading will be done

incrementally. Two T – shaped plates (a rectangular plate with flat

plate welded to the rectangular plate at its middle) were tied to the

support one at each side. The plates will be used as a torsion

restraint and will be fixed at the ends of beam using four bolts.

Torsion restraints to the ends of beam were provided by fixing the

T- Plates at its ends by bolds. Fig 13 shows the Schematic and

overall views of the test Setup.

Fig 13 Schematic and overall views of the setup

E. LOADING SYSTEM

Mahendran and Doam[8] used a loading system with

hydraulic jacks which had a disadvantage of restraining lateral

movement of the test beam. It did not allow the continuation of

loading into the post buckling range due to the fact that roller

bearings could slip out of position and cause injuries to people and

damage the components. Therefore a new gravity loading system

was designed to eliminate the above mentioned short comings. The

new loading system included the two rectangular box shaped

arrangements attached with chains to accommodate loading discs.

The rectangular boxes were suspended from the attachments which

were fixed at 1/3rd points of the test beam and ensured uniform

bending moment between the loading points. Previous researchers

have used both the overhang and quarter point loading methods to

investigate the lateral buckling behavior of various section types Put

et al.[8] used quarter point loading method to investigate the lateral

buckling of simply supported beams. In the overhang method, the

cantilever loads are applied to the test beam at a short distance from

the supports, which provide a Uniform bending moment within the

entire span on the other hand, the quarter point loading method

provides uniform bending moment only between the points of load

application. Therefore the overhang loading method was preferred

as it provides a uniform bending moment within the entire span, but

it has the possible undesirable effect of warping restraints due to the

overhang component of the test beam. In addition, it has the

limitation on its length due to fabrication difficulties. Hence, longer

test beams to accommodate cantilever loads in the overhang method

were not suitable in this test program. Therefore two point loading

method was adopted as shown in fig. 12 (a).

F.MEASURING SYSTEM

Vertical deflections were measured by affixing a needle at

1/3rd and mid span points which moves on a reference scale. Lateral

movements of beam were measured by mounting dial gauges on a

stand 1/3rd and mid span respectively. Strain readings were

recorded with the help of strain indicator. The location of strain

gauges is shown in fig. 14.

Fig 14 Schematic view for strain gauge loctions

………………............….. (7)

……………………............….. (8)

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TABLE.2.SPECIMEN DETAILS

Sl.

No Specimen id Size(mm) Thickness D/t B/t d/t

Boundary

conditions

1 Aw.N.11 100x50x10 1.6 62.5 31.3 6.3 Torsion Restrained

2 Aw.B.11 100x50x10 1.6 62.5 31.3 6.3

Torsion Restrained

and warping

Restrained at Bottom side

3 Aw.T.11 100x50x10 1.6 62.5 31.3 6.3

Torsion Restrained

and warping Restrained at

Topside

4 Aw.F.11 100x50x10 1.6 62.5 31.3 6.3

Torsion Restrained

and warping Restrained Fully


6 Aw.B.21 100x50x15 1.6 62.5 31.3 9.4

Torsion Restrained


Bottom side

7 Aw.T.21 100x50x15 1.6 62.5 31.3 9.4

Torsion Restrained and warping

Restrained at

Topside

8 Aw.F.21 100x50x15 1.6 62.5 31.3 9.4 Torsion Restrained and warping

Restrained Fully


10 Aw.B.22 100x50x15 2.0 50.0 25.0 7.5

Torsion Restrained

and warping

Restrained at Bottom side

11 Aw.T.22 100x50x15 2.0 50.0 25.0 7.5

Torsion Restrained

and warping

Restrained at Topside

12 Aw.F.22 100x50x15 2.0 50.0 25.0 7.5

Torsion Restrained

and warping Restrained Fully


14 Aw.B.32 100x50x20 2.0 50.0 25.0 10.0

Torsion Restrained


Bottom side

15 Aw.T.32 100x50x20 2.0 50.0 25.0 10.0

Torsion Restrained


Topside

16 Aw.F.32 100x50x20 2.0 50.0 25.0 10.0 Torsion Restrained and warping

Restrained Fully

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Table 2 lists the test specimens used in this program while

figure 15 shows a typical specimen arrangement for testing.

Fig 15 Test Setup

The cross section dimensions and material thicknesses of

each test specimen were measured using a vernier caliper and

tabulated.

The test specimen was placed in a position on Supports

and its ends were tied down with ‘T’ plates which were fixed at

beams end. The loading arms were then bolted to the test specimen

at each 1/3rd points. The loading boxes were hanged from the

loading arms by means of chains. Initial deflections and strains

were measured for loading box weight which of 400 N. Gravity

loads of 200N, 100N and 50N were purchased specifically for this

test am. The loads were applied at an increment of 200N till the test

specimen was failed and corresponding deflections and strains were

recorded. The Cross-Sectional rotation of specimen was measured

at 1/3rt span and corresponding rotations at mid span were extra-

polated. Test beams were allowed to deflect and rotate laterally and

loading was Inused until the Test beam failed by out-of-plane

buckling. The buckling behavior of the test beam shown in fig.16

was observed throughout the test and recorded.

