360
B. Young and G.J. Hancock
the measured material properties as detailed in Table 1. A value of 203,000 MPa specified in the AISI
Specification was used for the Young's modulus of elasticity (E) in calculating the design strength.
The current design strength (Pn) predicted by the standard and specification are unconservative, except
that they closely predicted the web crippling strengths for the EOF loading condition in most of the
cases. On average, the web crippling strength of a specimen subjected to either IOF or ETF loading
condition was reached in the test at 67% and 66% of the value predicted by the specifications
respectively, as shown in Table 2. For a specimen subjected to the ITF loading condition, the
corresponding value is 56%. It is noteworthy that a test strength as low as 43% of the current design
strength was obtained in the test for a certain specimen subjected to the ITF loading condition.
Figure 2: Mechanism model
PROPOSED DESIGN EQUATIONS
The nominal web crippling strength (P,,) of unlipped channels calculated according to the AS/NZS
4600 and AISI design rules are unconservative, as shown in Table 2, probably because they were
calibrated for sections with more slender webs
(h/t
> 60). Hence, design equations for unlipped
channels with stockier webs are proposed in this paper. It is assumed that the bearing load is applied
eccentrically to the web due to the presence of the comer radii, which produces bending of the web out
of its plane causing a plastic mechanism as shown in Fig. 2. A plastic mechanism model is used to
establish design equations, which account for the eccentric loading of the web. This approach is
similar to that used for square and rectangular hollow sections (SHS and RHS) by Zhao and Hancock
(1992 and 1995) to determine the web crippling strengths for both interior and end bearing loads. The
SHS and RHS tested by Zhao and Hancock (1992 and 1995) also had stockier webs than was intended
for the AS/NZS 4600 and AISI web crippling equations.
The proposed equations for channel sections are summarised as:
Pp,,,
= 1.44-0.0133 (1)
r
where

Web Crippling Tests of High Strength Cold-Formed Channels
f yt 2
mp= 4
t
r=r/+
2
t;
N,,, = ed
+
2
for Interior loading
for End loading
361
(2)
(3)
(4)
in which,
Ppm
is the web crippling strength predicted by using the plastic mechanism model,
Mp
is the
plastic moment per unit length, r and r~ are the centreline and inside comer radii respectively, h is the
depth of the flat portion of the web measured along the plane of the web, t is the thickness of the web,
fy is the yield stress, d is the overall depth of the web and N is the length of the bearing. In Eqn. 4,
Nm
is the assumed mechanism length, as shown in Figs 3a and 3b for interior and end loading respectively.
It is based on an assumption that the dispersion slope of the load through the corner and the web is 1:1
with correction factors i and e for interior and end loading respectively. The correction factors for
interior loading are i = 1.3 and 1.4 for IOF and ITF respectively, and the correction factors for end
loading are e = 1.0 and 0.6 for EOF and ETF respectively. Equation 1 also accounted for the web

slenderness
(h/t)
of the channel sections, and the equation is calibrated with the test results.
Figure 3: Assumed plastic hinge position and mechanism length,
Nm
COMPARISON OF TEST STRENGTHS WITH PROPOSED DESIGN STRENGTHS
The experimental ultimate web crippling loads per web
(PExp)
obtained from the tests are compared in
Table 3 with the proposed design strengths
(Ppm)
using the plastic mechanism model. The proposed
design strengths were calculated using the average measured cross-section dimensions and the
measured material properties as detailed in Table 1.
TABLE
2
COMPARISON OF WEB CRIPPLING TEST STRENGTHS WITH CURRENT DESIGN STRENGTHS
tc'
7
B
a
r,
*
%
c:
E
a
3
0
0

Note:
1
in,
=
25.4
mm;
1
ksi
=
6.89
MPa;
1
kip
=
4.45
kN
TABLE
3
COMPARISON
OF
WEB
CRIPPLING TEST STRENGTHS
WITH
PROPOSED
DESIGN
STRENGTHS
3
g
G%
3

s
%
3
""s
%
9
%
"rl
2
z
9
z
z
2
3
a
a
r,
6
Note:
1
in.
=
25.4
mrn;
1
ksi
=
6.89
MPa;

