Effects of stiffeners on the capacities of cold formed steel channel members

This paper investigates the effects of stiffeners on the compressive and flexural capacities of coldformed steel channel members. Stiffeners are added on the web of the channel section to form a new section called SupaCee. This new section is shown to be more innovative and stable than the traditional channel section. The structural advantages of this new section are investigated by comparing the capacities of SupaCee and channel members under compression and bending. The capacities are determined by using the direct strength method (DSM) according to ASNZS 4600:2018 with the support of THINWALL2, a buckling analysis program. It was found that the stiffeners are effective for small section dimensions and thicknesses, but become ineffective for large section dimensions.

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Steel Construction Design and Research

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Volume 14

November 2021

ISSN 1867-0520

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Content

Steel Construction 4/21

Volume 14

November 2021, No 4

ISSN 1867-0520 (print)

ISSN 1867-0539 (online)

www.ernst-und-sohn.de/steel-construction

http://wileyonlinelibrary.com/journal/stco

Steel Construction is indexed in Elsevier´s Scopus

CiteScore 2020: 1.9

Journal for ECCS members

EDITORIAL

Bernhard Hauke

221 European Steel Design Awards 2021

DESIGN & RESEARCH

Helen Bartsch, Felix Eyben, Simon Schaffrath, Markus Feldmann

222 On the plastic design of high-strength steel beams

Benjamin Newcomb, Kyle Tousignant

236 Optimized design of fillet welds in RHS joints for EN 1993-1-8

Alexander Britner, Corinne Dieu, Ralf Podleschny

250 Corrosion protection for cold-formed structural steel elements

Thomas Misiek, Bert Norlin, Reinhold Gitter, Torsten Höglund

258 Review of European design provisions for buckling of aluminium

members with longitudinal welds – part 1

Ngoc Hieu Pham, Quoc Anh Vu

270 Effects of stiffeners on the capacities of cold-formed steel channel

members

Asif Mohammed, Katherine Cashell

279 Cross-sectional behaviour and design of ferritic and duplex

stainless steel EHS in compression

288 ECCS news

293 Events A4 PRODUCTS & PROJECTS

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DOI: 10.1002/stco.202100003

ARTICLE

Effects of stiffeners on the capacities of cold-formed

steel channel members

Ngoc Hieu Pham, Quoc Anh Vu

This paper investigates the effects of stiffeners on the

com-pressive and flexural capacities of cold-formed steel channel

members Stiffeners are added on the web of the channel

sec-tion to form a new secsec-tion called SupaCee This new secsec-tion is

shown to be more innovative and stable than the traditional

channel section The structural advantages of this new section

are investigated by comparing the capacities of SupaCee and

channel members under compression and bending The

capac-ities are determined by using the direct strength method (DSM)

according to AS/NZS 4600:2018 with the support of

THIN-WALL-2, a buckling analysis program It was found that the

stiffeners are effective for small section dimensions and

thick-nesses, but become ineffective for large section dimensions

Keywords cold-formed steel; channel members; stiffeners; compressive

capacities; flexural capacities

1 Introduction

Cold-formed steel lipped channel and zed sections have

been available on the international markets for more than

30 years [1] The yield stresses of material properties

rang-ing from 450 to 550 MPa [2] depend on the thickness and

the cold-forming procedure The channel and zed

sec-tions in recent developments have stiffeners added on

their flanges, webs and lips to increase the buckling

ca-pacities, and such sections are known as SupaCee and

SupaZed The new sections have the following benefits

[3]:

1) The rounded lips of the sections (instead of sharp

edges) make handling safer on site

2) Better safety and reduced labour input can be

achie-ved while installing purlins

3) The strength performance is significantly improved,

resulting in considerable economic benefits

In terms of design methods, the effective width method

(EWM) was proposed by von Karman based on the flat

plate stability [4], then calibrated by Winter for

cold-formed steel members [5], [6] The interaction between

local and global buckling modes is accounted for in the

design, but this method becomes too complicated when

designing complex section shapes with multiple stiffeners

The limitation of the EWM can be solved by using the

di-rect strength method (DSM) The DSM was derived from

the design method for distortional buckling failures

pro-posed by Hancock et al [7] and then developed by

Scha-fer and Pekoz [8]–[10] This method is currently

formulat-ed in the Australian/New Zealand Standard AS/NZS 4600:2018 [11] and the North American Specification AISI S100-16 [12] for the design of cold-formed steel structures Compared with the EWM [8], the DSM has the following advantages:

– Design procedures are simple for complex sections with multiple stiffeners

– Elastic buckling analysis using numerical tools is uti-lized to consider the equilibrium between plate ele-ments not accounted for in the EWM

The development of the DSM provides deeper insights into the buckling behaviour of complex shapes [1] Elastic buckling analyses are compulsory, and can be carried out

by numerical software programs such as THIN-WALL-2 ([13], [14]) or CUFSM [15] The signature curve is one of the elastic buckling analysis results This curve shows the buckling stress versus buckling half-wavelength and can

be used to optimize the section shapes The DSM was used in this research

The addition of stiffeners to cold-formed steel sections has been investigated by many researchers In terms of compression members, Hancock et al ([7], [16]–[19]) per-formed a series of experiments on cold-per-formed steel stor-age racks with a variety of complex edge stiffeners The behaviour of members with edge stiffeners provided deeper insights into distortional buckling Seah and Rho-des [20] also conducted tests on isolated flanges with complex stiffeners to investigate their behaviour, which was followed by the modification of the British Standard using the effective width method with consideration of the distortional mode in design Wang et al., Yan and Young, and Xiang et al ([21]–[27]) investigated the behav-iour of cold-formed steel channel columns with complex edge stiffeners Manikandan et al [28] studied the behav-iour of three types of intermediate web stiffener on lipped channel sections under compression In addition, Chen et

al [29] presented a variety of stub column tests on cold-formed steel channel and zed sections with different stiff-eners The experimental results in Chen’s paper [29] were used to calibrate the finite element models that can be utilized to develop numerical studies to expand the data-base for a variety of sections and lengths The experimen-tal and numerical results were compared with the predic-tions from the current standards and the modificapredic-tions in design were then proposed The optimization of cold-formed steel channel columns was carried out by El-taly

et al [30] with combinations of edge and intermediate

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Steel Construction 14 (2021), No 4 271

N H Pham, Q A Vu: Effects of stiffeners on the capacities of cold-formed steel channel members ARTICLE

the American Society for Testing Materials (ASTM) In this paper, material grades according to AS 1397[2] de-scribe a range of coated steels from G250 to G550 A designation in the form G450-Z200 signifies a typical grade, where the letter G indicates heat treatment prior to hot-dipping, the first three-digit number (450) denotes the minimum yield stress in MPa, the letter Z indicates a zinc coating and the second three-digit number (200) denotes the coating mass in grams per square metre on both sides

of the steel sheet Six coating types are regulated: Z stands for zinc coating, ZF for zinc-iron alloy, ZA for zinc/aluminium coating, ZM for zinc/aluminium/magne-sium coating and AM for aluminium/zinc/magnezinc/aluminium/magne-sium, where aluminium prevails The stress-strain curve of G450 steel to AS 1397 [2] is illustrated in Fig 1, where the yield stress fy is based on a 0.2 % proof stress This

rounded curve and the low ratio of tensile strength to yield stress are due to the cold reduction processes Grade G450 was used for the investigations in this paper

The channel and SupaCee sections were commercial sec-tions provided by BlueScope Lysaght [3], and their dimen-sions are listed in Tab 1 The section properties and elas-tic buckling stresses were determined using THIN-WALL-2 ([13], [14]) The member lengths for each section varied from 2.0 to 8.0 m for compression or bending In order to evaluate the effectiveness of stiffeners, structural members using channel and SupaCee sections require the same amount of material The collected data is then used

to compare the capacities of SupaCee and channel sec-tion members under compression or bending This com-parison is presented in sections 4 and 5

structures

The direct strength method (DSM) is used to predict the ultimate strengths of cold-formed steel members based on

stiffeners The stiffeners to web openings were also

inves-tigated to find out their effects on the behaviour of

cold-formed steel channel sections under compression ([31],

[32])