Fig.16. Tested beam

(a) (b)

Fig 17.Loading pattern and the failure of the beam

Loading pattern was demonstrated in fig 12 (a) and the

pattern of failure was shown in fig 17 (a) and (b). The cb values for

different specimens under two point loading conditions are given in

Table.3. The effective length ratio determined experimentally for

different boundary conditions are shown in Table. 4.

TABLE.3.CALCULATION OF Cb* VALUE

Sl

No

Beam Id

Mmax

(KNM)

MA

(KNM)

MB

(KNM)

MC

(KNM)

Cb=(12.

5Mmax)/ (2.5Mma

x+3MA+

4MB+3MC)

1 Aw.N.11 2.7 2.025 2.7 2.025 1.136

2 Aw.B.11 3.1 2.325 3.1 2.325 1.136

3 Aw.T.11 3.3 2.475 3.3 2.475 1.136

4 Aw.F.11 3.5 2.625 3.5 2.625 1.136

5 Aw.N.21 3 2.25 3 2.25 1.136

6 Aw.B.21 3.4 2.55 3.4 2.55 1.136

7 Aw.T.21 3.6 2.7 3.6 2.7 1.136

8 Aw.F.21 3.7 2.775 3.7 2.775 1.136

9 Aw.N.22 3 2.25 3 2.25 1.136

10 Aw.B.22 3.4 2.55 3.4 2.55 1.136

11 Aw.T.22 3.7 2.775 3.7 2.775 1.136

12 Aw.F.22 4.1 3.075 4.1 3.075 1.136

13 Aw.N.32 3.2 2.4 3.2 2.4 1.136

14 Aw.B.32 3.7 2.775 3.7 2.775 1.136

15 Aw.T.32 4 3 4 3 1.136

16 Aw.T.32 4.3 3.225 4.3 3.225 1.136

Multiplying Factor to account for variation in moment along a

beam

TABLE.4. EFFECTIVE LENGTHS FOR DIFFERENT

BOUNDARY CONDITIONS

Sl No Beam Id Mmax

(KNM)

Exp.values for Effective Length as per

BS5950 Part 5 in mm

1 Aw.N.11 2.7 2254.94

2 Aw.B.11 3.1 2091.84

3 Aw.T.11 3.3 2022.481

4 Aw.F.11 3.5 1959.57

5 Aw.N.21 3 2286.44

6 Aw.B.21 3.4 2137.00

7 Aw.T.21 3.6 2072.45

8 Aw.F.21 3.7 2042.29

9 Aw.N.22 3 2625.90

10 Aw.B.22 3.4 2442.95

11 Aw.T.22 3.7 2328.11

12 Aw.F.22 4.1 2197.29

13 Aw.N.32 3.2 2688.80

14 Aw.B.32 3.7 2473.55

15 Aw.T.32 4 2366.60

16 Aw.T.32 4.3 2272.31

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G. VERTICAL DEFLECTION CURVES

The experimental curves of applied moment versus vertical

deflection and lateral deflection at mid span and 1/3rd span of test

beams were presented. From these figures, it could be seen that the

moment Vs vertical and lateral deflection curves were non-linear.

However, there was a linear relationship in moment Vs vertical

deflection up to 80% of the ultimate moment. For moment Vs lateral

deflections, there was a linear behavior in the beginning stage: The

lateral buckling tests of CFS beams by Bogdan et.al[8] and Cold-

Formed RHS beams presented by Zhao et al[5] had shown similar

relationships between the applied moment and deflections.

(a)

(b)

(c)

(d)

Fig.18. Moment Deflection Curves

From Figure 18, it can be noticed that the sections with

different slenderness have different in-plane and out-of-plane

stiffness. It was measured that the maximum in plane deflection

was achieved with the beam sections having less slenderness values

whereas the maximum out of plane deflection was achieved with

the more slender beam sections. This development was realized as

the less slender beams can resist larger moments than the more

slender beams before it fails by lateral distorsional buckling (i.e. out

of plane buckling). This could be due to certain experimental errors.

By comparing the load-deflection behavior of less slender beams

with more slender beams, less slender beams clearly demonstrate a

peak load and load drop corresponding graphs.