1
kip
=
4.45
kN
364
B. Young and G.J. Hancock
The proposed design strengths
(Ppm) are
generally conservative. The plastic mechanism model
approach therefore appears to be suitable for unlipped channels with a web slenderness
(h/t)
value of
less than or equal to 45.
TABLE 4
STATISTICAL PARAMETER FOR RELIABILITY ANALYSIS
Variables
Material
(Tensile Yield Stress)
Fabrication
(Mass)
Statistical Parameters
Mean Mm
COV VM
Mean F m
COV V F
Values
1.08
0.063
0.97

0.03i
RELIABILITY ANALYSIS
The safety index ([3) is a relative measure of the safety of the design. A lower target safety index of 2.5
for structural members is recommended as a lower limit for the AISI Specification. In general, if the
safety index is greater than 2.5 (13 > 2.5), then the design is considered to be reliable.
The existing resistance (capacity) factor (q~) of 0.75 for web crippling strength of single unreinforced
webs is given by the AS/NZS 4600 and the AISI Specification. This resistance (capacity) factor (q~ =
0.75) is used in the reliability analysis. A load combination of 1.25DL + 1.50LL is also used in the
analysis, where DL is the dead load and LL is the live load. Accordingly, the safety index may be
given as,
ln/MInFmPm /
0.691~
F = (5)
4V2M + V~ +CpV~ +0.212
The statistical parameters Mm, F m, V M and V F are mean values and coefficients of variation for
material properties and fabrication variables respectively, and these values are obtained from BHP
Structural and Pipeline Products (1998), as shown in Table 4. The statistical parameters Pm and Vp are
mean value and coefficient of variation for design equations, as shown in Tables 2 and 3 for current
design rules and proposed design equations respectively. The correction factor Cp is used to account
for the influence due to a small number of tests (Pek6z and Hall 1988, and Tsai 1992), and the factor
Cp is given in Eqn. Fl.l-3 of the AISI Specification. The safety index in Eqn. (5) is detailed in Rogers
and Hancock (1996).
The safety indices (13) of the current design rules to predict the web crippling strengths for the four
loading conditions are lower than the target safety index, except for the EOF loading condition as
shown in Table 2. Safety indices as low as 0.48 were calculated for the ITF loading condition.
However, this is not the case for the proposed design equations, the safety indices are higher than the
target value for the four loading conditions as shown in Table 3. Therefore, the proposed design
equations are much more reliable than the current design rules. The proposed design equations produce
good limit state design when calibrated with the existing resistance (capacity) factors (~ - 0.75).
CONCLUSIONS

Web Crippling Tests of High Strength Cold-Formed Channels
365
A series of web crippling tests has been conducted to examine the appropriateness of the current design
rules stipulated in the Australian/New Zealand Standard (AS/NZS 4600, 1996) and the American Iron
and Steel Institute (AISI, 1996) Specification for cold-formed steel structures. Tests were performed
on high strength cold-formed unlipped channels having nominal yield stress of 450 MPa, and the web
slenderness values ranged from 15.3 to 45. The specimens were tested using the four loading
conditions (EOF, IOF, ETF and ITF) according to the AISI Specification.
The test strengths were compared with the current design strengths obtained using AS/NZS 4600 and
the AISI Specification. It is demonstrated that the current design strengths predicted by the standard
and specification are unconservative for unlipped channels (single unreinforced webs), except that they
closely predicted the web crippling strengths for the EOF loading condition in most of the cases. For a
certain specimen subjected to ITF loading condition the test strength is only 43% of the current design
strength predicted by the standard and specification. Since the design strengths obtained using the
current design rules are generally unconservative for unlipped channels, therefore, a set of equations to
predict the web crippling strengths have been proposed in this paper. The proposed design equations
are derived based on a simple plastic mechanism model, and these equations are calibrated with the test
results. It has been shown that the proposed design strengths are generally conservative for unlipped
channels with web slenderness values of less than or equal to 45.
The reliability of the current design rules and the proposed design equations have been evaluated using
reliability analysis. In general, the safety indices of the current design rules are lower than the target
safety index of 2.5 as specified in the AISI Specification. Whereas the safety indices of the proposed
design equations are higher than the target value. Therefore, it has shown that the proposed design
equations are much more reliable than the current design rules for the prediction of web crippling
strength of the tested channels. The proposed design equations are capable of producing reliable limit
state designs when calibrated with the existing resistance (capacity) factors.
ACKNOWLEDGEMENTS
The authors are grateful to the Australian Research Council and BHP Structural and Pipeline Products
for their support through an ARC Collaborative Research Grant. Test specimens were provided by
BHP Steel.