In terms of flexural members, Ye et al [33] investigated

the more efficient cold-formed steel channel sections in

bending based on Eurocode 3 [34] It was found that the

intermediate web stiffeners did not increase the flexural

capacity of the channel sections, while complex edge

stiff-eners resulted in a considerable increase in the flexural

capacity of the sections Manikandan and Arun [35]

ex-amined the bending behaviour of cold-formed built-up

I-sections (back-to-back channel beam) with edge and

in-termediate web stiffeners The test and numerical results

were compared with the predictions from standards and

were used for design modifications Chun-gang et al [36]

also studied the effects of web stiffeners on the flexural

capacities of channel sections Their paper illustrated that

the intermediate web stiffeners did not increase the

bend-ing strengths of channel sections, as presented in the

work of Ye et al [33] The reason for this ineffectiveness is

that the flexural strengths of the sections investigated

were governed by distortional buckling, whereas the

in-termediate stiffeners were only useful for the local

buck-ling strength Chen also studied the behaviour of

cold-formed steel channel beams with edge-stiffened web holes

[37] Openings to accommodate technical services are

common in cold-formed steel members

Previous research has focused on experimental and

nu-merical studies of cold-formed steel sections with the

ad-dition of stiffeners that were used for optimizing sections

or design modifications However, the effectiveness of

additional stiffeners for member capacities remains a

question, particularly for commercial sections available

on the market This effectiveness is taken into account by

designers and can be evaluated based on the same

amount of material for the sections with and without

stiff-eners This paper attempts to answer this question by

in-vestigating the effects of complex stiffeners on the

capaci-ties of channel members under compression or bending

Channel and SupaCee sections were commercial sections

provided by BlueScope Lysaght [3], and their material

properties are regulated in AS 1397 [2] The capacities of

cold-formed steel members can be determined using the

DSM design equations formulated in AS/NZS 4600:2018

[11] with the support of THIN-WALL-2 ([13], [14]) in

sec-tional elastic buckling analyses The effectiveness of

stiff-eners is then evaluated by comparing the capacities of

SupaCee and channel members under compression or

bending

The material properties of cold-formed steel members are

regulated in Australian Steel Standard AS 1397 [2] or by

Fig 1 Stress-strain curve of G450 steel [1]

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272 Steel Construction 14 (2021), No 4

N H Pham, Q A Vu: Effects of stiffeners on the capacities of cold-formed steel channel members

buckling (Nce), local buckling (Ncl) and distortional buck-ling (Ncd)

(1)

(2)

(3) where:

c N Ny oc l Nce Nol d N Ny od

Ny nominal yield capacity of member in compression

Noc elastic compression buckling load

Nol elastic local buckling load

Nod elastic distortional buckling load

ce

y c

c2

y c

c

N

λ

=

















λ

for 0.776

cl

ce l ol

ce

0.4 ol ce

0.4

ce l

N

N N N

N

N N

λ

=

≤



 



























for 0.561

cd

y d od

y

0.6 od y

0.6

y d

N

N N N

N

N N

λ

=

≤



 

















  >











 the elastic buckling stresses (fo, fol, fod) and the yield stress

(fy) The non-dimensional slenderness values are

calculat-ed and uscalculat-ed directly to determine the global, local and

distortional buckling strengths as shown in Eqs (1)–(3)