TABLE.5 COMPARISON OF EFFECTIVE LENGTHS

FOR DIFFERENT BOUNDARY CONDITIONS

Sl.no

Boundary Conditions

Effective Length

ratio

( Experimental )

As per

IS 800

-2007

( Hot

Rolled )

Warping at

ends

Torsion at

ends

1 Free Restrained 0.82 1.00

2

Tension

Flange

Restrained

Restrained 0.76 0.75

3 Comp Flange

Restrained Restrained 0.73 0.85

4 Fully

Restrained Restrained 0.71 0.80

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100

Mo

men

t i

n k

Nm

Deflection in mm

Moment vs Vertical Deflection in mm

WFTR

WR©TR

WR(T)T

R

WRTR

Mid Span

0

1

2

3

4

0 10 20 30

Mo

men

t in

kN

m

Deflection in mm

Moment vs Vertical Deflection in mm

WFTR

WF©TR

WR(T)TR

WRTR

One Third

span

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6

Mo

men

t i

n k

Nm

Deflection in mm

Moment vs Lateral Deflection in mm

WR©TR

WR(T)TR

WRTR

Mid

span

0

0.5

1

1.5

2

2.5

3

3.5

0 0.5

Mo

mn

et

in k

Nm

Deflection in mm

Moment vs Lateral Deflection in mm

WR©TR

WR(T)TR

WRTR

One

Third

span

1293


ISBN 978-93-80609-17-1

VIII. RESULTS AND DISCUSSION

The resistance afforded by the supports can have a

substantial effect on the lateral buckling resistance of beams.

Warping and Torsion resistance increases in buckling resistance of a

beam. Restraint against rotation improves buckling resistance and in

such a case, the effective length is determined experimentally as 0.82

times the span length. In the most highly restrained condition (both

warping and torsion restraint) when all rotations are restrained, the

effective length is reduced to 0.706 times the actual length.

Restrained to compression flange reduces the effective length

substantially compared to the restraint provided by tension flange, ie

from 0.73 times to 0.76 times, BS5950; parts also cites the condition

regarding a beam which is part of a fully formed structure, and is

restrained at intervals by substantial connections under this condition,

the effective length may be taken as 0.8 times the distance between

restraints. If the connections are less substantial then the effective

length should be taken as 0.9 times the distance between restraints.

IX. CONCLUSIONS

It is observed that the methods used to impose restraint on

one form of rotation also have some effect on restraining other

rotations. It is the matter of engineering judgement as to how the

effective length should be used in different Circumstances. The

influence of warping and torsion restraints is investigated

experimentally and the ratios of effective length to actual lengths are

compared with BS 5950: parts. The results confirm the provisions of

BS 5950: parts.

ACKNOWLEDGEMENT

The author greatly acknowledges the contribution of

Dr L.S.Jeyagopal, Chairman, Mithren Structures, Coimbatore for his

novel of idea of setting up of Test Setup to this project. The

continuous encouragement of my supervisor Dr R. Thenmozhi is

highly appreciable. The management, particularly the then Principal

of Arulmigu Palaniandavar Polytechnic College has Permitted and

sanctioned the funds to carry out the experimental study.

REFERENCES

[1] John T.DeWolf and Clinton J.Gladding (1978), "Journal of the

Structural Division, Post-Buckling Behavior of Beam Webs in

Flexure", Vol.104, No.ST7, pp 1109-1122. [2] Roger A.LaBoube and Wei-Wen Yu(1982), "Bending Strength of

Webs of Cold-Formed Steel Beams", Vol.108, No.ST7, pp1589-

1604. [3] Muzaffer Yener, and Teoman Pekoz(1985), "Partial Moment

Redistribution in Cold-Formed Steel", Vol.111, No.6, pp 1187-

1203. [4] Y.L.Guo and S.F.Chen(1991), "Elasto-Plastic Interaction Buckling

of Cold-Formed Channel Columns", Vol.117, No.8, pp 2278-2298.

[5] Xiao-Ling Zhao, Gregory J.Hancock and Nicholas S.Trahair(1995), "Lateral-Buckling Tests of Cold-Formed RHS

Beams", Vol.121, No.11, pp 1565-1573.

[6] Reynaud L.Serrette and Teoman Pekoz(1995), "Distortional Buckling of Thin-Walled Beams/Panels. II Design Methods",

Vol.121, No.4, pp 767-775.

[7] B.W.Schafer and T.Pekoz(1999), "Laterally Braced Cold-Formed Steel Flexural Members with Edge Stiffened Fanges", Vol.125,

No.2, pp 118-127.

[8] Bogdan M.Put, Yong-Lin Pi and N.S.Trahair(1999), "Lateral Buckling Tests on Cold-Formed Channel Beams", Vol.125, No.5,

pp 532-539.

[9] Bogdan M.Put, Yong-Lin Pi and N.S.Trahair(1999), "Lateral Buckling Tests on Cold-Formed Z-Beams", Vol.125, No.11, pp

1277-1283.

[10] Cyrilus Winatama Kurniawan and Mahen Mahendran(2009), "Lateral Buckling Strength of Simply Supported LiteSteel Beams

Subject to Moment Gradient Effects", Vol.135, No.9, 135(9) pp

1058-1066.

[11] Rhodes. J.," Design of Cold Formed Steel Members ", Elsevier

Applied Science, London and New York.

1294


ISBN 978-93-80609-17-1

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