REFERENCES
American Iron and Steel Institute (1996). Specification for the Design of Cold-Formed Steel
Structural Members, AISI, Washington, DC.
Australian Standard (1991). Methods for Tensile Testing of Metals, AS 1391, Standards Association of
Australia, Sydney, Australia.
Australian/New Zealand Standard (1996).
Standards Australia, Sydney, Australia.
Cold-Formed Steel Structures, AS/NZS 4600:1996,
BHP Structural and Pipeline Products (1998). Pipe, Tube and Structural Products - Mechanical Test
Data. Somerton plant, NSW, Australia.
366
B. Young and G.J. Hancock
Hetrakul N. and Yu W.W. (1978). Structural Behavior of Beam Webs Subjected to Web Crippling and
a Combination of Web Crippling and Bending.
Final Report
Civil Engineering Study 78-4, University
of Missouri-Rolla, Mo, USA
Nash D. and Rhodes J. (1998). An Investigation of Web Crushing Behaviour in Thin-Wall Beams.
Thin-Walled structures
32, 207-230.
Pektsz T.B. and Hall W.B. (1988). Probabilistic Evaluation of Test Results. Proceedings of the 9th
International Specialty Conference on Cold-Formed Steel Structures, St. Louis, University of
Missouri-Rolla, Mo, USA.
Rogers C.A. and Hancock G.J. (1996). Ductility of G550 Sheet Steels in Tension-Elongation
Measurements and Perforated Tests.
Research Report
R735, Department of Civil Engineering,
University of Sydney, Australia.
Tsai M. (1992). Reliability Models of Load Testing. PhD dissertation, Department of Aeronautical
and Astronautical Engineering, University of Illinois at Urbana-Champaign.

Winter G. and Pian R.H.J. (1946). Crushing Strength of Thin Steel Webs. Cornell
Bulletin
35, Part 1,
Comell University, Ithaca, NY, USA.
Young B. and Hancock G.J. (1998). Web Crippling Behaviour of Cold-Formed Unlipped Channels.
Proceedings of the 14th International Specialty Conference on Cold-Formed Steel Structures, St.
Louis, University of Missouri-Rolla, Mo, USA, 127-150.
Zetlin L. (1955). Elastic Instability of Flat Plates Subjected to Partial Edge Loads.
Journal of the
Structural Division,
ASCE 81:795, 1-24.
Zhao X.L. and Hancock G.J. (1992). Square and Rectangular Hollow Sections Subject to Combined
Actions.
Journal of Structural Engineering,
ASCE 118:3, 648-668.
Zhao X.L. and Hancock G.J. (1995). Square and Rectangular Hollow Sections under Transverse End-
Bearing Force.
Journal of Structural Engineering,
ASCE 121:9, 1323-1329.
LOCAL AND DISTORTIONAL BUCKLING OF
PERFORATED STEEL WALL STUDS
Jyrki Kesti 1 and J. Michael Davies 2
~Laboratory of Steel Structures, Helsinki University of Technology,
P.O. Box 2100, FIN-02015 HUT, Finland
2Manchester School of Engineering, University of Manchester,
Manchester, M 13 9PL, UK
ABSTRACT
This paper considers the compression capacity of web-perforated steel wall studs. The web
perforations decrease the local buckling strength of the web and the distortional buckling strength of
the section. An analytical prediction of the compression capacity is described. Local and distortional

buckling stresses are determined by replacing the perforated part of the web with plain plate of
equivalent thickness. The effective area approach is used to consider local and distortional buckling.
Comparison between the test results for short columns and the corresponding predictions shows that
the method used gives reasonable results for web-perforated C-sections with or without web-stiffeners.
KEYWORDS
Cold-formed steel, wall stud, perforation, compression, local buckling, distortional buckling.
INTRODUCTION
Web-perforated steel wall studs are especially used in the Nordic countries as structural components in
steel-framed housing. The slotted thermal stud offers a considerable improvement in thermal
performance over a solid steel stud. The wall structure consists of web-perforated C-section studs with
U-section tracks top and bottom and, for example, gypsum wallboards attached to the stud flanges.
The sections investigated in this paper are shown in Figure 1. Both types of stud had six rows of slots
with dimensions as shown in the Figure.
The perforations reduce the elastic local buckling stress of the web and also reduce the bending
stiffness of the web which, in turn, results in decreased distortional buckling strength. The aim of this
paper is to analyse the local and distortional buckling strength of the perforated steel stud. The local
and distortional buckling modes are taken into account in design by using the effective area approach.
367
368
J. Kesti and J.M. Davies
Figure 1: Web-perforated C-section and web-stiffened C-section (Dimensions in mm)
ELASTIC BUCKLING STRESSES
Local Buckling Stress of the Web of a Perforated C-Section
The depth of the sections considered varied between 150 and 225 mm with a thickness between 1 and
2 mm. The overall depth of the perforations was 58 mm. Local buckling of the perforated region was
studied using the elastic buckling analysis available in the NISA finite element software (1996). The
analyses were carried out for both the isolated web element, which was assumed to be simply
supported, and for the whole section, including the edge-stiffened flanges. The width of the flanges
was 50 mm and the width of the stiffeners was 15 mm. Individual plate elements and the complete
sections of 800 mm in length were modelled, including the perforations. A sufficient length was