and (4)–(6) for compression and bending respectively

The nominal capacity of compression members is

calcu-lated as the minimum of the nominal strengths for global

Tab 1 Nominal dimensions of channel and SupaCee sections

SC/C15012

SC/C15015

SC/C15019

SC/C15024

1.2 1.5 1.9 2.4

152 152 152 152

64 64 64 64

7.5 7.5 7.5 7.5

14.5 14.5 14.5 14.5

64 64 64 64

42 42 42 42

5 5 5 5

35 35 35 35 SC/C20012

SC/C20015

SC/C20019

SC/C20024

1.2 1.5 1.9 2.4

203 203 203 203

76 76 76 76

10 10 10 10

19.5 19.5 19.5 19.5

115 115 115 115

42 42 42 42

5 5 5 5

35 35 35 35 SC/C25015

SC/C25019

SC/C25024

1.5 1.9 2.4

254 254 254

76 76 76

11 11 11

21.5 21.5 21.5

166 166 166

42 42 42

5 5 5

35 35 35 SC/C30019

SC/C30024

SC/C30030

1.9 2.4 3.0

300 300 300

96 96 96

14 14 14

27.5 27.5 27.5

212 212 212

42 42 42

5 5 5

35 35 35 SC/C35019

SC/C35024

SC/C35030

1.9 2.4 3.0

350 350 125

125 125 125

15 15 15

30.0 30.0 30.0

262 262 262

42 42 42

5 5 5

35 35 35 SC/C40019

SC/C40024

SC/C40030

1.9 2.4 3.0

400 400 400

125 125 125

15 15 15

30.0 30.0 30.0

312 312 312

42 42 42

5 5 5

35 35 35 Note: inner radius r 1 = r 2 = 5 mm; t, D, B, L 1 , L 2 , GS, S (mm); α 1 , α 2 ( 0 )

Fig 2 Nomenclature for channel and SupaCee sections

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where:

l Mbe Mol d M My od

My yield moment

Mo elastic lateral-torsional buckling moment

Mol elastic local buckling moment

Mod elastic distortional buckling moment Note that local buckling strengths (Ncl, Mcl) consider the interactions between local and global buckling modes The pure local buckling strengths were only determined for a fully braced column and beam by replacing Nce and

Mbe by Ny and My in Eqs (2) and (5) respectively

For singly symmetric sections subjected to torsional or flexural-torsional buckling, the global buckling stresses under compression and bending are presented in Appen-dix D of AS/NZS 4600:2018 [11] Sectional buckling stresses, including local and distortional buckling

stress-es, can be determined using the elastic buckling formulae presented in Appendix D [11] or by using numerical tools such as ABAQUS [38], CUFSM [15], or THIN-WALL-2 ([13], [14])

The nominal moment capacity (Mb) is the minimum of

the nominal strengths for lateral-torsional buckling (Mbe),

local buckling (Mbl) and distortional buckling (Mbd)

(4)

(5)

(6)

10

9 1

10

be

o o y y

o y y o y

y o y

M

=

<

−













>













for 0.776

bl

be l ol

be

0.4 ol be

0.4

be l

M

M M M

M

M M

λ

=

≤



 



























for 0.673

bd

y d od

y

0.5 od y

0.5

y d

M

M M M

M

M M

λ

=

≤



 

















  >











Tab 2 Sectional buckling stresses under compression

Note: D% is the buckling stress deviation between SupaCee and channel sections (in %).

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Sectional buckling stresses, including local and

distor-tional buckling stresses, under compression and bending

were determined using THIN-WALL-2 ([13], [14]), as

pre-sented in Tabs 2 and 3

The local buckling stresses fol of SupaCee sections

in-creased significantly compared with those of channel

sec-tions for compression or bending due to the effect of web

stiffeners, especially for small and thin cross-sections (see

section SC15012)

In terms of compression, the distortional buckling

stress-es of SupaCee sections are slightly lower (< 5 %) than

those of channel sections This reduction is insignificant,

and the distortional buckling stresses fod are still much

higher than the local buckling stresses fol This reduction

has no impact on the member capacities because member

strengths are governed by local buckling strengths, as

pre-sented in section 5

In terms of bending, the distortional buckling stresses fod

of SupaCee sections are generally higher than those of

Tab 3 Sectional buckling stresses under bending

Note: D% is the buckling stress deviation between SupaCee and channel sections (in %).

Fig 3 Model configuration for compression members

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umn/beam to reduce the effective length in the weak-axis direction The results are plotted in percentage diagrams, where the horizontal axis is for channel member capaci-ties and the vertical axis is for capacity deviations in per-cent (%) between SupaCee and channel members, as shown in Figs 5 and 6

channel sections, with a maximum deviation of 10.81 %

for the C25019 section This deviation undergoes

reduc-tion trends if the secreduc-tions vary from C250 to C150 or

C250 to C400 These stresses in SupaCee sections are

even smaller than those of channel sections, especially for

the C/SC350 and C/SC400 sections

capacities of cold-formed steel channel members

The DSM was used to determine the compressive and

flexural capacities of channel and SupaCee section

mem-bers with a variety of member lengths The model

configu-rations are shown in Figs 3 and 4 for compression and

bending respectively, where L is the member length or

span Bracing was placed at the mid-length of the

col-Fig 4 Model configuration for flexural members

Fig 5 Compressive capacities of cold-formed steel channel columns

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Fig 5b shows that most of the local buckling strengths

of SupaCee members are higher than those of channel members under compression Several local buckling strength values of SupaCee members are still lower than those of channel members although the local buckling stresses of the former are higher than those of the latter The reason is that the global buckling strengths (Nce) of the SupaCee members are significantly smaller than those of channel members, resulting in the considerable reduction in Ncl for those SupaCee members, as shown

by Eq (2)

Similarly to compressive members, almost all local buck-ling moments of SupaCee members are higher than those

of channel members, with a maximum deviation of 17 %,

as shown in Fig 6b Local buckling moments of SupaCee

As shown in Figs 5a and 6a, the global buckling strengths

of SupaCee members are much lower than those of

chan-nel members, reaching 15 % lower for compression or

bending This is explained by the fact that the section

properties Ix, Iy, Iw and J of SupaCee sections are smaller

than those of channel sections This deviation increases

for long members

The distortional buckling strengths (Ncd) of SupaCee

members are slightly lower than those of channel

mem-bers under compression (see Fig 5c) because the fod

val-ues of SupaCee sections are smaller than those of channel

sections, as presented in section 4 In terms of bending,

distortional buckling moments (Mbd) of the two types of

section members are approximative as the deviation

fluc-tuates between –1.72 % and 2.14 %, as presented in Fig 6c

Fig 6 Flexural capacities of cold-formed steel channel beams

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6 Conclusions

This paper investigates the effects of stiffeners on the ca-pacities of channel members under compression or bend-ing Commercial channel and SupaCee sections were provided by BlueScope Lysaght [3] The investigation was carried out by comparing the capacities of channel and SupaCee members The capacities were determined using the direct strength method (DSM) formulated in AS/NZS 4600: 2018 [11] with the support of THIN-WALL-2 soft-ware ([13], [14]) in elastic buckling analyses Based on the results, the following conclusions can be drawn:

– The stiffeners have significantly beneficial effects on thin and small section members, and marginal effects

on thicker and larger sections

– The global buckling capacities of SupaCee members are lower than those of channel members, particularly those of slender members

Based on these remarks, the following recommendation can be given for engineers and designers: Stiffeners should be used for sections with depths ≤ 300 mm, but are ineffective for large sections with depths > 300 mm

members are smaller than those of channel members for

several sections although the local buckling stresses of

the former are higher than those of the latter for the

fol-lowing reason: The global bucking moments of long-span

SupaCee beams are much smaller than those of channel

beams, which results in the significant reduction in local

buckling strengths of SupaCee beams, as shown by Eq

(5)

In general, the compressive and flexural capacities (Nc

and Mb) of SupaCee members are higher than those of

channel members, with a maximum deviation of 20 % and

9 % for compression and bending respectively (see Figs 5d

and 6d) However, the capacities of several SupaCee

members are still smaller than those of channel members

for the following reasons:

1) Member capacities are governed by global buckling

for thick sections and long members

2) The reduction of the global buckling strengths results

in the significant decrease of local buckling strengths

of SupaCee members, as discussed

3) Member capacities are governed by the distortional

buckling strengths for thin and short members

References

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Australia Elsevier Ltd.

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[15] Li, Z.; Schafer, B W (2010) Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM: Conventional and constrained finite strip methods Saint Louis, Missouri, USA.

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