chosen so that the minimum local buckling stress could be achieved.
The elastic local buckling stress,
l~rcr.perf,
for simply supported perforated plate elements of different
widths and thicknesses was determined using the finite element method (FEM). An analytical
expression for the local buckling of a perforated plate may be achieved using a buckling factor of k =
4.0 and an equivalent thickness,
tr, to~, for the whole plate. The equivalent thickness was determined in
a manner similar to Salmi (1998):
/
O'cr
,perf.
t
r ,loc " ,tl
|1| O'cr ,entire
t (1)
where
O'cr,pe~
is the elastic buckling stress of the perforated plate and O'cr, entire is the elastic buckling
stress of the entire plate. The elastic buckling stress of the equivalent plate with reduced thickness
trtoc
is thus the same as that of the perforated plate. The value for tr.toc was found to be in the range 0.72t-
0.75t for the plates studied. Thus, for design purposes, the equivalent thickness value,
tr.toc = 0.72t
could be used for the whole range of sections.
Local buckling stresses for the whole of the perforated sections, including the flanges, were on average
75% higher than those of the simply supported perforated plates. This indicates that assuming the web
part to be simply supported leads to quite conservative results and the contribution of the flanges to the
local buckling of the web should generally be considered.
Distortional Buckling Stress

Because of the perforation of the web, the, transverse bending stiffness of the section is rather low and
the section is sensitive to distortional buckling under compressive load. In the distortional mode of
buckling, the edge-stiffened flange elements of the section tend to deform by rotation of the flange
about the flange-web junction. The distortional buckling mode occurs at longer wavelengths than
local buc.t-!ing. Numerical methods, such as the finite strip method (FSM), may be used to determine
Local and Distortional Buckling of Perforated Steel Wall Studs
369
the distortional buckling stress of the section. The Generalized Beam Theory (GBT) provides a
particularly good tool with which to analyse distortional buckling in isolation and in combination with
other modes. Some approximate manual methods have also been presented, namely the Eurocode 3
(1996) method, which is based on flexural buckling of the stiffener, and a more sophisticated model
developed by Lau and Hancock (1987). The most recent method has been presented by Schafer and
Pektiz (1999). Schafer's method was used in this study and it was modified to cover the perforated C-
sections, as shown in Figure 2.
Figure 2: Notations for the perforated C-section and for the flange part alone
In the Schafer method, the closed-form prediction of the distortional buckling stress is based on the
rotational restraint at the web/flange junction. The rotational stiffness may be expanded as a
summation of the elastic and stress-dependent geometric stiffness terms with contributions from the
flange and the web,
+k,)e-(k,
(2)
where the subscript f indicates the flange and w the web. Buckling takes place when the elastic
stiffness at the web/flange junction is eroded by the geometric effect, i.e.,
Q =0. (3)
Using (3) and writing the stress-dependent portion of the geometric stiffness explicitly,
ks = kcfe +kc~e fcr,d
('kofg -at-
k~c~g
):0.
(4)

Therefore, the distortional buckling stress,f~r,a, is
k cge + k c~e
f cr ,d -'~ "~
k c/g + k c,,e '
(5)
where the stiffness terms with the notations given in Figure 2 are:
1 ;4i 2 11 12
kc/e = EIx: (Xo: _hx: )2 + EIw: _Elx~ (xo: _hx: )2 + G1r
(6)
lyy
'[{ ! I 1
k#g (L ! A: (Xo/-h~zy( I~ ~I~l+ +Ix:+
(7)
= _2yo(Xoi_h~ f 2
[, I~ [ Iy: ) h2x: +YoI Iyl